AutoMathText / data /code /gap /0.50-0.55.jsonl

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	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nDeclare(VTensor, RCVTensor, VTensorInd);\n\n# A x I_v\nClass(VTensor, Tensor, rec(\n new := (self, L) >> SPL(WithBases(self, rec(\n _children := [L[1]],\n dimensions := When(IsBound(L[1].dims), L[1].dims(), L[1].dimensions) * L[2],\n vlen := L[2]))),\n # NOTE: vlen not exposed to rChildren\n from_rChildren := (self, rch) >> ObjId(self)(rch[1], self.vlen),\n\n normalizedArithCost := (self) >> self.vlen * self.child(1).normalizedArithCost(),\n print := (self,i,is) >> Print(self.name, \"(\",\n self.child(1).print(i+is,is), \", \", self.vlen, \")\"),\n toAMat := self >> Tensor(self.child(1), I(self.vlen)).toAMat(),\n sums := self >> Inherit(self, rec(_children := [self.child(1).sums()])),\n isPermutation := False,\n dims := self >> self.child(1).dims() * self.vlen,\n needInterleavedLeft := False,\n needInterleavedRight := False,\n transpose := self >> VTensor(self.child(1).transpose(), self.vlen),\n # for BlockSums\n isBlockTransitive := true,\n area := self >> self.child(1).area() * self.vlen,\n #NOTE: check if these two should be set to true or false\n cannotChangeDataFormat := False,\n totallyCannotChangeDataFormat := False\n));\n\n\n# RC(A x I_v)\nClass(RCVTensor, Tensor, rec(\n new := (self, L) >> SPL(WithBases(self, rec(\n _children := [L[1]],\n dimensions := 2 * L[1].dimensions * L[2],\n vlen := L[2]))),\n # NOTE: vlen not exposed to rChildren\n from_rChildren := (self, rch) >> ObjId(self)(rch[1], self.vlen),\n print := (self,i,is) >> Print(self.name, \"(\",\n self.child(1).print(i+is,is), \", \", self.vlen, \")\"),\n toAMat := self >> RC(Tensor(self.child(1), I(self.vlen)).toAMat()),\n sums := self >> Inherit(self, rec(_children := [self.child(1).sums()])),\n isPermutation := False,\n dims := self >> self.child(1).dims() * self.vlen * 2,\n needInterleavedLeft := True,\n needInterleavedRight := True,\n transpose := self >> RCVTensor(self.child(1).transpose(), self.vlen),\n # for BlockSums\n isBlockTransitive := true\n));\n\n\nClass(VTensorInd, Tensor, rec(\n new := (self, L) >> SPL(WithBases(self, rec(\n _children := [L[1]],\n dimensions := When(IsBound(L[1].dims), L[1].dims(), L[1].dimensions) * L[2].range,\n vlen := L[2]))),\n from_rChildren := (self, rch) >> ObjId(self)(rch[1], self.vlen),\n\n rChildren := self >> [self._children[1], self.vlen],\n\n rSetChild := meth ( self, n, what )\n if n=1 then\n self._children[1] := what;\n elif n=2 then\n self.vlen := what;\n else\n Error(\"VTensorInd only has 2 rChildren\");\n fi;\n end,\n# from_rChildren := (self, rch) >> ObjId(self)(rch[1], rch[2]),\n\n print := (self,i,is) >> Print(self.name, \"(\",\n self.child(1).print(i+is,is), \", \", self.vlen, \")\"),\n toAMat := self >> let(d := self.child(1).dims(), v := self.vlen.range, L(d[1]v, d[1]).toAMat() IDirSum(self.vlen, self.child(1)).toAMat() * L(d[2]v, v).toAMat()),\n sums := self >> Inherit(self, rec(_children := [self.child(1).sums()])),\n isPermutation := False,\n dims := self >> self.child(1).dims() self.vlen.range,\n needInterleavedLeft := False,\n needInterleavedRight := False,\n transpose := self >> VTensorInd(self.child(1).transpose(), self.vlen),\n # for BlockSums\n isBlockTransitive := true,\n area := self >> self.child(1).area() * self.vlen.range,\n free := meth(self)\n local fvar;\n fvar := self.child(1).free();\n SubtractSet(fvar, Set([self.vlen]));\n return fvar;\n end\n));\n", "meta": {"hexsha": "93fe07cea6f2a16ed7075cb18ff2f6a9f7cc5277", "size": 3677, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/vector/sigmaspl/vtensor.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/paradigms/vector/sigmaspl/vtensor.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/paradigms/vector/sigmaspl/vtensor.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 37.9072164948, "max_line_length": 170, "alphanum_fraction": 0.5765569758, "num_tokens": 1124, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. 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	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nDeclare(DFT_Rader, DFT_GoodThomas);\n\n_accurate_dft := vec -> List(TransposedMat(MatSPL(transforms.DFT(Length(vec)))TransposedMat([vec]))[1], ComplexCyc);\n\nClass(fdft, FuncExp, rec(\n computeType := self >> self.args[1].t\n));\n\nClass(fDFT, DiagFunc, rec(\n abbrevs := [ func -> Checked(IsFunction(func), [func]) ],\n range := self >> TComplex, \n domain := self >> self.params[1].domain(), \n\n lambda := self >> fdft(self.params[1].lambda()),\n\n tolist := self >> let(\n\telts := List(self.params[1].tolist(), x->Complex(EvalScalar(x))),\n\tComplexFFT(elts))\n));\n\nNewRulesFor(DFT, rec(\n #F DFT_Base: DFT_2 = F_2\n #F\n DFT_Base := rec(\n info := \"DFT_2 -> F_2\",\n forTransposition := false,\n applicable := nt -> nt.params[1] = 2 and not nt.hasTags(),\n apply := (nt, C, cnt) -> F(2)\n ),\n\n DFT_Base1 := rec(\n info := \"DFT_1 -> I(1)\",\n forTransposition := false,\n applicable := nt -> nt.params[1] = 1 and not nt.hasTags(),\n apply := (nt, C, cnt) -> I(1)\n ),\n\n #F DFT_Canonize: DFT_n_k = perm DFT_n\n #F\n DFT_Canonize := rec(\n switch := false,\n info := \"DFT_n_k -> perm * DFT_n\",\n forTransposition := false,\n applicable := nt -> nt.params[1] > 2 and nt.params[2] <> 1 and not nt.hasTags(),\n children := nt -> [[ DFT(nt.params[1], 1) ]],\n apply := (nt, C, cnt) -> OddStride(nt.params[1], nt.params[2]) * C[1]\n ),\n\n #F DFT_CT: 1965\n #F General Cooley-Tukey Rule\n #F DFT_n = (DFT_n/d tensor I_d) * diag * (I_n/d tensor F_d) * perm\n #F\n #F Cooley/Tukey:\n #F An Algorithm for the Machine Calculation of Complex Fourier Series.\n #F Mathematics of Computation, Vol. 19, 1965, pp. 297--301.\n #F\n DFT_CT := rec(\n info := \"DFT(mn,k) -> DFT(m, k%m), DFT(n, k%n)\",\n\n maxSize := false,\n forcePrimeFactor := false,\n\n applicable := (self, nt) >> nt.params[1] > 2\n and not nt.hasTags()\n and (self.maxSize=false or nt.params[1] <= self.maxSize)\n and not IsPrime(nt.params[1])\n and When(self.forcePrimeFactor, not DFT_GoodThomas.applicable(nt), true),\n\n children := nt -> Map2(DivisorPairs(nt.params[1]),\n (m,n) -> [ DFT(m, nt.params[2] mod m), DFT(n, nt.params[2] mod n) ]\n ),\n\n apply := (nt, C, cnt) -> let(mn := nt.params[1], m := Rows(C[1]), n := Rows(C[2]),\n Tensor(C[1], I(n)) \n Diag(fPrecompute(Tw1(mn, n, nt.params[2]))) \n Tensor(I(m), C[2]) \n L(mn, m)\n )\n ),\n\n DFT_CT_Mincost := rec(\n maxSize := false,\n applicable := (self, nt) >> let(N := nt.params[1],\n\t N > 2 and not nt.hasTags() and IsEvenInt(N) and\n (self.maxSize = false or nt.params[1] <= self.maxSize)),\n\n children := nt -> let(N := nt.params[1], k := nt.params[2], Map2( \n\t Filtered(DivisorPairs(N), divpair -> IsEvenInt(divpair[2])),\n (m,n) -> [ DFT(m, k mod m), DFT3(m, k mod (2m)), DFT(n, k mod n) ])),\n\n apply := (nt, C, cnt) -> let(\n\t N := nt.params[1], m := Rows(C[1]), n := Rows(C[3]), k := nt.params[2],\n hf := (n-2)/2, i := Ind(hf), j := Ind(hf),\n\n SUM( _hhi(N, m, 0, n, C[1]), # first iteration has no twiddles\n When(hf=0, [],\n\t\tISum(i, _hhi(N, m, i+1, n, C[1] * Diag(fPrecompute(Twid(N,m,k,0,0,i+1)))))),\n _hhi(N, m, hf+1, n, C[2]), # middle is a DFT3\n\t When(hf=0, [],\n\t\tISum(j, _hhi(N, m, j+hf+2, n, C[1] * Diag(fPrecompute(Twid(N,m,k,0,0,j+2+hf))))))\n ) \n Tensor(I(m), C[3]) \n Tr(n, m)\n )\n ),\n\n #F DFT_CosSinSplit:\n #F\n #F DFT_n = CosDFT_n + i * SinDFT_n\n #F\n #F This rule has been restricted in applicability to small size\n #F (see config.g), Connects to Vetterli rules for CosDFT/SinDFT.\n #F\n DFT_CosSinSplit := rec(\n info := \"DFT_n -> CosDFT_n, SinDFT_n\",\n forTransposition := false,\n maxSize := 64,\n\n applicable := (self, nt) >> let(N:=nt.params[1], rot:=nt.params[2],\n N > 2 and N <= self.maxSize and Is2Power(N) and AbsInt(rot)=1 \n\t and not nt.hasTags()),\n\n children := nt -> [[ CosDFT(nt.params[1]), SinDFT(nt.params[1]) ]],\n\n apply := (nt, C, cnt) -> let(N := nt.params[1], rot := nt.params[2],\n\t Tensor(Mat([[1,1]]), I(N)) * \n VStack(C[1], (E(4)^rot) * C[2])\n\t)\n ),\n\n #F DFT_Rader: Rader's Algorithm for Prime size DFT\n #F\n #F DFT(p) -> P(g)' * (1 dirsum DFT(p-1)) * Tp * (1 dirsum DFT(p-1)) * P(g)\",\n #F P(g) = perm\n #F Tp = [[1,1],[1,-1/(p-1)]] dirsum diag\n #F\n DFT_Rader := rec(\n info := \"DFT(p) -> P(g)' * DFT(p-1) * Tp \",\n forTransposition := false,\n minSize := 3,\n maxSize := 64,\n accurate := true,\n\n raderDiag := (self, N, k, root) >> let(\n\t dft := When(self.accurate, _accurate_dft, vec->ComplexFFT(List(vec,ComplexCyc))),\n SubList(dft(List([0..N-2], x -> E(N)^(kroot^x mod N))), 2) / (N-1)),\n\n raderMid := (self, N, k, root) >>\n DirectSum(Mat([[1, 1], [1, -1/(N-1)]]),\n Diag(FData(self.raderDiag(N, k, root)))),\n\n applicable := (self, nt) >> let(n:=nt.params[1],\n n >= self.minSize and n <= self.maxSize and IsPrime(EvalScalar(n)) \n\t and not nt.hasTags()),\n\n children := nt -> [[ DFT(nt.params[1]-1, -1), DFT(nt.params[1]-1, -1) ]],\n\n apply := (self, nt, C, cnt) >> let(\n\t N := EvalScalar(nt.params[1]), k := EvalScalar(nt.params[2]), root := PrimitiveRootMod(N),\n RR(N, 1, root).transpose() \n DirectSum(I(1), C[1]) \n self.raderMid(N,k,root) \n DirectSum(I(1), C[2]) \n RR(N, 1, root)\n )\n ),\n\n DFT_RealRader := CopyFields(~.DFT_Rader, rec(\n children := nt -> [[ PRDFT1(nt.params[1]-1).transpose(), PRDFT1(nt.params[1]-1) ]],\n\n realRaderDiag := (self, N, k, root) >> let(cdiag := self.raderDiag(N, k, root),\n # cdiag is of length N-2.\n # cdiag = sublist( DFT_{N-1} omega_vector, [2..N-1])\n # now we want to obtain\n # rdiag = sublist( RDFT_N * omega_vector, [2..N-1]), we can do this using\n # the property RDFT = (1 dirsum (I tensor [[1, 1], [-j, j]]) dirsum 1) * LIJ * DFT\n # which means that rdiag = (1 dirsum (I tensor [[1, 1], [-j, j]]) dirsum 1) * LIJ * cdiag\n # the code below does this ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ plus pads a zero (for PRDFT)\n # and also the following trick.\n\n # The expected rdiag steady state is [[a, b], [b, -a]], we convert this to rotations (=RCDiag)\n # by applying J(2), ie we get [[b, -a], [a, b]], which would be a rotation by b + E(4)a,\n # but in this case both a and b are complex, so its not. We still use RCDiag though.\n #\n Concatenation(\n ConcatList([1..(N-3)/2], i -> Reversed([cdiag[i]+cdiag[N-1-i], -E(4)(cdiag[i]-cdiag[N-1-i])])), # DFT->RDFT\n [0, cdiag[(N-3)/2+1]])),\n\n raderMid := (self, N, k, root) >>\n DirectSum(Mat([[1, 1, 0], [1, -1/(N-1), 0], [0, 0, 0]]), # zero padding for PRDFT\n Tensor(I((N-1)/2), J(2))\n RCDiag(FData(self.realRaderDiag(N, k, root))).toloop()), \n # RCDiag with complex entries, max weird :) !\n # .toloop() is used because in vector code RCDiag is \n # converted to VRCDiag which is confused by complex entries AFAIK\n apply := (self,nt,C,cnt) >> let(\n N := EvalScalar(nt.params[1]), k := EvalScalar(nt.params[2]), root := PrimitiveRootMod(N),\n RR(N, 1, root).transpose() \n DirectSum(I(1), C[1]) \n self.raderMid(N,k,root) \n DirectSum(I(1), C[2]) \n RR(N, 1, root))\n )),\n\n #F DFT_Bluestein : Convert FFT to Toeplitz matrix, then embed in a larger Circulant\n #F\n #F DFT_n -> diag Toeplitz * diag\n #F\n # DFT on inputs, some of which are 0:\n #\n DFT_Bluestein := rec(\n info := \"DFT_n -> diag * Toeplitz * diag\",\n forTransposition := false,\n minSize := 3,\n maxSize := false,\n switch := false,\n\n # Applicable only for non-powers of 2 to prevent cycles\n applicable := (self, nt) >> let(N := nt.params[1],\n IsSymbolic(N) or \n\t (N >= self.minSize and When(IsInt(self.maxSize), N <= self.maxSize, true) and not Is2Power(N)\n\t\tand not nt.hasTags())),\n\n\t# NOTE: extend this to be a true degree of freedom\n\tfreedoms := t -> let(min := 2t.params[1]+1,\n\t [ integersBetween(min, 4 pow(2, floor(log(t.params[1])/log(2)))) ]),\n\n child := (t, fr) -> let(\n\t N := t.params[1], Ncirc := fr[1], \n [ DFT(Ncirc, -1).withTags(t.getTags()), DFT(Ncirc, 1).withTags(t.getTags()) ]),\n\n diag := (N, k) -> let(i:=Ind(N), Lambda(i, omegapi(fdiv(i^2 * k, N)))),\n\n\tcirc := (N, k, circsize) -> let(\n\t j1 := Ind(N),\n\t j2 := Ind(N-1),\n\t diagDirsum(\n\t\tLambda(j1, fdiv(omegapi(fdiv(-j1^2k, N)), circsize)),\n\t\tfConst(TReal, circsize-2N+1, 0),\n\t\tLambda(j2, fdiv(omegapi(fdiv(-(N-j2-1)^2k, N)), circsize)))),\n\n apply := (self, nt, C, cnt) >> let(\n N := nt.params[1],\n k := nt.params[2],\n Ncirc := Rows(C[1]),\n diag := fPrecompute(self.diag(N,k)),\n\t pad := spiral.paradigms.common.TRDiag(Ncirc, N, diag).withTags(nt.getTags()),\n\n\t #Diag(diag) Gath(fCompose(fAdd(Ncirc, N, 0))).toloop(1) * \n\t pad.transpose() * \n\t Inplace(Grp(C[1] * Diag(fPrecompute(fDFT(self.circ(N, k, Ncirc)))))) \n\t Inplace(C[2]) \n\t pad\n\t #Scat(fAdd(Ncirc, N, 0)).toloop(1) * Diag(diag) ##, O(Ncirc-N, N))\n\t)\n ),\n\n #F DFT_GoodThomas : Prime Factor FFT\n #F\n #F DFT_nk -> perm (DFT_n_a tensor DFT_k_b) * perm\n #F when gcd(n,k) = 1\n #F\n DFT_GoodThomas := rec(\n info := \"DFT_nk -> perm (DFT_n_a tensor DFT_k_b) * perm\",\n forTransposition := false,\n applicable := (self, nt) >> let(N := nt.params[1],\n\t N > 2 and DivisorPairsRP(N) <> [] and N <= self.maxSize and\n\t not nt.hasTags()),\n\n maxSize := 64,\n\n children := nt -> let(mn := nt.params[1], k:= nt.params[2], Map2(DivisorPairsRP(mn),\n (m,n) -> [ DFT(m, kn mod m), DFT(n, km mod n) ])),\n\n apply := (nt, C, cnt) -> let(\n r := Rows(C[1]),\n s := Rows(C[2]),\n alpha := 1 / s mod r,\n beta := 1 / r mod s,\n CRT(r,s,1,1).transpose() * Tensor(C[1], C[2]) * CRT(r,s,1,1)\n )\n ),\n\n #F DFT_PFA_SUMS : Prime Factor FFT using Sigma-SPL and cyclic shifts\n #F\n #F DFT_nk -> perm (DFT_n_a tensor DFT_k_b) * perm\n #F when gcd(n,k) = 1\n #F\n DFT_PFA_SUMS := CopyFields(~.DFT_GoodThomas, rec(\n apply := (nt, C, cnt) -> let(\n\t r := Rows(C[1]), s := Rows(C[2]),\n\t j := Ind(s), k := Ind(r),\n\t alpha := (1/s) mod r, beta := (1/r) mod s,\n\t ISum(j,\n Scat(fTensor(fId(r), fBase(j))) \n (C[1] ^ Z(r, -alphaj)) \n Gath(fTensor(fId(r), fBase(j)))) \n\t ISum(k,\n Scat(fTensor(fId(s), fBase(k))) \n (C[2] ^ Z(s, -betak)) \n Gath(fTensor(fId(s), fBase(k))))\n\t)\n )),\n\n DFT_PFA_RaderComb := rec(\n forTransposition := false,\n applicable := nt -> let(N := nt.params[1], divs := DivisorPairsRP(N),\n N > 2 and Length(divs)=2 and N mod 2 = 1 and\n IsPrime(divs[1][1]) and IsPrime(divs[1][2]) \n\t and not nt.hasTags()),\n\n children := nt -> let(\n\t N:=nt.params[1], k:=nt.params[2], divs := DivisorPairsRP(nt.params[1]),\n r := divs[1][1], s := divs[1][2],\n [ [DFT(r-1,-1), DFT(r-1,-1), DFT(s-1,-1), DFT(s-1,-1)],\n\t\t [DFT(s-1,-1), DFT(s-1,-1), DFT(r-1,-1), DFT(r-1,-1)] ]),\n\t\n apply := (nt, C, cnt) -> let(\n r := Rows(C[1])+1,\n s := Rows(C[3])+1,\n er := ChineseRem([r,s], [1,0]),\n es := ChineseRem([r,s], [0,1]),\n dr := DFT_Rader.raderMid(r, nt.params[2]s), # * er/s mod r),\n ds := DFT_Rader.raderMid(s, nt.params[2]r), # es/r mod s),\n\n CRT(r,s,1,1).transpose() \n Tensor(RR(r).transpose(), RR(s).transpose()) \n Tensor(\n DirectSum(I(1), C[1]) * dr * DirectSum(I(1), C[2]),\n DirectSum(I(1), C[3]) * ds * DirectSum(I(1), C[4])\n ) \n Tensor(RR(r), RR(s)) \n CRT(r,s,1,1)\n )\n ),\n\n #F DFT_SplitRadix: 1984\n #F\n #F DFT_n = B * (DFT_n/2 dirsum DFT_n/4 dirsum DFT_n/4) * perm\n #F\n #F B = (DFT_2 tensor I_n/2) * S * diag\n #F S = (I_n/2 dirsum (diag([1,E(4)] tensor I_n/4))\n #F\n #F Duhamel, Pierre:\n #F Split Radix FFT Algorithm, Electronics Letters, Vol. 20, No. 1,\n #F pp. 14--16, 1984\n #F\n DFT_SplitRadix := rec(\n info := \"DFT_n -> DFT_n/2, DFT_n/4, DFT_n/4\",\n forTransposition := true,\n maxSize := 64,\n\n applicable := (self, nt) >> let(N := nt.params[1],\n N >= 8 and N mod 4 = 0 and N <= self.maxSize and not nt.hasTags()\n ),\n\n children := nt -> let(N := nt.params[1], w := nt.params[2],\n [[ DFT(N/2, w), DFT(N/4, w) ]]\n ),\n\n apply := (nt, C, cnt) -> let(N := nt.params[1], w := nt.params[2],\n Tensor(F(2), I(N/2)) \n DirectSum(\n C[1],\n Tensor(Diag([1, E(4)^w]) F(2), I(N/4)) \n Diag(fPrecompute(fCompose(Tw3(N/2, 2, w), L(N/2, 2)))) \n Tensor(I(2), C[2])L(N/2,2)\n ) \n L(N, 2)\n )\n ),\n\n #F DFT_DCT1andDST1: 1984\n #F\n #F DFT_n = blocks * (DCT1_(n/2+1) dirsum DST1_(n/2-1)) * blocks\n #F\n #F Wang:\n #F Fast Algorithms for the Discrete W Transform and the\n #F Discrete Fourier Transform.\n #F IEEE Trans. on ASSP, 1984, pp. 803--814\n #F Britanak/Rao:\n #F The fast generalized discrete Fourier transforms: A unified\n #F approach to the discrete sinusoidal transforms computation.\n #F Signal Processing 79, 1999, pp. 135--150\n #F\n DFT_DCT1andDST1 := rec(\n info := \"DFT_n -> DCT1_(n/2+1), DST1_(n/2-1)\",\n maxSize := 64,\n\n applicable := (self, nt) >> let(N:=nt.params[1], k:=nt.params[2],\n N > 2 and N <= self.maxSize and Is2Power(N) and AbsInt(k)=1) and not nt.hasTags(),\n\n children := nt -> \n\t [[ DCT1( nt.params[1]/2 + 1 ), DST1( nt.params[1]/2 - 1 ) ]],\n\n apply := (nt, C, cnt) -> let(N:=nt.params[1], w:=nt.params[2],\n DirectSum(I(1), blocks4(N - 1, w)) \n DirectSum(C[1], C[2] ^ J(N/2 - 1)) \n DirectSum(I(1), blocks1(N - 1))\n )\n )\n));\n", "meta": {"hexsha": "82016fa0f99087cfa0769e5c46054dfc2445a24c", "size": 15239, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/dft/dft_rules.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/transforms/dft/dft_rules.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/transforms/dft/dft_rules.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 37.3504901961, "max_line_length": 124, "alphanum_fraction": 0.4860555155, "num_tokens": 5155, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. 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	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n#P SPL Parametrized Symbols\n#P ========================\n#P\n#P This package contains parametrized symbols - shortcut notation for common\n#P idiomatic constructs.\n#P\n\n#F -----------------------------------------------------------------------------\n#F I(N) : NxN identity matrix\n#F -----------------------------------------------------------------------------\nClass(I, Sym, rec(\n abbrevs := [ (x,y) -> Checked(x=y, IsPosInt0Sym(x), x),\n (n) -> Checked(IsPosInt0Sym(n), n) ],\n def := n -> Perm((), n),\n transpose := self >> self,\n conjTranspose := self >> self,\n inverse := self >> self,\n isIdentity := True,\n isSymmetric := True,\n doNotMeasure := true,\n printlatex := self >> Print(\" \\\\one_{\",self.params[1],\"} \"),\n area := self >> self.params[1],\n normalizedArithCost := self >> 0,\n));\n\n#F -----------------------------------------------------------------------------\n#F O(M,N) : MxN matrix of zeros\n#F -----------------------------------------------------------------------------\nClass(O, BaseMat, rec(\n abbrevs := [ n -> Checked(IsPosInt(n), [n,n]) ],\n\n new := (self, r, c) >> SPL(WithBases(self, rec(\n params := [r, c], dimensions := [r, c]))),\n\n isReal := True,\n isPermutation := False,\n arithmeticCost := (self, costMul, costAddMul) >> costMul(0) - costMul(0),\n\n transpose := self >> ObjId(self)(self.params[2], self.params[1]), \n conjTranspose := self >> ObjId(self)(self.params[2], self.params[1]), \n\n area := self >> Maximum(self.dimensions),\n\n toAMat := self >> AMatMat(NullMat(\n\tEvalScalar(self.params[1]), EvalScalar(self.params[2]))),\n\n print := Sym.print,\n dims := self >> [ self.params[1], self.params[2] ],\n rChildren := Sym.rChildren,\n rSetChild := Sym.rSetChild\n));\n\n#F -----------------------------------------------------------------------------\n#F RI(M,N) : MxN rectangular identity\n#F MIN(M,N) x MIN(M,N) identity padded with 0s\n#F -----------------------------------------------------------------------------\nClass(RI, Sym, rec(\n def := (r, c) -> Checked(IsPosInt(r), IsPosInt(c),\n Cond(r = c, I(r),\n r < c, Gath(fAdd(c,r,0)),\n Scat(fAdd(r,c,0)))),\n\n transpose := self >> ApplyFunc(self.__bases__[1], Reversed(self.params)),\n conjTranspose := self >> ApplyFunc(self.__bases__[1], Reversed(self.params)),\n));\n\n#F -----------------------------------------------------------------------------\n#F F(N) - NxN Discrete Fourier Transform matrix\n#F -----------------------------------------------------------------------------\nClass(F, Sym, rec(\n def := size -> Checked(IsPosInt(size),\n Cond(size = 1, Mat([[1]]),\n size = 2, Mat([[1,1], [1,-1]]),\n Mat(Global.DFT(size)))),\n\n isReal := self >> self.params[1] <= 2,\n isPermutation := False,\n transpose := self >> self,\n conjTranspose := self >> self,\n inverse := self >> let(n:=self.params[1], Cond(n=1, self, n=2, 1/2F(2), Error(\"Inverse not supported\"))),\n toAMat := self >> DFTAMat(self.params[1]),\n printlatex := (self) >> Print(\" F_{\", self.params[1], \"} \")\n));\n\n#F -----------------------------------------------------------------------------\n#F R(a) : 2x2 rotation matrix with angle api, namely\n#F\n#F cos(a) sin(a)\n#F -sin(a) cos(a)\n#F\n#F alternatively:\n#F\n#F R(c,s) : specified by a pair such as c^2 + s^2 = 1\n#F <c> <s>\n#F -<s> <c>\n#F\n#F -----------------------------------------------------------------------------\nClass(Rot, Sym, rec(\n abbrevs := [ (a) -> [cospi(a), sinpi(a)] ],\n\n def := (a,b) ->\n Mat( [[a, b], [-b, a]] ),\n\n transpose := self >>\n self.__bases__[1](self.params[1], -self.params[2]),\n\n conjTranspose := self >> self.transpose(),\n inverse := self >> self.transpose(),\n\n toAMat := self >> let(a := self.params[1], b := self.params[2],\n When(IsScalar(a) and IsScalar(b) and ScalarIsCos(a) and ScalarIsSin(b),\n RotationAMat(EvalScalar(ScalarCosArg(a))),\n AMatMat([[EvalScalar(a), EvalScalar(b)],\n [EvalScalar(-b), EvalScalar(a)]]))),\n\n #-----------------------------------------------------------------------\n # Expansions\n expandLifting := self >>\n let(c := self.params[1],\n s := self.params[2],\n ev := (not IsScalar(c) or CanBeFullyEvaluated(c.val)) and\n (not IsScalar(s) or CanBeFullyEvaluated(s.val)),\n Cond(ev and c = s, c * F(2) * Perm((1,2), 2),\n ev and c = -s, c * Perm((1,2), 2) * F(2),\n Mat([[1,1,0], [0,-1,1]]) \n Diag([c-s, s, c+s]) \n Mat([[1,0], [1,1], [0,1]]))),\n\n expandWinograd:= self >>\n let(c := self.params[1],\n s := self.params[2],\n ev := (not IsScalar(c) or CanBeFullyEvaluated(c.val)) and\n (not IsScalar(s) or CanBeFullyEvaluated(s.val)),\n Cond(ev and c = s, c * F(2) * Perm((1,2), 2),\n ev and c = -s, c * Perm((1,2), 2) * F(2),\n Mat([[1, (1-c)/s], [0, 1]]) \n Mat([[1, 0], [-s, 1]]) \n Mat([[1, (1-c)/s], [0, 1]]))),\n\n expandDef := self >> self.obj,\n));\n\n\nDeclare(toeplitz);\n\n#F -----------------------------------------------------------------------------\n#F toeplitz(elements) : toeplitz matrix given by elements of the first row and\n#F column, starting from the upper right corner\n#F -----------------------------------------------------------------------------\n#F NOTE: use generating function not list (see 'Toeplitz')\nClass(toeplitz, Sym, rec(\n abbrevs := [ arg -> When(Length(arg) > 1 or not IsList(arg[1]), [arg], arg) ],\n\n def := function(elements)\n local n;\n Constraint(IsList(elements) and Length(elements) > 0);\n Constraint(IsOddInt(Length(elements)));\n DoForAll(elements, x->Constraint(IsScalarOrNum(x)));\n n := (Length(elements) + 1) / 2;\n return Mat(ToeplitzMat(elements));\n end,\n\n transpose := self >> toeplitz(Reversed(self.params[1])),\n conjTranspose := self >> toeplitz(List(Reversed(self.params[1]), x->Global.Conjugate(x))),\n isReal := True,\n isPermutation := False,\n area := self >> Product(self.dimensions)\n));\n", "meta": {"hexsha": "45ccd2d376b88be494d53750fb01fb67aff72075", "size": 6354, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/spl/symbols.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/spl/symbols.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/spl/symbols.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 36.5172413793, "max_line_length": 110, "alphanum_fraction": 0.4557758892, "num_tokens": 1660, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. 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	{"text": "# Copyright (c) 2018-2020, Carnegie Mellon University\n# See LICENSE for details\n#\n# n-qubit Z transforms\n#\n\n\n#F qZT( n ) - Z Gate non-terminal\n#F Definition: (2^n x 2^n)-matrix that applies an n-point Z Transform to the target qubits\n#F Note: qZT(1) denotes the matrix[[1, 0], [0, -1]],\n#F qZT(_) is symmetric.\n#F\n#F qZT( n ) -> an n-qubit Z transform\nClass(qZT, TaggedNonTerminal, rec(\n abbrevs := [ n -> Checked(IsPosInt(n), [n]) ],\n dims := self >> let(size := 2^self.params[1], [size, size]),\n terminate := self >> Tensor(Replicate(self.params[1], qZ())),\n isReal := self >> true,\n groups := self >> [Replicate(self.params[1], 1)],\n rChildren := self >> self.params,\n from_rChildren := (self, rch) >> self.__bases__[1](rch[1]),\n recursive_def := (self, arch) >> self.__bases__[1](self.params[1]),\n SmallRandom := () -> Random([2..5]),\n LargeRandom := () -> Random([6..15]),\n normalizedArithCost := self >> Error(\"ArithCost not implemented\"),\n TType := T_Complex(64)\n));\n\n\nNewRulesFor(qZT, rec(\n\n # qZT_BinSplit rule\n # qzT_BinSplit qZT_(k) -> (qZT_(k1) tensor I) (I tensor qZT_(k2))\n # k1 + k2 = k\n qZT_BinSplit := rec (\n forTransposition := false,\n minSize := 2, \n applicable := (self, nt) >> nt.params[1] > 1,\n children := nt -> List( [1..nt.params[1] - 1], i -> [ Tensor(qZT(i), qZT(nt.params[1]-i)).withTags(nt.getTags()) ] ), \n apply := (nt, c, cnt) -> c[1],\n switch := true,\n ),\n\n #F qZT_Base: qZT(1) = qZ() SPL object\n #F Directly represent as an implementable gate\n qZT_Base := rec(\n info := \"qZT_(1) -> qZ()\",\n forTransposition := false,\n applicable := (self, nt) >> nt.params[1]=1,\n apply := (nt, c, cnt) -> qZ(),\n )\n\n));", "meta": {"hexsha": "bd38528ff429045a6363e2cfe516287711ca231b", "size": 1841, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "qzt.gi", "max_stars_repo_name": "spiral-software/spiral-package-quantum", "max_stars_repo_head_hexsha": "dd2323983495adbbc6261c0cdf840320d19d099d", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "qzt.gi", "max_issues_repo_name": "spiral-software/spiral-package-quantum", "max_issues_repo_head_hexsha": "dd2323983495adbbc6261c0cdf840320d19d099d", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "qzt.gi", "max_forks_repo_name": "spiral-software/spiral-package-quantum", "max_forks_repo_head_hexsha": "dd2323983495adbbc6261c0cdf840320d19d099d", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 34.7358490566, "max_line_length": 136, "alphanum_fraction": 0.5486148832, "num_tokens": 608, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8333246118695629, "lm_q2_score": 0.6548947290421275, "lm_q1q2_score": 0.5457398958944535}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n# ==========================================================================\n# RowTensor\n# ==========================================================================\nClass(RowTensor, BaseOverlap, rec(\n #-----------------------------------------------------------------------\n dims := self >> let(D := self._children[1].dimensions, \n [ self.isize * D[1],\n\t D[2] + AbsInt((D[2] - self.overlap) * (self.isize - 1)) ]),\n #-----------------------------------------------------------------------\n toAMat := self >> let(n := EvalScalar(self.isize),\n TensorProductAMat(AMatSPL(I(n)), AMatSPL(self._children[1])) \n\tAMatSPL(Sparse(\n\t\tself._rowoverlap(\n\t\t List([1..n], i-> EvalScalar(Cols(self._children[1]))),\n\t\t EvalScalar(self.overlap)\n\t\t)))\n ),\n #-----------------------------------------------------------------------\n arithmeticCost := (self, costMul, costAddMul) >>\n self.isize self._children[1].arithmeticCost(costMul, costAddMul)\n));\n\n# ==========================================================================\n# ColTensor\n# ==========================================================================\nClass(ColTensor, BaseOverlap, rec(\n #-----------------------------------------------------------------------\n dims := self >> let(D := self._children[1].dimensions,\n [ D[1] + AbsInt((D[1] - self.overlap) * (self.isize - 1)),\n\t self.isize * D[2] ]),\n #-----------------------------------------------------------------------\n toAMat := self >> let(n := _unwrap(self.isize),\n AMatSPL(Sparse(\n\t\tself._coloverlap(\n\t\t List([1..n], i->self._children[1].dimensions[1]),\n\t\t self.overlap\n\t\t))) * \n\tTensorProductAMat(AMatSPL(I(n)), AMatSPL(self._children[1]))\n )\n));\n\nColTensor._transpose_class := RowTensor;\nRowTensor._transpose_class := ColTensor;\n", "meta": {"hexsha": "997cb8c53fb77caf7b7e68f7047fa4f4f64f607b", "size": 1909, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/spl/RowColTensor.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/spl/RowColTensor.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/spl/RowColTensor.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 38.9591836735, "max_line_length": 76, "alphanum_fraction": 0.3986380304, "num_tokens": 418, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8333245787544824, "lm_q2_score": 0.6548947290421275, "lm_q1q2_score": 0.5457398742075619}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nRulesFor(DFT, rec(\n #F DFT_DFT1and3 : DFT1_2n -> L (DFT1_n dirsum DFT3_n) L (I2 tensor F2) L\n #F Derived using polynomial factorization:\n #F x^2n -> (x^n-1) (x^n+1)\n #F\n DFT_DFT1and3 := rec(\n isApplicable := P -> P[1] > 2 and P[1] mod 2 = 0,\n allChildren := P -> [[ DFT1(P[1]/2, P[2]), DFT3(P[1]/2, P[2]) ]],\n rule := (P,C) -> let(n := P[1]/2, \n L(2n, n) DirectSum(C[1], C[2]) * L(2n, 2) \n Tensor(I(n), F(2)) \n L(2n, n))\n )\n));\n\nlperm := p -> Z(p, (p-1)/2); \nrperm := p -> Z(p, (p+1)/2);\npdiag := (p,k) -> When(IsEvenInt(k), \n I(p),\n Diag(List([0..p-1], i -> (-1)^i)));\n\nRulesFor(DFT2, rec(\n DFT2_CT := Inherit(DFT_CT, rec(\n\tswitch := false,\n\tallChildren := P -> Map2(DivisorPairs(P[1]), \n\t (m,n) -> [ DFT2(m, P[2]), DFT(n, P[2]) ]),\n \n\trule := (P,C) -> let(mn := P[1], m := Rows(C[1]), n := Rows(C[2]), \n\t Tensor(C[1], I(n)) * Diag(fPrecompute(Tw2(mn, n, P[2]))) \n\t Tensor(I(m), C[2]) L(mn, m))\n )),\n));\n\nNewRulesFor(DFT2, rec(\n DFT2_PF := rec(\n \tinfo := \"DFT2_nk -> diag perm * (DFT2_n_a tensor DFT2_k_b) * perm\",\n \tforTransposition := true,\n \tapplicable := nt -> nt.params[1] > 2 and DivisorPairsRP(nt.params[1]) <> [] and not nt.hasTags(),\n \tallChildren := nt -> let(N := nt.params[1], k:= nt.params[2], Map2(DivisorPairsRP(N), \n \t\t(r,s) -> [ DFT2(r, 1/s mod r), DFT2(s, 1/r mod s) ])),\n \t\n apply := (nt, C, cnt) -> let(\n \t N := nt.params[1],\n \t r := Rows(C[1]), \n \t s := Rows(C[2]),\n \t alpha := 1 / s mod r,\n \t beta := 1 / r mod s,\n \t i := Ind(rs),\n \n \t CRT(r,s).transpose() \n \t Diag(Lambda(i, -sign(imod(salphaidiv(i,s) + rbetaimod(i,s), 2N) - N))) \n \t Tensor(C[1], C[2]) * CRT(r,s)\n \t)\n#D \tisApplicable := P -> P[1] > 2 and DivisorPairsRP(P[1]) <> [] and Length(P[3]) = 0,\n#D \tallChildren := P -> let(N := P[1], k:= P[2], Map2(DivisorPairsRP(N), \n#D \t\t(r,s) -> [ DFT2(r, 1/s mod r), DFT2(s, 1/r mod s) ])),\n#D \t\n#D \trule := (P,C) -> let(\n#D \t N := P[1],\n#D \t r := Rows(C[1]), \n#D \t s := Rows(C[2]),\n#D \t alpha := 1 / s mod r,\n#D \t beta := 1 / r mod s,\n#D \t i := Ind(rs),\n#D \n#D \t CRT(r,s).transpose() \n#D \t Diag(Lambda(i, -sign(imod(salphaidiv(i,s) + rbetaimod(i,s), 2N) - N))) \n#D \t Tensor(C[1], C[2]) * CRT(r,s)\n#D \t)\n )\n));\n\nRulesFor(DFT3, rec(\n DFT3_Base := BaseRule(DFT3, [2, ...]),\n\n DFT3_CT := Inherit(DFT_CT, rec(\n\tswitch := false,\n\tallChildren := P -> Map2(DivisorPairs(P[1]), \n\t (m,n) -> [ DFT(m, P[2]), DFT3(n, P[2]) ]),\n \n\trule := (P,C) -> let(mn := P[1], m := Rows(C[1]), n := Rows(C[2]), \n\t Tensor(C[1], I(n)) * Diag(fPrecompute(Tw3(mn, n, P[2]))) \n\t Tensor(I(m), C[2]) L(mn, m))\n )),\n\n DFT3_CT_Radix2 := rec(\n\tisApplicable := P -> P[1] > 2 and (P[1] mod 2) = 0,\n\tallChildren := P -> [[ DFT(P[1]/2, P[2]) ]], \n\trule := (P,C) -> let(n := P[1]/2,\n\t Tensor(C[1], I(2)) * Diag(fPrecompute(Tw3(2n, 2, P[2]))) \n\t Tensor(I(n), F(2)Diag(1,E(4)^P[2])) L(2n, n))\n ),\n\n DFT3_OddToDFT1 := rec(\n\tisApplicable := P -> IsOddInt(P[1]),\n\tallChildren := P -> [[ DFT(P[1], P[2]) ]],\n\trule := (P, C) -> rperm(P[1]) C[1] * pdiag(P[1], P[2])\n ),\n\n DFT3_2xOddToDFT1 := rec(\n\tisApplicable := P -> P[1] mod 4 = 2 and P[1] > 2,\n\tallChildren := P -> [[ DFT(P[1], P[2]) ]],\n\trule := (P, C) -> let(n:=P[1], k:=P[2],\n\t Z(n,-(n-2)/4) * C[1] * Diag(List([0..n-1], x->E(4)^(kx))))\n )\n\n));\n\nRulesFor(DFT4, rec(\t\n DFT4_Base := rec(\n\tisApplicable := P -> P[1]=2,\n\tforTransposition := false,\n\trule := (P,C) -> E(8)Mat((1/E(8))MatSPL(ApplyFunc(DFT4, P)))\n ),\n\n DFT4_CT := Inherit(DFT_CT, rec(\n\tallChildren := P -> Map2(DivisorPairs(P[1]), \n\t (m,n) -> [ DFT2(m, P[2]), DFT3(n, P[2]) ]),\n \n\trule := (P,C) -> let(mn := P[1], m := Rows(C[1]), n := Rows(C[2]), \n\t Tensor(C[1], I(n)) Diag(fPrecompute(Tw4(mn, n, P[2]))) \n\t Tensor(I(m), C[2]) L(mn, m))\n )),\n));\n\nNewRulesFor(DFT4, rec(\n DFT4_PF := rec(\n \tinfo := \"DFT4_nk -> diag perm * (DFT4_n_a tensor DFT4_k_b) * perm\",\n \tforTransposition := true,\n \tapplicable := nt -> nt.params[1] > 2 and DivisorPairsRP(nt.params[1]) <> [] and not nt.hasTags(),\n children := nt -> let(N := nt.params[1], k:= nt.params[2], Map2(DivisorPairsRP(N), \n \t\t(r,s) -> [ DFT4(r, 1/s mod r), DFT4(s, 1/r mod s) ])),\n \t\n apply := (nt, C, cnt) -> let(\n \t N := nt.params[1],\n \t r := Rows(C[1]), \n \t s := Rows(C[2]),\n \t alpha := 1 / s mod r,\n \t beta := 1 / r mod s,\n \t i := Ind(rs),\n \t d := Diag(Lambda(i, -sign(imod(salphaidiv(i,s) + rbetaimod(i,s), 2N) - N))),\n \t CRT(r,s).transpose() * \n \t d * (-E(4))\n \t Tensor(C[1], C[2]) \n \t d \n \t CRT(r,s)\n \t)\n#D \tisApplicable := P -> P[1] > 2 and DivisorPairsRP(P[1]) <> [] and Length(P[3]) = 0,\n#D \tallChildren := P -> let(N := P[1], k:= P[2], Map2(DivisorPairsRP(N), \n#D \t\t(r,s) -> [ DFT4(r, 1/s mod r), DFT4(s, 1/r mod s) ])),\n#D \t\n#D \trule := (P,C) -> let(\n#D \t N := P[1],\n#D \t r := Rows(C[1]), \n#D \t s := Rows(C[2]),\n#D \t alpha := 1 / s mod r,\n#D \t beta := 1 / r mod s,\n#D \t i := Ind(rs),\n#D \t d := Diag(Lambda(i, -sign(imod(salphaidiv(i,s) + rbetaimod(i,s), 2N) - N))),\n#D \t CRT(r,s).transpose() \n#D \t d * (-E(4))\n#D \t Tensor(C[1], C[2]) \n#D \t d *\n#D \t CRT(r,s)\n#D \t)\n )\n));\n\n", "meta": {"hexsha": "4e01c26420d3d8f474a10afc1e1f3171714b9f0c", "size": 5673, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/dft/dft234.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/transforms/dft/dft234.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/transforms/dft/dft234.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 32.6034482759, "max_line_length": 106, "alphanum_fraction": 0.4465009695, "num_tokens": 2287, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8376199633332891, "lm_q2_score": 0.6513548714339144, "lm_q1q2_score": 0.5455878435274346}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n# Here I define the new layer of \"index-free\" Sigma-SPL. I will use\n# this for library generation. The goal of index-free formulas is to\n# eliminate loop indices completely. In such formulas objects may\n# still depend on the loop indices, because gather/scatter/diagonal\n# functions become multivariate (vs. univariate) functions, taking\n# loop indices + point index as arguments. \n#\n# See \"Generalized Problem Spec\" write-up.\n#\n\nClass(GTIndexFunction, FuncClass, rec(\n isGTIndexFunction := true,\n\n # .upRank (=lift in spl.maude) is is the inverse of reduction .downRank, \n # it adds implicit dependency on the (new) inner loop, this happens when, eg.\n # gather is pulled into a loop: Gath(f) ISum(s) => ISum(Gath(f.upRank()) * s)\n upRank := self >> Error(\"Not implemented\"),\n\n upRankBy := (self, n) >> Checked(IsPosInt0(n), \n FoldL([1..n], (f, i) -> f.upRank(), self)),\n\n # .downRank (=red in spl.maude) is the \"reduction\" operator for\n # index mapping functions it eliminates implicit deendencies on loops \n # by introducing explicit references to loop variables ind(..)\n #\n # Eliminates dependency on loop <loopid>, 1 denotes innermost loop\n # <ind> is a loop index\n downRank := (self, loopid, ind) >> Error(\"Not implemented\"),\n\n # returns the rank, i.e., the number of implicit nested loops\n rank := self >> Error(\"Not implemented\"),\n\n # eliminated all loop dependencies \n downRankFull := (self, inds) >> \n FoldL(Reversed([1..Length(inds)]), (f, i) -> f.downRank(i, inds[i]), self),\n\n # split a loop, increase rank by 1, \n # if a loop had n iterations, the new outer loop will have <outer_its> iterations, \n # and next inner <inner_its> iterations\n split := (self, loopid, inner_its, outer_its) >> Error(\"not implemented\"),\n\n # rotate the ranks (see Doc(frotate) for explanation)\n rotate := (self, n) >> Error(\"not implemented\"),\n\n isUnitStride := self >> false,\n vecStride := (self, rank) >> self.params[4][rank+1],\n\n));\n\nClass(GTOps, rec(\n Print := PrintOps.Print,\n \\= := (a,b) -> When(IsBound(a.equals), a.equals(b), b=a)\n));\n\nIsGTIndexFunction := o -> IsRec(o) and IsBound(o.isGTIndexFunction) and o.isGTIndexFunction;\n\n# slow implementation, Haskell would love this\n_dropTail := (lst, arg) -> Cond(Length(lst)=0,lst,Cond(Last(lst)=arg, _dropTail(DropLast(lst, 1),arg), lst));\n\nClass(HHBase, GTIndexFunction, rec(\n abbrevs := [ (N,n,b,strides) -> [toExpArg(N), toExpArg(n), toExpArg(b), \n List(_dropTail(strides, 0), toExpArg)] ],\n def := (N, n, b, strides) -> Checked(IsList(strides), ForAll(strides, IsPosInt0Sym), \n\trec(N := N, n := n)), \n\n nloops := self >> Length(self.params[4]),\n free := self >> FreeVars(self.params),\n\n toSpl := (self, inds, kernel_size) >> self.downRankFull(inds),\n rank := self >> Maximum(0, Length(self.params[4])-1), # rank = number of implicit loop dependencies\n\n domain := self >> When(IsValue(self.params[2]), self.params[2].v, self.params[2]),\n range := self >> When(IsValue(self.params[1]), self.params[1].v, self.params[1]),\n\n base := self >> self.params[3],\n strides := self >> Cond(self.params[4] = [], [0], self.params[4]),\n\n # rotate(<n>)\n # switch the order of loops (represented by ranks), by making <n>-th loop innermost\n rotate := meth(self, n)\n local params, strides, rank;\n rank := self.rank();\n if rank<=1 and n<=1 then return self; \n elif n > rank then return self.upRank(); \n fi;\n \n params := ShallowCopy(self.params);\n strides := ShallowCopy(params[4]);\n strides := [strides[1], strides[n+1]] :: strides{[2..n]} :: strides{[n+2 .. rank+1]};\n params[4] := strides;\n return self.from_rChildren(params);\n end,\n\n isUnitStride := self >> false, # redefine if unit stride is possible\n));\n\nDeclare(KH, BHH, HH, HHZ);\n\n#F HH(<N>, <n>, <b>, <strides>) - generalized stride index mapping function\n#F N - range\n#F n - domain\n#F\n#F HH represents a multivariate function (j1 .. jn are indices of enclosing loops)\n#F (i, j1, ..., jn) -> b + strides[1]i + strides[2]j1 + ... + strides[n+1]jn\n#F\n#F Observe that dependence on the loop indices exists, even though no explicit\n#F loop index is present. This is how index free representation works.\n#F\nClass(HH, HHBase, rec(\n upRank := self >> let(s:=self.strides(), \n\tHH(self.params[1], self.params[2], self.params[3], Concatenation([s[1], 0], Drop(s, 1)))),\n\n downRank := (self, loopid, ind) >> Cond(loopid > self.rank(), self, let(s:=self.strides(),\n\tHH(self.params[1], self.params[2], s[loopid+1] ind + self.params[3], ListWithout(s, loopid+1)))),\n \n split := (self, loopid, inner_its, outer_its) >> Cond(loopid > self.rank(), self, let(\n strides := self.params[4],\n vs := self.params[4][1+loopid],\n\tHH(self.params[1], \n self.params[2], \n self.params[3], \n Concatenation(strides{[1..loopid+1]}, [inner_its * vs], strides{[loopid+2..Length(strides)]})))),\n \n lambda := self >> let(\n n := self.params[2],\n b := self.params[3],\n s := self.strides(),\n ind := List([1..Length(s)], i -> When(i=1, Ind(n), var.fresh_t(\"q\", TInt))),\n Lambda(Reversed(ind), b + Sum([1..Length(s)], i -> s[i] * ind[i]))),\n\n isUnitStride := self >> self.strides()[1] = 1\n));\n\nClass(BHH, HHBase, rec(\n abbrevs := [ (N,n,b,strides,refl) -> [toExpArg(N), toExpArg(n), toExpArg(b), List(_dropTail(strides,0), toExpArg), toExpArg(refl)] ],\n def := (N, n, b, strides, refl) -> Checked(\n IsList(strides), ForAll(strides, IsPosInt0Sym), IsPosIntSym(refl), \n\trec(N := N, n := n)), \n\n upRank := self >> let(s:=self.strides(), \n\tBHH(self.params[1], self.params[2], self.params[3], Concatenation([s[1], 0], Drop(s, 1)), self.params[5])),\n\n downRank := (self, loopid, ind) >> Cond(loopid > self.rank(), self, let(s:=self.strides(),\n\tBHH(self.params[1], self.params[2], self.params[3] + s[loopid+1] * ind, \n ListWithout(s, loopid+1), self.params[5]))),\n \n split := (self, loopid, inner_its, outer_its) >> Cond(loopid > self.rank(), self, let(\n strides := self.strides(),\n vs := self.params[4][1+loopid],\n\tBHH(self.params[1], \n self.params[2], \n self.params[3], \n Concatenation(strides{[1..loopid+1]}, [inner_its * vs], strides{[loopid+2..Length(strides)]}),\n self.params[5]))),\n \n lambda := self >> let(\n n := self.params[2],\n b := self.params[3],\n s := self.strides(),\n refl := self.params[5],\n inds := List([1..Length(s)], i -> When(i=1, Ind(n), var.fresh_t(\"q\", TInt))),\n res := b + Sum([1..Length(s)], i -> s[i] * inds[i]),\n Lambda(Reversed(inds), cond(leq(inds[1], idiv(n-1,2)), res, refl-res))\n ),\n));\n\n#F KH(<N>, <n>, <b>, <strides>, <corr>) - generalized (I_m dirsum J_m dirsum I_m ...) L^mn_n thingy\n#F N - range\n#F n - domain\n#F\n#F KH represents a multivariate function (j1 .. jn are indices of enclosing loops)\n#F (i, j1, ..., jn) -> b + strides[1]i + strides[2]j1 + ... + strides[n+1]jn\n#F\n#F Observe that dependence on the loop indices exists, even though no explicit\n#F loop index is present. This is how index free representation works.\n#F\nClass(KH, HHBase, rec(\n abbrevs := [ (N,n,b,strides,corr) -> [toExpArg(N), toExpArg(n), toExpArg(b), List(_dropTail(strides,0), toExpArg), List(corr, toExpArg)] ],\n def := (N, n, b, strides, corr) -> Checked(\n IsList(strides), ForAll(strides, IsPosInt0Sym), \n IsList(corr), ForAll(corr, IsIntSym), Length(corr) = 2, \n\trec(N := N, n := n)), \n\n upRank := self >> let(s:=self.strides(), \n\tKH(self.params[1], self.params[2], self.params[3], \n Concatenation([s[1], 0], Drop(s, 1)), \n self.params[5])),\n\n downRank := (self, loopid, ind) >> Checked(loopid=1, self.rank()=1, let(\n s:=self.strides(), corr:=self.params[5], b:=self.params[3],\n\tKH(self.params[1], \n self.params[2], \n b,\n [s[1]], \n [ s[2]ind + cond(neq(imod(ind,2),0), corr[2], corr[1]), \n s[1]-s[2]-ind + cond(neq(imod(ind,2),0), corr[1], corr[2]) ]))),\n \n lambda := self >> Checked(Length(self.strides())=1, let(\n n := self.params[2], \n b := self.params[3], \n s := self.strides()[1],\n i := Ind(n),\n corr_even := self.params[5][1], corr_odd := self.params[5][2],\n Lambda(i, b + si + imod(i+1, 2)corr_even + imod(i, 2)corr_odd)))\n));\n\n#F HHZ(<N>, <n>, <b>, <strides>) - generalized stride mod N index mapping (prime-factor FFT)\n#F N - range\n#F n - domain\n#F\n#F HHZ represents a multivariate function (j1 .. jn are indices of enclosing loops)\n#F (i, j1, ..., jn) -> (b + strides[1]i + strides[2]j1 + ... + strides[n+1]jn) mod N\n#F\n#F Observe that dependence on the loop indices exists, even though no explicit\n#F loop index is present. This is same as in HH. \n#F\nClass(HHZ, HHBase, rec(\n split := (self, loopid, inner_its, outer_its) >> Cond(loopid > self.rank(), self, let(\n strides := self.params[4],\n vs := self.params[4][1+loopid],\n\tHHZ(self.params[1], \n self.params[2], \n self.params[3], \n Concatenation(strides{[1..loopid+1]}, [inner_its * vs], strides{[loopid+2..Length(strides)]})))),\n\n upRank := self >> let(s:=self.strides(), \n\tHHZ(self.params[1], self.params[2], self.params[3], Concatenation([s[1], 0], Drop(s, 1)))),\n\n downRank := (self, loopid, ind) >> Cond(loopid > self.rank(), self, let(s:=self.strides(),\n\tHHZ(self.params[1], self.params[2], self.params[3] + s[loopid+1]ind, ListWithout(s, loopid+1)))),\n\n lambda := self >> let(hlambda := ApplyFunc(HH, self.params).lambda(),\n CopyFields(hlambda, rec(expr := imod(hlambda.expr, self.params[1]))))\n));\n\nDeclare(UU);\n\n## UU(<N>,<n>,<base>,<stride>,<columns>,<leading_dim>,\n## < <vstride_cols, vstride_rows>, ... > )\n## \n## index mapping: \n## (i, j1, ..., jn) -> \n## base + stride (i / columns) + leading_dim * (i mod columns)\n## + vstride_cols[1]j1 + ... + vstride_cols[n]jn\n## + (vstride_rows[1]j1 + ... + vstride_rows[n]jn)* leading_dim\n##\n## This is roughly the equivalent of an HH function for 2D inputs.\n\nClass(UU, GTIndexFunction, rec(\n abbrevs := [ (N, n, bX, bY, s, c, ld, strides) -> [toExpArg(N), toExpArg(n), toExpArg(bX), toExpArg(bY),\n toExpArg(s), toExpArg(c), toExpArg(ld),\n List(_dropTail(strides,[0,0]), x->List(x,toExpArg))] ],\n def := (N, n, bX, bY, s, c, ld, strides) -> Checked(IsList(strides), ForAll(strides, x-> \n IsList(x) and Length(x)=2 and ForAll(x,IsPosInt0Sym)), \n rec(N := N, n := n)), \n\n nloops := self >> Length(self.params[8]),\n free := self >> FreeVars(self.params),\n\n toSpl := (self, inds, kernel_size) >> self.downRankFull(inds),\n rank := self >> Length(self.params[8]), # rank = number of implicit loop dependencies\n\n domain := self >> When(IsValue(self.params[2]), self.params[2].v, self.params[2]),\n range := self >> When(IsValue(self.params[1]), self.params[1].v, self.params[1]),\n\n upRank := self >> let(ss:=self.params[8], \n\tUU(self.params[1], self.params[2], self.params[3], self.params[4], self.params[5], self.params[6], self.params[7], \n Concatenation([[0,0]], ss))),\n\n downRank := (self, loopid, ind) >> Cond(loopid > self.rank(), self, let(ss:=self.params[8],\n\tUU(self.params[1], self.params[2], self.params[3] + ss[loopid][1] * ind, self.params[4] + ss[loopid][2] * ind * self.params[7],\n self.params[5], self.params[6], self.params[7], ListWithout(ss, loopid)))),\n\n split := (self, loopid, inner_its, outer_its) >> Cond(loopid > self.rank(), self, let(\n strides := self.params[8],\n vs := self.params[8][loopid],\n UU(self.params[1], \n self.params[2], \n self.params[3], \n self.params[4],\n self.params[5],\n self.params[6],\n self.params[7],\n Concatenation(strides{[1..loopid]}, [inner_its * vs], strides{[loopid+1..Length(strides)]})))),\n\n \n lambda := self >> let(\n n := self.params[2],\n bX := self.params[3],\n bY := self.params[4],\n s := self.params[5],\n c := self.params[6],\n ld := self.params[7],\n ss := self.params[8],\n ind := List([1..Length(ss)], i -> var.fresh_t(\"q\", TInt)),\n index := Ind(n),\n Lambda(Concatenation(Reversed(ind),[index]), (bX + imod(index,c) * s) + (bY+idiv(index,c) * ld) + Sum([1..Length(ss)], i -> ss[i][1] * ind[i]) + Sum([1..Length(ss)], i -> ss[i][2] * ind[i] * ld))),\n\n isUnitStride := self >> Error(\"isUnitStride is not supported for now with UU\"),\n));\n\nDeclare(XChain);\n\n#F XChain( <permuted [1..n]> ) - fTensor chain of fBase's and single fId.\n#F\n#F This represents a subset of functions captured by HH. Namely those\n#F functions that described tightly packed index space, i.e.,\n#F if f is an XChain in k-nested loop with dimensions in loop_dims, then\n#F\n#F domain(f) * Product(loop_dims) = range(f)\n#F\nClass(XChain, GTIndexFunction, rec(\n def := perm -> Checked(IsList(perm), ForAll(perm, IsPosInt0), \n\tSet(Copy(perm))=[0..Length(perm)-1],\n rec()),\n\n range := self >> 0,\n domain := self >> 0,\n\n equals := (self, o) >> ObjId(self)=ObjId(o) and self.params[1]=o.params[1],\n\n printFull := self >> Print(self.name, \"(\", self.params[1], \")\"),\n printShort := self >> Print(\"x(\", PrintCS(self.params[1]), \")\"),\n\n toSpl := (self, inds, kernel_size) >> let(fbases := List(inds, fBase),\n\tApplyFunc(fTensor, List(self.params[1], i -> When(i=0, fId(kernel_size), fbases[i])))),\n\n toDiag := (self, loop_dims, kernel) >> let(fconst := List(loop_dims, d->fConst(d,1)),\n\tApplyFunc(diagTensor, List(self.params[1], i -> When(i=0, kernel, fconst[i])))),\n\n without := (self, loopid) >> Checked(loopid >= 1, loopid <= Length(self.params[1])-1, let(\n\tlst := ListWithout(self.params[1], Position(self.params[1], loopid)),\n\tXChain(List(lst, x -> When(x < loopid, x, x-1))))),\n\n part := (self, loopid, ind, kernel_size, loop_dims) >> \n ApplyFunc(fTensor, List(self.params[1], i ->\n\t Cond(i=0, fId(kernel_size),\n\t\t i=loopid, fBase(ind),\n\t\t fId(loop_dims[i])))),\n \n composeWith := (self, f) >> When(ObjId(f)<>XChain, Error(\"Can only compose with another XChain\"),\n\tlet(fperm := f.params[1], \n\t myperm := self.params[1],\n\t pos := Position(myperm, 0),\n\t XChain(Concatenation(1+myperm{[1..pos-1]}, fperm, 1+myperm{[pos+1..Length(myperm)]})))),\n));\n\n\n# NOTE: toSpl -> SubstTopDown( ind -> inds[i] )\n# Normal functions retrofitted for GT\nfId.toSpl := (self, inds, ksize) >> self; \nfId.without:= (self, loopid) >> self;\nfId.part := (self, loopid, loopvar, kernel_size, loop_dims) >> self;\n#fId.toDiag := (self, loop_dims) >> fConst(TReal, self.params[1], 1);\n\nfBase.toSpl := (self, inds, ksize) >> Cond(\n ObjId(self.params[2])=ind, fBase(inds[self.params[2].n]), \n self);\n\nfBase.without := (self, loopid) >> Cond(\n self.params[2]=ind(self.params[1], loopid), fBase(self.params[1], 0),\n self);\n\nfBase.part := (self, loopid, loopvar, ksize, loop_dims) >> Cond(\n self.params[2]=ind(self.params[1], loopid), fAdd(self.params[1], self.params[1], loopvar), \n fId(self.params[1]));\n\nfTensor.part := (self, loopid, loopvar, ksize, loop_dims) >>\n ApplyFunc(fTensor, List(self.children(), c -> c.part(loopid, loopvar, ksize, loop_dims)));\n\nfTensor.without := (self, loopid) >> \n ApplyFunc(fTensor, List(self.children(), c -> c.without(loopid)));\n\nfTensor.toSpl := (self, inds, ksize) >> \n ApplyFunc(ObjId(self), List(self.children(), c -> c.toSpl(inds, ksize)));\n\nfCompose.toSpl := (self, inds, ksize) >> \n ApplyFunc(fCompose, List(self.children(), c -> c.toSpl(inds, ksize)));\n\nFuncClass.toSpl := (self, inds, ksize) >> self;\n\n#FuncClassOper.rank := self >> Maximum(List(self.children(), x->x.rank()));\n#FuncClass.rank := self >> 0;\n#DiagFunc.rank := self >> 0;\n\nFuncClassOper.isUnitStride := self >> false; \nFuncClass.isUnitStride := self >> false;\nfId.isUnitStride := self >> true;\nfTensor.isUnitStride := self >> ForAll(self._children, x->x.isUnitStride());\n#fBase.toDiag := (self, loop_dims) >> fConst(TReal, self.params[1], 1);\n#fId.part := (self, loopid, ind, kernel_size, loop_dims) >> self;\n\nListAddP := function(l1, l2, c)\n local i, lenl1, lenl2, res, maxlen, minlen;\n lenl1 := Length(l1);\n lenl2 := Length(l2);\n minlen := Minimum(lenl1, lenl2);\n maxlen := Maximum(lenl1, lenl2);\n res := Concatenation(l1, Replicate(maxlen-lenl1, c)); \n for i in [1..lenl2] do \n res[i] := res[i] + l2[i];\n od;\n return res;\nend;\n\nListAddZP := (l1, l2) -> ListAddP(l1,l2,0);\nListAddLP := (l1, l2) -> ListAddP(l1,l2,[0,0]);\n\n", "meta": {"hexsha": "1823df912da8b34df8e5c51d2afb7a1b1e626cf5", "size": 17199, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/spl/gtfuncs.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/spl/gtfuncs.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/spl/gtfuncs.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 41.5434782609, "max_line_length": 206, "alphanum_fraction": 0.5891040177, "num_tokens": 5322, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. 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	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nImportAll(spiral.formgen);\nImportAll(spiral.transforms);\nImportAll(spiral.compiler);\n\ndoScalarDft := function(arg)\n\tlocal szs, userOpts, isSingle, opts, direction, func, file, t, rt, ir, N, cycles, flops;\n\t\n\tif not (Length(arg) in [1..2]) then\n\t\tError(\"usage: doScalarDft(sizes, [userOptions])\");\n\tfi;\n\t\n\tszs := When(IsList(arg[1]), arg[1], [ arg[1] ]);\n\tuserOpts := When(IsBound(arg[2]), arg[2], rec());\n\t\n\tisSingle := IsBound(userOpts.precision) and userOpts.precision = \"single\";\n\t\n\topts := CopyFields(SpiralDefaults, rec(\n\t\t\t\tprecision := When(isSingle, \"single\", \"double\"),\n\t\t\t\tTRealCtype := When(isSingle, \"float\", \"double\"),\n\t\t\t));\n\t\n\topts.globalUnrolling := 512;\n\t\t\n\tdirection := When(IsBound(userOpts.transInverse) and userOpts.transInverse, 1, -1);\n\t\n\tfor N in szs do\n\t\tif IsBound(userOpts.functionNameRoot) then\n\t\t\tfunc := ReplaceAll(userOpts.functionNameRoot, \"%sz1\", StringInt(N));\n\t\telse\n\t\t\tfunc := When(direction=1,\"i\",\"\")::\"DFT\"::When(isSingle, \"_SC\", \"_DC\")::StringInt(N);\n\t\tfi;\n\t\t\n\t\tfile := func::\".c\";\n\t\t\n\t\tt := DFT(N, direction);\n\t\trt := RandomRuleTree(t, opts);\n\t\tir := CodeRuleTree(rt, opts);\n\t\t\n\t\tPrintTo(file, PrintCode(func, ir, opts));\n\t\t\n\t\tcycles := CMeasure(ir, opts);\n\t\tflops:= t.normalizedArithCost();\n\t\tPrintLine(t, \" \", cycles, \" [cyc] \", _compute_gflops(flops, cycles), \" [Gf/s]\");\n\tod;\n\t\n\treturn true;\nend;\n\n\ndoScalar2DDft := function(arg)\n\tlocal szs, userOpts, isSingle, opts, direction, func, file, t, rt, ir, dims, cycles, flops;\n\t\n\tif not ((Length(arg) in [1..2]) and IsList(arg[1]) and Length(arg[1]) > 0) then\n\t\tError(\"usage: doScalar2DDft(sizes, [userOptions])\");\n\tfi;\n\t\n\tszs := arg[1];\n\tif Length(szs) = 2 and IsInt(szs[1]) and IsInt(szs[2]) then\n\t\tszs := [ szs ];\n\telif not ForAll(szs, dims -> Length(dims) = 2 and IsInt(dims[1]) and IsInt(dims[2])) then\n\t\tError(\"sizes must be one or more pairs of integers\");\n\tfi;\n\t\n\tuserOpts := When(IsBound(arg[2]), arg[2], rec());\n\t\n\tisSingle := IsBound(userOpts.precision) and userOpts.precision = \"single\";\n\t\n\topts := CopyFields(SpiralDefaults, rec(\n\t\t\t\tprecision := When(isSingle, \"single\", \"double\"),\n\t\t\t\tTRealCtype := When(isSingle, \"float\", \"double\"),\n\t\t\t));\n\t\t\t\t\n\topts.globalUnrolling := 128;\n\t\n\tdirection := When(IsBound(userOpts.transInverse) and userOpts.transInverse, 1, -1);\n\t\n\tfor dims in szs do\n\t\tif IsBound(userOpts.functionNameRoot) then\n\t\t\tfunc := ReplaceAll(userOpts.functionNameRoot, \"%sz1\", StringInt(dims[1]));\n\t\t\tfunc := ReplaceAll(func, \"%sz2\", StringInt(dims[2]));\n\t\telse\n\t\t\tfunc := When(direction=1,\"i\",\"\")::\"DFT\"::When(isSingle, \"_SC\", \"_DC\")::StringInt(dims[1])::\"x\"::StringInt(dims[2]);\n\t\tfi;\n\t\t\n\t\tfile := func::\".c\";\n\t\t\n\t\tt := MDDFT(dims, direction);\n\t\trt := RandomRuleTree(t, opts);\n\t\tir := CodeRuleTree(rt, opts);\n\t\t\n\t\tPrintTo(file, PrintCode(func, ir, opts));\n\t\t\n\t\tcycles := CMeasure(ir, opts);\n\t\tflops:= t.normalizedArithCost();\n\t\tPrintLine(t, \" \", cycles, \" [cyc] \", _compute_gflops(flops, cycles), \" [Gf/s]\");\n\tod;\n\t\n\treturn true;\nend;\n\n\n\nClass(ScriptGenScalar, ScriptGenBase, rec(\n\n\t_arch := () -> \"Scalar\",\n\n\n\t_init := meth(self)\n\t\tself._setTransform(SGKEY_FFT);\n\t\tself._setType(SGKEY_SPCX);\n\t\tself._setSize(16);\n\t\tself._setFilename(\"\");\n\tend,\n\t\n\t\n\t_validTransforms := meth(arg)\n\t\treturn [SGKEY_FFT, SGKEY_IFFT, SGKEY_FFT_2D, SGKEY_IFFT_2D];\n\tend,\n\t\n\t\n\t_validSizes := meth(arg)\n\t\tlocal self, szs, xform, type;\n\t\tself := arg[1];\n\t\tszs := [];\n\t\txform := self.getSettingsValue(SGKEY_TRANSFORM);\n\t\ttype := self.getSettingsValue(SGKEY_DATATYPE);\n\t\t\n\t\tif xform in [SGKEY_FFT, SGKEY_IFFT] then\n\t\t\tszs := Filtered([2..512], i->ForAll(Factors(i), j->j<=19));\n\t\t\tAppend(szs, Filtered([513..1024], i->ForAll(Factors(i), j->j<=19) and IsInt(i/16)));\n\t\t\tAppend(szs, List([11..16], i->2^i));\n\t\telif xform in [SGKEY_FFT_2D, SGKEY_IFFT_2D] then\n\t\t\tszs := List(Filtered([2..360], i->ForAll(Factors(i), j->j<=19)), n -> [n, n]);\n\t\telif xform = SGKEY_WHT then\n\t\t\tif type = SGKEY_DPCX then\n\t\t\t\tszs := List([2..10], i->2^i);\n\t\t\telse\n\t\t\t\tszs := List([4..10], i->2^i);\n\t\t\tfi;\n\t\tfi;\n\t\t\t\t\n\t\treturn szs;\n\tend,\n\t\n\t\n\t_validTypes := meth(arg)\n\t\treturn [SGKEY_SPCX, SGKEY_DPCX];\n\tend,\n\n\t\n\tgetScriptChoices := (self) >> [SGSTR_RUNRANDOMALL], \n\t\n\t\n\t_genScript := meth(self, runType)\n\t\tlocal scrstr, xform, type, szs, tempopts, optrec, optstr, funcstr;\n\t\t\n\t\txform\t := self.getSettingsValue(SGKEY_TRANSFORM);\n\t\ttype\t := self.getSettingsValue(SGKEY_DATATYPE);\n\t\tszs := self.getSettingsValue(SGKEY_SIZE);\n\t\t\n\t\ttempopts := \"scriptOpts\";\n\t\t\n\t\toptrec\t := rec(\n\t\t\t\t\t\tprecision := When(type=SGKEY_SPCX, \"single\", \"double\"),\n\t\t\t\t\t\tsearchType := runType,\n\t\t\t\t\t);\n\t\tif IsBound(self._settings.(SGKEY_FUNCNAME)) then\n\t\t\toptrec.functionNameRoot := self._settings.(SGKEY_FUNCNAME);\n\t\tfi;\n\t\tif xform in [SGKEY_IFFT, SGKEY_IFFT_2D] then\n\t\t\toptrec.transInverse := true;\n\t\tfi;\n\t\t\t\t\n\t\tif xform in [SGKEY_FFT, SGKEY_IFFT] then\n\t\t\tfuncstr := \"doScalarDft(\"::String(szs)::\", \"::tempopts::\")\";\n\t\telif xform in [SGKEY_FFT_2D, SGKEY_IFFT_2D] then\n\t\t\tfuncstr := \"doScalar2DDft(\"::String(szs)::\", \"::tempopts::\")\";\n\t\telse\n\t\t\treturn \"\";\n\t\tfi;\n\t\t\t\t\n\t\toptstr := StringPrint(optrec);\n\t\t\n\t\tscrstr := \"Import(scriptgen);;\\n\";\n\t\tAppend(scrstr, tempopts::\" := \"::optstr::\";;\\n\");\n\t\tAppend(scrstr, funcstr::\";;\\n\");\n\t\t\t\n\t\treturn scrstr;\n\tend,\n)); # Class ScriptGenScalar\n\n\nSetScriptGenConstructor(ScriptGenScalar);\n\n", "meta": {"hexsha": "d0e22d1fc5a012fb20fda58fd1c15a4e7ebb3799", "size": 5387, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/scriptgen/scalar.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/scriptgen/scalar.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", 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YES\n2. YES\n\n", "lm_q1_score": 0.7931059414036511, "lm_q2_score": 0.6859494678483918, "lm_q1q2_score": 0.5440305984532323}}
	{"text": "#############################################################################\n##\n## This file is part of GAP, a system for computational discrete algebra.\n## This file's authors include Alexander Hulpke.\n##\n## Copyright of GAP belongs to its developers, whose names are too numerous\n## to list here. Please refer to the COPYRIGHT file for details.\n##\n## SPDX-License-Identifier: GPL-2.0-or-later\n##\n## This file contains the methods for the construction of the basic fp group\n## types.\n##\n\n\n \n#############################################################################\n##\n#M TrivialGroupCons( <IsPcGroup> )\n##\nInstallMethod( TrivialGroupCons, \"fp group\",\n [ IsFpGroup and IsTrivial ],\n filter -> FreeGroup(0));\n\n\n#############################################################################\n##\n#M AbelianGroupCons( <IsFpGroup and IsFinite>, <ints> )\n##\nInstallMethod( AbelianGroupCons, \"fp group\", true,\n [ IsFpGroup and IsAbelian, IsList ], 0,\nfunction( filter, ints )\nlocal f,g,i,j,rels,gfam,fam;\n\n if Length(ints)=0 or not ForAll( ints, x -> IsInfinity(x) or (IsInt(x) and x >= 0) ) then\n Error( \"<ints> must be a list of integers\" );\n fi;\n\n f := FreeGroup(IsSyllableWordsFamily, Length(ints));\n g := GeneratorsOfGroup(f);\n rels:=[];\n for i in [1..Length(ints)] do\n for j in [1..i-1] do\n Add(rels,Comm(g[i],g[j]));\n od;\n if IsPosInt(ints[i]) then\n Add(rels,g[i]^ints[i]);\n fi;\n od;\n\n g:=f/rels;\n\n if ForAll(ints,IsPosInt) then\n SetSize( g, Product(ints) );\n else\n SetSize( g, infinity );\n fi;\n\n fam:=FamilyObj(One(f));\n gfam:=FamilyObj(One(g));\n gfam!.redorders:=ints;\n SetFpElementNFFunction(gfam,function(x)\n local u,e,i,j,n;\n u:=UnderlyingElement(x);\n e:=ExtRepOfObj(u); # syllable form\n\n # bring in correct order and reduction\n n:=ListWithIdenticalEntries(Length(gfam!.redorders),0);\n for i in [1,3..Length(e)-1] do\n j:=e[i];\n if IsPosInt(gfam!.redorders[j]) then\n\tn[j]:=n[j]+e[i+1] mod gfam!.redorders[j];\n else\n\tn[j]:=n[j]+e[i+1];\n fi;\n od;\n\n e:=[];\n for i in [1..Length(gfam!.redorders)] do\n if n[i]<>0 then\n\tAdd(e,i);\n\tAdd(e,n[i]);\n fi;\n od;\n\n return ObjByExtRep(fam,e);\n end);\n\n SetReducedMultiplication(g);\n SetIsAbelian( g, true );\n\n return g;\nend );\n\n#############################################################################\n##\n#M CyclicGroupCons( <IsFpGroup>, <n> )\n##\nInstallOtherMethod( CyclicGroupCons, \"fp group\", true,\n [ IsFpGroup and IsCyclic, IsObject ], 0,\nfunction( filter, n )\nlocal f,g,fam,gfam;\n if n=infinity then\n return FreeGroup(\"a\");\n elif not IsPosInt(n) then\n TryNextMethod();\n fi;\n f:=FreeGroup( IsSyllableWordsFamily, \"a\" );\n g:=f/[f.1^n];\n SetSize(g,n);\n fam:=FamilyObj(One(f));\n gfam:=FamilyObj(One(g));\n SetFpElementNFFunction(gfam,function(x)\n local u,e;\n u:=UnderlyingElement(x);\n e:=ExtRepOfObj(u); # syllable form\n if Length(e)=0 or (e[2]>=0 and e[2]<n) then\n return u;\n elif e[2] mod n=0 then\n return One(f);\n else\n e:=[e[1],e[2] mod n];\n return ObjByExtRep(fam,e);\n fi;\n end);\n\n SetReducedMultiplication(g);\n return g;\nend );\n\n\n#############################################################################\n##\n#M DihedralGroupCons( <IsFpGroup and IsFinite>, <n> )\n##\nInstallMethod( DihedralGroupCons,\n \"fp group\",\n true,\n [ IsFpGroup and IsFinite,\n IsInt and IsPosRat ],\n 0,\n\nfunction( filter, n )\nlocal f,rels,g;\n\n if n mod 2 = 1 then\n TryNextMethod();\n elif n = 2 then return\n CyclicGroup( IsFpGroup, 2 );\n fi;\n f := FreeGroup( IsSyllableWordsFamily, \"r\", \"s\" );\n rels:= [f.1^(n/2),f.2^2,f.1^f.2f.1];\n g := f/rels;\n SetSize(g,n);\n SetReducedMultiplication(g);\n return g;\n\nend );\n\nInstallOtherMethod( DihedralGroupCons,\n \"fp group\",\n true,\n [ IsFpGroup and IsFinite,\n IsInfinity ],\n 0,\n\nfunction( filter, inf )\nlocal f,rels,g;\n\n f := FreeGroup( IsSyllableWordsFamily, \"r\", \"s\" );\n rels:= [f.2^2,f.1^f.2f.1];\n g := f/rels;\n SetSize(g,infinity);\n SetReducedMultiplication(g);\n return g;\n\nend );\n\n#############################################################################\n##\n#M DicyclicGroupCons( <IsFpGroup and IsFinite>, <n> )\n##\nInstallMethod( DicyclicGroupCons,\n \"fp group\",\n true,\n [ IsFpGroup and IsFinite,\n IsInt and IsPosRat ],\n 0,\nfunction( filter, n )\nlocal f,rels,g;\n if 0 <> n mod 4 then\n TryNextMethod();\n elif n = 4 then return\n CyclicGroup( IsFpGroup, 4 );\n fi;\n f := FreeGroup( IsSyllableWordsFamily, \"r\", \"s\" );\n rels:= [ f.1^2/f.2^(n/4), f.2^(n/2), f.2^f.1*f.2 ];\n g := f/rels;\n SetSize(g,n);\n if n <= 10^4 then SetReducedMultiplication(g); fi;\n return g;\nend );\n\n#############################################################################\n##\n#M ElementaryAbelianGroupCons( <IsFpGroup and IsFinite>, <n> )\n##\nInstallMethod( ElementaryAbelianGroupCons,\n \"fp group\",\n true,\n [ IsFpGroup and IsFinite and IsElementaryAbelian,\n IsInt and IsPosRat ],\n 0,\n\nfunction( filter, n )\n if n = 1 then\n return CyclicGroupCons( IsFpGroup, 1 );\n elif not IsPrimePowerInt(n) then\n Error( \"<n> must be a prime power\" );\n fi;\n n:= AbelianGroupCons( IsFpGroup, Factors(n) );\n SetIsElementaryAbelian( n, true );\n return n;\nend );\n\n\n#############################################################################\n##\n#M FreeAbelianGroupCons( <IsFpGroup>, <rank> )\n##\nInstallMethod( FreeAbelianGroupCons,\n \"fp group\",\n true,\n [ IsFpGroup and IsAbelian,\n IsInt and IsPosRat ],\n 0,\n\nfunction( filter, rank )\n return AbelianGroupCons( filter, ListWithIdenticalEntries(rank, 0) );\n # TODO: Add the following if it ever moves from Polycyclic to the GAP core:\n #SetIsFreeAbelian( G, true );\nend );\n\n", "meta": {"hexsha": "ee11009956f70afcb4fb3b8cc06d5e5979c32076", "size": 5839, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "test_files/gap.gi", "max_stars_repo_name": "pheonixo/file_info", "max_stars_repo_head_hexsha": "1585f9938e591ea92312f49d9d2d7481951d9e18", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "test_files/gap.gi", "max_issues_repo_name": "pheonixo/file_info", "max_issues_repo_head_hexsha": "1585f9938e591ea92312f49d9d2d7481951d9e18", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "test_files/gap.gi", "max_forks_repo_name": "pheonixo/file_info", "max_forks_repo_head_hexsha": "1585f9938e591ea92312f49d9d2d7481951d9e18", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 23.9303278689, "max_line_length": 92, "alphanum_fraction": 0.5521493406, "num_tokens": 1795, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. 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	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nClass(LoopGath, Gath);\nClass(LoopScat, Scat);\nClass(LoopPrm, Prm);\n\nFuncClass.gath := self >> Gath(self);\nFuncClass.scat := self >> Scat(self);\n\nfId.gath := self >> I(self.params[1]);\nfId.scat := self >> I(self.params[1]);\n\nL.scat := self >> let(m:=self.params[2], n:=self.params[1]/self.params[2], j:=Ind(m), fid := fId(n), fbase := fBase(m,j),\n gath := Gath(fTensor(fid, fbase)), scat := Scat(fTensor(fbase, fid)),\n ISum(j, m, scatgath));\n\nL.gath := self >> let(m:=self.params[2], n:=self.params[1]/self.params[2], j:=Ind(n), fid := fId(m), fbase := fBase(n,j),\n gath := Gath(fTensor(fbase, fid)), scat := Scat(fTensor(fid, fbase)),\n ISum(j, n, scatgath));\n\nfCompose.gath := self >> Compose(Reversed(List(self.children(), i->i.gath())));\nfCompose.scat := self >> Compose(List(self.children(), i->i.scat()));\n\nfTensorBuf := function(func, combine)\n local ch, n, loopvars, i, lv, newch1, newch2, res; \n ch := func.children();\n n := Length(ch);\n loopvars := List(Filtered(ch, c -> ObjId(c)=fId), c -> Ind(c.size));\n \n lv := 1; newch1 := []; newch2 := [];\n for i in [1..n] do\n if ObjId(ch[i]) <> fId then\n\t Add(newch1, ch[i]);\n\telse\n\t Add(newch1, fBase(loopvars[lv]));\n\t Add(newch2, fBase(loopvars[lv]));\n\t lv := lv+1;\n\tfi;\n od;\n\n res := combine(fTensor(newch1), fTensor(newch2));\n\n # lv here is number of loopvars + 1\n for i in Reversed([1..lv-1]) do\n res := ISum(loopvars[i], res);\n\t# unroll inner loop\n\t#if i=lv-1 then res:=BB(res); fi;\n od;\n return res;\nend;\n\n#fTensor.gath := self >> Tensor(List(self.children(), i->i.gath()));\n\nfTensor.scat := self >> fTensorBuf(self, (f1, f2) -> BB(Scat(f1) * Gath(f2)));\nfTensor.gath := self >> fTensorBuf(self, (f1, f2) -> BB(Scat(f2) * Gath(f1)));\n\n", "meta": {"hexsha": "4f89fd32e5386ba906724a93425be4250bfc5d8e", "size": 1925, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/loops/sigmaspl.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/paradigms/loops/sigmaspl.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/paradigms/loops/sigmaspl.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 32.0833333333, "max_line_length": 121, "alphanum_fraction": 0.5688311688, "num_tokens": 632, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7662936430859597, "lm_q2_score": 0.7090191214879992, "lm_q1q2_score": 0.5433168456226456}}
	{"text": "# Built-in\nA := [[1, 2], [3, 4], [5, 6], [7, 8]];\nB := [[1, 2, 3], [4, 5, 6]];\n\nPrintArray(A);\n# [ [ 1, 2 ],\n# [ 3, 4 ],\n# [ 5, 6 ],\n# [ 7, 8 ] ]\n\nPrintArray(B);\n# [ [ 1, 2, 3 ],\n# [ 4, 5, 6 ] ]\n\nPrintArray(A * B);\n# [ [ 9, 12, 15 ],\n# [ 19, 26, 33 ],\n# [ 29, 40, 51 ],\n# [ 39, 54, 69 ] ]\n", "meta": {"hexsha": "3367ffc2635a5f7bf5c19cff40d3a3b7f0f01fc8", "size": 340, "ext": "gap", "lang": "GAP", "max_stars_repo_path": "Task/Matrix-multiplication/GAP/matrix-multiplication.gap", "max_stars_repo_name": "LaudateCorpus1/RosettaCodeData", "max_stars_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_stars_repo_licenses": ["Info-ZIP"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2018-11-09T22:08:38.000Z", "max_stars_repo_stars_event_max_datetime": "2018-11-09T22:08:38.000Z", "max_issues_repo_path": "Task/Matrix-multiplication/GAP/matrix-multiplication.gap", "max_issues_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_issues_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_issues_repo_licenses": ["Info-ZIP"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Task/Matrix-multiplication/GAP/matrix-multiplication.gap", "max_forks_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_forks_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_forks_repo_licenses": ["Info-ZIP"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2018-11-09T22:08:40.000Z", "max_forks_repo_forks_event_max_datetime": "2018-11-09T22:08:40.000Z", "avg_line_length": 17.0, "max_line_length": 38, "alphanum_fraction": 0.2764705882, "num_tokens": 204, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8933094003735664, "lm_q2_score": 0.6076631698328916, "lm_q1q2_score": 0.5428312218725211}}
	{"text": "# Solving equations over Free Groups\n\nInstallGlobalFunction(FreeGroupEquationSolve,\nfunction(w,u)\n local vars, consts;\n\n vars := GeneratorsOfGroup(FreeGroupOfWord(w));\n consts := GeneratorsOfGroup(FreeGroupOfWord(u));\n\nend);\n\n\n#\tex and ey are the x- and y-exponent sums of the word w respectively.\n#\tq is the quotient of the exponent sums, e.g. if exponent sums are 3 and 7 then q=2, as 2x3+1=7\n#\taut:=[x', y'] is a list consisting of the Neilsen generating pair corresponding to the Moldovanskii rewriting.\n#\tThat is, if w' is the rewritten form of w then there exists an automorphism\n#\t\\phi of F(x, y) such that \\phi(w)=w'. In aut, x' and y' are such that\n#\t\\phi(x)=x', \\phi(y)=y'. For example, for mold:=Moldovanskii(u); where u is\n#\tsome word over x and y, then mold[1]; and MappedWord(u, [x, y], mold[2]); are\n#\tthe same word.\n# NOTE: It may be that MappedWord is better than Eliminated word\n#\tfor our purposes? As might not use syllable notation! (Section 36.3-1 of GAP\n#\tdocumentation.)\n\n# TODO: Tests: Some words to rewrite + test that applying the auotmorphism\n# stabilises them.\n# Check whether w is a commutator, and error if it is\n# Error(\"w is a commutator\");\n# Error(\"\");\n\nInstallGlobalFunction(MoldovanskiiRewritingByGenerators,\nfunction(w,x,y)\n\t local ex, ey, q, aut;\n\n\t ex := ExponentSumWord(w, x);\n\t ey := ExponentSumWord(w, y);\n\t aut := [x, y];\n\n\t while ex<>0 and ey<>0 do\n\t\t if AbsInt(ey)>=AbsInt(ex) then\n\t\t\t q := -QuoInt(ey, ex); # QuoInt is quotient of integers\n\t\t\t w := MappedWord(w, [x], [xy^q] );\n\t\t\t aut[1] := MappedWord(aut[1], [x], [xy^q] );\n\t\t\t aut[2] := MappedWord(aut[2], [x], [xy^q] );\n\t\t\t ey := ExponentSumWord(w, y);\n\t\t elif AbsInt(ex)>AbsInt(ey) then\n\t\t\t q := -QuoInt(ex, ey);\n\t\t\t w := MappedWord(w, [y], [yx^q] );\n\t\t\t aut[1] := MappedWord(aut[1], [y], [yx^q] );\n\t\t\t aut[2] := MappedWord(aut[2], [y], [yx^q] );\n\t\t\t ex := ExponentSumWord(w, x);\n\t\t fi;\n\t od;\n\t return [w, aut];\nend);\n\n# We're looking for solutions to w(x,y) = u(a,b)\n# 1. Rewrite w(x,y) as w_0(xy^-1x, y)\n# If expoent sum of x <> 0 or y <> 0 then do\n# Moldovanski rewriting to get one of htem to 0.\n# Also remember the rewriting step\n# 2. If w_0 is in <x^eps y x, y> or <y^eps x y, x >\n# (If w_0 in <y^-1xy, x> then reinterpret x->x_0, y->x_0y_0\n\n# Solves the equation w(x,y) = u(a,b) where w in F(x,y) :wq\n# There is no real reason to not use\n# list and not just 2 variables\nInstallGlobalFunction(IsSolution,\nfunction(w, u, xs, ixs)\n return MappedWord(w, xs, ixs) = u;\nend);\n\nInstallGlobalFunction(SubwordLength,\nfunction(word_string, i)\n\tlocal subword, exp, next_exp, subcount, letter, j;\n\tsubcount := 0;\n\twhile i <= Length(word_string) do\n\t\tnext_exp := 0;\n\t\tletter := word_string[i];\n\t\tif IsAlphaChar(letter) then\n\t\t\tif word_string[i+1] = '^' then\n\t\t\t\tnext_exp := Int([word_string[i+2]]);\n\t\t\t\ti := i + 3;\n\t\t\t\twhile IsDigitChar(word_string[i]) do\n\t\t\t\t\tnext_exp := 10next_exp;\n\t\t\t\t\tnext_exp := next_exp + Int([word_string[i]]);\n\t\t\t\t\ti := i + 1;\n\t\t\t\tod;\n\t\t\t\tsubcount := subcount + next_exp;\n\t\t\telse\n\t\t\t\tsubcount := subcount + 1;\n\t\t\t\ti := i + 1;\n\t\t\tfi;\n\t\telif letter = ')' then\n\t\t\treturn subcount;\n\t\telif letter = '(' then\n\t\t\tsubword := SubwordLength(word_string, i + 1);\n\t\t\tj := 0;\n\t\t\twhile word_string[i + j] <> ')' do\n\t\t\t\tj := j + 1;\n\t\t\tod;\n\t\t\ti := i + j + 1;\n\t\t\texp := 1;\n\t\t\tif i >= Length(word_string) then\n\t\t\t\treturn -1;\n\t\t\tfi;\n\t\t\tif word_string[i] = '^' then\n\t\t\t\texp := Int([word_string[i + 1]]);\n\t\t\t\ti := i + 2;\n\t\t\t\twhile IsDigitChar(word_string[i]) do\n\t\t\t\t\texp := 10exp;\n\t\t\t\t\texp := exp + Int([word_string[i]]);\n\t\t\t\t\ti := i + 1;\n\t\t\t\tod;\n\t\t\tfi;\n\t\t\tsubcount := subcount + (exp * subword);\n\t\t\tif i >= Length(word_string) then\n\t\t\t\treturn -1;\n\t\t\tfi;\n\t\telse\n\t\t\ti := i + 1;\n\t\tfi;\n\tod;\nend);\n\n# Find solutions to an equation w(x,y) = u(a,b)\n# up to length n by brute force\n# w(x, y) is a function of variables\n# u(a, b) is a function of constants\n# Trying to solve for x and y\n\nInstallGlobalFunction(ShortSolutions,\nfunction(w, u, n)\n local variables, constants, f, gens, const, consts, vars, copy, solutions, tree, c1, c2, c3, c4, nodes, word_string, letter, subcount, i, next_exp, start_consts, exps;\n\tsolutions := [];\n\ttree := rec();\n\tnodes := [1];\n\n variables := FreeGroupOfWord(w);\n\tconstants := FreeGroupOfWord(u);\n\n\tf := FreeGroup(Concatenation(List(GeneratorsOfGroup(constants), String),\n\t\t\t\t\t\t\t\t List(GeneratorsOfGroup(variables), String)));\n\tgens := GeneratorsOfGroup(f){[1 .. Length(GeneratorsOfGroup(variables))]};\n\tvars := GeneratorsOfGroup(f){[Length(GeneratorsOfGroup(variables)) + 1 ..\n\t\t\t\t\t\t\t\t Length(GeneratorsOfGroup(f))]};\n\tconsts := Concatenation(gens, List(gens, Inverse));\n\tstart_consts := Concatenation(consts, [f.1f.1^-1]);\n\ttree.children := List(start_consts, x -> rec(value := x, parent := tree));\n\ttree.value := f.1 f.1^-1;\n\tw := MappedWord(w, GeneratorsOfGroup(variables), vars);\n\tu := MappedWord(u, GeneratorsOfGroup(constants), consts);\n\n\tif u = f.1 * f.1^-1 then\n\t\tword_string := String(w);\t\t\n\t\tif IsDigitChar(word_string[Length(word_string)]) then\n\t\t\tif word_string[1] = '(' then\n\t\t\t\tsubcount := SubwordLength(word_string, 2);\n\t\t\t\tif subcount > 0 then\n\t\t\t\t\tw := Subword(w, 1, subcount);\n\t\t\t\tfi;\n\t\t\tfi;\n\t\tfi;\n\t\texps := ExponentSums(w);\n\t\tif RemInt(exps[3], exps[4]) <> 0 and RemInt(exps[4], exps[3]) <> 0 then\n\t\t\treturn [[f.1 * f.1^-1, f.1 * f.1^-1]];\n\t\tfi;\n\tfi;\n\n\tfor const in start_consts do\n\t\tcopy := MappedWord(w, [vars[1]], [const]);\n\t\tif copy = u then\n\t\t\tAdd(solutions, [const, 0]);\n\t\tfi;\n\t\tsolutions := BuildTree(const, consts, tree, copy, u, f, solutions, 0, n, nodes);\n\tod;\n\t# Print(nodes[1]);\n\t# Print(\"\\n\");\n\treturn solutions;\nend);\n\nInstallGlobalFunction(BuildTree,\nfunction(x, consts, node, copy, u, f, solutions, n, limit, nodes)\n\tlocal child, const, word, grandchild, c, child_rec;\n\tnodes[1] := nodes[1] + 1;\n\tif n > limit then\n\t\treturn solutions;\n\tfi;\n\tfor child in node.children do\n\t\tchild.children := [];\n\t\tc := MappedWord(copy, [f.4], [child.value]);\n\t\tif c = u then\n\t\t\tAdd(solutions, [x, child.value]);\n\t\tfi;\n\t\tif child.value <> (f.1f.1^-1) then\n\t\t\tfor const in consts do\n\t\t\t\tword := child.value const;\n\t\t\t\tif word = child.parent.value then\n\t\t\t\t\tcontinue;\n\t\t\t\tfi;\n\t\t\t\tchild_rec := rec();\n\t\t\t\tchild_rec.value := word;\n\t\t\t\tchild_rec.parent := child;\n\t\t\t\tAdd(child.children, child_rec);\n\t\t\tod;\n\t\tfi;\n\tod;\n\tfor child in node.children do\n\t\tBuildTree(x, consts, child, copy, u, f, solutions, n + 1, limit, nodes);\n\tod;\n\treturn solutions;\nend);\n\nInstallMethod(FreeGroupOfWord, \"for a word over the free group\",\n [IsWord], w -> FamilyObj(w)!.freeGroup);\n\nGreenTest := function(n)\n local w, u, F, U, x, y, a, b;\n\n F := FreeGroup(\"x\", \"y\");\n x := F.1; y := F.2;\n\n\n w := x * y * x;\n u := a^2 * b^2 * a^2;\n\n return ShortSolutions(w, u, n);\nend;\n\n", "meta": {"hexsha": "4acbd80dffc1495df5d70a8390b32ff854e09f74", "size": 6861, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "gap/Equations.gi", "max_stars_repo_name": "db213/GreenMachine", "max_stars_repo_head_hexsha": "fbed716dbd4332ba0deb5110eb7f5a00335b12c8", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "gap/Equations.gi", "max_issues_repo_name": "db213/GreenMachine", "max_issues_repo_head_hexsha": "fbed716dbd4332ba0deb5110eb7f5a00335b12c8", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2018-01-14T00:50:08.000Z", "max_issues_repo_issues_event_max_datetime": "2018-01-14T00:50:08.000Z", "max_forks_repo_path": "gap/Equations.gi", "max_forks_repo_name": "db213/GreenMachine", "max_forks_repo_head_hexsha": "fbed716dbd4332ba0deb5110eb7f5a00335b12c8", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 29.8304347826, "max_line_length": 171, "alphanum_fraction": 0.6152164408, "num_tokens": 2243, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7772998714925402, "lm_q2_score": 0.6959583250334526, "lm_q1q2_score": 0.5409683166126662}}
	{"text": "# De Caen, Mathon and Moorhouse's Preparata graph Pr(t, e)\nBindGlobal(\"PreparataGraph\", function(arg)\n local t, e, q, s, F, K, dp;\n if Length(arg) < 1 then\n Error(\"at least one argument expected\");\n return fail;\n fi;\n t := arg[1];\n if Length(arg) > 1 then\n e := arg[2];\n else\n e := 1;\n fi;\n q := 2^(2t-1);\n s := 2^e;\n F := GF(q);\n dp := DirectProduct(FieldMultiplicationPermutationGroup(q),\n FieldAdditionPermutationGroup(2),\n FieldAdditionPermutationGroup(q),\n FieldExponentiationPermutationGroup(q));\n return Graph(dp, Cartesian(F, GF(2), F), OnPreparata(q, s, dp),\n function(x,y)\n return x <> y\n and x[3]+y[3] = x[1]^s y[1] + x[1] * y[1]^s + (x[2]+y[2])(x[1]^(s+1) + y[1]^(s+1));\n end, true);\nend);\n\n# Quotient graph of the Preparata graph\nBindGlobal(\"PreparataQuotientGraph\", function(arg)\n local h, s, t, e, B, G, H, K, T, V;\n if Length(arg) < 2 then\n Error(\"at least two arguments expected\");\n return fail;\n fi;\n h := arg[1];\n if IsGraph(arg[2]) then\n G := arg[2];\n if IsFFE(G.names[1][3]) then\n s := 1;\n else\n s := Size(G.names[1][3]);\n fi;\n t := Log2Int(2sG.order)/4;\n else\n t := arg[2];\n if Length(arg) > 2 then\n e := arg[3];\n else\n e := 1;\n fi;\n G := PreparataGraph(t, e);\n fi;\n B := BasisVectors(Basis(GF(2^(2t-1))));\n if IsFFE(G.names[1][3]) then\n K := AdditiveGroup(B{[1..h]});\n V := List(G.names, x -> [x[1], x[2], x[3]+K]);\n else\n K := AdditiveGroup(B{[1..h+Log2Int(s)]});\n V := List(G.names, x -> [x[1], x[2], Elements(x[3])[1]+K]);\n fi;\n T := Set(List(V, x -> Positions(V, x)));\n H := Graph(Stabilizer(G.group, T, OnSetsSets), T, OnSets, function(x,y)\n return IsSubset(DistanceSet(G, 1, x), y);\n end, true);\n AssignVertexNames(H, List(T, x -> V[x[1]]));\n return H;\nend);\n\n# The coset graph of a Kasami code over an odd power extension\n# of a binary field.\nBindGlobal(\"KasamiGraph\", function(i, j, m)\n local q, s, t, dp, G;\n q := 2^i;\n s := q^(2*j+1);\n t := q^m + 1;\n G := FieldAdditionPermutationGroup(s);\n dp := DirectProduct(G, G, FieldExponentiationPermutationGroup(s));\n return Graph(dp, Elements(GF(s)^2), OnKasami(s, s, dp),\n function(x, y)\n return x <> y and x[1]+y[1] = (x[2]+y[2])^t;\n end, true);\nend);\n\n# The coset graph of an extended Kasami code over an odd power extension\n# of a binary field.\nBindGlobal(\"ExtendedKasamiGraph\", function(i, j, m)\n return ExtendedBipartiteDoubleGraph(KasamiGraph(i, j, m));\nend);\n\n# The coset graph of a Kasami code over a quadratic extension\n# of a binary field.\nBindGlobal(\"QuadraticKasamiGraph\", function(i)\n local q, s, t, dp;\n q := 2^i;\n s := q^2;\n t := q + 1;\n dp := DirectProduct(FieldAdditionPermutationGroup(q),\n FieldAdditionPermutationGroup(s),\n FieldExponentiationPermutationGroup(s));\n return Graph(dp, Cartesian(GF(q), GF(s)), OnKasami(q, s, dp),\n function(x, y)\n return x <> y and x[1]+y[1] = (x[2]+y[2])^t;\n end, true);\nend);\n\n# The coset graph of an extended Kasami code over a quadratic extension\n# of a binary field.\nBindGlobal(\"ExtendedQuadraticKasamiGraph\", function(i)\n return ExtendedBipartiteDoubleGraph(QuadraticKasamiGraph(i));\nend);\n", "meta": {"hexsha": "65dd07938c7043f00dccf9eac629de0881becf3b", "size": 3530, "ext": "gap", "lang": "GAP", "max_stars_repo_path": "lib/CodeGraphs.gap", "max_stars_repo_name": "jaanos/gap-graphs", "max_stars_repo_head_hexsha": "18dd56c9b90a12a717a0cc893fdd72c6343ee79b", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2015-10-27T15:54:29.000Z", "max_stars_repo_stars_event_max_datetime": "2016-11-07T14:09:44.000Z", "max_issues_repo_path": "lib/CodeGraphs.gap", "max_issues_repo_name": "jaanos/gap-graphs", "max_issues_repo_head_hexsha": "18dd56c9b90a12a717a0cc893fdd72c6343ee79b", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2015-04-20T23:13:11.000Z", "max_issues_repo_issues_event_max_datetime": "2015-04-20T23:13:11.000Z", "max_forks_repo_path": "lib/CodeGraphs.gap", "max_forks_repo_name": "jaanos/gap-graphs", "max_forks_repo_head_hexsha": "18dd56c9b90a12a717a0cc893fdd72c6343ee79b", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 31.8018018018, "max_line_length": 102, "alphanum_fraction": 0.5512747875, "num_tokens": 1131, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8840392756357327, "lm_q2_score": 0.6113819732941511, "lm_q1q2_score": 0.5404856768077062}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n#P Parametrized permutation classes\n#P --------------------------------\n#P\n\n## -----------------------------------------------------------------------------\n#F L(<n>, <str>) - stride permutation\n##\nClass(L, PermClass, rec(\n def := (n,str) -> Checked(IsPosIntSym(n), IsPosIntSym(str),\n (not (IsInt(n) and IsInt(str)) or n mod str = 0), rec()),\n\n domain := self >> self.params[1],\n range := self >> self.params[1],\n\n lambda := self >> let(\n n := self.params[1], str := self.params[2], i := Ind(n),\n Lambda(i, idiv(i, n/str) + str * imod(i, n/str))),\n\n transpose := self >> self.__bases__[1](self.params[1], self.params[1] / self.params[2]),\n isSymmetric := self >> (self.params[1] = self.params[2]^2) or (self.params[2] = 1) or (self.params[2] = self.params[1]),\n printlatex := self >> Print(\" \\\\stride^{\", self.params[1], \"}_{\",self.params[2],\"} \")\n\n));\n\n## -----------------------------------------------------------------------------\n#F Tr(<k>, <str>) - stride permutation L(kstr, str),\n##\n## This L equivalent is used to simplify rewriting, since k is not explicit in L,\n## and if symbolics are used, to extract it we have to do simplification tricks,\n## eg. n/f1(n) = f2(n).\n##\n## Tr stands for Transpose.\n##\nClass(Tr, PermClass, rec(\n def := (k,str) -> Checked(IsPosIntSym(k), IsPosIntSym(str), rec()),\n\n lambda := self >> let(\n k := self.params[1], str := self.params[2], i := Ind(kstr),\n Lambda(i, idiv(i, k) + str * imod(i, k))),\n\n domain := self >> self.params[1] * self.params[2],\n range := self >> self.params[1] * self.params[2],\n\n dims := self >> [self.range(), self.domain()],\n \n transpose := self >> self.__bases__[1](self.params[2], self.params[1])\n));\n\n## -----------------------------------------------------------------------------\n#F Z(N,k) : Cyclic shift by <k>, permutation {0, ..., n-1} -> {k,...,n-1, 0,...,k-1}\n##\n# if one redefines .lambda, then .transposed should be also handled in custom .lambda\nClass(Z, PermClass, rec(\n abbrevs := [ n -> [n,1] ],\n def := (n,k) -> rec(), \n domain := self >> self.params[1],\n range := self >> self.params[1],\n lambda := self >> let(n:=self.params[1], k:=self.params[2], i := Ind(n),\n Lambda(i, imod(i + k, n))),\n transpose := self >> self.__bases__[1](self.params[1], self.params[1] - self.params[2])\n));\n\n## -----------------------------------------------------------------------------\n#F J(N) : NxN reverse identity, also known as reversal permutation (1,n)(2,n-1)...\n##\nClass(J, PermClass, rec(\n def := n -> rec(), \n lambda := self >> let(i := Ind(self.params[1]), Lambda(i,self.params[1]-i-1)),\n domain := self >> self.params[1],\n range := self >> self.params[1],\n transpose := self >> self,\n isSymmetric := True\n));\n\n## -----------------------------------------------------------------------------\n#F OddStride(<n>, <str>)\n#F OS(<n>, <str>) - odd stride permutation (i -> i * str mod n)\n##\nClass(OS, PermClass, rec(\n isCyclic := true,\n def := (n,str) -> Checked(IsPosIntSym(n), IsIntSym(str), n > 0,\n AnySyms(n,str) or (Gcd(EvalScalar(n),EvalScalar(str))=1), rec()),\n domain := self >> self.params[1],\n range := self >> self.params[1],\n lambda := self >> let(i := Ind(self.params[1]),\n Lambda(i, imod(self.params[2] * i, self.params[1]))),\n transpose := self >> self.__bases__[1](self.params[1], self.params[2]^-1 mod self.params[1])\n));\nOddStride := OS;\n\nDeclare(gammaTensor);\n## -----------------------------------------------------------------------------\n#F CRT(<r>, <s>) - Chinese remainder theorem permutation function of size rs\n##\nClass(CRT, PermClass, rec(\n isCyclic := true,\n\n abbrevs := [ (r, s) -> Checked(IsPosIntSym(r), IsPosIntSym(s), AnySyms(r,s) or Gcd(r,s)=1,\n let(alpha := 1/s mod r,\n beta := 1/r mod s,\n [r, s, alpha, beta])) ],\n\n toGammaTensor := self >> gammaTensor(\n OddStride(self.params[1], self.params[3]),\n OddStride(self.params[2], self.params[4])),\n\n def := (r, s, alpha, beta) -> Checked(\n IsPosIntSym(r), IsPosIntSym(s), AnySyms(r, s) or Gcd(r,s)=1,\n rec()),\n\n domain := self >> self.params[1] self.params[2],\n range := self >> self.params[1] * self.params[2],\n\n lambda := self >> let(\n r := self.params[1], s := self.params[2], N := rs,\n alpha := self.params[3], beta := self.params[4],\n aa := (1/s/alpha) mod r, bb := (1/r/beta) mod s,\n i := Ind(N),\n When(not self.transposed,\n Lambda(i, ((salphaidiv(i, s)) + (rbetaimod(i, s))) mod N),\n Lambda(i, s(imod(iaa, r)) + (imod(ibb, s))))),\n));\n\nClass(fCond, FuncClass, rec(\n def := (cond, f1, f2) -> Checked(\n f1.range() = f2.range(),\n f1.domain() = f2.domain(),\n\trec()),\n\n domain := self >> self.params[1].domain(),\n range := self >> self.params[2].range(),\n\n lambda := self >> let(f1 := self.params[2], f2:= self.params[3], mycond := self.params[1],\n i := Ind(f1.domain()),\n Lambda(i, cond(mycond.lambda().at(i), f1.lambda().at(i), f2.lambda().at(i)))),\n\n transpose := self >> let(base := self.__bases__[1],\n base(self.params[1], self.params[2].transpose(), self.params[3].transpose()))\n));\n\n# ----------------------------------------------------------\n# Bit and Digit reversals\n# ----------------------------------------------------------\n\n# Return x as a b-bit value, formed as a vector\n_numToBits := (k, b) >> Reversed(List([1..b], i-> imod(idiv(k, 2^(i-1)), 2)));\n\n# Return number corresponding to bit vector b\n_bitsToNum := b -> let(\n l := Reversed(b),\n Sum([1..Length(l)], i -> 2^(i-1) * l[i]));\n\n# Calculate base-r digit reversed value of k, where k is between 0 and n-1\n_digitRev := function(k, n, r)\n local bitval, numbits, bitsperchunk, numchunks, res_bits, i, s; \n\n numbits := Log2Int(n);\n bitsperchunk := Log2Int(r);\n numchunks := numbits / bitsperchunk;\n\n bitval := _numToBits(k, numbits);\n \n res_bits := [];\n for i in Reversed([1..numchunks]) do\n s := bitval{([bitsperchunki-(bitsperchunk-1) .. bitsperchunk i])};\n Append(res_bits, s);\n od;\n\n return _bitsToNum(res_bits);\nend;\n\n#F DR(<k, r>) - digit reversal permutation R^k_r\n##\nClass(DR, PermClass, rec(\n def := (k, r) -> Checked(IsInt(k), Is2Power(k), (r^(LogInt(k,r)) = k), rec()),\n\n domain := self >> self.params[1],\n range := self >> self.params[1],\n # This is very slow because of how Gap evaluates functions\n # lambda := self >> let(\n # n := self.params[1], base := self.params[2], t := LogInt(n, base),\n # rev := List([1..t], i-> fTensor(fId(base^(t-i)), L(base^i, base))),\n # fCompose(Reversed(rev)).lambda()),\n\n# This is faster but a little bit uglier.\n lambda := self >> let(\n i := Ind(self.params[1]),\n Lambda(i, _digitRev(i, self.params[1], self.params[2]))),\n\n transpose := self >> self\n));\n\n#F BR(<k>) - bit reversal permutation\n##\nClass(BR, PermClass, rec(\n def := k -> Checked(IsInt(k), Is2Power(k), rec()), \n domain := self >> self.params[1],\n range := self >> self.params[1],\n lambda := self >> DR(self.params[1], 2).lambda(),\n transpose := self >> self\n));\n", "meta": {"hexsha": "b51bed1eb9909529221d07ab10fdf162020a2a5c", "size": 7353, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/spl/perms.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/spl/perms.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/spl/perms.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 35.5217391304, "max_line_length": 124, "alphanum_fraction": 0.517747858, "num_tokens": 2109, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7718434873426303, "lm_q2_score": 0.6959583187272711, "lm_q1q2_score": 0.5371708957715707}}
	{"text": "################################################################################\r\n##\r\n#W GroupTheoretical_data.gi GroupTheoretical Package\r\n##\r\n#W Paul Bruillard, Cesar Galindo, Siu-Hung Ng, Julia Plavnik, Eric Rowell,\r\n#W Zhenghan Wang\r\n##\r\n## Installation file for functions in the GroupTheoretical_data portion of the GroupTheoretical package\r\n##\r\n#Y Copyright (C) 2016, Battelle Memorial Institute\r\n##\r\n################################################################################\r\n\r\n\r\n################################################################################\r\n##\r\n#F DG_S_and_T(<group>,<bool>) Computes Simples, S, T, FPdim(Xi), FPdimC for D(G)\r\n##\r\nInstallGlobalFunction(DG_S_and_T, function(G,display)\r\n local g, elmsG, R, r, tbl, chi, Simples, x, y, S, s, T, rank, x_idx, y_idx, FPdim, FPdimC,l,pseudounitary_data,sorted_data;\r\n elmsG := Elements(G);\r\n if display then \r\n Print(\"\\nG = \", StructureDescription(G), \" \", IdGroup(G), \"\\n\");\r\n fi;\r\n\r\n # compute the simples\r\n R := List(ConjugacyClasses(G), Representative);\r\n Simples := [];\r\n for r in R do\r\n tbl := CharacterTable(Centralizer(G, r));\r\n for chi in Irr(tbl) do\r\n Add(Simples, [r, chi, ConjugacyClasses(tbl)]);\r\n od;\r\n od;\r\n rank:=Size(Simples);\r\n\r\n if display then\r\n Print(\"Rank is\\n\\n\");\r\n Display(rank);\r\n Print(\"Computing S matrix\\n\");\r\n fi;\r\n\r\n # compute the S-matrix\r\n # since s is symmetric we can half the size of the inner loop\r\n #S := NullMat(rank,rank);\r\n S:=[];\r\n# for x_idx in [1..rank] do\r\n# x:=Simples[x_idx];\r\n for x in Simples do\r\n l:=[];\r\n #for y_idx in [x_idx..rank] do\r\n# for y_idx in [1..rank] do\r\n# y:=Simples[y_idx];\r\n for y in Simples do\r\n s := 0;\r\n for g in elmsG do\r\n if x[1]gy[1]Inverse(g) = gy[1]Inverse(g)x[1] then\r\n s := s + ComplexConjugate(x[2][Position(x[3], \r\n ConjugacyClass(Centralizer(G, x[1]), gy[1]Inverse(g)))])\r\n * ComplexConjugate(y[2][Position(y[3], \r\n ConjugacyClass(Centralizer(G, y[1]), Inverse(g)x[1]g))]);\r\n fi;\r\n od;\r\n s := s * (1/(Size(Centralizer(G, x[1])) * Size(Centralizer(G, y[1])))) * Size(G);\r\n #S[x_idx][y_idx] := s;\r\n #S[y_idx][x_idx] := s;\r\n Add(l,s);\r\n od;\r\n Add(S,l);\r\n od;\r\n\r\n # compute the T-matrix\r\n T := [];\r\n for x in Simples do\r\n Add(T, x[2][Position(x[3], ConjugacyClass(Centralizer(G, x[1]), x[1]))]/x[2][1]);\r\n od;\r\n\r\n if display then\r\n Print(\"\\n The S-matrix is: \\n\\n\");\r\n Print(S);\r\n Print(\"\\n\\n The T-matrix is: \\n\\n\");\r\n Print(T);\r\n Print(\"\\n\\n\");\r\n fi;\r\n\r\n pseudounitary_data := pseudounitary_sort(S,T,Simples);\r\n Simples := pseudounitary_data[1];\r\n S := pseudounitary_data[2];\r\n T := pseudounitary_data[3];\r\n FPdim := pseudounitary_data[4];\r\n FPdimC := pseudounitary_data[5];\r\n\r\n # sort by dimensions (if two objects have the same dimension, their\r\n # relative order is unchanged).\r\n sorted_data := dimension_sort(S,T,Simples,FPdim);\r\n Simples:=sorted_data[1];\r\n S:=sorted_data[2];\r\n T:=sorted_data[3];\r\n FPdim:=sorted_data[4];\r\n\r\n return [Simples, S, T, FPdim, FPdimC];\r\nend);\r\n\r\n################################################################################\r\n##\r\n#F DG_data(<group>) . . . . . . . . . . . . . . .Computes modular data for D(G).\r\nInstallGlobalFunction(DG_data, function(G)\r\n local Simples, S, T, FPdim, FPdimC, N, data;\r\n data:=DG_S_and_T(G,false);\r\n Simples:=data[1];\r\n S:=data[2];\r\n T:=data[3];\r\n FPdim:=data[4];\r\n FPdimC:=data[5];\r\n N:=compute_fusion_rules(S,FPdimC);\r\n return [Simples,S,T,N,FPdim,FPdimC];\r\nend);\r\n\r\n#E DG_data.gi . . . . . . . . . . . . . . . . . . . . . . . . . . . . .ends here\r\n", "meta": {"hexsha": "524cdaabfc6052a2244fe094aeb5fa8890a367dd", "size": 3729, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "lib/DG_data.gi", "max_stars_repo_name": "pnnl/GroupTheoretical", "max_stars_repo_head_hexsha": "d60aaec27d2ca98ec55b12b78213538a346eef27", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "lib/DG_data.gi", "max_issues_repo_name": "pnnl/GroupTheoretical", "max_issues_repo_head_hexsha": "d60aaec27d2ca98ec55b12b78213538a346eef27", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2021-05-20T21:43:28.000Z", "max_issues_repo_issues_event_max_datetime": "2021-05-20T21:43:28.000Z", "max_forks_repo_path": "lib/DG_data.gi", "max_forks_repo_name": "pnnl/GroupTheoretical", "max_forks_repo_head_hexsha": "d60aaec27d2ca98ec55b12b78213538a346eef27", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 2, "max_forks_repo_forks_event_min_datetime": "2017-12-07T13:46:25.000Z", "max_forks_repo_forks_event_max_datetime": "2020-12-12T22:39:35.000Z", "avg_line_length": 31.075, "max_line_length": 126, "alphanum_fraction": 0.5258782515, "num_tokens": 1141, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. 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	{"text": "# Using SageMath interface for GAP\n# To start GAP inside of SageMath:\n# gap.console()\n#\n# Defining groups in GAP:\n# PSL := FreeProduct(CyclicGroup(2),CyclicGroup(3))\n#\n# Using SageMath to access GAP's\n# finitely presented groups functionality\n# https://doc.sagemath.org/html/en/reference/groups/sage/groups/finitely_presented.html\n\n# from sage.interfaces.gap import get_gap_memory_pool_size, set_gap_memory_pool_size\n# set_gap_memory_pool_size(20000000000)\n\nk := 4;\n\nF := FreeGroup(\"t_k\", \"c\", \"d\");\n\nG := F / [F.3^(-1)F.1(F.3F.2^(-1))^(-k+1)F.1(F.3F.2^(-1))^(k-1)(F.1^(-1)),\n F.2^(-1)F.1F.2F.3^(-1)(F.1)^(-1)F.3F.1F.3F.2^(-1)(F.1)^(-1)];\n\nRelatorsOfFpGroup(G);\n\nAllHomomorphismClasses(G, SymmetricGroup(3));\n# AllHomomorphisms(G, SymmetricGroup(3));\n\n", "meta": {"hexsha": "a13c755d5a4c8a81a1d5cbf91636ab811bc8cff4", "size": 777, "ext": "gap", "lang": "GAP", "max_stars_repo_path": "src/gap_tests.gap", "max_stars_repo_name": "ben300694/knot-theory", "max_stars_repo_head_hexsha": "f4d889466495da3bc42f6808c9c4a1f5940480eb", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2022-03-23T17:47:05.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-23T17:47:05.000Z", "max_issues_repo_path": "src/gap_tests.gap", "max_issues_repo_name": "ben300694/knot-theory", "max_issues_repo_head_hexsha": "f4d889466495da3bc42f6808c9c4a1f5940480eb", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "src/gap_tests.gap", "max_forks_repo_name": "ben300694/knot-theory", "max_forks_repo_head_hexsha": "f4d889466495da3bc42f6808c9c4a1f5940480eb", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 28.7777777778, "max_line_length": 87, "alphanum_fraction": 0.6692406692, "num_tokens": 286, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8128673087708699, "lm_q2_score": 0.6584175072643415, "lm_q1q2_score": 0.5352060671775899}}
	{"text": "# Constants\nBindGlobal(\"Graph6ByteInteger\", 62);\nBindGlobal(\"Graph6WordInteger\", 258047);\nBindGlobal(\"Graph6DwordInteger\", 68719476735);\nBindGlobal(\"Graph6MaxInteger\", Graph6DwordInteger);\nBindGlobal(\"Graph6BitVector\", List([0..5], i -> 2^(5-i)));\nBindGlobal(\"Graph6IntVector\", List([0..5], i -> 64^(5-i)));\n\n# graph6 integer encoding\nBindGlobal(\"Graph6EncodeInteger\", function(x)\n if not IsInt(x) or x < 0 or x >= Graph6MaxInteger then\n Error(\"not an integer in allowed range\");\n return fail;\n fi;\n if x <= Graph6ByteInteger then\n return [x+63];\n elif x <= Graph6WordInteger then\n return [63, Int(x/4096), Int(x/64), x] mod 64 + 63;\n else\n return Concatenation([126, 126],\n List(Graph6IntVector, y -> Int(x/y) mod 64 + 63));\n fi;\nend);\n\n# graph6 integer decoding\nBindGlobal(\"Graph6DecodeInteger\", function(i, s)\n if s[i] <> 126 then\n return [i+1, s[i] - 63];\n elif s[i+1] <> 126 then\n return [i+4, (s{[i+1..i+3]} - 63)Graph6IntVector{[4..6]}];\n else\n return [i+8, (s{[i+2..i+7]} - 63)Graph6IntVector];\n fi;\nend);\n\n# Convert an integer to a bitstring of length w\nBindGlobal(\"IntToBits\", function(x, w)\n return List([1..w], i -> Int(x / 2^(w-i)) mod 2);\nend);\n\n# Convert a bitstring to a list of integers given the width w\nBindGlobal(\"BitsToInt\", function(b, w)\n local out, i;\n out := [];\n i := 0;\n while i+w <= Length(b) do\n Add(out, b{[i+1..i+w]} * List([1..w], j -> 2^(w-j)));\n i := i+w;\n od;\n return out;\nend);\n\n# Convert a bitstring to a graph6 string with padding p\nBindGlobal(\"BitsToString\", function(b, p)\n local c;\n c := Concatenation(b, ListWithIdenticalEntries(-Length(b) mod 6, p));\n return List([0,6..Length(c)-6], i -> c{[i+1..i+6]}Graph6BitVector + 63);\nend);\n\n# Convert a graph6 string to a bitstring\nBindGlobal(\"StringToBits\", function(s)\n return Concatenation(List(s, x -> List(Graph6BitVector, y -> Int((x-63)/y) mod 2)));\nend);\n\n# graph6 string\nBindGlobal(\"Graph6String\", function(G)\n local A, s;\n A := CollapsedAdjacencyMat(Group(()), G);\n s := Concatenation(Graph6EncodeInteger(G.order),\n BitsToString(Concatenation(List([1..G.order], i -> A[i]{[1..i-1]})), 0));\n return List(s, CharInt);\nend);\n\n# Read graph from graph6 string\nBindGlobal(\"GraphFromGraph6String\", function(s)\n local A, b, n, i, j, t;\n s := List(s, IntChar);\n t := Graph6DecodeInteger(1, s);\n i := t[1];\n n := t[2];\n b := StringToBits(s{[i..Length(s)]});\n A := NullMat(n, n);\n i := 1;\n for j in [2..n] do\n A[j]{[1..j-1]} := b{[i..i+j-2]};\n A{[1..j-1]}[j] := b{[i..i+j-2]};\n i := i+j-1;\n od;\n return AdjFunGraph([1..n], MatrixAdjacency(A));\nend);\n\n# sparse6 string\nBindGlobal(\"Sparse6String\", function(G)\n local i, j, b, c, v, w;\n w := Log2Int(G.order-1)+1;\n b := [];\n v := 1;\n for i in [1..G.order] do\n for j in [1..i] do\n if IsVertexPairEdge(G, i, j) then\n if i = v+1 then\n c := 1;\n else\n if i > v then\n Add(b, 1);\n Append(b, IntToBits(i-1, w));\n fi;\n c := 0;\n fi;\n Add(b, c);\n Append(b, IntToBits(j-1, w));\n v := i;\n fi;\n od;\n od;\n if G.order in [2,4,8,16] and (-Length(b)) mod 6 > w\n and Length(Adjacency(G, G.order-1)) > 0\n and Length(Adjacency(G, G.order)) = 0 then\n Add(b, 0);\n fi;\n return List(Concatenation([58], Graph6EncodeInteger(G.order),\n BitsToString(b, 1)), CharInt);\nend);\n\n# Read graph from sparse6 string\nBindGlobal(\"GraphFromSparse6String\", function(s)\n local A, b, t, i, m, n, v, w, c, x, y, z;\n if s[1] = ':' then\n s := s{[2..Length(s)]};\n fi;\n s := List(s, IntChar);\n t := Graph6DecodeInteger(1, s);\n i := t[1];\n n := t[2];\n w := Log2Int(n-1)+1;\n b := StringToBits(s{[i..Length(s)]});\n A := List([1..n], j -> []);\n i := 1;\n v := 1;\n z := BitsToInt(b, w+1);\n m := 2^w;\n for y in z do\n c := Int(y/m);\n x := y mod m + 1;\n if c = 1 then\n v := v+1;\n fi;\n if v > n or x > n then\n break;\n fi;\n if x > v then\n v := x;\n else\n Add(A[x], v);\n Add(A[v], x);\n fi;\n od;\n return AdjFunGraph([1..n], ListAdjacency(A));\nend);\n\n# sparse6 string\nBindGlobal(\"IncrementalSparse6String\", function(G, H)\n local i, j, b, c, v, w;\n if G.order <> H.order then\n Error(\"graphs have different orders\");\n return fail;\n fi;\n w := Log2Int(G.order-1)+1;\n b := [];\n v := 1;\n for i in [1..G.order] do\n for j in [1..i] do\n if IsVertexPairEdge(G, i, j) <> IsVertexPairEdge(H, i, j) then\n if i = v+1 then\n c := 1;\n else\n if i > v then\n Add(b, 1);\n Append(b, IntToBits(i-1, w));\n fi;\n c := 0;\n fi;\n Add(b, c);\n Append(b, IntToBits(j-1, w));\n v := i;\n fi;\n od;\n od;\n if G.order in [2,4,8,16] and (-Length(b)) mod 6 > w\n and Adjacency(G, G.order-1) = Adjacency(H, G.order-1)\n and Adjacency(G, G.order) = Adjacency(H, G.order) then\n Add(b, 0);\n fi;\n return List(Concatenation([59], BitsToString(b, 1)), CharInt);\nend);\n\n# Read graph from incremental sparse6 string\nBindGlobal(\"GraphFromIncrementalSparse6String\", function(s, H)\n local A, B, b, i, m, v, w, c, x, y, z;\n if s[1] = ';' then\n s := s{[2..Length(s)]};\n fi;\n B := List([1..H.order], j -> Adjacency(H, j));\n A := List(B, ShallowCopy);\n s := List(s, IntChar);\n w := Log2Int(H.order-1)+1;\n b := StringToBits(s);\n i := 1;\n v := 1;\n z := BitsToInt(b, w+1);\n m := 2^w;\n for y in z do\n c := Int(y/m);\n x := y mod m + 1;\n if c = 1 then\n v := v+1;\n fi;\n if v > H.order or x > H.order then\n break;\n fi;\n if x > v then\n v := x;\n elif x in A[v] then\n Remove(A[x], Position(A[x], v));\n if x <> v then\n Remove(A[v], Position(A[v], x));\n fi;\n else\n Add(A[x], v);\n Add(A[v], x);\n fi;\n od;\n return AdjFunGraph([1..H.order], ListAdjacency(A));\nend);\n\n# auto6 string\nBindGlobal(\"Auto6String\", function(G)\n local b, g, h, i, l, p, r, s, w, x, sch;\n g := GeneratorsOfGroup(G.group);\n l := [1..Length(g)];\n i := 0;\n for p in [1..Length(g)] do\n if g[p] = () then\n i := i+1;\n else\n l[p] := l[p] - i;\n fi;\n od;\n sch := List(G.schreierVector, function(y)\n if y < 0 then\n return y;\n else\n return l[y];\n fi;\n end);\n g := Filtered(g, y -> y <> ());\n w := Log2Int(G.order-1)+1;\n r := Length(G.representatives);\n b := IntToBits(r, w);\n for i in [1..r] do\n Append(b, IntToBits(G.representatives[i]-1, w));\n Append(b, IntToBits(Length(G.adjacencies[i]), w));\n for x in G.adjacencies[i] do\n Append(b, IntToBits(x-1, w));\n od;\n od;\n for h in g do\n for i in [1..G.order] do\n Append(b, IntToBits(i^h - 1, w));\n od;\n od;\n if Length(g) > 1 then\n s := Log2Int(Length(g)) + 1;\n for i in [1..G.order] do\n if sch[i] < 0 then\n Append(b, IntToBits(0, s));\n else\n Append(b, IntToBits(sch[i], s));\n fi;\n od;\n fi;\n return List(Concatenation([33], Graph6EncodeInteger(G.order),\n Graph6EncodeInteger(Length(g)), BitsToString(b, 0)), CharInt);\nend);\n\n# Read graph from auto6 string\nBindGlobal(\"GraphFromAuto6String\", function(s)\n local G, A, R, S, a, b, d, r, t, g, i, j, k, n, v, w;\n if s[1] = '!' then\n s := s{[2..Length(s)]};\n fi;\n s := List(s, IntChar);\n t := Graph6DecodeInteger(1, s);\n i := t[1];\n n := t[2];\n w := Log2Int(n-1)+1;\n t := Graph6DecodeInteger(i, s);\n i := t[1];\n g := t[2];\n b := StringToBits(s{[i..Length(s)]});\n d := BitsToInt(b, w);\n r := d[1];\n if r = 0 then\n r := n;\n fi;\n i := 2;\n R := [];\n A := [];\n for j in [1..r] do\n Add(R, d[i]+1);\n Add(A, d{[i+2..i+d[i+1]+1]}+1);\n i := i + d[i+1] + 2;\n od;\n if g = 0 then\n G := ();\n v := List([1..n], x -> -Position(R, x));\n else\n G := [];\n for j in [1..g] do\n Add(G, PermList(d{[i..i+n-1]}+1));\n i := i+n;\n od;\n if g = 1 then\n v := List([1..n], function(x)\n local y;\n y := Position(R, x);\n if y = fail then\n return 1;\n else\n return -y;\n fi;\n end);\n else\n k := w(i-1);\n t := Log2Int(g)+1;\n v := BitsToInt(b{[k+1..k+n*t]}, t);\n for j in [1..r] do\n v[R[j]] := -j;\n od;\n fi;\n fi;\n return rec(\n isGraph := true,\n order := n,\n names := [1..n],\n representatives := Immutable(R),\n adjacencies := A,\n group := Group(G),\n schreierVector := Immutable(v)\n );\nend);\n", "meta": {"hexsha": "8cee5edc4931010811ef544fefc461f2f8a2265b", "size": 9802, "ext": "gap", "lang": "GAP", "max_stars_repo_path": "lib/Graph6.gap", "max_stars_repo_name": "jaanos/gap-graphs", "max_stars_repo_head_hexsha": "18dd56c9b90a12a717a0cc893fdd72c6343ee79b", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2015-10-27T15:54:29.000Z", "max_stars_repo_stars_event_max_datetime": "2016-11-07T14:09:44.000Z", "max_issues_repo_path": "lib/Graph6.gap", "max_issues_repo_name": "jaanos/gap-graphs", "max_issues_repo_head_hexsha": "18dd56c9b90a12a717a0cc893fdd72c6343ee79b", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2015-04-20T23:13:11.000Z", "max_issues_repo_issues_event_max_datetime": "2015-04-20T23:13:11.000Z", "max_forks_repo_path": "lib/Graph6.gap", "max_forks_repo_name": "jaanos/gap-graphs", "max_forks_repo_head_hexsha": "18dd56c9b90a12a717a0cc893fdd72c6343ee79b", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 27.8465909091, "max_line_length": 88, "alphanum_fraction": 0.4531728219, "num_tokens": 3088, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8397339596505966, "lm_q2_score": 0.6334102636778403, "lm_q1q2_score": 0.5318961088015213}}
	{"text": "# The vector product of two vectors with 3 elements.\nBindGlobal(\"VectorProduct\", function(u, v)\n return [u[2]v[3]-u[3]v[2], u[3]v[1]-u[1]v[3], u[1]v[2]-u[2]v[1]];\nend);\n\n# Multiplication in Hall algebras\nBindGlobal(\"HallMultiplication\", function(p)\n local r;\n r := CoefficientsOfUnivariatePolynomial(p)[2];\n return function(x, y)\n if IsZero(y[2]) then\n return xy[1];\n else\n return [x[1]y[1] - x[2]/y[2]Value(p, y[1]),\n x[1]y[2] - x[2](y[1] + r)];\n fi;\n end;\nend);\n\n# Multiplication in Dickson near-fields\nBindGlobal(\"DicksonMultiplication\",\n q -> function(x, y)\n if IsZero(y) then\n return 0Z(q);\n else\n return x^(q^LogFFE(y, Z(q^2))) * y;\n fi;\n end);\n\n# Right division in Dickson near-fields\nBindGlobal(\"DicksonRightDivision\",\n q -> function(x, y)\n if IsZero(x) then\n return 0Z(q);\n else\n return (x / y)^(q^LogFFE(y, Z(q^2)));\n fi;\n end);\n\n# Multiplication in exceptional near-fields\nBindGlobal(\"ExceptionalMultiplication\", function(q, F, B)\n local mat;\n mat := ToExceptionalMatrix(q, F, B);\n return function(x, y)\n local M;\n M := mat(x) mat(y);\n return M[1]B;\n end;\nend);\n\n# Right division in exceptional near-fields\nBindGlobal(\"ExceptionalRightDivision\", function(q, F, B)\n local mat;\n mat := ToExceptionalMatrix(q, F, B);\n return function(x, y)\n local M;\n M := mat(x) mat(y)^-1;\n return M[1]*B;\n end;\nend);\n\n# Normalize a vector over a semifield given the semifield right division.\nBindGlobal(\"NormalizeSemifieldVector\",\n div -> function(v)\n local n;\n n := First(v, x -> not IsZero(x));\n return List(v, x -> div(x, n));\n end);\n", "meta": {"hexsha": "8f27104f607d8e8ad8864ef6ba0c7d2a691091d0", "size": 1864, "ext": "gap", "lang": "GAP", "max_stars_repo_path": "lib/Operations.gap", "max_stars_repo_name": "jaanos/gap-graphs", "max_stars_repo_head_hexsha": "18dd56c9b90a12a717a0cc893fdd72c6343ee79b", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2015-10-27T15:54:29.000Z", "max_stars_repo_stars_event_max_datetime": "2016-11-07T14:09:44.000Z", "max_issues_repo_path": "lib/Operations.gap", "max_issues_repo_name": "jaanos/gap-graphs", "max_issues_repo_head_hexsha": "18dd56c9b90a12a717a0cc893fdd72c6343ee79b", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2015-04-20T23:13:11.000Z", "max_issues_repo_issues_event_max_datetime": "2015-04-20T23:13:11.000Z", "max_forks_repo_path": "lib/Operations.gap", "max_forks_repo_name": "jaanos/gap-graphs", "max_forks_repo_head_hexsha": "18dd56c9b90a12a717a0cc893fdd72c6343ee79b", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 27.0144927536, "max_line_length": 75, "alphanum_fraction": 0.5461373391, "num_tokens": 547, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7745833737577158, "lm_q2_score": 0.6859494550081925, "lm_q1q2_score": 0.5313250430875123}}
	{"text": "InsertionSort := function(L)\n local n, i, j, x;\n n := Length(L);\n for i in [ 2 .. n ] do\n x := L[i];\n j := i - 1;\n while j >= 1 and L[j] > x do\n L[j + 1] := L[j];\n j := j - 1;\n od;\n L[j + 1] := x;\n od;\nend;\n\ns := \"BFKRIMPOQACNESWUTXDGLVZHYJ\";\nInsertionSort(s);\ns;\n# \"ABCDEFGHIJKLMNOPQRSTUVWXYZ\"\n", "meta": {"hexsha": "8ea81dd042ef9a4b87b81fc7f45ab938d64eaa05", "size": 324, "ext": "gap", "lang": "GAP", "max_stars_repo_path": "Task/Sorting-algorithms-Insertion-sort/GAP/sorting-algorithms-insertion-sort.gap", "max_stars_repo_name": "LaudateCorpus1/RosettaCodeData", "max_stars_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_stars_repo_licenses": ["Info-ZIP"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2018-11-09T22:08:38.000Z", "max_stars_repo_stars_event_max_datetime": "2018-11-09T22:08:38.000Z", "max_issues_repo_path": "Task/Sorting-algorithms-Insertion-sort/GAP/sorting-algorithms-insertion-sort.gap", "max_issues_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_issues_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_issues_repo_licenses": ["Info-ZIP"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Task/Sorting-algorithms-Insertion-sort/GAP/sorting-algorithms-insertion-sort.gap", "max_forks_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_forks_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_forks_repo_licenses": ["Info-ZIP"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2018-11-09T22:08:40.000Z", "max_forks_repo_forks_event_max_datetime": "2018-11-09T22:08:40.000Z", "avg_line_length": 17.0526315789, "max_line_length": 34, "alphanum_fraction": 0.4845679012, "num_tokens": 130, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7690802370707281, "lm_q2_score": 0.6893056104028797, "lm_q1q2_score": 0.5301313222628298}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nvtransposelo := (l1,l2,n) -> Flat(List([1..n/2], i-> [l1[2i-1],l2[2i-1]]\n));\n\nvtransposehi := (l1,l2,n) -> Flat(List([1..n/2], i-> [l1[2i],l2[2i]]\n));\n\nvrev64 := (l1,n) -> Flat(List([1..n/2], i-> [l1[2i],l1[2i-1]]\n));\n", "meta": {"hexsha": "ccf3ee9fb0f0f51460e7d74514c0a764dd7e693e", "size": 307, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/platforms/neon/misc.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/platforms/neon/misc.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/platforms/neon/misc.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 21.9285714286, "max_line_length": 74, "alphanum_fraction": 0.5472312704, "num_tokens": 139, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.72487026428967, "lm_q2_score": 0.7279754489059774, "lm_q1q2_score": 0.5276877560448671}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n# alpha is a function of P (divisor of N)\n# m = N/P\n\n# Frequency domain, u in [0, N)\n# Per processor, total pts=2m, total useful pts=m\n# We start to see aliasing at 3m/2, m=N/P.\nW := (alpha, u) -> exp(-alpha * u^2);\n\n# Time domain, t in [0, 1]\nw := (alpha, t) -> sqrt(d_PI / alpha) * exp(-d_PI^2 * t^2 / alpha);\n\n# digits - eg. 17, number of exact (unaffected by aliasing) decimal digits\ngauss_alpha := (N, p, digits) -> let(m := N/p, 4/9 * digits * d_log(10) / m^2);\n\n# how many samples of the filter to keep in the time domain, assuming gauss_alpha(N, p, digits)\n# was used.\nedge := digits -> IntDouble(d_ceil(2/(3d_PI) d_log(10) * digits));\n\n\nClass(fPerExt, FuncClass, rec(\n def := (N, l, r) -> rec(N:=N, n:=N+l+r),\n lambda := self >> let(N := self.params[1], l:=self.params[2], r:=self.params[3],\n \tj := Ind(self.n),\n\tLambda(j, imod(j-l, N)))\n));\n\n# below we should not use HZ, since HZ assumes that n * stride = N, and if used as below\n# assumption will be violated\n#RewriteRules(RulesFuncSimp, rec(\n# fPerExt_H := ARule(fCompose, [@(1,fPerExt), @(2,H)], e -> \n#\tlet(base := @(2).val.params[3], stride := @(2).val.params[4], \n#\t[ HZ(@(1).val.N, @(2).val.n, base - @(1).val.params[2], stride) ]))\n#));\n\n\nNewRulesFor(DFT, rec(\n\n DFT_Gauss := rec(\n\tforTransposition := true,\n\tminSize := 4,\n\tmaxSize := false,\n\tp := 4,\n\tdigits := 15,\n\n\tapplicable := (self, t) >> (self.minSize<>false and Rows(t) > self.minSize) and\n\t not IsPrime(Rows(t)) and t.params[2] in [1,-1 mod Rows(t)],\n\n libApplicable := (self, t) >> eq(imod(t.params[1], self.p), 0),\n\tfreedoms := (self, t) >> [],\n\n\tchild := (self, t, freedoms) >> let(N := Rows(t), p := self.p,\n\t [ DFT(2N/p, t.params[2]), DFT(p, t.params[2]) ]), \n \n\tapply := meth(self, t,C,Nonterms) \n\t local N, m, n, rot, k, p, alpha, time_filter, freq_filter, j;\n\t N := Rows(t); \n\t n := Rows(C[2]);\n\t k := edge(self.digits);\n\t p := self.p;\n\t m := N/p;\n\t alpha := gauss_alpha(N, p, self.digits);\n\n\t time_filter := let(i:=Ind(2kp), Lambda(i, w(alpha, (i-kp)/N)).setRange(TDouble));\n\t freq_filter := let(i:=Ind(m), Lambda(i, p/(2NW(alpha, i-m/2))).setRange(TDouble)); \n\t \n\t j := Ind(p);\n\t return \n\t Grp(\n\t\tIterDirectSum(j, j.range, \n\t\t Diag(freq_filter) * \n\t\t Gath(H(2m, m, mimod(j,2), 1)).toloop(4) * C[1]\n\t\t) \n\t\t(Tr(2N/p, p))\n\t ) * \n\t RowTensor(2N/p, 2kp-p/2, \n\t\tC[2] \n\t\tlet(i:=Ind(p), Diag(Lambda(i, omega(2p, i)).setRange(TComplex))) \n\t\tTensor(RowVec(List([0..2k-1], x->(-1)^x)), I(p)) \n\t\tDiag(time_filter)\n\t ) * \n\t Gath(fPerExt(N, kp, kp-p/2));\n\tend\n\t \n )\n));\n\n# scaling by p/(2N) belongs to the time_filter, but freq_filter is shorter\n#\t time_filter := List([-kp .. kp-1], i-> w(alpha, i/N));\n#\t freq_filter := List([-m/2..m/2-1], i-> p/(2NW(alpha, i))); \n\n#\t return\n#\t Z(N, m/2) \n#\t Tensor(I(p/2), \n#\t\t DirectSum(\n#\t\t Diag(freq_filter) * Gath(fStack(H(2m, m/2, 3m/2, 1), H(2m, m/2, 0, 1))) C[1],\n#\t\t Diag(freq_filter) * Gath(H(2m, m, m/2, 1)) C[1])\n#\t ) * \n\n\ntestGauss := function(N, p, k)\n local s, me, them;\n DFT_Gauss.p := p;\n SwitchRulesByNameQuiet(DFT, [DFT_Gauss]);\n s := SPLRuleTree(ExpandSPL(DFT(N,k))[1]);\n me := MatSPL(s);\n them := MatSPL(DFT(N,k));\n VisualizeMat(me-them, \" \");\n return [s, me, them];\nend;\n\nsplGauss := function(N, p, k)\n local s, me, them;\n DFT_Gauss.p := p;\n SwitchRulesByNameQuiet(DFT, [DFT_Gauss]);\n s := SPLRuleTree(ExpandSPL(DFT(N,k))[1]);\n return s;\nend;\n\nsums := function(s, opts)\n local real;\n real := s.isReal();\n s := SumsSPL(s);\n s := SubstBottomUp(s, @.cond(IsNonTerminal), x->RecursStep(0,0,x));\n s := ApplyStrategy(s, opts.formulaStrategies.sigmaSpl, UntilDone);\n if not opts.generateComplexCode and not real then\n s := ApplyStrategy(RC(s), opts.formulaStrategies.rc, UntilDone); fi;\n return ApplyStrategy(s, opts.formulaStrategies.postProcess, UntilDone);\nend;\n\n# opts := CopyFields(SpiralDefaults, rec(generateComplexCode := true));\n# opts := CopyFields(opts, rec(unparser := CMacroUnparser));\n\n# N := 128;\n# k := edge(17);\n# p := 4;\n# alpha := alpha(N, p, 17);\n\nNewRulesFor(DFT, rec(\n\n DFT_PrunedGauss := rec(\n\tforTransposition := true,\n\tminSize := 4,\n\tmaxSize := false,\n\tp := 2,\n\tdigits := 15,\n\n\tapplicable := (self, t) >> (self.minSize<>false and Rows(t) > self.minSize) and\n\t not IsPrime(Rows(t)) and t.params[2] in [1,-1 mod Rows(t)],\n\n\tchildren := (self, t) >> let(N := Rows(t), p := self.p,\n\t [[ DFT(2N/p, t.params[2]), DFT3(p, t.params[2]) ]]), #DFT3\n \n\tapply := meth(self, t,C,Nonterms) \n\t local N, m, n, mat, rot, k, p, alpha, time_filter, freq_filter, freq_filter2;\n\t N := Rows(t); \n\t n := Rows(C[2]);\n mat := MatSPL(C[2]);\n\t k := edge(self.digits);\n\t p := self.p;\n\t m := N/p;\n\t alpha := gauss_alpha(N, p, self.digits);\n\t time_filter := List([-kp .. kp-1], i-> w(alpha, i/N).eval());\n\t freq_filter := List([-m/2..m/2-1], i-> p/(2NW(alpha, i).eval())); \n\n\t return \n\t Diag(freq_filter) Gath(H(2m, m, 0, 1)) C[1] \n\t RowTensor(2N/p, 2kp-p/2, \n\t\tRowVec(mat[1]) \n\t\tTensor(RowVec(List([0..2k-1], x->(-1)^x)), I(p)) * \n\t\tDiag(time_filter)) \n\t transforms.filtering.Ext(N, transforms.filtering.per(k p), \n\t\t transforms.filtering.per(k * p - p/2));\n\tend\n )\n));\n\n#2N/p * 2kp\n#4Nk complex fmas overhead for filter (one stripe out), k=edge(digits)\n", "meta": {"hexsha": "b87d7e2d96d04f6a0277fb3227c2fbffd2ae7205", "size": 5624, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/dft/gauss.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/transforms/dft/gauss.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/transforms/dft/gauss.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 30.5652173913, "max_line_length": 95, "alphanum_fraction": 0.5554765292, "num_tokens": 1979, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8056321843145404, "lm_q2_score": 0.6548947357776795, "lm_q1q2_score": 0.5276042764806658}}
	{"text": "# return a list of two lists :\n# first is the list of months with five weekends between years y1 and y2 (included)\n# second is the list of years without such months, in the same interval\nFiveWeekends := function(y1, y2)\n local L, yL, badL, d, m, y;\n L := [ ];\n badL := [ ];\n for y in [y1 .. y2] do\n yL := [ ];\n for m in [1, 3, 5, 7, 8, 10, 12] do\n if WeekDay([1, m, y]) = \"Fri\" then\n d := StringDate([1, m, y]);\n Add(yL, d{[4 .. 11]});\n fi;\n od;\n if Length(yL) = 0 then\n Add(badL, y);\n else\n Append(L, yL);\n fi;\n od;\n return [ L, badL ];\nend;\n\nr := FiveWeekends(1900, 2100);;\nn := Length(r[1]);\n# 201\nLength(r[2]);\n# 29\nr[1]{[1 .. 5]};\n# [ \"Mar-1901\", \"Aug-1902\", \"May-1903\", \"Jan-1904\", \"Jul-1904\" ]\nr[1]{[n-4 .. n]};\n# [ \"Mar-2097\", \"Aug-2098\", \"May-2099\", \"Jan-2100\", \"Oct-2100\" ]\n", "meta": {"hexsha": "f48e053e413dd8407e8ba9d60dc9101392fef4d9", "size": 842, "ext": "gap", "lang": "GAP", "max_stars_repo_path": "Task/Five-weekends/GAP/five-weekends.gap", "max_stars_repo_name": "mullikine/RosettaCodeData", "max_stars_repo_head_hexsha": "4f0027c6ce83daa36118ee8b67915a13cd23ab67", "max_stars_repo_licenses": ["Info-ZIP"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2018-11-09T22:08:38.000Z", "max_stars_repo_stars_event_max_datetime": "2018-11-09T22:08:38.000Z", "max_issues_repo_path": "Task/Five-weekends/GAP/five-weekends.gap", "max_issues_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_issues_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_issues_repo_licenses": ["Info-ZIP"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Task/Five-weekends/GAP/five-weekends.gap", "max_forks_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_forks_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_forks_repo_licenses": ["Info-ZIP"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2018-11-09T22:08:40.000Z", "max_forks_repo_forks_event_max_datetime": "2018-11-09T22:08:40.000Z", "avg_line_length": 24.7647058824, "max_line_length": 83, "alphanum_fraction": 0.5213776722, "num_tokens": 341, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7371581741774411, "lm_q2_score": 0.7154239957834733, "lm_q1q2_score": 0.5273806464944745}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nDeclare(DWTper);\n\n#F DWTper(<n>, <j>, [<h(z)>,<g(z)>])\n#F DWTper(<n>, <j>, <L>, <V>)\n#F returns a 2-channel <j>-stage discrete wavelet transform with periodic extensions \n#F (circulant transforms) where the \n#F low pass and the high pass analysis filters given by polynomials \n#F [<h(z)>,<g(z)>] \n#F\n#F <L> = [<Lh>,<Lg>] - coefficient lists for h and g\n#F <V> = [<vh>,<vg>] - valuation for h and g\n#F\n#F <n> - size of the output of the reconstructed sequence\n#F <j> - number of filter bank stages\nClass(DWTper, NonTerminal, rec(\n\n abbrevs := [\n function(n,j,M)\n local S,L,V, j;\n if IsList(M[1]) then\n S:=List([1,2], j->FillZeros([M[1][j],M[2][j]]));\n V:=List(S, j->j[2]);\n L:=List(S, j->j[1]);\n return [n,j,L,V];\n else \n Checked(IsPosInt(n), Checked(ForAll(M,i->IsPolynomial(i)),true));\n S:=List(M, i-> FillZeros(i));\n V:=List(S, i->i[2]);\n L:=List(S, i->i[1]);\n return [n,j,L,V];\n fi;\n end,\n function(n,j,L,V)\n local S,V,L,i,j;\n S:=List([1,2], j->FillZeros([L[j],V[j]]));\n V:=List(S, j->j[2]);\n L:=List(S, j->j[1]);\n return [n,j,L,V];\n end\n ],\n\n dims := self >> [self.params[1], self.params[1]],\n\n half1 := self >> let(\n n := self.params[1],\n l1 := self.params[3][1],\n v1 := self.params[4][1],\n DownSample(n,2,0) * Circulant(n,l1,v1).terminate() ),\n\n half2 := self >> let(\n n := self.params[1],\n l2 := self.params[3][2], \n v2 := self.params[4][2],\n DownSample(n,2,0) * Circulant(n,l2,v2).terminate() ),\n \n terminate := self >> let(\n n := self.params[1],\n j := self.params[2],\n L := self.params[3],\n V := self.params[4], \n # DWT as filter bank stage + downsampling\n res := Cond(j = 1, I(n), \n\t DirectSum(DWTper(n/2,j-1,L,V).terminate(), I(n/2))) * \n VStack(self.half1(), self.half2()),\n When(self.transposed, res.transpose(), res)\n ),\n\n LiftingScheme := self >> self.lifting(),\n\n lifting := meth(self)\n local n,j,LS,h,g,he,ho,ge,go; \n n := self.params[1]; \n j := self.params[2];\n h := DownsampleTwo([self.params[3][1],self.params[4][1]]);\n g := DownsampleTwo([self.params[3][2],self.params[4][2]]);\n # Lifting scheme does not converge for wavelets longer than 9 \n # (need to be fixed)\n if (Maximum(List(h, i-> Length(i[1])))>9 or \n Maximum(List(g, i-> Length(i[1])))>9) then return [[]];fi;\n he := Poly(h[1][1],h[1][2]); \n ho := Poly(h[2][1],h[2][2]); \n ge := Poly(g[1][1],g[1][2]); \n go := Poly(g[2][1],g[2][2]); \n LS := LiftingScheme([[he,ho],[ge,go]]);\n return LS;\n end,\n\n isReal := True,\n));\n\n\n#F RuleFilter_DWT: (base case) DWT -> Mat, \n#F Computes filter by definition\n#F\nRulesFor(DWTper, rec(\n #F RuleFilt_Mallat_2:\n #F \n #F DWTper(n,j,[h,g])->DWTper(n/2,j-1,[h,g]),DWTper(n,1,[h,g]) \n #F\n #F Mallat rule recursive (single stage DWT)\n #F The I(n/2) is inefficient because it copies the output\n #F However, this rule allows application of Lifting, POlyphase, etc. \n #F on DWTper(n,1,[h,g])\n #F \n DWTper_Mallat_2 := rec(\n\tinfo := \"DWTper(n,j,[h,g])->DWTper(n,j-1,[h,g])\",\n\tforTransposition := false,\n\tisApplicable := P -> P[1] > 2 and P[1] mod 2 =0 and P[2] > 1,\n\n\tallChildren := P -> [[ DWTper(P[1]/2,P[2]-1,P[3],P[4]), DWTper(P[1],1,P[3],P[4]) ]],\n\n\trule := (P, C) -> DirectSum(C[1],I(P[1]/2))C[2]\n ),\n\n #F DWTper_Mallat:\n #F \n #F DWTper(n,j,[h,g])->DWTper(n/2,j-1,[h,g]), DSCirculant \n #F \n DWTper_Mallat := rec(\n info := \"DWTper(n,j,[h,g])->DWTper(n/2,j-1,[h,g])\",\n forTransposition := false,\n isApplicable := P -> P[1]>2 and P[1] mod 2 = 0,\n\n allChildren := P -> let(\n\t n := P[1],\n\t dcirc1 := DSCirculant(n, P[3][1], P[4][1], 2, 0),\n\t dcirc2 := DSCirculant(n, P[3][2], P[4][2], 2, 0),\n\t When(P[2]=1, [[ dcirc1, dcirc2 ]],\n\t\t [[ dcirc1, dcirc2, DWTper(P[1]/2, P[2]-1, P[3], P[4]) ]])),\n\n rule := (P, C) -> When(P[2]=1, VStack(C[1], C[2]),\n VStack(C[3]C[1], C[2]))\n ),\n\n #F DWTper_Polyphase:\n #F \n #F DWTper(n,1,[h,g])->[ [Circulant(he), Circulant(ho)],\n #F [Circulant(ge), Circulant(go)] ]\n #F\n #F Single-stage periodic DWT into a matrix of circulants of downsampled filters \n #F \n DWTper_Polyphase := rec(\n\tinfo := \"DWTper(n,1,[h,g]) -> [[Circ(he), Circ(ho)], [Circ(ge), Circ(go)]]\",\n\tforTransposition := false,\n\tisApplicable := P -> P[1]>2 and P[1] mod 2 =0 and P[2]=1,\n\tallChildren := function(P)\n\t local n,h,g,he,ho,ge,go; \n\t n := P[1]; \n\t h := DownsampleTwo([P[3][1], P[4][1]]);\n\t g := DownsampleTwo([P[3][2], P[4][2]]);\n\t he := Circulant(n/2, h[1][1], h[1][2]); \n\t ho := Circulant(n/2, h[2][1], h[2][2]);\n\t ge := Circulant(n/2, g[1][1], g[1][2]);\n\t go := Circulant(n/2, g[2][1], g[2][2]);\n\t return [[ he, ho, ge, go ]];\n\tend,\n\trule := (P, C) -> BlockMat( [[ C[1], C[2] ],\n\t\t [ C[3], C[4] ]] ) * L(P[1],2)\n ),\n\n #F RuleDWTper_Lifting:\n #F \n DWTper_Lifting := rec(\n info := \"DWTper(n,1,[h,g]) -> Lifting steps\",\n forTransposition := false,\n isApplicable := ( L ) -> L[1]>2 and L[1] mod 2 =0 and L[2]=1,\n\n allChildren := function ( P )\n local n,j,LS,Lc,scheme,step,pol; \n n := P[1];\n LS := Copy(HashLookupWav(HashTableWavelets, [P[3],P[4]]));\n Lc := List(LS, scheme->\n List(scheme{[2..Length(scheme)]}, step->\n let(pol := FillZeros(ListPoly(step)),\n Circulant(n/2,pol[1],pol[2]))));\n\n for i in [1..Length(LS)] do \n # attach the indicator of the type of the first liftings step\n Lc[i][1].lift :=LS[i][1];\n\n # fuse in the constants/shifts in the last lifting step\n #if (LS[i][1]=0 or LS[i][1]=-2) then LS[i][4]:=LS[i][4]LS[i][3];\n #else LS[i][4]:=LS[i][4]LS[i][2];\n #fi;\n\n pol := FillZeros(ListPoly(LS[i][4]));\n Lc[i][3] := Circulant(n/2,pol[1],pol[2]);\n od;\n return Lc;\n end,\n\n rule := function ( P, C, Nonterms )\n local n, i, ind, b, l, M, first, last, ind0, ind1, lstep, last_ls;\n n := P[1]; \n b := Nonterms[1].lift;\n l:=Length(C);\n\n\t ind0 := fTensor(fBase(2,0), fId(Rows(C[3])));\n\t ind1 := fTensor(fBase(2,1), fId(Rows(C[3])));\n\t lstep := (f,b) -> When(b=0, \n\t\tLStep(Scat(ind0) * f * Gath(ind1)),\n\t\tLStep(Scat(ind1) * f * Gath(ind0)));\n\n M := When(b < 0, \n\t\tSUM(Scat(ind0)C[2]Gath(ind1), Scat(ind1)C[1]Gath(ind0)),\n\t\tSUM(Scat(ind0)C[2]Gath(ind0), Scat(ind1)C[1]Gath(ind1)));\n\n\t b := (b+2) mod 2; # make b positive\n\t for i in [1 .. l-2] do\n\t M := M * lstep(C[i+2], b);\n\t\tb := (b+1) mod 2;\n od; \n\n\t first := M.child(1);\n\t M := Inplace(Compose(Drop(M.children(),1)));\n\t return first * M * L(n,2);\n end\n )\n));\n", "meta": {"hexsha": "e92cd99a45008cdefa6116bdba6fbebc294ab217", "size": 7432, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/filtering/dwt_per.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/transforms/filtering/dwt_per.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/transforms/filtering/dwt_per.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 33.0311111111, "max_line_length": 89, "alphanum_fraction": 0.4765877287, "num_tokens": 2613, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8418256313782276, "lm_q2_score": 0.626124191181315, "lm_q1q2_score": 0.5270873925623926}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\nClass(PrunedMDDFT, TaggedNonTerminal, rec(\n abbrevs := [\n (n,k,blk,pat) -> Checked(ForAll(n, IsPosIntSym), IsIntSym(k), IsPosIntSym(blk), ForAll(pat, IsList), \n [_unwrap(n), _unwrap(k), _unwrap(blk), pat, ]),\n ],\n dims := self >> [Product(self.params[1]), self.params[3]Product(self.params[4], i->Length(i))],\n isReal := self >> false,\n normalizedArithCost := self >> let(n := self.params[1], IntDouble(5 n * d_log(n) / d_log(2))),\n TType := TComplex,\n terminate := self >> let(nlist := self.params[1],\n blk := self.params[3], pat_md := self.params[4],\n scat3d := Tensor(List(Zip2(pat_md, nlist), j->let(pat := j[1], size := j[2],\n Tensor(Mat(List(pat, i->BasisVec(size/blk, i))).transpose(), I(blk)).terminate()))),\n dft3d := MDDFT(nlist, self.params[2]),\n t := dft3d * scat3d,\n t.terminate()\n )\n \n));\n\nClass(PrunedIMDDFT, TaggedNonTerminal, rec(\n abbrevs := [\n (n,k,blk,pat) -> Checked(ForAll(n, IsPosIntSym), IsIntSym(k), IsPosIntSym(blk), ForAll(pat, IsList), \n [_unwrap(n), _unwrap(k), _unwrap(blk), pat, ]),\n ],\n dims := self >> [ self.params[3]Product(self.params[4], i->Length(i)), Product(self.params[1]) ],\n isReal := self >> false,\n normalizedArithCost := self >> let(n := self.params[1], IntDouble(5 n * d_log(n) / d_log(2))),\n TType := TComplex,\n terminate := self >> let(nlist := self.params[1],\n blk := self.params[3], pat_md := self.params[4],\n gath3d := Tensor(List(Zip2(pat_md, nlist), j->let(pat := j[1], size := j[2],\n Tensor(Mat(List(pat, i->BasisVec(size/blk, i))), I(blk)).terminate()))),\n dft3d := MDDFT(nlist, self.params[2]),\n t := gath3d * dft3d,\n t.terminate()\n )\n \n));\n\n\n\n\n\nNewRulesFor(PrunedMDDFT, rec(\n PrunedMDDFT_Base := rec(\n info := \"PrunedMDDFT -> PrunedDFT\",\n applicable := nt -> Length(nt.params[1])=1,\n children := nt -> let(P := nt.params, tags := nt.getTags(), [[ PrunedDFT(P[1][1], P[2], P[3], P[4][1]).withTags(tags) ]]),\n apply := (nt, C, Nonterms) -> C[1]\n ),\n PrunedMDDFT_RowCol := rec (\n info := \"PrunedMDDFT_n -> PrunedMDDFT_n/d, PrunedMDDFT_d\",\n applicable := nt -> Length(nt.params[1]) > 1 and not nt.hasTags(),\n\n children := nt -> let(\n dims := nt.params[1],\n len := Length(dims),\n pats := nt.params[4],\n List([1..len-1],\n i -> [ PrunedMDDFT(dims{[1..i]}, nt.params[2], nt.params[3], pats{[1..i]}), \n PrunedMDDFT(dims{[i+1..len]}, nt.params[2], nt.params[3], pats{[i+1..len]}) ])),\n\n apply := (nt, C, Nonterms) -> let(\n n1 := Cols(Nonterms[1]),\n n2 := Rows(Nonterms[2]),\n Tensor(C[1], I(n2)) \n Tensor(I(n1), C[2])\n )\n )\n));\n\nNewRulesFor(PrunedIMDDFT, rec(\n PrunedIMDDFT_Base := rec(\n info := \"PrunedIMDDFT -> PrunedIDFT\",\n applicable := nt -> Length(nt.params[1])=1,\n children := nt -> let(P := nt.params, tags := nt.getTags(), [[ PrunedIDFT(P[1][1], P[2], P[3], P[4][1]).withTags(tags) ]]),\n apply := (nt, C, Nonterms) -> C[1]\n ),\n PrunedIMDDFT_RowCol := rec (\n info := \"PrunedIMDDFT_n -> PrunedIMDDFT_n/d, PrunedIMDDFT_d\",\n applicable := nt -> Length(nt.params[1]) > 1 and not nt.hasTags(),\n\n children := nt -> let(\n dims := nt.params[1],\n len := Length(dims),\n pats := nt.params[4],\n List([1..len-1],\n i -> [ PrunedIMDDFT(dims{[1..i]}, nt.params[2], nt.params[3], pats{[1..i]}), \n PrunedIMDDFT(dims{[i+1..len]}, nt.params[2], nt.params[3], pats{[i+1..len]}) ])),\n\n apply := (nt, C, Nonterms) -> let(\n n1 := Cols(Nonterms[1]),\n n2 := Rows(Nonterms[2]),\n Tensor(C[1], I(n2)) \n Tensor(I(n1), C[2])\n )\n )\n));\n\n", "meta": {"hexsha": "f5d9699fcf8aed2d778a9f94727b4b62d7e764c0", "size": 4454, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/dft/mdprune.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, 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	{"text": "# Copyright (c) 2018-2020, Carnegie Mellon University\n# See LICENSE for details\n\n# Radix N kernel for FFTE\n\nbuildScalarKernel_a := function(n, kk, conf, opts)\n local name, suffix, filesuffix, j, k, l, m, tmp1, tmp2, tmp3, i1, i2, gf, sf, gath, scat,\n gc, sc, dft, rts, rt, opcnts, dfts, dftc, i3, twt, twf, twl, tws, twc,\n cl, cc, c, cx, lp, mp;\n\n name := DFTnameStr(n, kk);\n suffix := \"a\";\n filesuffix := \"c_\";\n# suffix := \"_j\";\n Print(\"\\n\\n// == Generating \\\"\", name, \"\\\" ==================================================\\n\\n\"); \n\n # variables\n #t := var.fresh_t(\"t\", TInt);\n j := var.fresh_t(\"j\", TInt);\n# k := var.fresh_t(\"k\", TInt);\n k := V(0);\n l := var.fresh_t(\"l\", TInt);\n # m := var.fresh_t(\"m\", TInt);\n m := V(1);\n lp := var.fresh_t(\"lp\", TPtr(TInt));\n mp := var.fresh_t(\"mp\", TPtr(TInt));\n \n # temp arrays\n tmp1 := var.fresh_t(\"R\", TArray(TReal, 2n));\n tmp2 := var.fresh_t(\"S\", TArray(TReal, 2n));\n tmp3 := var.fresh_t(\"T\", TArray(TReal, 2n));\n \n # gather and scatter\n i1 := var.fresh_t(\"i\", n);\n i2 := var.fresh_t(\"i\", n);\n gf := fTensor(Lambda(i1, k + jm + i1lm), fId(2));\n sf := fTensor(Lambda(i2, k+njm + i2m), fId(2));\n gath := Gath(gf);\n scat := Scat(sf);\n\n # generate gather and scatter code\n gc := BlockUnroll(unroll_cmd(opts.codegen(gath, tmp1, X, opts)), opts);\n sc := BlockUnroll(unroll_cmd(opts.codegen(scat, Y, tmp3, opts)), opts);\n \n # generate DFT kernel\n dft := RC(DFT(n, kk));\n rts := AllRuleTrees(dft, opts);\n opcnts := List(rts, r -> [ Length(Collect(CodeRuleTree(r, opts), @(1, [add, sub, mul], e->e.t=TReal))), r]);\n rt := Minimum(opcnts)[2];\n dfts := SumsRuleTree(rt, opts);\n dftc := BlockUnroll(opts.codegen(dfts, tmp2, tmp1, opts), opts);\n \n # twiddles as lookup table\n i3 := var.fresh_t(\"i\", 2n);\n twt := var.fresh_t(\"TW\", TPtr(TReal)); \n twf := Lambda(i3, cond(eq(i3, 0), 1, eq(i3, 1), 0, nth(twt, 2((n-1)j) + 2 * idiv(i3, 2) + (imod(i3, 2) - 2))));\n \n # debug twiddles\n twl := Map(twf.tolist(), RulesStrengthReduce);\n DoForAll([0..Length(twl)-1], _i->Unparse(assign(nth(Y, _i), twl[_i+1]), CUnparser, 0, 1));\n\n tws := RCDiag(twf);\n twc :=BlockUnroll(unroll_cmd(opts.codegen(tws, tmp3, tmp2, opts)), opts);\n \n # stitch code fragments together\n cl := func(TVoid, \"transform\", [Y, X, twt, j, k, l, m], \n decl([tmp1, tmp2, tmp3], chain(gc, dftc, twc, sc)));\n cc := Compile(cl, opts);\n \n # fixup to push decls inside (?)\n c := func(TVoid, \"transform\", [Y, X, twt, j, k, lp], \n decl(cc.vars::[l], \n chain(\n assign(l, deref(lp)),\n cc.cmd.cmds[1].cmd\n )\n )\n );\n \n # print Radix N FFTE kernel as function\n# PrintCode(name, c, opts);\n# PrintTo(name::\".c\", PrintCode(name, c, opts));\n \n # function with j and k loop in the function call\n cl := func(TVoid, \"transform\", [Y, X, twt, lp], \n decl(c.cmd.vars::c.free(), \n chain(\n assign(l, deref(lp)),\n loopn(j, l, \n c.cmd.cmd)\n )\n )\n );\n \n # print Radix N FFTE kernel as function\n PrintCode(opts.FortranIze(name::suffix), cl, opts);\n PrintTo(name::filesuffix::suffix::\".c\", PrintCode(opts.FortranIze(name::suffix), cl, opts));\nend;\n\n\n", "meta": {"hexsha": "52fa530ad06f26a8021a9c884034c208915587b9", "size": 3436, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "kernelgen/scalar_a.gi", "max_stars_repo_name": "spiral-software/spiral-package-ffte", "max_stars_repo_head_hexsha": "19f751776c117e28bdbcc3d2530c895ad554d855", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "kernelgen/scalar_a.gi", "max_issues_repo_name": "spiral-software/spiral-package-ffte", "max_issues_repo_head_hexsha": "19f751776c117e28bdbcc3d2530c895ad554d855", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "kernelgen/scalar_a.gi", "max_forks_repo_name": "spiral-software/spiral-package-ffte", "max_forks_repo_head_hexsha": "19f751776c117e28bdbcc3d2530c895ad554d855", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2021-06-15T12:41:51.000Z", "max_forks_repo_forks_event_max_datetime": "2021-06-15T12:41:51.000Z", "avg_line_length": 34.0198019802, "max_line_length": 117, "alphanum_fraction": 0.5209545984, "num_tokens": 1165, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.815232489352, "lm_q2_score": 0.6442251064863697, "lm_q1q2_score": 0.5251932372639404}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nClass(PkRDFT12_Base, PRDFT_Base, rec(\n dims := self >> [self.params[1], self.params[1]],\n terminate := self >> let(N := self.params[1], k := self.params[2], \n\trr := When(self.transposed, Cols(self), Rows(self)), \n\tmat := Cond(IsEvenInt(N), \n Mat(Concatenation(\n [List([0..N-1], c-> When(IsEvenInt(c), 1,1))],\n [List([0..N-1], c-> When(IsEvenInt(c), 1,-1))],\n List([2..rr-1], r -> When(r mod 2 = 0, \n List([0..N-1], c -> self.projRe(self.omega(N,k,Int(r/2),c))),\n List([0..N-1], c -> self.projIm(self.omega(N,k,Int(r/2),c))))))),\n Mat(Concatenation(\n [List([0..N-1], c -> 1)],\n List([2..rr], r -> When(r mod 2 = 0, \n List([0..N-1], c -> self.projRe(self.omega(N,k,Int(r/2),c))),\n List([0..N-1], c -> self.projIm(self.omega(N,k,Int(r/2),c)))))))),\n When(self.transposed, mat.transpose(), mat)),\n));\n\nClass(PkRDFT1, PkRDFT12_Base, rec(\n abbrevs := [ (n) -> Checked(IsPosInt(n), [n, 1]),\n (n,k) -> Checked(IsPosIntSym(n), IsIntSym(k), \n IsSymbolic(n) or IsSymbolic(k) or Gcd(n,k)=1, [n, k mod n]) ],\n omega := (N,k,r,c) -> E(N)^(krc)\n));\nClass(PkRDFT2, PkRDFT12_Base, rec(\n abbrevs := [ (n) -> Checked(IsPosIntSym(n), [n, 1]),\n (n,k) -> Checked(IsPosIntSym(n), IsIntSym(k), \n IsSymbolic(n) or IsSymbolic(k) or Gcd(n,k)=1, [n, k mod (2n)]) ],\n omega := (N,k,r,c) -> E(2N)^(kr(2c+1))\n));\n\nClass(PkDHT1, PkRDFT1, rec(\n terminate := self >> let(n := self.params[1], k := self.params[2], i := When(IsEvenInt(n), 2, 1),\n DirectSum(I(i), Tensor(I(Int((n-1)/2)), F(2))) \n PkRDFT1(n, k).terminate()\n )\n));\n\nClass(PkDHT2, PkRDFT2, rec(\n terminate := self >> let(n := self.params[1], k := self.params[2], i := When(IsEvenInt(n), 2, 1),\n DirectSum(I(i), Tensor(I(Int((n-1)/2)), Diag(1,-1)F(2))) \n PkRDFT2(n, k).terminate()\n )\n));\n\nClass(URealDFT_Base, NonTerminal, rec(\n abbrevs := [ (n) -> Checked(IsPosInt(n), [n, 1]),\n (n,k) -> Checked(IsPosInt(n), IsInt(k), Gcd(n,k)=1, [n, k mod n]) ],\n terminate := self >> let(N := self.params[1], k := self.params[2], \n\trr := When(self.transposed, Cols(self), Rows(self)),\n\tMat(Concatenation(\n\t [List([0..N-1], c-> When(IsEvenInt(c), 1,0))],\n\t [List([0..N-1], c-> When(IsOddInt(c), 1,0))],\n\t List([2..rr-1], r -> When(r mod 2 = 0, \n\t\t List([0..N-1], c -> self.projRe(self.omega(N,k,Int(r/2),c))),\n\t\t List([0..N-1], c -> self.projIm(self.omega(N,k,Int(r/2),c)))))))),\n isReal := True,\n SmallRandom := () -> Random([2..16]), \n LargeRandom := () -> 2 ^ Random([6..15])\n));\n\nClass(URDFT_Base, URealDFT_Base, rec(\n projRe := Re,\n projIm := Im,\n hashAs := self >> self\n));\n\nClass(URDFT, URDFT_Base, rec(\n dims := self >> let(n:=self.params[1], [ 2(Int((n+1)/2)), n ]),\n omega := (N,k,r,c) -> E(N)^(krc),\n));\n\nURDFT1:=URDFT;\n\n# Regularized Rules\n# R1 -> (R1, C1) (R1')\n# R2 -> (R2, C2) (R1')\nPRF12_CTReg_Children := (N,k,PRFt,DFTt,PRF1prime, maxRadix) -> Map2(\n Filtered(DivisorPairs(N),d->d[1] <= maxRadix/2 and d[2]<>2),\n (m,n) -> When(IsEvenInt(n),\n\t[ PRFt(2m,k), DFTt(m,k), PRF1prime(n,k) ],\n\t[ PRFt(m,k), DFTt(m,k), PRF1prime(n,k) ] )\n);\n\nPRF12_CTReg_Rule := (N,k,C,Conj,Tw) -> let(mm:=Cols(C[1]), m:=When(IsEvenInt(N), mm/2, mm),\n n:=Cols(C[3]), Nf:=Int(N/2), Nc:=Int((N+1)/2),\n nf:=Int(n/2), nc:=Int((n+1)/2), mf:=Int(m/2), mc:=Int((m+1)/2), j:=Ind(nc-1),\n\n SUM(\n\tBB(RC(Scat(H(Nc,m,0,n/2))) * C[1] * L(mm,2) * RC(Gath(H(ncm, m, 0, nc)))),\n\n\tWhen(nc=1, [], \n\tISum(j, BB(\n\t RC(Scat(BH(Nc,N,m,j+1,n))) \n\t Conj * RC(C[2]) * Tw(j) \n\t RC(Gath(H(ncm, m, j+1, nc))))))\n ) * \n Tensor(I(m), C[3]) * L(N,m)\n);\n\nPRF12_CTReg2_Rule := (N,k,C,Conj,Tw) -> let(mm:=Cols(C[1]), m:=When(IsEvenInt(N), mm/2, mm),\n n:=Cols(C[3]), Nf:=Int(N/2), Nc:=Int((N+1)/2),\n nf:=Int(n/2), nc:=Int((n+1)/2), mf:=Int(m/2), mc:=Int((m+1)/2), j:=Ind(nc-1),\n\n SUM(\n\tRC(Scat(H(Nc,m,0,n/2))) * C[1] * RC(Gath(H(ncm, m, 0, 1))),\n\n\tWhen(nc=1, [], \n\tISum(j, \n\t RC(Scat(BH(Nc,N,m,j+1,n))) \n\t Conj * RC(C[2]) * Tw(j) * L(2m, m) \n\t RC(Gath(H(ncm, m, m(j+1), 1)))))\n ) * \n Tensor(C[3], I(m)) \n);\n\nPRF12_CTReg3_Rule := (N,k,C,Conj,Tw) -> let(mm:=Cols(C[1]), m:=When(IsEvenInt(N), mm/2, mm),\n n:=Cols(C[3]), Nf:=Int(N/2), Nc:=Int((N+1)/2),\n nf:=Int(n/2), nc:=Int((n+1)/2), mf:=Int(m/2), mc:=Int((m+1)/2), j:=Ind(nc-1),\n\n SUM(\n\tRC(Scat(H(Nc,m,0,n/2))) * C[1] * L(2m, 2) Gath(H(N, 2m, 0, nc)),\n\n\tWhen(nc=1, [], \n\tISum(j, \n\t RC(Scat(BH(Nc,N,m,j+1,n))) \n\t Conj * RC(C[2]) * Tw(j) \n\t Gath(H(N, 2m, j+1, nc))))\n ) * \n Tensor(I(m), L(n,2)C[3]) L(N,m)\n);\n\nPRF12_CTReg4_Rule := (N,k,C,Conj,Tw) -> let(mm:=Cols(C[1]), m:=When(IsEvenInt(N), mm/2, mm),\n n:=Cols(C[3]), Nf:=Int(N/2), Nc:=Int((N+1)/2),\n nf:=Int(n/2), nc:=Int((n+1)/2), mf:=Int(m/2), mc:=Int((m+1)/2), j:=Ind(nc-1),\n\n RC(Tensor(I(m/2), DirectSum(I(n/2+1), J(n/2-1)))) \n RC(L(N/2, m)) \n DirectSum(\n C[1] * L(2m, 2),\n\tIterDirectSum(j, RC(M(m,m/2)) Conj * RC(C[2]) * Tw(j))\n ) * \n L(N, nc) * \n Tensor(I(m), L(n,2)C[3]) L(N,m)\n);\n\nPRF12_CTReg5_Rule := (N,k,C,Conj,Tw) -> let(mm:=Cols(C[1]), m:=When(IsEvenInt(N), mm/2, mm),\n n:=Cols(C[3]), Nf:=Int(N/2), Nc:=Int((N+1)/2),\n nf:=Int(n/2), nc:=Int((n+1)/2), mf:=Int(m/2), mc:=Int((m+1)/2), j:=Ind(nc-1),\n\n RC(Tensor(I(m/2), DirectSum(I(n/2+1), J(n/2-1)))) \n RC(L(N/2, m)) \n DirectSum(\n C[1],\n\tIterDirectSum(j, RC(M(m,m/2)) * Conj * RC(C[2]) * Tw(j) * L(2m, m))\n ) \n Tensor(C[3], I(m))\n);\n\nunrc := m -> let(r := Dimensions(m)[1], c := Dimensions(m)[2],\n MatSPL(Gath(H(r,r/2,0,2))) * m * MatSPL(Scat(H(c,c/2,0,2))));\n\nRulesFor(URDFT1, rec(\n URDFT1_Base1 := BaseRule(URDFT1, [1, @]),\n URDFT1_Base2 := BaseRule(URDFT1, [2, @]),\n URDFT1_Base4 := BaseRule(URDFT1, [4, @]),\n\n URDFT1_CT := rec(\n maxRadix := 32,\n\tisApplicable := P -> not IsPrime(P[1]) and not (IsEvenInt(P[1]) and IsPrime(P[1]/2)),\n\tallChildren := (self, P) >> PRF12_CTReg_Children(P[1], P[2], URDFT1, DFT1, URDFT1, self.maxRadix), \n\trule := (P,C) -> let(N:=P[1], k:=P[2], m:=When(IsEvenInt(N), Cols(C[1])/2, Cols(C[1])),\n\t PRF12_CTReg_Rule(N, k, C, Diag(BHD(m,1,-1)), \n j -> RC(DirectSum(I(1), Diag(fPrecompute(fCompose(Twid(N,m,k,0,0,j+1), fAdd(m, m-1, 1))))))))),\n\n # slightly different variant of same rule, \n URDFT1_CT2 := rec(\n\tisApplicable := P -> not IsPrime(P[1]) and not (IsEvenInt(P[1]) and IsPrime(P[1]/2)),\n\tallChildren := P -> PRF12_CTReg_Children(P[1], P[2], URDFT1, DFT1, URDFT1), \n\trule := (P,C) -> let(N:=P[1], k:=P[2], m:=When(IsEvenInt(N), Cols(C[1])/2, Cols(C[1])),\n\t PRF12_CTReg2_Rule(N, k, C, Diag(BHD(m,1,-1)), j->RC(Diag(fPrecompute(Twid(N,m,k,0,0,j+1))))))),\n\n URDFT1_CT3 := rec(\n\tisApplicable := P -> not IsPrime(P[1]) and not (IsEvenInt(P[1]) and IsPrime(P[1]/2)),\n\tallChildren := P -> PRF12_CTReg_Children(P[1], P[2], URDFT1, DFT1, URDFT1), \n\trule := (P,C) -> let(N:=P[1], k:=P[2], m:=When(IsEvenInt(N), Cols(C[1])/2, Cols(C[1])),\n\t PRF12_CTReg3_Rule(N, k, C, Diag(BHD(m,1,-1)), j->RC(Diag(fPrecompute(Twid(N,m,k,0,0,j+1))))))),\n\n URDFT1_CT4 := rec(\n\tisApplicable := P -> not IsPrime(P[1]) and not (IsEvenInt(P[1]) and IsPrime(P[1]/2)),\n\tallChildren := P -> PRF12_CTReg_Children(P[1], P[2], URDFT1, DFT1, URDFT1), \n\trule := (P,C) -> let(N:=P[1], k:=P[2], m:=When(IsEvenInt(N), Cols(C[1])/2, Cols(C[1])),\n\t PRF12_CTReg4_Rule(N, k, C, Diag(BHD(m,1,-1)), j->RC(Diag(fPrecompute(Twid(N,m,k,0,0,j+1))))))),\n\n URDFT1_CT5 := rec(\n\tisApplicable := P -> not IsPrime(P[1]) and not (IsEvenInt(P[1]) and IsPrime(P[1]/2)),\n\tallChildren := P -> PRF12_CTReg_Children(P[1], P[2], URDFT1, DFT1, URDFT1), \n\trule := (P,C) -> let(N:=P[1], k:=P[2], m:=When(IsEvenInt(N), Cols(C[1])/2, Cols(C[1])),\n\t PRF12_CTReg5_Rule(N, k, C, Diag(BHD(m,1,-1)), j->RC(Diag(fPrecompute(Twid(N,m,k,0,0,j+1))))))),\n\n));\n\n\n", "meta": {"hexsha": "26b9fc720d4eb4e52a5dfdb89952450231ee799b", "size": 8226, "ext": "gi", "lang": "GAP", "max_stars_repo_path": 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	{"text": "# Copyright (c) 2018-2020, Carnegie Mellon University\n# See LICENSE for details\n#\n# Contains the CNOT and SWAP non-terminals and rewrite rules\n#\n\n##\n#F qSWAPT( <qi>, <qj>, <n>,, <arch> ) Object\n##\n#F Awaps qi and qj in a system of n qubits, with architecture arch\n#F Definition: (2^n x 2^n)-matrix \n#F that swaps qubit qi and qubit qj, with the identity operation applied to all others\nClass(qSWAPT, TaggedNonTerminal, rec(\n abbrevs := [ (qi, qj, n, arch) -> Checked(IsPosInt(n), [qi, qj, n, arch]) ],\n dims := self >> let(size := 2^self.params[3], [size, size]),\n terminate := self >> GenSwapMat(self.params[1], self.params[2], self.params[3]), \n isReal := self >> true,\n rChildren := self >> self.params,\n from_rChildren := (self, rch) >> self.__bases__[1](rch[1], rch[2], rch[3], rch[4]),\n SmallRandom := () -> Random([2..5]),\n LargeRandom := () -> Random([6..15]),\n normalizedArithCost := self >> Error(\"ArithCost not implemented\"),\n TType := T_Real(64)\n));\n\n##\n#F CnotTerm( <i>, <j>, <n> )\n##\n## .terminate() function for the qCNOT Non-terminal. Expands qCNOT non-terminal into a 2^n by 2^n matrix\nCnotTerm := function (i, j, n)\n return When(i < j, Tensor(Tensor(I(2^(i)), GenCnotMat(j, 0)), I(2^(n-j))), Tensor(Tensor(I(2^(j)), GenCnotMat(i, 1)), I(2^(n-i)))); # create the intended cnot matrix\nend;\n\n##\n#F CnotSPL( <i>, <j>, <n> )\n##\n## Used for the qCNOT_Base breakdown rule. Represents a qCNOT Non-terminal as a tensor of CNOT and I SPL objects\nCnotSPL := function (i, j, n)\n return When(i < j, Tensor(Tensor(I(2^(i)), CNOT(j-i, 0)), I(2^(n-1-j))), Tensor(Tensor(I(2^(j)), CNOT(i-j, 1)), I(2^(n-1-i)))); # create the intended cnot matrix\nend;\n\n##\n#F qCNOT( <qj>, <dir>, <arch> ) Object\n##\n#F CNOT Non-terminal\n#F Definition: (2^n x 2^n)-matrix that applies a CNOT from qubit 0 to j \nClass(qCNOT, TaggedNonTerminal, rec(\n abbrevs := [ (qj, dir, arch) -> Checked([qj, dir, arch]) ],\n dims := self >> let(size := 2^(self.params[1]+1), [size, size]),\n terminate := self >> GenCnotMat(self.params[1], self.params[2]),\n isReal := self >> true,\n groups := self >> [[2]],\n recursive_def := (self, arch) >> self.__bases__[1](self.params[1], self.params[2], arch),\n rChildren := self >> self.params,\n from_rChildren := (self, rch) >> self.__bases__[1](rch[1], rch[2], rch[3]),\n connected := self >> true,\n SmallRandom := () -> Random([2..5]),\n LargeRandom := () -> Random([6..15]),\n normalizedArithCost := self >> Error(\"ArithCost not implemented\"),\n TType := T_Real(64)\n));\n\n\n##\n#F qCNOT Breakdown Rules\n## \nNewRulesFor(qCNOT, rec(\n \n #F qCNOT_Base: qCNOT(_) = CNOT() SPL object\n #F Directly represent as an implementable gate, if a proper edge exists\n qCNOT_Base := rec(\n info := \"qCNOT_(_) -> CNOT(_)\",\n forTransposition := false,\n applicable := (self, nt) >> (HasEdge(0, nt.params[1], nt.params[3]) = 1),\n apply := (nt, c, cnt) -> CNOT(nt.params[1], nt.params[2]),\n )\n\n));\n\n##\n#F CnotSPL( <i>, <j>, <n> )\n##\n## Used for the qSWAP_Base breakdown rule. Represents a qCNOT Non-terminal as a tensor of CNOT and I SPL objects\nCnotSPL := function (i, j, n)\n return When(i < j, Tensor(Tensor(I(2^(i)), CNOT(j-i, 0)), I(2^(n-1-j))), Tensor(Tensor(I(2^(j)), CNOT(i-j, 1)), I(2^(n-1-i)))); # create the intended cnot matrix\nend;\n\n##\n#F SwapGenChildren( <start>, <ending>, <n>, <arch> )\n##\n## decompose a qSWAPT transform into smaller qSWAPT transforms\nSwapGenChildren := function (start, ending, n, arch)\n local move, children;\n move := Best_Move(start, ending, arch);\n children := [];\n Add(children, [qSWAPT(start, move, n, arch) * qSWAPT(move, ending, n, arch) * qSWAPT(start, move, n, arch)]);\n return children;\nend;\n\n##\n#F qSWAPT Breakdown Rules\n## \nNewRulesFor(qSWAPT, rec(\n\n #F qSWAPT_Base: qSWAPT(_) = qCNOT() SPL objects\n #F SWAP to CNOT conversion, only if an edge exists\n #F represent a swap as a series of 3 CNOTs with the middle being an alternate direction\n qSWAPT_Base := rec(\n info := \"qSWAPT() -> CNOT * CNOT * CNOT \",\n forTransposition := false,\n applicable := (self, nt) >> ( (HasEdge(nt.params[1], nt.params[2], nt.params[4]) = 1) and (nt.params[1] <> nt.params[2])),\n children := nt -> List( [ [ (CnotSPL(nt.params[1], nt.params[2], nt.params[3]))(CnotSPL(nt.params[2], nt.params[1], nt.params[3]))(CnotSPL(nt.params[1], nt.params[2], nt.params[3])) ] , [ (CnotSPL(nt.params[2], nt.params[1], nt.params[3]))(CnotSPL(nt.params[1], nt.params[2], nt.params[3]))(CnotSPL(nt.params[2], nt.params[1], nt.params[3])) ] ] ), \n apply := (nt, c, cnt) -> c[1],\n ),\n\n\n #F qSWAPT_ID: qSWAPT(_) = I() SPL object\n #F SWAP to Identity conversion if the swap is trivial\n qSWAPT_Id := rec(\n info := \"qSWAPT() -> Identity \",\n forTransposition := false,\n applicable := (self, nt) >> (nt.params[1] = nt.params[2]),\n apply := (nt, c, cnt) -> I(2^(nt.params[3])),\n ),\n\n #F qSWAPT_Rec: qSWAPT(_) = qSWAPT(_) * qSWAPT(_) \n #F Break down an unimplementable qSWAP into an implementable swap and a swap that is 1 step closer to being implementable\n #F TODO, make this a bit more intelligent, right now SwapGenChildren just does a random walk\n qSWAPT_Rec := rec(\n info := \"qSWAPT() -> qSWAPT() * qSWAPT()\",\n forTransposition := false,\n applicable := (self, nt) >> ((nt.params[1] <> nt.params[2]) and (HasEdge(nt.params[1], nt.params[2], nt.params[4]) = 0)),\n children := nt -> SwapGenChildren(nt.params[1], nt.params[2], nt.params[3], nt.params[4]), \n apply := (nt, c, cnt) -> c[1],\n )\n\n));\n\n##\n#F ShiftMat( <swap1>, <swap2>, <arch>, <n> )\n##\n## generates a martix of SWAP operations that swap the qubit groups swap1 and swap2 in parallel\n## swap1 is the target position, and swap2 are original positions\nShiftMat := function (swap1, swap2, arch, n)\n local idx, format, backmat, targets, t, positions, e, sw1, sw2, s, i, test, already_swapped;\n idx := 1;\n format := I(2^(n));\n backmat := I(2^(n));\n positions := [];\n targets := [];\n for s in swap1 do \n Add(positions, s);\n od;\n for t in swap2 do \n Add(targets, t);\n od;\n for s in swap1 do\n if ((targets[idx] <> positions[idx])) then # just save the extra trouble, if the swap is trivial\n format := format * qSWAPT(positions[idx], targets[idx], n ,arch);\n backmat := qSWAPT(positions[idx], targets[idx], n , arch) * backmat;\n sw1 := targets[idx];\n sw2 := positions[idx];\n i := 1;\n for e in positions do \n if e = sw1 then \n positions[i] := sw2;\n fi;\n if e = sw2 then \n positions[i] := sw1;\n fi;\n i := i + 1;\n od;\n fi;\n idx := idx + 1;\n od;\n return [format, backmat];\nend;\n\n", "meta": {"hexsha": "e6e0a9e052a85ebd01190f5f8557feb2da43ee4d", "size": 7072, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "qcnot.gi", "max_stars_repo_name": "spiral-software/spiral-package-quantum", "max_stars_repo_head_hexsha": "dd2323983495adbbc6261c0cdf840320d19d099d", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "qcnot.gi", "max_issues_repo_name": "spiral-software/spiral-package-quantum", "max_issues_repo_head_hexsha": "dd2323983495adbbc6261c0cdf840320d19d099d", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "qcnot.gi", "max_forks_repo_name": "spiral-software/spiral-package-quantum", "max_forks_repo_head_hexsha": "dd2323983495adbbc6261c0cdf840320d19d099d", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 39.5083798883, "max_line_length": 370, "alphanum_fraction": 0.5764988688, "num_tokens": 2233, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.8289387998695209, "lm_q2_score": 0.6297746074044134, "lm_q1q2_score": 0.5220446072501131}}
	{"text": "#\n# cls 17: A_2\n#\nhandle17char3:=function()\n local tmp1,tmp2,o,info,rep,cent,uu;\n o:=AllClasses(orbs)[17];\n info:=infos[17];\n \n rep:=Representative(o);\n #pr[15]=[0,0,1,1,1,0]\n #pr[13]=[0,1,1,1,0,0]\n #pr[26]=[1,1,1,2,1,0]\n tmp1:=ApplyRootsReflections(rep,[15,13,26]);\n uu:=Unipotent(chevalleyAdj(rep),[[3,1]]);\n tmp1:=Conj(tmp1,uu);\n tmp1:=ConjugateByTori(tmp1,[3],[-1]);\n \n cent:=FromPositiveBorel(o,info[2]);\n tmp2:=ApplyRootsReflections(cent,[15,13,26]);\n uu:=Unipotent(chevalleyAdj(cent),[[3,1]]);\n tmp2:=Conj(tmp2,uu);\n tmp2:=ConjugateByTori(tmp2,[3],[-1]);\n\n return [tmp1,tmp2];\nend;\n\n\n#\n# cls 10: D_4(a_1)\n#\nhandle10char3:=function()\n local tmp1,tmp2,tmp3,tmp4,o,info,rep,cent,uu;\n o:=AllClasses(orbs)[10];\n info:=infos[10];\n \n rep:=Representative(o);\n #pr[4] =[0,0,0,1,0,0]\n #pr[32]=[1,1,2,2,1,1]\n #pr[33]=[1,1,1,2,2,1]\n tmp1:=ApplyRootsReflections(rep,[4,32,33]);\n uu:=Unipotent(chevalleyAdj(rep),[[3,-1],[5,1]]);\n tmp1:=Conj(tmp1,uu);\n tmp1:=ConjugateByTori(tmp1,[4,1,2,6],[-1,-1,-1,-1]);\n\n #pr[20]=[0,1,0,1,1,1]\n #pr[21]=[0,0,1,1,1,1]\n tmp3:=ApplyRootsReflections(rep,[20,21]);\n uu:=Unipotent(chevalleyAdj(rep),[[3,1],[4,1],[5,-1],[9,1],[10,-1]]);\n tmp3:=Conj(tmp3,uu);\n tmp3:=ConjugateByTori(tmp3,[2,4],[-1,-1,-1,-1]);\n \n \n cent:=FromPositiveBorel(o,info[2]);\n tmp2:=ApplyRootsReflections(cent,[4,32,33]);\n uu:=Unipotent(chevalleyAdj(cent),[[3,-1],[5,1]]);\n tmp2:=Conj(tmp2,uu);\n tmp2:=ConjugateByTori(tmp2,[4,1,2,6],[-1,-1,-1,-1]);\n\n tmp4:=ApplyRootsReflections(cent,[20,21]);\n uu:=Unipotent(chevalleyAdj(cent),[[3,1],[4,1],[5,-1],[9,1],[10,-1]]);\n tmp4:=Conj(tmp4,uu);\n tmp4:=ConjugateByTori(tmp4,[2,4],[-1,-1,-1,-1]);\n \n return [tmp1,tmp3,tmp2,tmp4];\nend;\n\n\n#\n# cls 4: E_6(a_3) [13,1,15,6,14,4] \n#\nhandle4char3:=function()\n local tmp1,tmp2,o,info,rep,cent;\n o:=AllClasses(orbs)[4];\n info:=infos[4];\n \n rep:=Representative(o);\n tmp1:=ConjugateByTorus(rep,4,-1);# h_1 --> h_4\n \n cent:=FromPositiveBorel(o,info[2]);\n tmp2:=ConjugateByTorus(cent,4,-1);# h_1 --> h_4\n \n return [tmp1,tmp2];\nend;\n", "meta": {"hexsha": "8ec938e65ac3ed44c0dfe428fd8ce78a98d62efc", "size": 2187, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "lib/components/E6char3.gi", "max_stars_repo_name": "iuliansimion/Chevalley.gap", "max_stars_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "lib/components/E6char3.gi", "max_issues_repo_name": "iuliansimion/Chevalley.gap", "max_issues_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "lib/components/E6char3.gi", "max_forks_repo_name": "iuliansimion/Chevalley.gap", "max_forks_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 26.0357142857, "max_line_length": 73, "alphanum_fraction": 0.5729309556, "num_tokens": 934, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7606506635289836, "lm_q2_score": 0.685949467848392, "lm_q1q2_score": 0.5217679178662326}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n# equality of scalars\nscalareq := (a,b) -> AbsFloat(a-b) < 1e-10;\n# equality of lists\nlseq := (a,b) -> Length(a)=Length(b) and ForAll([1..Length(a)], scalareq(a[i], b[i]));\n\nlequiv := (a,b) -> Cond(\n lseq(a,b), \"eq\", \n lseq(a, -b), \"eqneg\",\n lseq(a, Reversed(b)), \"rev\", \n lseq(a, -Reversed(b)), \"revneg\",\n \"none\");\n\ntovec := lst -> TransposedMat([lst]);\ntolst := vec -> TransposedMat(vec)[1];\nrpart := vec -> List(vec, x->ReComplex(Complex(x)));\nipart := vec -> List(vec, x->ImComplex(Complex(x)));\n\nrand := arg -> RandomList([-100..100]);\n#rand := x->x;\n\n##\n## Constructors for symmetric sequences\n##\nreal := n -> List([1..n], rand);\ncplx := (rsym, isym) -> (n -> rsym(n) + E(4)isym(n));\n\neven0 := n -> let(len := Int((n-1)/2), lst := List([2..len+1], rand),\n Flat([rand(1), lst, When(IsEvenInt(n),rand(len+2),[]), Reversed(lst)]));\n\neven00 := n -> let(len := Int((n-1)/2), lst := List([1..len], rand),\n Flat([0, lst, When(IsEvenInt(n),rand(len+1),[]), Reversed(lst)]));\nodd0 := n -> let(len := Int((n-1)/2), lst := List([2..len+1], rand),\n Flat([rand(1), lst, When(IsEvenInt(n),0,[]), -Reversed(lst)]));\nodd00 := n -> let(len := Int((n-1)/2), lst := List([1..len], rand),\n Flat([0, lst, When(IsEvenInt(n),0,[]), -Reversed(lst)]));\n\neven1 := n -> let(len := Int(n/2), lst := List([1..len], rand),\n Flat([lst, When(IsOddInt(n),rand(len+1),[]), Reversed(lst)]));\nodd1 := n -> let(len := Int(n/2), lst := List([1..len], rand),\n Flat([lst, When(IsOddInt(n),0,[]), -Reversed(lst)]));\n\njeven1 := n -> Checked(IsEvenInt(n), let(lst:=List([1..n/2], rand), Flat([lst,lst])));\njodd1 := n -> Checked(IsEvenInt(n), let(lst:=List([1..n/2], rand), Flat([lst,-lst])));\njeven0 := n -> Checked(IsOddInt(n), Concatenation([rand(0)], jeven1(n-1)));\njeven00 := n -> Checked(IsOddInt(n), Concatenation([0], jeven1(n-1)));\njodd0 := n -> Checked(IsOddInt(n), Concatenation([rand(0)], jodd1(n-1)));\njodd00 := n -> Checked(IsOddInt(n), Concatenation([0], jodd1(n-1)));\n\nce0 := cplx(even0, odd00);\nco0 := cplx(odd0, even00);\nce1 := cplx(even1, odd1);\nco1 := cplx(odd1, even1);\n\njce0 := cplx(jeven0, jodd00);\njco0 := cplx(jodd0, jeven00);\njce1 := cplx(jeven1, jodd1);\njco1 := cplx(jodd1, jeven1);\n\nraderce0 := n -> Checked(IsPrime(n+1), Drop(\n tolst(MatSPL(DFT_Rader.raderMid(n+1,1,PrimitiveRootMod(n+1))) \n\t tovec(Concat([rand(0)], ce0(n)))), 1));\n\nupsample0 := n -> Checked(IsEvenInt(n), List([1..n], i -> When(IsEvenInt(i),0,rand())));\n\nupsample1 := n -> Checked(IsEvenInt(n), List([1..n], i -> When(IsOddInt(i),0,rand())));\n\n_even := n -> ((n+1) mod 2);\n_odd := n -> (n mod 2);\n\n_minsetPoints := function(points, n)\n local uniq, cur, p;\n cur := []; uniq := Set([]);\n for p in points do\n if not (p in uniq) and p < n then \n\t Add(cur, p); \n\t AddSet(uniq, p); \n\tfi;\n od;\n return cur;\nend;\n\n_CommuteExt := function(perm, sym, refl_diff, n, drop0) \n local mat, N, ext, points, minset, pmat;\n mat:=MatSPL(Prm(perm));\n N := perm.domain();\n ext := sym.ext(N,false);\n points := List(Refl(n, N-refl_diff, N, perm).tolist(), x->x.ev());\n minset := When(not drop0, _minsetPoints(points, n), Drop(_minsetPoints(points,n), 1)-1);\n pmat := MatSPL(Scat(FList(minset).setRange(Cols(ext))));\n return \n mat * MatSPL(ext) * pmat;\nend;\n\n\n# CommuteExt(spl, sym, scaled) - find X, such that spl * sym.ext(n, scaled) = X * pspl\n# X = spl * sym.ext(n, scaled) * pspl^-1\n#\n\nCommuteExt1 := (perm, sym) -> _CommuteExt(perm, sym, -1, Cols(sym.ext(perm.domain(),false)), false);\nCommuteExt0 := (perm, sym) -> _CommuteExt(perm, sym, 0, Cols(sym.ext(perm.domain(),false)), false);\nCommuteExt00 := (perm, sym) -> _CommuteExt(perm, sym, 0, 1+Cols(sym.ext(perm.domain(),false)), true);\n\n##\n## Constructors for symmetric sequences\n##\nClass(Symmetry, rec(\n isSymmetry := true,\n __call__ := (self, n) >> self.seq(n),\n red := (self, n, scaled) >> self.ext(n, scaled).transpose(),\n verify := (self, n) >> MatSPL(self.red(n,false)self.ext(n, true))\n));\n\nIsSymmetry := x -> IsRec(x) and IsBound(x.isSymmetry) and x.isSymmetry;\n\n_gathI := (nn, top_hole, bot_hole) -> let(n:=Int(nn), Gath(fAdd(n, n-top_hole-bot_hole, top_hole)));\n_gathI2 := (nn, top_hole, bot_hole) -> let(n:=Int(nn), Gath(H(n, Int((n-top_hole-bot_hole+1)/2), top_hole, 2)));\n_gathJ := (nn, top_hole, bot_hole) -> let(n:=Int(nn), Gath(fCompose(fAdd(n, n-top_hole-bot_hole, top_hole), J(n-top_hole-bot_hole))));\n\nClass(GathExtend, Sym, rec(def := (n, symmetry) -> symmetry.ext(n, true)));\nClass(GathExtendU, Sym, rec(def := (n, symmetry) -> symmetry.ext(n, false)));\nClass(GathExtendZ, Sym, rec(def := (n, symmetry) -> DirectSum(I(1),-J(n-1))symmetry.ext(n, true)));\nClass(GathExtendZU, Sym, rec(def := (n, symmetry) -> DirectSum(I(1),-J(n-1))symmetry.ext(n, false)));\nClass(ScatReduce, Sym, rec(def := (n, symmetry) -> symmetry.red(n, true)));\nClass(ScatReduceU, Sym, rec(def := (n, symmetry) -> symmetry.red(n, false)));\n\n\nClass(EOSymmetry, Symmetry, rec(tsize := \"cols\"));\n\nClass(Upsample0, EOSymmetry, rec(\n seq:= n -> Checked(IsEvenInt(n), List([1..n], i -> When(IsEvenInt(i),0,rand()))),\n ext := (n, scaled) -> Checked(IsEvenInt(n), Tensor(I(n/2),Mat([[1],[0]]))),\n red := (n, scaled) -> Checked(IsEvenInt(n), Tensor(I(n/2),Mat([[1,0]]))),\n));\n\nClass(Upsample1, EOSymmetry, rec(\n seq:= n -> Checked(IsEvenInt(n), List([1..n], i -> When(IsEvenInt(i),0,rand()))),\n ext := (n, scaled) -> Checked(IsEvenInt(n), Tensor(I(n/2),Mat([[0],[1]]))),\n red := (n, scaled) -> Checked(IsEvenInt(n), Tensor(I(n/2),Mat([[0,1]]))),\n));\n\nClass(Even0, EOSymmetry, rec(\n seq := n -> let(len := Int((n-1)/2), lst := List([2..len+1], rand),\n\tFlat([rand(1), lst, When(IsEvenInt(n),rand(len+2),[]), Reversed(lst)])),\n ext := (n, scaled) -> let(hf := When(scaled, 1/2, 1), \n\tDirectSum(I(1), \n\t VStack(\n\t\t\tDirectSum(hfI(Int((n-1)/2)), I(_even(n))),\n\t\t\thf_gathJ(n/2, 0, _even(n))))),\n# red := n -> Gath(fAdd(n, Int((n+2)/2), 0))\n));\n\nClass(Even0star, EOSymmetry, rec(\n seq := n -> let(len := Int((n-1)/2), lst := List([2..len+1], rand),\n\tFlat([rand(1), lst, When(IsEvenInt(n),0,[]), Reversed(lst)])),\n ext := (n, scaled) -> let(hf := When(scaled, 1/2, 1), \n\tDirectSum(I(1), \n\t VStack(\n\t\t\thfI(Int((n-1)/2)), \n When(IsEvenInt(n), O(1, Int((n-1)/2)), []), \n\t\t\thfJ(Int((n-1)/2))))),\n# red := n -> Gath(fAdd(n, Int((n+2)/2), 0))\n));\n\nClass(Even00, EOSymmetry, rec(\n seq := n -> let(len := Int((n-1)/2), lst := List([2..len+1], rand),\n\tFlat([0, lst, When(IsEvenInt(n),rand(len+2),[]), Reversed(lst)])),\n ext := (n, scaled) -> let(hf := When(scaled, 1/2, 1), \n\tVStack(O(1,Int(n/2)), \n\t DirectSum(hfI(Int((n-1)/2)), I(_even(n))),\n\t hf_gathJ(n/2, 0, _even(n)))),\n# red := n -> Gath(fAdd(n, Int(n/2), 1))\n));\n\nClass(Even00star, EOSymmetry, rec(\n seq := n -> let(len := Int((n-1)/2), lst := List([2..len+1], rand),\n\tFlat([0, lst, When(IsEvenInt(n),0,[]), Reversed(lst)])),\n ext := (n, scaled) -> let(hf := When(scaled, 1/2, 1), \n\tVStack(O(1,Int(n/2)), \n\t DirectSum(hfI(Int((n-1)/2)), O(_even(n))),\n\t hf_gathJ(n/2, 0, _even(n)))),\n# red := n -> Gath(fAdd(n, Int(n/2), 1))\n));\n\nClass(Even1, EOSymmetry, rec(\n seq := n -> let(len := Int(n/2), lst := List([1..len], rand),\n\tFlat([lst, When(IsOddInt(n),rand(len+1),[]), Reversed(lst)])),\n ext := (n, scaled) -> let(hf := When(scaled, 1/2, 1), \n\tWhen(IsEvenInt(n), \n\t hf VStack(I(n/2), J(n/2)), \n\t VStack(DirectSum(hfI((n-1)/2), I(1)), hf_gathJ((n+1)/2, 0, 1))))\n# red := n -> Gath(fAdd(n, Int((n+1)/2), 0))\n));\n\n\nClass(Odd0, EOSymmetry, rec(\n seq := n -> let(len := Int((n-1)/2), lst := List([2..len+1], rand),\n\tFlat([rand(1), lst, When(IsEvenInt(n),0,[]), -Reversed(lst)])),\n ext := (n, scaled) -> let(hf := When(scaled, 1/2, 1),\n\tDirectSum(I(1), \n\t hfVStack(I(Int((n-1)/2)), \n\t\t When(IsEvenInt(n), O(1, Int((n-1)/2)), []), \n\t\t\t -J(Int((n-1)/2))))) \n# red := n -> Gath(fAdd(n, Int((n+2)/2), 0))\n));\n\nClass(Odd00, EOSymmetry, rec(\n seq := n -> let(len := Int((n-1)/2), lst := List([2..len+1], rand),\n\tFlat([0, lst, When(IsEvenInt(n),0,[]), -Reversed(lst)])),\n ext := (n, scaled) -> let(hf := When(scaled, 1/2, 1), \n\t hf VStack(O(1,Int((n-1)/2)), \n\t I(Int((n-1)/2)),\n\t\t\t When(IsEvenInt(n), O(1,Int((n-1)/2)), []), \n\t -J(Int((n-1)/2)))),\n# red := n -> Gath(fAdd(n, Int((n-1)/2), 1))\n));\n\nClass(Odd00star, EOSymmetry, rec(\n seq := n -> let(len := Int((n-1)/2), lst := List([2..len+1], rand),\n\tFlat([0, lst, When(IsEvenInt(n),rand(len+2),[]), -Reversed(lst)])),\n ext := (n, scaled) -> let(hf := When(scaled, 1/2, 1), \n\t hf * VStack(O(1,Int((n-1)/2)), \n\t I(Int((n-1)/2)),\n When(IsEvenInt(n), RowVec( Replicate(Int((n-3)/2),0)::[1] ), []), \n -J(Int((n-1)/2)))),\n# red := n -> Gath(fAdd(n, Int((n-1)/2), 1))\n));\n\n\nClass(Odd1, EOSymmetry, rec(\n seq := n -> let(len := Int(n/2), lst := List([1..len], rand),\n\tFlat([lst, When(IsOddInt(n),0,[]), -Reversed(lst)])),\n ext := (n, scaled) -> let(hf := When(scaled, 1/2, 1), \n\t hf * VStack(I(Int(n/2)), \n\t\t When(IsOddInt(n), O(1, Int(n/2)),[]), \n\t\t\t -J(Int(n/2)))),\n# red := n -> Gath(fAdd(n, Int(n/2), 0))\n));\n\n\nClass(Real, EOSymmetry, rec(\n seq := n -> List([1..n], rand),\n ext := (n, scaled) -> I(n),\n tsize := \"rows\", # does not matter, since ext is square\n));\n\n# NOTE: red != ext^T, how to handle?\n# - silently drop scaling?\n\n# DirectSum((I tensor W), j * I(1))\n#\nClass(Conj_Base, Symmetry, rec(\n __call__ := (self, w, j) >> Checked(IsMat(w), DimensionsMat(w)=[2,2], \n\tWithBases(self, rec(\n\t\tw := w, \n\t\tj := j, \n\t\toperations := PrintOps\n ))),\n tsize := \"rows\",\n print := self >> Print(self.name, \"(\", self.w, \", \", self.j, \")\"),\n W := self >> When(IsBound(self.isOdd) and self.isOdd, self.w * DiagonalMat([1, -1]), self.w),\n invertW := self >> let(base := self.__bases__[1], base(TransposedMat(self.w^-1), 1/self.j)),\n seq := (self, n) >> self.re.seq(n) + E(4) * self.im.seq(n),\n verify := (self, n) >> MatSPL(self.red(n,false)self.ext(n, false))\n));\n\nClass(Conj0_Base, Conj_Base, rec(\n P := n -> DirectSum(I(1), L_or_OS(n-1, Int(n/2)) DirectSum(I(Int(n/2)), J(Int((n-1)/2)))),\n ext := (self, n, scaled) >> self.invertW().red(n, scaled).transpose(),\n red := (self, n, scaled) >> let(\n\tW := Mat(When(scaled, self.W(), self.W())),\n self.PP(n) * DirectSum(I(1), Tensor(I(Int((n-1)/2)), W), self.j * I(_even(n))) * self.P(n)\n )\n));\n\nClass(Conj1_Base, Conj_Base, rec(\n P := n -> L_or_OS(n, Int((n+1)/2)) * DirectSum(I(Int((n+1)/2)), J(Int(n/2))),\n seq := (self, n) >> self.re.seq(n) + E(4) * self.im.seq(n),\n ext := (self, n, scaled) >> self.invertW().red(n, scaled).transpose(),\n red := (self, n, scaled) >> let(\n\tW := Mat(When(scaled, self.W(), self.W())),\n self.PP(n) * DirectSum(Tensor(I(Int(n/2)), W), self.j * I(_odd(n))) * self.P(n)\n )\n));\n\nClass(Conj0_R2R, Conj0_Base, rec(PP := (self, n) >> self.P(n).transpose()));\nClass(Conj1_R2R, Conj1_Base, rec(PP := (self, n) >> self.P(n).transpose()));\n\nClass(CE0_R2R, Conj0_R2R, rec(re := Even0, im := Odd00, isOdd := false));\nClass(CO0_R2R, Conj0_R2R, rec(re := Odd0, im := Even00, isOdd := true, j := -E(4)));\nClass(CE1_R2R, Conj1_R2R, rec(re := Even1, im := Odd1, isOdd := false));\nClass(CO1_R2R, Conj1_R2R, rec(re := Odd1, im := Even1, isOdd := true, j := -E(4)));\n\n_m := n -> When(n=1, Mat([[1], [0]]), I(0));\n_mj := n -> When(n=1, Mat([[0], [1]]), I(0));\n\nClass(Conj0_R2Cpx, Conj0_Base, rec(PP := (self, n) >> \n\tDirectSum(_m(1), I(n-1-_even(n)), _m(_even(n)))));\n\nClass(Conj1_R2Cpx, Conj1_Base, rec(PP := (self, n) >> \n\tDirectSum(I(n-_odd(n)), When(self.isOdd, _mj(_odd(n)), _m(_odd(n))))));\n\nClass(CE0_R2Cpx, Conj0_R2Cpx, rec(re := Even0, im := Odd00, isOdd := false));\nClass(CO0_R2Cpx, Conj0_R2Cpx, rec(re := Odd0, im := Even00, isOdd := true, j := -E(4)));\nClass(CE1_R2Cpx, Conj1_R2Cpx, rec(re := Even1, im := Odd1, isOdd := false));\nClass(CO1_R2Cpx, Conj1_R2Cpx, rec(re := Odd1, im := Even1, isOdd := true, j := -E(4)));\n\nW_RFT := 1/2[[1, 1], [-E(4), E(4)]];\nW_RFTT := 1/2[[1, 1], [E(4), -E(4)]];\nW_URFT := [[1, 1], [-E(4), E(4)]];\nW_URFTT := [[1, 1], [E(4), -E(4)]];\nW_DHT := 1/2[[1-E(4), 1+E(4)], [1+E(4), 1-E(4)]];\n\nrsym := function(x)\n local n, nc, nf, mid, uniq, zeros, fst_0, mid_0, fstmid;\n n := Length(x); nc := Int((n+1)/2); nf := Int(n/2); mid := nf;\n if n=0 then return \"empty\"; fi;\n\n fst_0 := scalareq(x[1], 0);\n mid_0 := scalareq(x[nf+1], 0);\n fstmid := [Cond(fst_0,0, 1), Cond(mid_0, 0, 1)];\n\n if ForAll(x, e->scalareq(e,0)) then return \"zero\";\n\n # normal symmetries\n elif ForAll([1..nc-1], i->scalareq(x[1+ i], x[1+ (n-i) mod n])) then\n fstmid[2] := Cond(IsOddInt(n), 1, fstmid[2]);\n if fstmid=[0,0] then return \"even00\"; \n\telif fstmid=[0,1] then return \"even00\"; \n elif fstmid=[1,0] then return \"even0\"; \n elif fstmid=[1,1] then return \"even0\"; \n fi;\n elif ForAll([1..nc-1], i->scalareq(x[1+ i], -x[1+ (n-i) mod n])) then\n fstmid[2] := Cond(IsOddInt(n), 0, fstmid[2]);\n if fstmid=[0,0] then return \"odd00\"; \n\telif fstmid=[0,1] then return \"odd00\"; \n elif fstmid=[1,0] then return \"odd0\"; \n elif fstmid=[1,1] then return \"odd0\"; \n fi;\n elif ForAll([0..mid-1], i->scalareq(x[1+ i], x[1+ (n-1-i)])) then \n if IsOddInt(n) and mid_0 then return \"even1\"; \n else return \"even1\";\n fi;\n elif ForAll([0..mid-1], i->scalareq(x[1+ i], -x[1+ (n-1-i)])) then \n if IsOddInt(n) and not mid_0 then return \"odd1\"; \n else return \"odd1\";\n fi;\n\n # symmetries with flipped bottom, i.e. abcabc\n elif n>2 and IsOddInt(n) and ForAll([1..nc-1], i->scalareq(x[1+ i], x[1+ mid+i])) then\n\tif fst_0 then return \"jeven00\"; else return \"jeven0\"; fi;\n elif n>2 and IsOddInt(n) and ForAll([1..nc-1], i->scalareq(x[1+ i], -x[1+ mid+i])) then\n\tif fst_0 then return \"jodd00\"; else return \"jodd0\"; fi;\n elif n>2 and ForAll([0..mid-1], i->scalareq(x[1+ i], x[1+ mid+i])) then return \"jeven1\";\n elif n>2 and ForAll([0..mid-1], i->scalareq(x[1+ i], -x[1+ mid+i])) then return \"jodd1\";\n\n # rader symmetries, similar to normal but every other sample in bottom half is negated\n elif ForAll([1..nc-1], i->scalareq(x[1+i], (-1)^i x[1+(n-i) mod n])) then\n\tif fst_0 then return \"rader_even00\"; else return \"rader_even0\"; fi;\n elif ForAll([1..nc-1], i->scalareq(x[1+i], - (-1)^i * x[1+(n-i) mod n])) then\n\tif fst_0 then return \"rader_odd00\"; else return \"rader_odd0\"; fi;\n\n # symmetries with normal shape, but elements negated in some non-recognized way\n elif ForAll([1..nc-1], i->scalareq(x[1+i], x[1+(n-i) mod n]) or scalareq(x[1+i], -x[1+(n-i) mod n])) then\n\tif fst_0 then return \"eo00\"; else return \"eo0\"; fi;\n elif ForAll([0..mid-1], i->scalareq(x[1+i], x[1+(n-1-i)]) or scalareq(x[1+i], -x[1+(n-1-i)])) then\n\treturn \"eo1\"; \n else\n\tuniq := Length(Set(List(x, e->V(AbsFloat(e)))));\n\tzeros := Length(Filtered(x, e->scalareq(e,0)));\n\tif uniq <= Int((n+2)/2) then\n # no obvious symmetry, but only approx half unique elements\n\t # so sequence is still redundant\n\t return Concat(\"red_\", String(uniq-zeros), \"/\", String(zeros), \"/\",String(Length(x))); \n\telse return \"none\";\n\tfi;\n fi;\nend;\n\nrisym := function(x)\n local rs, is, re, im;\n re := List(x, e->ReComplex(Complex(e)));\n im := List(x, e->ImComplex(Complex(e)));\n rs := rsym(re);\n is := rsym(im);\n return [rs,is];\nend;\n\ncsym := function(x)\n local s;\n s := sym(x);\n if s = [\"even0\", \"odd00\"] then return \"ce0\";\n elif s = [\"odd0\", \"even00\"] then return \"co0\";\n elif s = [\"even1\", \"odd1\"] then return \"ce1\";\n elif s = [\"odd1\", \"even1\"] then return \"co1\";\n elif s = [\"jeven1\", \"jodd1\"] then return \"jce1\";\n elif s = [\"jodd1\", \"jeven1\"] then return \"jco1\";\n elif s = [\"rader_even0\", \"rader_odd00\"] then return \"rader_ce0\";\n elif s = [\"rader_odd0\", \"rader_even00\"] then return \"rader_co0\";\n elif s = [\"none\", \"zero\"] then return \"real\";\n elif s = [\"zero\", \"none\"] then return \"imag\";\n elif s = [\"zero\", \"zero\"] then return \"zero\";\n elif s = [\"none\", \"none\"] then return \"cplx\";\n else return s;\n fi;\nend;\n\n \npart := (v, str, n) -> v{1 + [ 0 .. (Length(v) / str - 1) ] * str + n};\n \nfxi_inputs := (inp, fsize) -> let(\n m := Length(inp)/fsize, \n List([0..m-1], x->part(inp,m,x)));\n\nfxi_rsyms := (inp, fsize) -> List(fxi_inputs(inp, fsize), rsym);\nfxi_syms := (inp, fsize) -> List(fxi_inputs(inp, fsize), risym);\n\ntransf_syms := (n, transforms, syms) -> \n List(syms, s ->\n List(transforms, transform -> \n\t let(inpvec := TransposedMat([s(n)]),\n\t outvec := TransposedMat(MatSPL(transform(n))inpvec)[1],\n\t outsym := sym(outvec),\n\t Cond(outsym[2]=\"zero\", outsym[1],\n\t\t outsym[1]=\"zero\", Concat(\"j\", outsym[2]),\n\t\t \"none\"))));\n\nctransf_syms := (n, transforms, syms) -> \n List(syms, s ->\n List(transforms, transform -> \n\t let(inpvec := TransposedMat([s(n)]),\n\t outvec := TransposedMat(MatSPL(transform(n))inpvec)[1],\n\t risym(outvec))));\n\n\n# transf_syms(18, [ DFT1, DFT2, DFT3, DFT4 ], [even00, even1, odd00, odd1]);\n\n# fxi_syms(even0(36),6);\n# fxi_syms(even00(36),6);\n# fxi_syms(even1(36),6);\n# fxi_syms(odd0(36),6);\n# fxi_syms(odd00(36),6);\n# fxi_syms(odd1(36),6);\n\n\n# if rs=\"none\" and is=\"none\" then return \"none\";\n# elif rs=\"none\" and is=\"zero\" then return \"real\";\n# elif rs=\"even\" and is=\"odd\" then return \"ce\";\n# elif rs=\"even\" and is=\"odd\" then return \"ce\";\n#end;\ntwpow := (N,n) -> List([0..N-1], j -> (j mod n) Int(j / n));\n\ntw1 := (N,n) -> List([0..N-1], j -> E(4N)^((2(j mod n)) * (2Int(j / n))));\ntw2 := (N,n) -> List([0..N-1], j -> E(4N)^((2(j mod n)) (2Int(j / n)+1)));\ntw3 := (N,n) -> List([0..N-1], j -> E(4N)^((2(j mod n)+1) (2Int(j / n))));\ntw4 := (N,n) -> List([0..N-1], j -> E(4N)^((2(j mod n)+1) (2Int(j / n)+1)));\ndct2diag := N -> List([0..N-1], i->E(2N)^i);\ndct4diag := N -> List([0..N-1], i->E(4N)^(2i+1));\nidct2diag := N -> List([0..N-1], i->E(2N)^-i);\nlistmul := (l1,l2) -> List([1..Length(l1)], i->l1[i]l2[i]);\n\nComplexFFT2 := input -> TransposedMat(MatSPL(DFT2(Length(input))) * TransposedMat([input]))[1];\nComplexFFT3 := input -> TransposedMat(MatSPL(DFT3(Length(input))) * TransposedMat([input]))[1];\nComplexFFT4 := input -> TransposedMat(MatSPL(DFT4(Length(input))) * TransposedMat([input]))[1];\n\n\n# Macro Extensions\n#\nMacroExt0 := (k,a,b,c,d) -> Checked(IsSymmetry(a), IsSPL(b), IsSPL(d), b.dims()=d.dims(),\n IsOddInt(k) or IsSymmetry(c), \n Cond(IsOddInt(k),\n let(kk := (k-1)/2, n := Cols(b), \n top := DirectSum(GathExtendU(n, a), Tensor(I(kk), b)),\n VStack(top,\n Tensor(J(kk), d) * Gath(fAdd(Cols(top), kkCols(d), Cols(a.ext(n,true)))))),\n let(kk := (k-2)/2, n := Cols(b), \n top := DirectSum(GathExtendU(n, a), Tensor(I(kk), b), GathExtendU(n, c)),\n VStack(top, \n Tensor(J(kk), d) Gath(fAdd(Cols(top), kkCols(d), Cols(a.ext(n,true))))))\n ));\n\nMacroExt1 := (k,b,c,d) -> Checked(IsSPL(b), IsSPL(d), b.dims()=d.dims(),\n IsEvenInt(k) or IsSymmetry(c), \n Cond(IsOddInt(k),\n let(kk := (k-1)/2, n := Cols(b), \n top := DirectSum(Tensor(I(kk), b), GathExtendU(n, c)),\n VStack(top,\n Tensor(J(kk), d) Gath(fAdd(Cols(top), kkCols(d), 0)))),\n let(kk := k/2, \n VStack(Tensor(I(kk), b),\n Tensor(J(kk), d)))\n ));\n\nJp := x -> OS(x, -1);\n\nlistExtMat := mat -> List(mat, row -> let(n:=PositionProperty(row, x->x<>0), \n Cond(n=false, 0, \n row[n]<0, -n,\n +n)));\n\nanalyze := (stride, extmat) -> let(\n lst := listExtMat(MatSPL(extmat)),\n fsize := Length(lst)/stride,\n rec(inp := fxi_inputs(lst, fsize),\n sym := fxi_rsyms(lst, fsize)));\n\nanalyzeT := (stride, extmat, partsizes) -> let(\n fsize := Rows(extmat)/stride,\n lst := listExtMat(TransposedMat(MatSPL(L(fsizestride, stride)*extmat))),\n part := Drop(ScanL(partsizes, (p, x) -> [Last(p)+1..Last(p)+x], [0]), 1),\n rec(out := List(part, p->lst{p}))); \n\npanalyze := function(stride, extmat) \n local r, zip, i, e, sym, n, mid, j, cur, absprev, prev, sign;\n r := analyze(stride, extmat);\n zip := Zip2(r.sym, r.inp);\n n := Length(zip);\n mid := Int((n+1)/2);\n for i in [1..Length(zip)] do\n e := zip[i];\n if e[1] = \"none\" then \n sym := \"I\";\n if i > mid then\n cur := List(e[2], AbsInt);\n for j in [1..mid] do \n prev := r.inp[j];\n absprev := List(r.inp[j], AbsInt);\n if cur=Reversed(absprev) then \n prev := Reversed(prev);\n sign := Cond(e[2]=prev, \"\", e[2]=-prev, \"-\", \"#\");\n sym := sign :: \"J/\" :: StringInt(j); \n elif cur=[absprev[1]]::Reversed(Drop(absprev, 1)) then \n prev := [prev[1]]::Reversed(Drop(prev, 1)); \n sign := Cond(e[2]=prev, \"\", e[2]=-prev, \"-\", \"#\");\n sym := sign :: \"J'/\"::StringInt(j); \n fi;\n od;\n fi;\n else\n sym := YellowStr(e[1]);\n fi;\n Print(sym, \": \", e[2], \"\\n\");\n od;\nend;\n\n", "meta": {"hexsha": "ceb65da08038283bed81c7f49c2f7ac966c24a36", "size": 21670, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/sym/symmetries.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/sym/symmetries.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/sym/symmetries.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 39.4, "max_line_length": 134, "alphanum_fraction": 0.5359021689, "num_tokens": 7984, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7606506526772883, "lm_q2_score": 0.6859494485880928, "lm_q1q2_score": 0.5217678957721588}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nClass(RealDFT_Base, TaggedNonTerminal, rec(\n abbrevs := [ (n) -> Checked(IsPosInt(n), [n, 1]),\n (n,k) -> Checked(IsPosInt(n), IsInt(k), Gcd(n,k)=1, [n, k]) ],\n \n terminate := self >> let(N := self.params[1], k := self.params[2], \n\trr := When(self.transposed, Cols(self), Rows(self)),\n\tmat := Mat(List([0..rr-1], r -> When(r mod 2 = 0, \n List([0..N-1], c -> self.projRe(self.omega(N,k,Int(r/2),c))),\n List([0..N-1], c -> self.projIm(self.omega(N,k,Int(r/2),c)))))),\n When(self.transposed, mat.transpose(), mat)),\n\n toAMat := self >> self.terminate().toAMat(), \n\n isReal := True,\n SmallRandom := () -> Random([2..16]), \n LargeRandom := () -> 2 ^ Random([6..15]),\n\n normalizedArithCost := self >> let(n := self.params[1], \n floor(2.5 * n * log(n) / log(2.0))),\n\n hashAs := self >> let(t:=ObjId(self)(self.params[1], 1).withTags(self.getTags()),\n When(self.transposed, t.transpose(), t))\n\n));\n\n\nClass(PDHT13_Base, RealDFT_Base, rec(\n projRe := w -> Re(w)+Im(w),\n projIm := w -> Re(w)-Im(w)\n));\n\nClass(PDHT24_Base, RealDFT_Base, rec(\n projRe := w -> Re(w)+Im(w),\n projIm := w -> -Re(w)+Im(w)\n));\n\nClass(PRDFT_Base, RealDFT_Base, rec(\n projRe := Re,\n projIm := Im\n));\n\nClass(IPRDFT_Base, TaggedNonTerminal, rec(\n abbrevs := [ (n) -> Checked(IsPosInt(n), [n, 1]),\n\t (n,k) -> Checked(IsPosInt(n), IsInt(k), Gcd(n,k)=1, [n, k]) ],\n terminate := self >> let(n:=self.params[1], k:=self.params[2],\n\tself.rdft(n, -k).terminate().transpose() * self.diag(n)),\n isReal := True,\n SmallRandom := () -> Random([2..16]), \n LargeRandom := () -> 2 ^ Random([6..15]),\n\n diag0 := n -> When(n=2, I(4), \n Diag(diagDirsum(fConst(TReal, 2, 1), fConst(TReal, 2Int((n-1)/2), 2), \n When(IsEvenInt(n), fConst(TReal, 2, 1), [])))),\n\n diag1 := n -> Diag(diagDirsum(fConst(TReal, 2Int(n/2), 2), \n When(IsOddInt(n), fConst(TReal, 2, 1), []))),\n\n normalizedArithCost := self >> let(n := self.params[1], \n floor(2.5 * n * log(n) / log(2.0))),\n\n hashAs := self >> let(t:=ObjId(self)(self.params[1], 1).withTags(self.getTags()),\n When(self.transposed, t.transpose(), t))\n));\n\nDeclare(IPRDFT, IPRDFT1, IPRDFT2, IPRDFT3, IPRDFT4);\n\n# PRDFT(<N>, <k>) - Packed Real DFT Nonterminal\n# Is a N+2 x N real matrix. N+2 outputs correspond\n# to Floor(N/2)+1 complex outputs of complex DFT\n# the other half of complex DFT outputs are complex\n#\nClass(PRDFT, PRDFT_Base, rec(\n abbrevs := [ (n) -> Checked(IsPosInt(n), [n, 1]),\n (n,k) -> Checked(IsPosInt(n), IsInt(k), Gcd(n,k)=1, [n, k mod n]) ],\n dims := self >> let(n:=self.params[1], d := [2(Int(n/2)+1), n], When(self.transposed, Reversed(d), d)),\n omega := (N,k,r,c) -> E(N)^(krc),\n inverse := self >> IPRDFT1(self.params[1], -self.params[2]),\n inverseViaDiag := self >> self.transpose() IPRDFT.diag(self.params[1])\n));\nPRDFT1 := PRDFT;\n\nClass(PRDFT2, PRDFT_Base, rec(\n abbrevs := [ (n) -> Checked(IsPosInt(n), [n, 1]),\n (n,k) -> Checked(IsPosInt(n), IsInt(k), Gcd(n,k)=1, [n, k mod (2n)]) ],\n dims := self >> let(n:=self.params[1], d := [2(Int(n/2)+1), n], When(self.transposed, Reversed(d), d)),\n omega := (N,k,r,c) -> E(2N)^(kr(2c+1)),\n inverse := self >> IPRDFT3(self.params[1], -self.params[2])\n));\n\nClass(PRDFT3, PRDFT_Base, rec(\n abbrevs := [ (n) -> Checked(IsPosInt(n), [n, 1]),\n (n,k) -> Checked(IsPosInt(n), IsInt(k), Gcd(n,k)=1, [n, k mod (2n)]) ],\n dims := self >> let(n:=self.params[1], d := [2(Int((n+1)/2)), n], When(self.transposed, Reversed(d), d)),\n omega := (N,k,r,c) -> E(2N)^(k(2r+1)c),\n inverse := self >> IPRDFT2(self.params[1], -self.params[2])\n));\n\nClass(PRDFT4, PRDFT_Base, rec(\n abbrevs := [ (n) -> Checked(IsPosInt(n), [n, 1]),\n (n,k) -> Checked(IsPosInt(n), IsInt(k), Gcd(n,k)=1, [n, k mod (4n)]) ],\n dims := self >> let(n:=self.params[1], d := [2(Int((n+1)/2)), n], When(self.transposed, Reversed(d), d)),\n omega := (N,k,r,c) -> E(4N)^(k(2r+1)(2c+1)),\n inverse := self >> IPRDFT4(self.params[1], -self.params[2])\n));\n\n# Class(SkewRDFT3, PRDFT_Base, rec(\n# abbrevs := [ (n) -> Checked(IsPosInt(n), [n, 1, 0, 0]),\n# (n,k) -> Checked(IsPosInt(n), IsInt(k), Gcd(n,k)=1, [n, k, 0, 0]), \n# (n,k,lr,rr) -> Checked(IsPosInt(n), IsInt(k), IsRat(lr), IsRat(rr), \n# \t Gcd(n,k)=1, [n, k, lr, rr])\n# ],\n# dims := self >> let(n:=self.params[1], [ 2Int((n+1)/2), n ]),\n# omega := (self,N,k,r,c) >> let(\n# \tlnum:=Numerator(self.params[3]), lden:=Denominator(self.params[3]),\n# \trnum:=Numerator(self.params[4]), rden:=Denominator(self.params[4]),\n# \tE(2Nldenrden) ^ (k(lden(2r+1)+lnum)(rdenc+rnum)))\n# ));\n# Class(SkewRDFT4, SkewRDFT3, rec(\n# dims := self >> let(n:=self.params[1], [ 2Int((n+1)/2), n ]),\n# omega := (self,N,k,r,c) >> let(\n# \tlnum:=Numerator(self.params[3]), lden:=Denominator(self.params[3]),\n# \trnum:=Numerator(self.params[4]), rden:=Denominator(self.params[4]),\n# \tE(4Nldenrden) ^ (k(lden(2r+1)+lnum)(rden(2c+1)+rnum)))\n# ));\n\n#\n# Hartley\n#\nClass(PDHT, PDHT13_Base, rec(\n abbrevs := [ (n) -> Checked(IsPosInt(n), [n, 1]),\n (n,k) -> Checked(IsPosInt(n), IsInt(k), Gcd(n,k)=1, [n, k mod (n)]) ],\n dims := self >> let(n:=self.params[1], d := [2(Int(n/2)+1), n], When(self.transposed, Reversed(d), d)),\n omega := PRDFT.omega\n));\nPDHT1 := PDHT;\n\nClass(PDHT2, PDHT24_Base, rec(\n abbrevs := [ (n) -> Checked(IsPosInt(n), [n, 1]),\n (n,k) -> Checked(IsPosInt(n), IsInt(k), Gcd(n,k)=1, [n, k mod (2n)]) ],\n dims := self >> let(n:=self.params[1], d := [2(Int(n/2)+1), n], When(self.transposed, Reversed(d), d)),\n omega := PRDFT2.omega\n));\n\nClass(PDHT3, PDHT13_Base, rec(\n abbrevs := [ (n) -> Checked(IsPosInt(n), [n, 1]),\n (n,k) -> Checked(IsPosInt(n), IsInt(k), Gcd(n,k)=1, [n, k mod (2n)]) ],\n dims := self >> let(n:=self.params[1], d := [2(Int((n+1)/2)), n], When(self.transposed, Reversed(d), d)),\n omega := PRDFT3.omega\n));\n\nClass(PDHT4, PDHT24_Base, rec(\n abbrevs := [ (n) -> Checked(IsPosInt(n), [n, 1]),\n (n,k) -> Checked(IsPosInt(n), IsInt(k), Gcd(n,k)=1, [n, k mod (4n)]) ],\n dims := self >> let(n:=self.params[1], d := [2(Int((n+1)/2)), n], When(self.transposed, Reversed(d), d)),\n omega := PRDFT4.omega\n));\n\n\n# IPRDFT(<N>, <k>) - Inverse Packed Real DFT Nonterminal\n# Is a N x N+2 real matrix. When applied to N+2 outputs\n# of PRDFT yields the original real input.\nClass(IPRDFT, IPRDFT_Base, rec(\n abbrevs := [ (n) -> Checked(IsPosInt(n), [n, 1]),\n (n,k) -> Checked(IsPosInt(n), IsInt(k), Gcd(n,k)=1, [n, k mod (n)]) ],\n dims := self >> let(n:=self.params[1], d := [n, 2(Int(n/2)+1)], When(self.transposed, Reversed(d), d)),\n rdft := PRDFT,\n diag := IPRDFT_Base.diag0\n));\nIPRDFT1 := IPRDFT;\n\n# IPRDFT2 is inverse if PRDFT3\nClass(IPRDFT2, IPRDFT_Base, rec(\n abbrevs := [ (n) -> Checked(IsPosInt(n), [n, 1]),\n (n,k) -> Checked(IsPosInt(n), IsInt(k), Gcd(n,k)=1, [n, k mod (2n)]) ],\n dims := self >> let(n:=self.params[1], d := [n, 2(Int((n+1)/2))], When(self.transposed, Reversed(d), d)),\n rdft := PRDFT3,\n diag := IPRDFT_Base.diag1\n)); \n\n# IPRDFT3 is inverse if PRDFT2\nClass(IPRDFT3, IPRDFT_Base, rec(\n abbrevs := [ (n) -> Checked(IsPosInt(n), [n, 1]),\n (n,k) -> Checked(IsPosInt(n), IsInt(k), Gcd(n,k)=1, [n, k mod (2n)]) ],\n dims := self >> let(n:=self.params[1], d := [n, 2(Int(n/2)+1)], When(self.transposed, Reversed(d), d)),\n rdft := PRDFT2,\n diag := IPRDFT_Base.diag0\n));\n\nClass(IPRDFT4, IPRDFT_Base, rec(\n abbrevs := [ (n) -> Checked(IsPosInt(n), [n, 1]),\n (n,k) -> Checked(IsPosInt(n), IsInt(k), Gcd(n,k)=1, [n, k mod (4n)]) ],\n dims := self >> let(n:=self.params[1], d := [n, 2(Int((n+1)/2))], When(self.transposed, Reversed(d), d)),\n rdft := PRDFT4,\n diag := IPRDFT_Base.diag1\n));\n\n", "meta": {"hexsha": "c4d71d0561b9e221efd2ea1480b1e2f81d11da90", "size": 8171, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/realdft/prdft.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/transforms/realdft/prdft.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/transforms/realdft/prdft.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 40.4504950495, "max_line_length": 110, "alphanum_fraction": 0.5372659405, "num_tokens": 3006, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. 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	{"text": "# The tetrahedron with v=4, k=3, lm=2.\nBindGlobal(\"TetrahedronGraph\", CompleteGraph(SymmetricGroup(4)));\n\n# The octahedron with v=6, k=4, lm=2, mu=4.\nBindGlobal(\"OctahedronGraph\", CocktailPartyGraph(3));\n\n# The Petersen graph with v=10, k=3, lm=0, mu=1.\nBindGlobal(\"PetersenGraph\", OddGraph(2));\n\n# The Clebsch graph with v=16, k=10, lm=6, mu=6.\nBindGlobal(\"ClebschGraph\", HalvedCubeGraph(5));\n\n# The Schlaefli graph with v=27, k=16, lm=10, mu=8.\nBindGlobal(\"SchlaefliGraph\",\n Graph(DirectProduct(SymmetricGroup(6), SymmetricGroup(2)),\n [[-3,-3,1,1,1,1,1,1], [3,-1,-1,-1,-1,-1,-1,3]],\n OnRoots, RootAdjacency));\n\n# The Hoffman-Singleton graph with v=50, k=7, lm=0, mu=1.\nBindGlobal(\"HoffmanSingletonGraph\", List([function()\n local G, dp, p1, p2, p3, p4;\n G := Group((1, 2, 3, 4, 5));\n dp := DirectProduct(G, G, G, Group((1, 2)));\n p1 := Projection(dp, 1);\n p2 := Projection(dp, 2);\n p3 := Projection(dp, 3);\n p4 := Projection(dp, 4);\n return Graph(dp, Cartesian(GF(5), GF(5), [1, 2]),\n function(x, g)\n local g4, j, s, u, v;\n u := 5^Image(p2, g) * Z(5)^0;\n v := 5^Image(p3, g) * Z(5)^0;\n g4 := Image(p4, g);\n s := x[3]^2;\n j := [1, 2x[3]];\n return [1^g4(x[1]+x[2](u-sv)+s(u^2-v^2)/2)+5^Image(p1, g),\n j[1^g4](x[2]+su+v), x[3]^g4];\n end, function(x, y)\n return (x{[2,3]} = y{[2,3]} and y[1] in [x[1]-x[3], x[1]+x[3]])\n or x[3] <> y[3] and y[1] = x[1] + x[2]y[2]x[3]^2;\n end, true);\n end])[1]());\n\n# The Gewirtz graph with v=56, k=10, lm=0, mu=2.\nBindGlobal(\"GewirtzGraph\", Graph(MathieuGroup(21), [[1,2,3,7,10,20]],\n OnSets, DisjointSets));\n\n# The strongly regular Witt graph with v=77, k=16, lm=0, mu=4.\nBindGlobal(\"WittStronglyRegularGraph\", Graph(MathieuGroup(22),\n [[1,2,3,7,10,20]], OnSets, DisjointSets));\n\n# The graph with v=210, k=99, lm=48, mu=45 constructed by M. Klin\nBindGlobal(\"KlinGraph\", List([function()\n local G, H, N, V;\n H := Group([(1,2,3,4,5,6), (1,4)]);\n V := Set(List(SymmetricGroup(7), g -> Hg));\n N := Position(V, H());\n G := EdgeOrbitsGraph(Action(SymmetricGroup(7), V, OnRight),\n List([(3,4,5,6,7), (2,4,6,3,5,7), (3,5,6,7), (2,4,5,6,7,3),\n (2,3,5,6,7), (2,4,5,6), (2,3,5,6)],\n g -> [N, Position(V, Hg)]));\n AssignVertexNames(G, V);\n return G;\n end])[1]());\n\n# The cube with intersection array {3, 2, 1; 1, 2, 3}\nBindGlobal(\"CubeGraph\", HammingGraph(3, 2));\n\n# The Heawood graph with intersection array {3, 2, 2; 1, 1, 3}.\nBindGlobal(\"HeawoodGraph\", DesarguesianPlaneIncidenceGraph(2));\n\n# The icosahedron with intersection array {5, 2, 1; 1, 2, 5}.\nBindGlobal(\"IcosahedronGraph\", Graph(DirectProduct(AlternatingGroup(5),\n Group((1, 2))),\n [(1,3,5,2,4)], function(p, g)\n return (p^g)^((-1)^(6^g));\n end, function(x, y)\n return Order(x*y) = 3;\n end));\n\n# The Sylvester graph with intersection array {5, 4, 2; 1, 1, 4}\nBindGlobal(\"SylvesterGraph\", Graph(SymmetricGroup(6),\n [[1, [[[1,2], [3,4], [5,6]],\n [[1,3], [2,5], [4,6]],\n [[1,4], [2,6], [3,5]],\n [[1,5], [2,4], [3,6]],\n [[1,6], [2,3], [4,5]]]]],\n function(x, g)\n return [x[1]^g,\n Set(List(x[2], l -> OnSetsSets(l, g)))];\n end, function(x, y)\n return x[1] <> y[1] and x[2] <> y[2] and\n Set([x[1], y[1]]) in Intersection(x[2], y[2])[1];\n end));\n\n# The Perkel graph with intersection array {6, 5, 2; 1, 1, 3}.\nBindGlobal(\"PerkelGraph\", Graph(PSL(2, 19),\n Elements(Filtered(ConjugacyClassesSubgroups(PSL(2, 19)),\n x -> Size(x) = 57 and Order(x[1]) = 60)[1]),\n ConjugateGroup, function(x, y)\n return Order(Intersection(x, y)) = 10;\n end, true));\n\n\n# The Gosset graph with intersection array {27, 10, 1; 1, 10, 27}.\nBindGlobal(\"GossetGraph\",\n Graph(DirectProduct(SymmetricGroup(8), SymmetricGroup(2)),\n [[-3,-3,1,1,1,1,1,1]], OnRoots, RootAdjacency));\n\n# The truncated Witt graph with intersection array {15, 14, 12; 1, 1, 9}.\nBindGlobal(\"Witt23Graph\", Graph(MathieuGroup(23), [[1,4,8,12,13,19,21,23]],\n OnSets, DisjointSets));\n\n# The large Witt graph with intersection array {30, 28, 24; 1, 3, 15}.\nBindGlobal(\"Witt24Graph\", Graph(MathieuGroup(24), [[1,4,8,12,13,19,21,23]],\n OnSets, DisjointSets));\n\n# The bipartite graph associated to Higman's design\n# with intersection array {50, 49, 36; 1, 14, 50}.\nBindGlobal(\"HigmanGraph\", Graph(Stabilizer(MathieuGroup(24), [23, 24], OnSets),\n [[1,4,8,12,13,19,21,23]], OnSets,\n function (x, y)\n return Length(Difference(Intersection(x, y),\n [23, 24])) in [0, 4];\n end));\n\n# The Coxeter graph with intersection array {3,2,2,1; 1,1,1,2}.\nBindGlobal(\"CoxeterGraph\", PolarGraphNOorth(1, 3, 7));\n\n# The doubly truncated Witt graph with intersection array {7,6,4,4; 1,1,1,6}.\nBindGlobal(\"Witt22Graph\", Graph(MathieuGroup(22), [[1,2,3,4,5,10,18,21]],\n OnSets, DisjointSets));\n\n# The dodecahedron with intersection array {3,2,1,1,1; 1,1,1,2,3}.\nBindGlobal(\"DodecahedronGraph\", List([function()\n local G, O, act, dp, p1, p2, u, v;\n dp := DirectProduct(AlternatingGroup(5), Group((1, 2)));\n p1 := Projection(dp, 1);\n p2 := Projection(dp, 2);\n act := function(t, g)\n return OnTuples(t{Permuted([1,2], Image(p2, g))}, Image(p1, g));\n end;\n u := [1, 2];\n v := [3, 4];\n O := Arrangements([1..5], 2);\n G := EdgeOrbitsGraph(Action(dp, O, act),\n [Position(O, u), Position(O, v)]);\n AssignVertexNames(G, O);\n return G;\n end])[1]());\n\n# The Desargues graph with intersection array {3,2,2,1,1; 1,1,2,2,3}.\nBindGlobal(\"DesarguesGraph\", DoubledOddGraph(2));\n\n# The Biggs-Smith graph with intersection array {3,2,2,2,1,1,1; 1,1,1,1,1,1,3}.\nBindGlobal(\"BiggsSmithGraph\", Graph(PSL(2, 17),\n Elements(Filtered(ConjugacyClassesSubgroups(PSL(2, 17)),\n x -> Size(x) = 102 and Order(x[1]) = 24)[1]),\n ConjugateGroup, function(x, y)\n return Order(Intersection(x, y)) = 8;\n end, true));\n", "meta": {"hexsha": "7df3549810daa46886654b27cdb837f4e5b45f5e", "size": 7140, "ext": "gap", "lang": "GAP", "max_stars_repo_path": "lib/NamedGraphs.gap", "max_stars_repo_name": "jaanos/gap-graphs", "max_stars_repo_head_hexsha": "18dd56c9b90a12a717a0cc893fdd72c6343ee79b", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2015-10-27T15:54:29.000Z", "max_stars_repo_stars_event_max_datetime": "2016-11-07T14:09:44.000Z", "max_issues_repo_path": "lib/NamedGraphs.gap", "max_issues_repo_name": "jaanos/gap-graphs", "max_issues_repo_head_hexsha": "18dd56c9b90a12a717a0cc893fdd72c6343ee79b", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2015-04-20T23:13:11.000Z", "max_issues_repo_issues_event_max_datetime": "2015-04-20T23:13:11.000Z", "max_forks_repo_path": "lib/NamedGraphs.gap", "max_forks_repo_name": "jaanos/gap-graphs", "max_forks_repo_head_hexsha": "18dd56c9b90a12a717a0cc893fdd72c6343ee79b", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 44.0740740741, "max_line_length": 79, "alphanum_fraction": 0.4894957983, "num_tokens": 2344, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7879311956428946, "lm_q2_score": 0.6619228691808012, "lm_q1q2_score": 0.521549677737004}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nDeclare(ImageData, ImageVar, ImageUnk);\n\nClass(ImageUnk, SumsBase, BaseContainer, rec(\n new := (self, dims) >> Checked(IsList(dims) and Length(dims) = 2 and ForAll(dims, IsPosInt),\n SPL(WithBases(self, rec(dimensions := dims, _children := [], dims := self >> self.dimensions)))),\n print := (self, i, is) >> Print(\"ImageUnk(\", self.dims(), \")\"),\n codeletShape := self >> let(d := self.dims(), Concat(\"ImageUnk_\", StringInt(d[1]),\"x\",StringInt(d[2]))),\n fftImage := self >> ApplyFunc(O, TRDFT2D(self.dims()).dims()/self.dims()[2]),\n freqImage := self >> let(lindims := Product(TRDFT2D(self.dims()).dims())/(2Product(self.dims())),\n fPrecompute(fConst(TComplex, lindims, 1+E(4)))),\n timeImage := self >> O(self.dims()[1], self.dims()[2]),\n randomImage := (self, m, n) >> ImageUnk(m, n),\n toAMat := self >> NullAMat(self.dimensions),\n unknownImage := self >> self\n));\n\nClass(ImageData, Mat, rec(\n print := (self, i, is) >> Print(\"ImageData(\", Mat(self.element).dims(), \")\"),\n codeletShape := self >> let(d := self.dims(), Concat(\"ImageData_\", StringInt(d[1]),\"x\",StringInt(d[2]))),\n fftImage := self >> TRDFT2D(self.dims()).compute(self.element),\n freqImage := self >> let(fftRData := 1/Product(self.dims()) Flat(self.fftImage()),\n fftCxData := List([1..Length(fftRData)/2], i->Complex(fftRData[2i-1], fftRData[2i])),\n FData(List(fftCxData, i->TComplex.value(i)))),\n timeImage := self >> self.element,\n randomImage := (self, m, n) >> let(data := List([1..m], i->List([1..n], j->FloatRat(Random([1..1000]/1000)))),\n ImageData(data)),\n unknownImage := self >> ImageUnk(self.dims())\n));\n\nClass(ImageVar, SumsBase, BaseContainer, rec(\n new := (self, dims) >> Checked(IsList(dims) and Length(dims) = 2 and ForAll(dims, IsPosInt),\n SPL(WithBases(self, rec(dimensions := dims, _children := [], dims := self >> self.dimensions)))),\n print := (self, i, is) >> Print(\"ImageVar(\", self.dims(), \")\"),\n codeletShape := self >> let(d := self.dims(), Concat(\"ImageVar_\", StringInt(d[1]),\"x\",StringInt(d[2]))),\n fftImage := self >> ApplyFunc(O, TRDFT2D(self.dims()).dims()/self.dims()[2]),\n freqImage := self >> let(lindims := Product(TRDFT2D(self.dims()).dims())/(2Product(self.dims())),\n type := TArray(TComplex, lindims), d := param(type, \"freqImage\"), FDataOfs(d, lindims, 0)),\n timeImage := self >> O(self.dims()[1], self.dims()[2]),\n randomImage := (self, m, n) >> ImageVar(m, n),\n toAMat := self >> NullAMat(self.dimensions),\n unknownImage := self >> ImageUnk(self.dims())\n));\n\n\n#F TRConv2D(img)\n# For an image\n# img := [ [ 1, 2, 3, 4 ],\n# [ 5, 6, 7, 8 ],\n# [ 9, 10, 11, 12 ],\n# [ 13, 14, 15, 16 ] ];\n#\n# MatSPL(TRConv2D(RealImage(img))) =\n#\n#[ [ 1, 4, 3, 2, 13, 16, 15, 14, 9, 12, 11, 10, 5, 8, 7, 6 ],\n# [ 2, 1, 4, 3, 14, 13, 16, 15, 10, 9, 12, 11, 6, 5, 8, 7 ],\n# [ 3, 2, 1, 4, 15, 14, 13, 16, 11, 10, 9, 12, 7, 6, 5, 8 ],\n# [ 4, 3, 2, 1, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5 ],\n# [ 5, 8, 7, 6, 1, 4, 3, 2, 13, 16, 15, 14, 9, 12, 11, 10 ],\n# [ 6, 5, 8, 7, 2, 1, 4, 3, 14, 13, 16, 15, 10, 9, 12, 11 ],\n# [ 7, 6, 5, 8, 3, 2, 1, 4, 15, 14, 13, 16, 11, 10, 9, 12 ],\n# [ 8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 14, 13, 12, 11, 10, 9 ],\n# [ 9, 12, 11, 10, 5, 8, 7, 6, 1, 4, 3, 2, 13, 16, 15, 14 ],\n# [ 10, 9, 12, 11, 6, 5, 8, 7, 2, 1, 4, 3, 14, 13, 16, 15 ],\n# [ 11, 10, 9, 12, 7, 6, 5, 8, 3, 2, 1, 4, 15, 14, 13, 16 ],\n# [ 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 14, 13 ],\n# [ 13, 16, 15, 14, 9, 12, 11, 10, 5, 8, 7, 6, 1, 4, 3, 2 ],\n# [ 14, 13, 16, 15, 10, 9, 12, 11, 6, 5, 8, 7, 2, 1, 4, 3 ],\n# [ 15, 14, 13, 16, 11, 10, 9, 12, 7, 6, 5, 8, 3, 2, 1, 4 ],\n# [ 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 ] ]\n#\nClass(TRConv2D, TaggedNonTerminal, rec(\n abbrevs := [ img -> [img]],\n dims := self >> self.params[1].dims(),\n isReal := True,\n terminate := self >>\n TIRDFT2D(self.params[1].dims()).terminate() \n RCDiag(FList(TReal, 1/Product(self.params[1].dims())Flat(self.params[1].fftImage()))) \n TRDFT2D(self.params[1].dims()).terminate(),\n normalizedArithCost := (self) >>\n TRDFT2D(self.params[1].dims()).normalizedArithCost() +\n TIRDFT2D(self.params[1].dims()).normalizedArithCost() +\n 3 * Rows(TRDFT2D(self.params[1].dims())),\n symTerminate := self >> let(N := self.params[1].dims(),\n imgv := Flat(self.params[1].timeImage()),\n tf := MDDFT(N),\n ti := MDDFT(N, -1),\n d := MatSPL(tf) * imgv,\n t := ti * (1/Product(N))Diag(d) tf,\n MatSPL(t)),\n forwardTransform := self >> let(t := TRDFT2D(self.params[1].dims()), tags := self.getTags(),\n When(\n Length(tags) >= 1 and ObjId(tags[1]) = paradigms.vector.AVecReg, let(n := t.dims()[1], v := tags[1].v,\n TCompose([TPrm(fTensor(fId(n/(2v)), L(2v, 2))), t]).withTags(tags)),\n t.withTags(tags))),\n\n HashId := self >> let(conv := self.params[1].dims(), When(IsBound(self.tags), Concatenation(conv, self.tags), conv)),\n\n hashAs := meth(self)\n local conv;\n conv := Copy(self);\n conv.params[1] := self.params[1].unknownImage();\n return conv;\n end\n));\n\n\n#F 2D RConv Rule\nNewRulesFor(TRConv2D, rec(\n TRConv2D_TRDFT2D_tSPL := rec(\n switch := true,\n applicable := (self, t) >> true,\n children := (self, t) >>\n [[\n TCompose([\n TIRDFT2D(t.params[1].dims()),\n TRCDiag(fPrecompute(t.params[1].freqImage())),\n TRDFT2D(t.params[1].dims())\n ]).withTags(t.getTags())\n ]],\n apply := (self, t, C, Nonterms) >> C[1]\n )\n));\n\n\n#Class(TRCorr2D, TaggedNonTerminal, rec(\n# abbrevs := [ img -> [img]],\n# dims := self >> self.params[1].dims(),\n# isReal := True,\n# terminate := self >> let(tf := TRDFT2D(self.params[1].dims()), d := 1/Product(self.params[1].dims()) * Flat(tf.compute(self.params[1].element)),\n# TIRDFT2D(self.params[1].dims()).terminate() \n# RCDiag(FList(TReal, List([1..Length(d)], j->When(IsOddInt(j), d[j], -d[j])))) \n# tf.terminate(),\n# normalizedArithCost := (self) >>\n# TRDFT2D(self.params[1].dims()).normalizedArithCost() +\n# TIRDFT2D(self.params[1].dims()).normalizedArithCost() +\n# 3 * Rows(TRDFT2D(self.params[1].dims()))),\n# symTerminate := self >> let(N := self.params[1].dims(),\n# img := self.params[1].element,\n# rimg := Reversed(List(img, Reversed)),\n# imgv := Flat(rimg),\n# tf := MDDFT(N),\n# ti := MDDFT(N, -1),\n# d := MatSPL(tf) * imgv,\n# t := ti * (1/Product(N))Diag(d) tf,\n# MatSPL(t))\n#));\n", "meta": {"hexsha": "25841b2d60712763a5ad488f606c793f39f635aa", "size": 6851, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/common/mdconv.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": 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	{"text": "################################################################################\n##\n#W pseudounitary_sort.gi GroupTheoretical Package\n##\n#W Paul Bruillard, Cesar Galindo, Siu-Hung Ng, Julia Plavnik, Eric Rowell, \n#W Zhenghan Wang\n##\n## Installation file for pseudounitary_sort functions of the GroupTheoretical Package\n##\n#Y Copyright (C) 2016, Battelle Memorial Institute\n##\n################################################################################\n\n################################################################################\n##\n#F pseudounitary_sort(<list>,<list>,<list>) . . . . sorts S and T to give pseudo\n##. . . . . . . . . . . . . . . . . . . . . .unitary data. FPdims are computed.\n##\nInstallGlobalFunction(pseudounitary_sort, function(S,T,Simples)\n local FPdim,FPdimC,x,r,i,FPRow,FPRow_idx,j,is_real,is_pos;\n #\n # look along the diagonal for 1's and check that the corresponding row is real\n # and positive\n FPRow:=[];\n r := Size(Simples);\n for i in [1..r] do\n if S[i][i] = 1 then\n is_real := true;\n is_pos := true;\n for j in [1..r] do\n if ImaginaryPart(S[i][j]) <> 0 then\n is_real := false;\n break;\n fi;\n if S[i][j] <= 0 then\n is_pos := false;\n break;\n fi;\n od;\n if is_real and is_pos then\n Add(FPRow,ShallowCopy(S[i]));\n fi;;\n fi;\n od;\n\n # find out which row is largest\n Sort(FPRow);\n FPRow:=Reversed(FPRow);\n FPRow_idx:=Position(S,FPRow[1]);\n\n # switch 1 with FPRow_idx\n if FPRow_idx <> 1 then\n S{[1,FPRow_idx]}:=S{[FPRow_idx,1]};\n S:=TransposedMatMutable(S);\n S{[1,FPRow_idx]}:=S{[FPRow_idx,1]};\n S:=TransposedMatMutable(S);\n Simples{[1,FPRow_idx]}:=Simples{[FPRow_idx,1]};\n T{[1,FPRow_idx]}:=T{[FPRow_idx,1]};\n fi;\n\n # get the FPdimension\n FPdim:=ShallowCopy(S[1]);\n FPdimC:=Sum(List(FPdim,x->x^2));\n\n return [Simples,S,T,FPdim,FPdimC];\nend);\n\n################################################################################\n##\n#F dimension_sort(<list>,<list>,<list>,<list>) . . . . sorts data by increasing\n# dimension.\n##\nInstallGlobalFunction(dimension_sort, function(S,T,Simples,FPdim)\n local made_switch, x, r;\n made_switch := true;\n r:=Size(FPdim);\n while made_switch do\n made_switch := false;\n for x in [3..r] do\n if FPdim[x] < FPdim[x-1] then\n S{[x,x-1]} := S{[x-1,x]};\n S:=TransposedMatMutable(S);\n S{[x,x-1]} := S{[x-1,x]};\n S:=TransposedMatMutable(S);\n T{[x,x-1]} := T{[x-1,x]};\n FPdim{[x,x-1]} := FPdim{[x-1,x]};\n Simples{[x,x-1]} := Simples{[x-1,x]};\n made_switch := true;\n fi;\n od;\n od;\n return [Simples,S,T,FPdim];\nend);\n#E pseudounitary_sort.gi . . . . . . . . . . . . . . . . . . . . . . . ends here\n", "meta": {"hexsha": "7b1b9f55ddebe597bcab93a9e8fcbd83ffc770ef", "size": 2829, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "lib/pseudounitary_sort.gi", "max_stars_repo_name": "pnnl/GroupTheoretical", "max_stars_repo_head_hexsha": "d60aaec27d2ca98ec55b12b78213538a346eef27", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "lib/pseudounitary_sort.gi", "max_issues_repo_name": "pnnl/GroupTheoretical", "max_issues_repo_head_hexsha": "d60aaec27d2ca98ec55b12b78213538a346eef27", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2021-05-20T21:43:28.000Z", "max_issues_repo_issues_event_max_datetime": "2021-05-20T21:43:28.000Z", "max_forks_repo_path": "lib/pseudounitary_sort.gi", "max_forks_repo_name": "pnnl/GroupTheoretical", "max_forks_repo_head_hexsha": "d60aaec27d2ca98ec55b12b78213538a346eef27", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 2, "max_forks_repo_forks_event_min_datetime": "2017-12-07T13:46:25.000Z", "max_forks_repo_forks_event_max_datetime": "2020-12-12T22:39:35.000Z", "avg_line_length": 29.7789473684, "max_line_length": 85, "alphanum_fraction": 0.5008837045, "num_tokens": 860, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.785308580887758, "lm_q2_score": 0.66192288918838, "lm_q1q2_score": 0.5198137247656515}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nClass(PrunedDFT, TaggedNonTerminal, rec(\n abbrevs := [\n (n,blk,pat) -> Checked(IsPosIntSym(n), IsPosIntSym(blk), IsList(pat),\n AnySyms(n,blk) or (IsInt(_unwrap(n)/_unwrap(blk)) and ForAll(pat, i->IsInt(i) and i < n/blk)),\n [_unwrap(n), 1, _unwrap(blk), pat]),\n (n,k,blk,pat) -> Checked(IsPosIntSym(n), IsIntSym(k), IsPosIntSym(blk), IsList(pat),\n AnySyms(n,k) or Gcd(_unwrap(n),_unwrap(k))=1,\n AnySyms(n,blk) or (IsInt(_unwrap(n)/_unwrap(blk)) and ForAll(pat, i->IsInt(i) and i < n/blk)),\n [_unwrap(n), When(AnySyms(n,k), k, k mod _unwrap(n)), _unwrap(blk), pat])\n ],\n\n dims := self >> let(\n size := self.params[1],\n d := [size, self.params[3]Length(self.params[4])],\n When(self.transposed, [d[2], d[1]], d)\n ),\n\n terminate := self >> let(\n size := self.params[1], blk := self.params[3], pat := self.params[4],\n res := DFT(size, self.params[2]).terminate() \n Tensor(Mat(List(pat, i->BasisVec(size/blk, i))).transpose(), I(blk)).terminate(),\n When(self.transposed, res.transpose(), res)\n ),\n\n isReal := self >> false,\n normalizedArithCost := self >> let(n := self.params[1], IntDouble(5 * n * d_log(n) / d_log(2))),\n TType := T_Complex(T_Real(64))\n));\n\n\n\nClass(PrunedIDFT, TaggedNonTerminal, rec(\n abbrevs := [\n (n,blk,pat) -> Checked(IsPosIntSym(n), IsPosIntSym(blk), IsList(pat),\n AnySyms(n,blk) or (IsInt(_unwrap(n)/_unwrap(blk)) and ForAll(pat, i->IsInt(i) and i < n/blk)),\n [_unwrap(n), 1, _unwrap(blk), pat]),\n (n,k,blk,pat) -> Checked(IsPosIntSym(n), IsIntSym(k), IsPosIntSym(blk), IsList(pat),\n AnySyms(n,k) or Gcd(_unwrap(n),_unwrap(k))=1,\n AnySyms(n,blk) or (IsInt(_unwrap(n)/_unwrap(blk)) and ForAll(pat, i->IsInt(i) and i < n/blk)),\n [_unwrap(n), When(AnySyms(n,k), k, k mod _unwrap(n)), _unwrap(blk), pat])\n ],\n\n dims := self >> let(\n size := self.params[1],\n d := [size, self.params[3]Length(self.params[4])],\n When(not self.transposed, [d[2], d[1]], d)\n ),\n\n terminate := self >> let(\n size := self.params[1], blk := self.params[3], pat := self.params[4],\n res := DFT(size, self.params[2]).terminate() \n Tensor(Mat(List(pat, i->BasisVec(size/blk, i))).transpose(), I(blk)).terminate(),\n When(not self.transposed, res.transpose(), res)\n ),\n\n isReal := self >> false,\n normalizedArithCost := self >> let(n := self.params[1], IntDouble(5 * n * d_log(n) / d_log(2))),\n TType := T_Complex(T_Real(64))\n));\n\n\n_pruned_children := function(m, n, scatpat, pdft)\n local pdfts, scatpats, iterparts, uspats, uuspats, uspats, spats;\n spats := Map([0..m-1], i->List(Intersection(scatpat, i+m[0..n-1]), j->j));\n uspats := Map([0..Length(spats)-1], i->(spats[i+1]-i)/m);\n uuspats := Set(uspats);\n\n # partition iterations into unique patterns\n iterparts := List([1..Length(uuspats)], j->Filtered([1..m], i->uspats[i] = uuspats[j])-1);\n Sort(iterparts);\n\n scatpats := List(iterparts, lst->uspats[lst[1]+1]);\n pdfts := Map(scatpats, sp->pdft(n, sp));\n return pdfts;\nend;\n\n_ctpr_applicable := function(m, n, scatpat)\n local spats, gpats, strides;\n spats := Map([0..m-1], i->List(Intersection(scatpat, i+m[0..n-1]), j->j));\n gpats := Map(spats, lst->Map(lst, i->Position(scatpat, i)-1));\n strides := Set(Flat(Map(gpats, lst->Map([1..Length(lst)-1], j->lst[j+1]-lst[j]))));\n return ForAll(spats, i->i<>[]) and (Length(strides) in [0, 1]);\nend;\n\n_build_basef := lst -> When(lst = lst[1] + [0..Length(lst)-1], let(i := Ind(Length(lst)), Lambda(i, lst[1] + i)), FData(Map(lst, V)));\n\n_build_stack := function(m, n, scatpat, pdfts, NI, gsop, istck, stck, cmpse)\n local stack, isu, is, itervars, gatscats, lbds, lbdvars, itercounts, iterbasesf, iterbases, iterparts, uuspats, uspats, bases, strides, stride, spats, gpats;\n spats := Map([0..m-1], i->List(Intersection(scatpat, i+m[0..n-1]), j->j));\n gpats := Map(spats, lst->Map(lst, i->Position(scatpat, i)-1));\n #When(ForAny(spats, i->i=[]), Error(\"need at least one element per child DFT\"));\n strides := Set(Flat(Map(gpats, lst->Map([1..Length(lst)-1], j->lst[j+1]-lst[j]))));\n stride := When(Length(strides) = 1, strides[1], 1);\n bases := Map(gpats, i->i[1]);\n\n uspats := Map([0..Length(spats)-1], i->(spats[i+1]-i)/m);\n uuspats := Set(uspats);\n\n iterparts := List([1..Length(uuspats)], j->Filtered([1..m], i->uspats[i] = uuspats[j])-1);\n Sort(iterparts);\n iterbases := Map(iterparts, lst->Map(lst, i->bases[i+1]));\n iterbasesf := List(iterbases, _build_basef);\n itercounts := List(iterparts, Length);\n itervars := List(iterparts, lst->Ind(Length(lst)));\n lbdvars := List(iterparts, lst->Ind(Length(gpats[lst[1]+1])));\n lbds := List([1..Length(itervars)], i->Lambda(lbdvars[i], stridelbdvars[i]+iterbasesf[i].at(itervars[i])).setRange(NI));\n gatscats := List(lbds, i->ApplyFunc(gsop, [i]));\n\n is := List([1..Length(itervars)], i->ApplyFunc(istck, [itervars[i], cmpse(pdfts[i], gatscats[i])]));\n isu := Map([1..Length(is)], i->When(itervars[i].range=1, is[i].unroll().child(1), is[i]));\n stack := When(Length(isu) = 1, isu[1], ApplyFunc(stck, isu));\n return stack;\nend;\n\n\nNewRulesFor(PrunedDFT, rec(\n PrunedDFT_base := rec(\n forTransposition := false,\n maxSize := 256,\n applicable := (self, nt) >> not nt.hasTags() and nt.params[1] <= self.maxSize and nt.params[3] = 1,\n children := nt -> [[DFT(nt.params[1], nt.params[2])]],\n apply := (nt, C, cnt) -> let(size := nt.params[1], blk := nt.params[3], pat := nt.params[4],\n C[1] * Tensor(Mat(List(pat, i->BasisVec(size/blk, i))).transpose(), I(blk)).terminate())\n ),\n PrunedDFT_DFT := rec(\n forTransposition := true,\n applicable := (self, nt) >> nt.params[1] = nt.params[3] and nt.params[4] = [0],\n children := nt -> [[ DFT(nt.params[1], nt.params[2]).withTags(nt.getTags()) ]],\n apply := (nt, C, cnt) -> C[1]\n ),\n PrunedDFT_CT := rec(\n forTransposition := true,\n applicable := (self, nt) >> nt.params[1] > 2\n and not nt.hasTags()\n and not IsPrime(nt.params[1])\n and nt.params[3] > 1,\n children := nt -> Map2(Filtered(DivisorPairs(nt.params[1]), (l) -> IsInt(nt.params[3]/l[1])),\n (m,n) -> [ DFT(m, nt.params[2] mod m), PrunedDFT(n, nt.params[2] mod n, nt.params[3]/m, nt.params[4]) ]\n ),\n apply := (nt, C, cnt) -> let(mn := nt.params[1], m := Rows(C[1]), n := Rows(C[2]),\n Tensor(C[1], I(n)) \n Diag(fPrecompute(Tw1(mn, n, nt.params[2]))) \n L(mn, m) * Tensor(C[2], I(m))\n )),\n PrunedDFT_CT_rec_block := rec(\n forTransposition := true,\n applicable := (self, nt) >> nt.params[1] > 2\n and not nt.hasTags()\n and not IsPrime(nt.params[1])\n and nt.params[3] = 1\n and Last(nt.params[4])+1-nt.params[4][1] = Length(Set(nt.params[4]))\n and ForAny(Map2(DivisorPairs(nt.params[1]), (m,n)->_ctpr_applicable(m, n, nt.params[4])), i->i),\n children := (nt) -> Filtered(Map2(DivisorPairs(nt.params[1]), (m, n) -> [ DFT(m, nt.params[2] mod m) ]::\n _pruned_children(m, n, nt.params[4], (r, sp) -> PrunedDFT(r, nt.params[2] mod n, nt.params[3], sp))),\n lst -> ForAll(Filtered(lst, i->ObjId(i) = PrunedDFT), j->j.params[4] <> [])),\n apply := (nt, C, cnt) -> let(mn := nt.params[1], m := Rows(C[1]), n := Rows(C[2]),\n Tensor(C[1], I(n)) \n Diag(fPrecompute(Tw1(mn, n, nt.params[2]))) \n _build_stack(m, n, nt.params[4], Drop(C, 1), nt.dims()[2], Gath, IterVStack, VStack, (a,b)->ab)\n )\n )\n));\n\nNewRulesFor(PrunedIDFT, rec(\n PrunedIDFT_base := rec(\n forTransposition := false,\n maxSize :=256,\n applicable := (self, nt) >> not nt.hasTags() and nt.params[1] <= self.maxSize and nt.params[3] = 1,\n children := nt -> [[DFT(nt.params[1], nt.params[2])]],\n apply := (nt, C, cnt) -> let(size := nt.params[1], blk := nt.params[3], pat := nt.params[4],\n Tensor(Mat(List(pat, i->BasisVec(size/blk, i))) C[1], I(blk)).terminate())\n ),\n PrunedIDFT_CT_rec_block := rec(\n forTransposition := true,\n applicable := (self, nt) >> nt.params[1] > 2\n and not nt.hasTags()\n and not IsPrime(nt.params[1])\n and nt.params[3] = 1\n and Last(nt.params[4])+1-nt.params[4][1] = Length(Set(nt.params[4]))\n and ForAny(Map2(DivisorPairs(nt.params[1]), (m,n)->_ctpr_applicable(m, n, nt.params[4])), i->i),\n children := (nt) -> Filtered(Map2(DivisorPairs(nt.params[1]), (n, m) ->\n _pruned_children(m, n, nt.params[4], (r, sp) -> PrunedIDFT(r, nt.params[2] mod n, nt.params[3], sp)) ::\n [ DFT(m, nt.params[2] mod m) ]),\n lst -> ForAll(Filtered(lst, i->ObjId(i) = PrunedIDFT), j->j.params[4] <> [])),\n apply := (nt, C, cnt) -> let(mn := nt.params[1], m := Rows(Last(C)), n := Cols(C[1]),\n _build_stack(m, n, nt.params[4], DropLast(C, 1), nt.dims()[1], Scat, IterHStack1, HStack1, (a,b)->ba) \n Diag(fPrecompute(Tw1(mn, n, nt.params[2]))) \n Tensor(Last(C), I(n))\n )\n )\n));\n\n\n\nClass(IOPrunedDFT, TaggedNonTerminal, rec(\n abbrevs := [\n (n,oblk,opat,iblk,ipat) -> Checked(IsPosIntSym(n), IsPosIntSym(oblk), IsList(opat), IsPosIntSym(iblk), IsList(ipat),\n AnySyms(n,iblk,oblk) or (IsInt(_unwrap(n)/_unwrap(iblk)) and IsInt(_unwrap(n)/_unwrap(oblk)) and\n ForAll(ipat, i->IsInt(i) and i < n/iblk) and ForAll(opat, i->IsInt(i) and i < n/oblk)),\n [_unwrap(n), 1, _unwrap(oblk), opat, _unwrap(iblk), ipat]),\n\n\n (n,k,oblk,opat,iblk,ipat) -> Checked(IsPosIntSym(n), IsIntSym(k), IsPosIntSym(oblk), IsList(opat), IsPosIntSym(iblk), IsList(ipat),\n AnySyms(n,k) or Gcd(_unwrap(n),_unwrap(k))=1,\n AnySyms(n,iblk,oblk) or (IsInt(_unwrap(n)/_unwrap(iblk)) and IsInt(_unwrap(n)/_unwrap(oblk)) and\n ForAll(ipat, i->IsInt(i) and i < n/iblk) and ForAll(opat, i->IsInt(i) and i < n/oblk)),\n [_unwrap(n), When(AnySyms(n,k), k, k mod _unwrap(n)), _unwrap(oblk), opat, _unwrap(iblk), ipat])\n ],\n dims := self >> [self.params[3]Length(self.params[4]), self.params[5]Length(self.params[6])],\n terminate := self >> let(size := self.params[1],\n oblk := self.params[3], opat := self.params[4], iblk := self.params[5], ipat := self.params[6],\n Tensor(Mat(List(opat, i->BasisVec(size/oblk, i))), I(oblk)).terminate() \n DFT(size, self.params[2]).terminate() \n Tensor(Mat(List(ipat, i->BasisVec(size/iblk, i))).transpose(), I(iblk)).terminate()),\n isReal := self >> false,\n normalizedArithCost := self >> let(n := self.params[1], IntDouble(5 n * d_log(n) / d_log(2))),\n TType := T_Complex(T_Real(64))\n));\n\n\nNewRulesFor(IOPrunedDFT, rec(\n IOPrunedDFT_base := rec(\n forTransposition := true,\n maxSize := 16,\n applicable := (self, nt) >> not nt.hasTags() and nt.params[1] <= self.maxSize and nt.params[3] = 1 and nt.params[5] = 1,\n children := nt -> [[DFT(nt.params[1], nt.params[2])]],\n apply := (nt, C, cnt) -> let(size := nt.params[1], oblk := nt.params[3], opat := nt.params[4], iblk := nt.params[5], ipat := nt.params[6],\n Tensor(Mat(List(opat, i->BasisVec(size/oblk, i))), I(oblk)).terminate() \n C[1] \n Tensor(Mat(List(ipat, i->BasisVec(size/iblk, i))).transpose(), I(iblk)).terminate())\n ),\n\n IOPrunedDFT__PrunedDFT := rec(\n forTransposition := true,\n applicable := (self, nt) >> nt.params[1] = nt.params[3] and nt.params[4] = [0],\n children := nt -> [[ PrunedDFT(nt.params[1], nt.params[2], nt.params[5], nt.params[6]).withTags(nt.getTags()) ]],\n apply := (nt, C, cnt) -> C[1]\n ),\n\n IOPrunedDFT__PrunedDFT_T := rec(\n forTransposition := true,\n applicable := (self, nt) >> nt.params[1] = nt.params[5] and nt.params[6] = [0],\n children := nt -> [[ PrunedDFT(nt.params[1], nt.params[2], nt.params[3], nt.params[4]).transpose().withTags(nt.getTags()) ]],\n apply := (nt, C, cnt) -> C[1]\n ),\n\n IOPrunedDFT__Gath_PrunedDFT := rec(\n forTransposition := true,\n maxSize := 16,\n applicable := (self, nt) >> not nt.hasTags() and nt.params[1] <= self.maxSize and\n ((nt.params[3] = 1 and not (nt.params[5] = 1)) or (nt.params[3] * nt.params[5] < nt.params[1])),\n children := nt -> [[ PrunedDFT(nt.params[1], nt.params[2], nt.params[5], nt.params[6]) ]],\n apply := (nt, C, cnt) -> let(size := nt.params[1], oblk := nt.params[3], opat := nt.params[4], iblk := nt.params[5], ipat := nt.params[6],\n Tensor(Mat(List(opat, i->BasisVec(size/oblk, i))), I(oblk)).terminate() * C[1])\n ),\n\n IOPrunedDFT__PrunedDFT_T_Scat := rec(\n forTransposition := true,\n maxSize := 16,\n applicable := (self, nt) >> not nt.hasTags() and nt.params[1] <= self.maxSize and\n (((not nt.params[3] = 1) and nt.params[5] = 1) or(nt.params[3] * nt.params[5] < nt.params[1])),\n children := nt -> [[ PrunedDFT(nt.params[1], nt.params[2], nt.params[3], nt.params[4]).transpose() ]],\n apply := (nt, C, cnt) -> let(size := nt.params[1], oblk := nt.params[3], opat := nt.params[4], iblk := nt.params[5], ipat := nt.params[6],\n C[1] * Tensor(Mat(List(ipat, i->BasisVec(size/iblk, i))).transpose(), I(iblk)).terminate())\n ),\n\n IOPrunedDFT_CT := rec(\n forTransposition := true,\n applicable := (self, nt) >> nt.params[1] > 2 and nt.params[3] * nt.params[5] >= nt.params[1]\n and not nt.hasTags()\n and not IsPrime(nt.params[1])\n and nt.params[3] > 1,\n children := nt -> Map2(Filtered(DivisorPairs(nt.params[1]), (mn) -> IsInt(nt.params[3]/mn[2]) and IsInt(nt.params[5]/mn[1])),\n (m,n) -> [\n PrunedDFT(m, nt.params[2] mod m, nt.params[3]/n, nt.params[4]).transpose(),\n PrunedDFT(n, nt.params[2] mod n, nt.params[5]/m, nt.params[6]) ]\n ),\n apply := (nt, C, cnt) -> let(mn := nt.params[1], m := Cols(C[1]), n := Rows(C[2]),\n Tensor(C[1], I(n)) \n Diag(fPrecompute(Tw1(mn, n, nt.params[2]))) \n L(mn, m) * Tensor(C[2], I(m))\n ))\n));\n", "meta": {"hexsha": "f1aebeee9b72de8fa95eeb44a9afb2777742fef3", "size": 14698, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/dft/prune.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", 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YES\n2. YES", "lm_q1_score": 0.7826624789529375, "lm_q2_score": 0.6619228691808012, "lm_q1q2_score": 0.5180621936686869}}
	{"text": "\nInstallMethod(TotalDegree,\n \"TotalDegree of multivariable polynomial\",\n [IsPolynomial],\n function(poly)\n local result;\n\n result:=ExtRepPolynomialRatFun(poly);\n result:=result{2[1..Length(result)/2]-1};\n result:=Maximum(List(result,j->Sum(j{2[1..Length(j)/2]})));\n return result;\nend);\n\nInstallMethod(ValuePoly,\n \"Value of multivariable polynomial\",\n [IsPolynomial,IsList,IsList],\n function(poly,vars,vals)\n local result,ext_rep,ext_vars,\n monom,pos,i,j;\n\n ext_rep:=ExtRepPolynomialRatFun(poly);\n ext_vars:=List(vars,i->ExtRepPolynomialRatFun(i));\n ext_vars:=List(ext_vars,i->i[1][1]);\n\n result:=Zero(poly);\n for i in 2[1..Length(ext_rep)/2]-1 do\n monom:=One(poly);\n for j in 2[1..Length(ext_rep[i])/2]-1 do\n pos:=Position(ext_vars,ext_rep[i][j]);\n monom:=monomvals[pos]^ext_rep[i][j+1];\n od;\n monom:=monom((ext_rep[i+1]One(poly)));\n result:=result+monom;\n od;\n\n return result;\nend);\n\npRadical:=function(poly,avars)\n local result,\n ext_rep,ext_avars,\n p,deg,deg_max,p_div,monom,i,j;\n\n #exterior reprezentation of polynomial and variables\n ext_rep:=ExtRepPolynomialRatFun(poly);\n ext_avars:=List(avars,i->ExtRepPolynomialRatFun(i));\n ext_avars:=List(ext_avars,i->i[1][1]);\n \n # degree of variables in monomials of poly\n deg:=List(ext_rep{2[1..Length(ext_rep)/2]-1},i->i{2[1..Length(i)/2]});\n\n # Adjustment: (poly)^p ---> poly\n p:=Characteristic(poly);\n if Concatenation(deg)=[] then return poly; fi;\n deg_max:=LogInt(Maximum(Concatenation(deg)),p);\n p_div:=Gcd(p^deg_max,Gcd(Concatenation(deg)));\n if p_div>1 then\n result:=Zero(poly);\n for i in 2[1..Length(ext_rep)/2]-1 do\n monom:=One(poly);\n for j in 2[1..Length(ext_rep[i])/2]-1 do\n monom:=monomavars[Position(ext_avars,ext_rep[i][j])]^(ext_rep[i][j+1]/p_div);\n od;\n result:=result+ext_rep[i+1]monom;\n od;\n return result;\n fi;\n return poly;\nend;\n\nSolve:=function(poly,avars)\n local ext_rep,vars,ext_avars,p,\n deg,tot_deg,poz1,pozm,xpoly,xall,x,\n taboo;\n\n # Adjustment: (poly)^p ---> poly\n poly:=pRadical(poly,avars);\n \n #exterior reprezentation of polynomial and variables\n ext_rep:=ExtRepPolynomialRatFun(poly);\n ext_avars:=List(avars,i->ExtRepPolynomialRatFun(i));\n ext_avars:=List(ext_avars,i->i[1][1]);\n \n # variables of poly\n vars:=Concatenation(ext_rep{2[1..Length(ext_rep)/2]-1});\n vars:=vars{2[1..Length(vars)/2]-1};\n # degree of variables in monomials of poly\n deg:=List(ext_rep{2[1..Length(ext_rep)/2]-1},i->i{2[1..Length(i)/2]});\n tot_deg:=List(deg,i->Sum(i));\n #ignor constants\n tot_deg:=Filtered(tot_deg,i->i<>0);\n\n # Restrict: x should not be deduced from x+x^p+y\n taboo:=[];\n if Length(Set(vars))>1 then\n for x in Set(vars) do\n xall:=ext_rep{2[1..Length(ext_rep)/2]-1};\n xall:=Filtered(xall,i->x in i);\n xpoly:=Filtered(xall,i->Length(i)=2);\n if Length(xpoly)>=2 then\n # if xall=xpoly then\n # return [Position(ext_avars,x),Zero(poly),avars[Position(ext_avars,x)]];\n # fi;\n Add(taboo,Positions(vars,x));\n fi;\n od;\n taboo:=Concatenation(taboo);\n fi;\n\n p:=Characteristic(poly);\n# if Length(vars)=1 then\n# return [Position(ext_avars,vars[1]),RootsOfUPol(poly)[1],true];\n# fi;\n#Error(\"!\");\n if 1 in tot_deg then\n # x^p+P(x)^p\n if Length(Set(vars)) = 1 and Length(Set(tot_deg))>=2 then\n# Print(poly,\"\\n\");\n return [Position(ext_avars,vars[1]),Zero(poly),avars[Position(ext_avars,vars[1])]];\n# return fail;\n fi;\n \n## if Length(Set(vars)) = 1 and not Difference(tot_deg,[1])[1] mod p =0 then\n# if Length(Set(vars)) = 1 and not Set(tot_deg)=[1,p] then\n# Print(poly,\"\\n\");\n# return [Position(ext_avars,vars[1]),Zero(poly),avars[Position(ext_avars,vars[1])]];\n## return fail;\n# fi;\n \n if Length(Set(vars)) = 1 and Maximum(tot_deg)>1 then return fail; fi; # such relations produce infinite loops\n \n # position of variables among monomials of poly\n poz1:=Positions(tot_deg,1);\n poz1:=Difference(poz1,taboo);\n # if all variables are taboo return fail\n if Length(poz1)=0 then return fail; fi;\n # else choose one which is not taboo\n poz1:=poz1[1];\n # position of monomial in ext_rep\n pozm:=Position(ext_rep,[vars[poz1],1]);\n return [Position(ext_avars,vars[poz1]),avars[Position(ext_avars,vars[poz1])]-(ext_rep[pozm+1]^(-1))poly,true];\n fi;\n return fail;\nend;\n\nSolveWithTorsion:=function(poly,avars)\n local ext_rep,vars,ext_avars,\n deg,tot_deg,poz1,pozm,xpoly,x,\n taboo;\n\n # Adjustment: (poly)^p ---> poly\n poly:=pRadical(poly,avars);\n \n #exterior reprezentation of polynomial and variables\n ext_rep:=ExtRepPolynomialRatFun(poly);\n ext_avars:=List(avars,i->ExtRepPolynomialRatFun(i));\n ext_avars:=List(ext_avars,i->i[1][1]);\n \n # variables of poly\n vars:=Concatenation(ext_rep{2[1..Length(ext_rep)/2]-1});\n vars:=vars{2[1..Length(vars)/2]-1};\n # degree of variables in monomials of poly\n deg:=List(ext_rep{2[1..Length(ext_rep)/2]-1},i->i{2[1..Length(i)/2]});\n tot_deg:=List(deg,i->Sum(i));\n #ignor constants\n tot_deg:=Filtered(tot_deg,i->i<>0);\n\n # Restrict: x should not be deduced from x+x^p+y\n taboo:=[];\n if Length(Set(vars))>1 then\n for x in Set(vars) do\n xpoly:=ext_rep{2[1..Length(ext_rep)/2]-1};\n xpoly:=Filtered(xpoly,i->x in i);\n xpoly:=Filtered(xpoly,i->Length(i)=2);\n if Length(xpoly)>=2 then\n Add(taboo,Positions(vars,x));\n fi;\n od;\n taboo:=Concatenation(taboo);\n fi;\n \n# if Length(vars)=1 then\n# return [Position(ext_avars,vars[1]),RootsOfUPol(poly)[1],true];\n# fi;\n#Error(\"!\");\n if 1 in tot_deg then\n # x^p+P(x)^p\n if Length(Set(vars)) = 1 and Length(Set(tot_deg))>=2 then\n return [Position(ext_avars,vars[1]),Zero(poly),avars[Position(ext_avars,vars[1])]];\n fi;\n \n if Length(Set(vars)) = 1 and Maximum(tot_deg)>1 then return fail; fi; # such relations produce infinite loops\n \n # position of variables among monomials of poly\n poz1:=Positions(tot_deg,1);\n poz1:=Difference(poz1,taboo);\n # if all variables are taboo return fail\n if Length(poz1)=0 then return fail; fi;\n # else choose one which is not taboo\n poz1:=poz1[1];\n # position of monomial in ext_rep\n pozm:=Position(ext_rep,[vars[poz1],1]);\n return [Position(ext_avars,vars[poz1]),avars[Position(ext_avars,vars[poz1])]-(ext_rep[pozm+1]^(-1))poly,true];\n fi;\n return fail;\nend;\n\nReduceRelations:=function(relations,avars,values,APR)\n local result,#relations,\n relations_len,schimbare,Ring,torsion,GB,\n index,sol,i,modulo;\n\n result:=ShallowCopy(values);\n relations:=List(relations,i->Value(i,avars,result)One(APR));\n relations:=Filtered(relations,i->i <> Zero(APR));\n relations:=Set(relations);\n# relations:=List(coefficients(u),i->i[2]);\n relations_len:=Length(relations);\n\n# i:=1;\n# while i<relations_len do\n# modulo:=Concatenation([1..i-1],[i+1..relations_len]);\n# modulo:=relations{modulo};\n# relations:=List(relations,i->PolynomialReducedRemainder(i,relations,MonomialLexOrdering()));\n# relations:=Set(Filtered(relations,i->i <> Zero(APR)));\n# if Length(relations)<relations_len then i:=1; fi;\n# relations_len:=Length(relations);\n# od;\n# Error(\"!\");\n#Print(\"...relations: \",relations,\"\\n\");\n schimbare:=true;\n while relations<>[] and schimbare do\n #Print(\"@@@\",relations_len,\" \");\n# Print(\"..relations: \",relations,\"\\n\");\n# Print(\"--->result: \",result,\"\\n\");\n #GB:=GroebnerBasis(relations,MonomialLexOrdering()); ## ATENTIE AICI\n result:=List(result,i->PolynomialReducedRemainder(i,relations,MonomialLexOrdering()));\n #result:=List(result,i->PolynomialReducedRemainder(i,GB,MonomialLexOrdering()));\n# Print(\"fresh result:\",result,\"\\n\");\n schimbare:=false;\n #Error(\"!!\");\n #refresh relations\n #relations:=List(relations,i->Value(i,avars,result)One(APR));\n relations:=List(relations,i->ValuePoly(i,avars,result)One(APR));\n# Print(\"fresh rels:\",relations,\"\\n\");\n relations:=Filtered(relations,i->i <> Zero(APR));\n schimbare:=Length(relations)<relations_len;\n relations_len:=Length(relations);\n od;\n#Error(\"!\");\n#Print(\".relations: \",relations,\"\\n\");\n relations:=Filtered(relations,i->i <> Zero(APR));\n \n return [result,relations];\nend;\n\nSolveRelations:=function(relations,avars,values,APR)\n local result,#relations,\n relations_len,schimbare,Ring,torsion,\n index,sol,i;\n\n result:=ShallowCopy(values);\n relations:=List(relations,i->Value(i,avars,result)One(APR));\n relations:=Filtered(relations,i->i <> Zero(APR));\n \n relations:=ReduceRelations(relations,avars,result,APR);\n# #Error(\"!\");\n result:=relations[1];\n relations:=relations[2];\n# #relations:=List(coefficients(u),i->i[2]);\n relations_len:=Length(relations);\n# Print(\"...relations: \",relations,\"\\n\");\n \n Ring:=CoefficientsRing(APR);\n schimbare:=true;\n torsion:=[];\n \n #Error(\"!\");\n while relations<>[] and schimbare do\n ##Print(\"len:=\",Length(relations),\"\\n\");\n schimbare:=false;\n index:=1;\n while index<=relations_len do\n #Print(\"len===\",Length(relations),\"\\n\",\"index===\",index,\"\\n\");\n sol:=Solve(relations[index],avars);\n #Print(\"solved \",relations[index],\"\\n\");\n #Error(\"!\");\n #sol:=fail;\n if sol<>fail then\n #change result\n result[sol[1]]:=sol[2];\n for i in [1..Length(result)] do\n if not result[i] in Ring and result[i]<>avars[i] then\n result[i]:=Value(result[i],avars,result)One(APR);\n fi;\n od;\n #refresh relations\n relations:=List(relations,i->Value(i,avars,result)*One(APR));\n relations:=Filtered(relations,i->i <> Zero(APR));\n #relations:=ReduceRelations(relations,avars,result,APR);\n #result:=relations[1];\n #relations:=relations[2];\n schimbare:=Length(relations)<relations_len or sol[2]=Zero(APR);\n relations_len:=Length(relations);\n\n if Length(sol)=3 and sol[3] in avars then Add(torsion,sol[3]); fi;\n fi;\n index:=index+1;\n od;\n od;\n\n return [result,relations,torsion];\nend;\n", "meta": {"hexsha": "c1603507f48fe21a27cdc1119ca2e94b517ed09b", "size": 11077, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "lib/poly.gi", "max_stars_repo_name": "iuliansimion/Chevalley.gap", "max_stars_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "lib/poly.gi", "max_issues_repo_name": "iuliansimion/Chevalley.gap", "max_issues_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "lib/poly.gi", "max_forks_repo_name": "iuliansimion/Chevalley.gap", "max_forks_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 35.2770700637, "max_line_length": 119, "alphanum_fraction": 0.592488941, "num_tokens": 3164, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7634837635542924, "lm_q2_score": 0.6757646140788307, "lm_q1q2_score": 0.5159353108337196}}
	{"text": "RequirePackage(\"grape\");\n\nGC := function(x,y,i,j) return x[i]y[j] - x[j]y[i]; end;\n\nG2 := function(q)\n local P, Q;\n if q mod 2 = 0 then\n Q := [[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1],[0,0,0,1,0,0,0],[0,0,0,0,0,0,0],[0,0,0,0,0,0,0],[0,0,0,0,0,0,0]]Z(q)^0;;\n else\n Q := [[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1],[0,0,0,1,0,0,0],[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0]]Z(q)^0;;\n fi;\n P := Filtered(List(Subspaces(GF(q)^7, 1), y -> Elements(y)[2]), x -> xQx = 0Z(q));;\n\n return Graph(Group(()), P, function(x,y) return x; end,\n function(x,y)\n return x <> y and xQy = 0Z(q) and yQx = 0*Z(q) and \n [ GC(x,y,2,3), GC(x,y,6,5), GC(x,y,3,1), GC(x,y,7,6), GC(x,y,1,2), GC(x,y,5,7) ] =\n [ GC(x,y,4,5), GC(x,y,4,3), GC(x,y,4,6), GC(x,y,4,1), GC(x,y,4,7), GC(x,y,4,2) ];\n end, true);;\nend;\n\n", "meta": {"hexsha": "f3ae8ce35da43d4a996cba2fcaffca2c2b3a4a53", "size": 892, "ext": "gap", "lang": "GAP", "max_stars_repo_path": "lib/g2.gap", "max_stars_repo_name": "jaanos/gap-graphs", "max_stars_repo_head_hexsha": "18dd56c9b90a12a717a0cc893fdd72c6343ee79b", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2015-10-27T15:54:29.000Z", "max_stars_repo_stars_event_max_datetime": "2016-11-07T14:09:44.000Z", "max_issues_repo_path": "lib/g2.gap", "max_issues_repo_name": "jaanos/gap-graphs", "max_issues_repo_head_hexsha": "18dd56c9b90a12a717a0cc893fdd72c6343ee79b", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2015-04-20T23:13:11.000Z", "max_issues_repo_issues_event_max_datetime": "2015-04-20T23:13:11.000Z", "max_forks_repo_path": "lib/g2.gap", "max_forks_repo_name": "jaanos/gap-graphs", "max_forks_repo_head_hexsha": "18dd56c9b90a12a717a0cc893fdd72c6343ee79b", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 40.5454545455, "max_line_length": 135, "alphanum_fraction": 0.4428251121, "num_tokens": 476, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8791467738423873, "lm_q2_score": 0.5851011542032312, "lm_q1q2_score": 0.5143897920892279}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nZeroCoef := function(p)\nlocal i, L;\nL:=p.coefficients;\nfor i in [1..Length(p.coefficients)] do\n if AbsFloat(ReComplex(ComplexAny(p.coefficients[i]))) < FloatString(\"1e-4\") then\n L[i] := p.baseRing.zero;\n fi;\nod;\nreturn Polynomial(p.baseRing, L, p.valuation);\nend;\n\n\n# Recursive implementation of the long division for Laurent polynomials h(z) and g(z)\n# There are deg(h)-deg(g)+2 different schemes for division \nLaurentRemainder := function ( arg )\n\nlocal a, b, q, q1, r1, q2, r2, Ls, Lt, z, \n deghigha, deglowa, deghighb, deglowb, dega, degb, coefa, coefb, divs;\n\nif IsList(arg[1]) then arg:=arg[1];fi;\na:=arg[1];\nb:=arg[2];\n\n#Print(\"check\");\nif not (IsPolynomial(a) and IsPolynomial(a)) then\n Error(\"<a> and <b> must be polynomials\");\nelif not a.baseRing.name = b.baseRing.name then\n Error(\"Both polynomials have to be over the same field\");\nelif not IsBound(PolynomialRing(a.baseRing).isEuclideanRing) then\n Error(\"Polymonials must be constructed over a field, not over a ring\");\nfi;\n\nz:=Indeterminate(a.baseRing);\nz.name:=\"z\";\nif Length(arg)=3 then q:=arg[3]; else q:=0z^0; fi;\n\ndeglowa := a.valuation;\ndeglowb := b.valuation;\ndega := Length(a.coefficients)-1;\ndegb := Length(b.coefficients)-1;\ndeghigha := deglowa + dega;\ndeghighb := deglowb + degb;\n\n\ncoefa := a.coefficients;\ncoefb := b.coefficients; \n\nif dega<degb then return [[q,a]];fi;\n\n q1 := Polynomial(a.baseRing,[coefa[dega+1]/coefb[degb+1]],deghigha-deghighb);\n r1 := a - q1 b;\n q1 := q1 + q;\n# Print(q1);\n# Print(\"\\n\");\n# Print(r1);\n#Print(\"\\n\");\n\n# q2 := coefa[1]/coefb[1] * z^(deglowa-deglowb);\n q2 := Polynomial(a.baseRing,[coefa[1]/coefb[1]],deglowa-deglowb);\n r2 := a - q2 * b;\n q2 := q2 + q;\n Ls := [];\n for divs in [[r1,b,q1],[r2,b,q2]] do\n Lt := LaurentRemainder(divs);\n Add(Ls,Lt);\n od;\n Ls := Flat(Ls);\n Ls := List([1..Length(Ls)/2], i->[Ls[2i-1],Ls[2i]]); \n Ls := List(Collected(Ls), col->col[1]);\n if not IsList(Ls[1]) then return [Ls];\n else return Ls;\n fi; \n \n\nend;\n\n#\n# Note:\n# ! Because we now use double floats, the LiftingScheme generates more LS than\n# possible because of finite precision. There will be a bunch of the same lifting\n# schemes generated multiple times with coefficients different after 10th\n# decimal or so. This requies fixing !\n#\n\n#F LiftingScheme( <poly1>, <poly2> )\n#F returns a list of Laurent polynomials that represent \n#F primal and dual lifting steps factorization of the polyphase \n#F matrix of polynomials <poly1> and <poly2>:\n#F P(z)= [[ <poly1_even>, <poly1_odd>],\n#F [ <poly2_even>, <poly2_odd>]]\n#F In Discrete Wavelet Transform notation, <poly1> represents\n#F a low-pass filter impulse response, whereas <poly2> represents\n#F a high-pass one. \n#F \n#F The output is in the following format:\n#F [ b, l1(z), l2(z), .... , ln(z), c1, c2]\n#F \n#F b - a binary symbol that determines the type of the \n#F initial lifting step (0 - primal, 1 - dual)\n#F li(z) - polynomial representing i-th lifting step\n#F c1, c2 - scaling constants\n#F\n#F Example:\n#F \n#F P(z)= [ c1, 0 ] * [ 1, l2(z)] * [ 1 , 0 ] \n#F [ 0, c2 ] [ 0, 1 ] [ l1(z), 1 ]\n#F ---------- ----------- ------------ \n#F scaling primal l.s. dual l.s. (b=1)\n#F\n#F Note: Factorization is implemented in Laurent Polynomial\n#F ring over the base field inherited from <poly1>, <poly2>.\n#F\n\nLiftingScheme := function ( M )\n\nlocal he, ho, ge, go, hen, hon, gen, gon, b, QR, z, Le, Lo, L, Lc, Ls, ve, vo, P, factor, scheme;\n\n\n#Print(\"Recursion \\n\");\n# Check if h(z) and g(z) in fact represent a perfect reconstruction \n# filter bank -> determinant of the polyphase matrix should be\n# a monomial \nhe := M[1][1];ho := M[1][2]; ge := M[2][1]; go := M[2][2];\n if not Length(ZeroCoef(Determinant([[he, ho],[ge, go]])).coefficients) = 1 then\n Error(\"h(z) and g(z) must satisfy the perfect reconstruction condition P(z)P'(z)^(-1) = I where P and P' are analysis and synthesis polyphase matrices\");\n fi;\n\n z:=Indeterminate(he.baseRing);\n z.name:=\"z\";\n# Factoring Algorithm\n b:=0;\n\n if LaurentDegree(he) >= LaurentDegree(ho) then b:=1; fi;\n\n if (ho=0z^0 or ge=0z^0) then\n L:=[];\n if ho=0z^0 then Add(L,ZeroCoef(ge)\n Polynomial(he.baseRing,[1/ ZeroCoef(go).coefficients[1]], -go.valuation));\n else Add(L,ho/he); fi;\n Add(L, he);\n Add(L, go);\n Add(L, b);\n return [Reversed(L)];\n fi;\n if (he=0z^0 or go=0z^0) then\n L:=[];\n if he=0z^0 then Add(L,ZeroCoef(go)\n Polynomial(he.baseRing,[1/ ZeroCoef(ge).coefficients[1]], -ge.valuation));\n else Add(L,he/ho); fi;\n Add(L, ho);\n Add(L, ge);\n Add(L, b-2);\n return [Reversed(L)];\n fi;\n L:=[]; \n if b=0 then\n QR:=LaurentRemainder(ho,he);\n for factor in QR do\n hon := factor[2];\n hon := ZeroCoef(hon);\n gon := go - ge factor[1];\n gon := ZeroCoef(gon);\n\n Lc:=LiftingScheme([[he,hon],[ge,gon]]);\n for scheme in Lc do Add(scheme,factor[1]); od;\n Append(L,Lc);\n od;\n\n\n else \n QR:=LaurentRemainder(he,ho);\n for factor in QR do\n hen := factor[2];\n hen := ZeroCoef(hen);\n gen := ge - go * factor[1];\n gen := ZeroCoef(gen);\n Lc:=LiftingScheme([[hen,ho],[gen,go]]);\n for scheme in Lc do Add(scheme,factor[1]); od;\n Append(L,Lc);\n od;\n\n fi;\n\nreturn(L);\n\nend;\n\n\nLifting := function(M)\nlocal Lt, Ls, L, factor, p, normM, normDiff;\n\nL:=LiftingScheme(M,[]);\nLt:=[];\nLs:=[];\n\nfor factor in L do \n Add(Ls, factor);\n if IsInt(factor) then Add(Lt, Ls); Ls:=[];fi;\nod;\nreturn Lt;\nend;\n\n\nVerifyLiftingScheme:=function(P,L2)\n\nlocal P, M, b, i, l,z,p, normM, normDiff;\n\n z:=Indeterminate(P[1].baseRing);\n z.name:=\"z\";\n\n#P:=[[P[1],P[2]],[P[3],P[4]]];\nM:= [[1, 0],[0,1]];\n\nL2:=Reversed(L2);\nl:=Length(L2);\nb:=L2[l];\nfor i in [1 .. l-3] do\n if b=-2 then \n M:= M * [[0z^0,1z^0 ], [1z^0, L2[l-i-2]]]; b:=1;\n elif b=-1 then \n M:= M [[L2[l-i-2],1z^0 ], [1z^0, 0z^0]]; b:=0;\n elif b=0 then\n M:= M [[1z^0, L2[l-i-2]], [0z^0, 1z^0]]; b:=1;\n else \n M:= M [[1z^0, 0z^0], [L2[l-i-2], 1z^0]]; b:=0;\n fi;\nod;\nM:=[[L2[l-2], 0z^0],[0z^0, L2[l-1]]]M;\n#Print([[P[1],P[2]],[P[3],P[4]]]);\nif Same(P[1][1].baseRing, Doubles) then \n normM:=Sum(M, l->Sum(l, p->(Sum(p.coefficients,i->i^2))^1/2))^1/2;\n normDiff:=Sum(M-P, l->Sum(l, p->(Sum(p.coefficients,i->i^2))^1/2))^1/2;\n Print(\"error: \",normDiff/normM,\"\\n\");\n if (normDiff/normM > FloatString(\"1e-4\")) then return false;\n else return true;\n fi;\nelse return[M,P,M=P];\nfi;\nend;\n\nArithmeticCostLS := function(L)\nlocal step, mult, add, i;\n\nmult:=0;\nadd:=0;\nL:=Reversed(L);\nfor step in [1..Length(L)-3] do\n for i in L[step].coefficients do\n if not i = 0 then mult:=mult+1; add:=add+1;fi;\n od;\nod;\nmult:=mult+2;\nreturn [add,mult,Length(L)-3];\nend;\n\n\n#F MatPoly := function(h,g)\n#F returns a matrix formed of two filters h(z) and g(z)\n#F also returns largest and the smallest degree of the \n#F coefficients in the matrix. \n#F Format: [<mat>, q, p]\n\nMatPoly := function(h,g)\n\nlocal hc, gc, hsmall, hlarge,\n gsmall, glarge, q, p, M;\n\n # Check the degrees of the filters \n hc := h.coefficients;\n gc := g.coefficients; \n hsmall := h.valuation;\n hlarge := Length(hc) + hsmall - 1;\n gsmall := g.valuation;\n glarge := Length(gc) + gsmall - 1;\n q := Minimum([hsmall,gsmall]);\n p := Maximum([hlarge,glarge]);\n \n# Construct the 2 x l matrix of filter coefficients\n\n M := \n [\n Concat(List([1..AbsInt(q-hsmall)],i->h.baseRing.zero),\n hc, List([1..p-hlarge],i->h.baseRing.zero)\n ),\n Concat(List([1..AbsInt(q-gsmall)],i->h.baseRing.zero),\n gc, List([1..p-glarge],i->h.baseRing.zero)\n )\n ];\n\n return ([M, hsmall, hlarge, gsmall, glarge]);\nend;\n\n\nPolyphase := function(p1,p2)\n\nlocal he, ho, ge, go, z, h, g;\n\nif not (IsPolynomial(p1) and IsPolynomial(p1)) then\n Error(\"<p1> and <p2> must be polynomials\");\nelif not p1.baseRing.name = p2.baseRing.name then\n Error(\"Both polynomials have to be over the same field\");\nelif not IsBound(PolynomialRing(p1.baseRing).isEuclideanRing) then\n Error(\"Polymonials must be constructed over a field, not over a ring\");\nfi;\n\n z:=Indeterminate(p1.baseRing);\n z.name:=\"z\";\n\n h := DownsampleTwo(ListPoly(p1));\n g := DownsampleTwo(ListPoly(p2));\n he := Polynomial(p1.baseRing, h[1][1], h[1][2]); \n ho := Polynomial(p1.baseRing, h[2][1], h[2][2]); \n ge := Polynomial(p1.baseRing, g[1][1], g[1][2]); \n go := Polynomial(p1.baseRing, g[2][1], g[2][2]); \n\n# Find he(z) and ho(z)\n# Lo:=Sublist(p1.coefficients, Filtered([1..Length(p1.coefficients)],IsEvenInt));\n# Le:=Sublist(p1.coefficients, Filtered([1..Length(p1.coefficients)],IsOddInt));\n# if (p1.valuation mod 2 = 1) then L:=Le; Le:=Lo; Lo:=L; \n# ve := Int((p1.valuation + 1)/2); vo := ve;\n# else ve := Int(p1.valuation/2); vo := ve + 1;\n# fi;\n# he:=Polynomial(p1.baseRing, Le, ve);\n# ho:=Polynomial(p1.baseRing, Lo, vo); \n# \n# Find ge(z) and go(z)\n\n# Lo:=Sublist(p2.coefficients, Filtered([1..Length(p2.coefficients)],IsEvenInt));\n# Le:=Sublist(p2.coefficients, Filtered([1..Length(p2.coefficients)],IsOddInt));\n# if (p2.valuation mod 2 = 1) then L:=Le; Le:=Lo; Lo:=L; \n# ve := Int((p2.valuation + 1)/2); vo := ve;\n# else ve := Int(p2.valuation/2); vo := ve+1;\n# fi;\n# ge:=Polynomial(p2.baseRing, Le, ve);\n# go:=Polynomial(p2.baseRing, Lo, vo); \n \nreturn [[he,ho],[ge,go]];\nend;\n\n\n# PolyPolyphaseMat:=function(M)\n# Returns a list of 2 polynomials from a polyphase matrix \n\nPolyPolyphaseMat:=function(M)\n\nlocal he,ho,ge,go,h,g,z;\n\nhe:=M[1][1];\nho:=M[1][2];\nge:=M[2][1];\ngo:=M[2][2];\nz:=Indeterminate(he.baseRing);\nz.name:=\"z\";\n\nh:=Upsample(he)+z^(1)Upsample(ho);\ng:=Upsample(ge)+z^(1)Upsample(go);\n\nreturn([h,g]);\nend;\n\n\n", "meta": {"hexsha": "d4967b1029a902ab2541f146c6068cab3de8c23a", "size": 9996, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/filtering/lifting.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/transforms/filtering/lifting.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/transforms/filtering/lifting.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 27.2370572207, "max_line_length": 159, "alphanum_fraction": 0.5948379352, "num_tokens": 3532, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. 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	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n#####################\n# General Rule\n#####################\n\nPRF34_CT_Children := (N,k,DFTp,PRF3,PRFt) -> Map2(DivisorPairs(N),\n (m,n) -> When(IsEvenInt(n),\n\t[ DFTp(m, k), PRF3(n, k) ],\n\t[ DFTp(m, k), PRF3(n, k), PRFt(m, k) ])\n);\n\nPRF34_CT_Rule := (N,k,C,Conj,Tw) -> let(\n m:=Rows(C[1]), n:=Cols(C[2]), Nc:=Int((N+1)/2), \n nf:=Int(n/2), nc:=Int((n+1)/2), mf:=Int(m/2), mc:=Int((m+1)/2), j:=Ind(nf),\n \n SUM(\n\tISum(j, RC(Scat(BH(Nc, N-1, m, j, n))) \n\t Conj RC(C[1]) * Tw(j) * \n\t\tRC(Gath(H(ncm, m, j, nc)))\n\t), \n\tWhen(IsEvenInt(n), [], \n\t RC(Scat(H(Nc, mc, nf, n))) C[3] * Gath(H(2ncm, m, 2nf, 2nc)))\n ) \n Tensor(I(m), C[2]) \n L(N,m)\n);\n\nIPRF34_CT_Rule := (N,k,C,Conj,Tw) -> let(\n m:=Rows(C[1]), n:=Rows(C[2]), Nc:=Int((N+1)/2), \n nf:=Int(n/2), nc:=Int((n+1)/2), mf:=Int(m/2), mc:=Int((m+1)/2), j:=Ind(nf),\n \n L(N,n) \n Tensor(I(m), C[2]) \n SUM(\n\tISum(j, \n\t RC(Scat(H(ncm, m, j, nc))) \n\t Tw(j) * \n\t RC(C[1]) * \n\t Conj * \n\t RC(Gath(BH(Nc, N-1, m, j, n)))\n\t), \n\tWhen(IsEvenInt(n), [], \n\t Scat(H(2ncm, m, 2nf, 2nc)) * C[3] * RC(Gath(H(Nc, mc, nf, n))))\n )\n);\n\n#####################\n# Special Cases\n#####################\n\nRulesFor(PRDFT4, rec(\n PRDFT4_Base1 := BaseRule(PRDFT4, [1, @]),\n PRDFT4_Base2 := rec( \n\tisApplicable := P -> P[1]=2,\n\trule := (P, C) -> F(2) * Mat(1/2MatSPL(PDHT4(2,P[2]))) # DHT4(2) is a diagonal\n ),\n PRDFT4_CT := rec(\n\tisApplicable := P -> not IsPrime(P[1]),\n\tallChildren := P -> PRF34_CT_Children(P[1], P[2], DFT2, PRDFT3, PRDFT4), \n\trule := (P,C) -> let(N:=P[1], k:=P[2], m:=Rows(C[1]),\n\t PRF34_CT_Rule(N, k, C, Diag(BHD(m,-1,1)), j->RC(Diag(fPrecompute(Twid(N,m,k,1/2,1/2,j))))))),\n PRDFT4_Trig := rec(\n\tisApplicable := P -> P[1] > 2 and IsEvenInt(P[1]) and P[2]=1,\n\tallChildren := P -> [[ DCT4(P[1]/2), DST4(P[1]/2) ]],\n\trule := (P, C) -> let(n:=P[1]/2, \n\t L(2n, n) * DirectSum(C[1], C[2]) * SymSplit4(n)))\n));\n\nRulesFor(IPRDFT4, rec(\n IPRDFT4_Base1 := BaseRule(IPRDFT4, [1, @]),\n IPRDFT4_Base2 := rec( \n\tisApplicable := P -> P[1]=2,\n\trule := (P, C) -> Mat(1/2MatSPL(PDHT4(2,P[2]))) F(2) # DHT4(2) is a diagonal\n ),\n IPRDFT4_CT := rec(\n\tisApplicable := P -> not IsPrime(P[1]),\n\tallChildren := P -> PRF34_CT_Children(P[1], P[2], DFT3, IPRDFT2, IPRDFT4), \n\trule := (P,C) -> let(N:=P[1], k:=P[2], m:=Rows(C[1]),\n\t IPRF34_CT_Rule(N, k, C, Diag(BHD(m,-1,1)), j->RC(Diag(fPrecompute(Twid(N,m,k,1/2,1/2,j)))))))\n));\n\nRulesFor(PRDFT3, rec(\n PRDFT3_Base1 := BaseRule(PRDFT3, [1, @]),\n PRDFT3_Base2 := rec(\n\tisApplicable := P -> P[1]=2,\n\trule := (P, C) -> Cond(\n\t P[2] mod 4 = 1, I(2), \n\t P[2] mod 4 = 3, Diag(1,-1), \n\t Error(\"Bad second parameter for PRDFT3(n,k), gcd(n,k)=1 does not hold\"))\n ),\n PRDFT3_CT := rec(\n\tisApplicable := P -> not IsPrime(P[1]),\n\tallChildren := P -> PRF34_CT_Children(P[1], P[2], DFT1, PRDFT3, PRDFT3), \n\trule := (P,C) -> let(N:=P[1], k:=P[2], m:=Rows(C[1]),\n\t PRF34_CT_Rule(N, k, C, Diag(BHD(m,1,-1)), j->RC(Diag(fPrecompute(Twid(N,m,k,1/2,0,j))))))),\n PRDFT3_Trig := rec(\n\tisApplicable := P -> P[1] > 2 and IsEvenInt(P[1]) and P[2]=1,\n\tallChildren := P -> [[ DCT3(P[1]/2), DST3(P[1]/2) ]],\n\trule := (P, C) -> let(n:=P[1]/2, \n\t L(2n, n) DirectSum(C[1], C[2]) * SymSplit3(n))),\n\n PRDFT3_OddToPRDFT1 := rec(\n\tisApplicable := P -> IsOddInt(P[1]),\n\tallChildren := P -> [[ PRDFT(P[1], P[2]) ]],\n\trule := (P, C) -> rperm_ev(P[1]) * C[1] * pdiag(P[1], P[2])\n )\n));\n\nRulesFor(IPRDFT2, rec(\n IPRDFT2_Base1 := BaseRule(IPRDFT2, [1, @]),\n IPRDFT2_Base2 := rec(\n\tisApplicable := P -> P[1]=2,\n\trule := (P, C) -> Cond(\n\t P[2] mod 4 = 1, Diag(2,-2),\n\t P[2] mod 4 = 3, Diag(2,2),\n\t Error(\"Bad second parameter for IPRDFT2(n,k), gcd(n,k)=1 does not hold\"))\n ),\n IPRDFT2_CT := rec(\n\tisApplicable := P -> not IsPrime(P[1]),\n\tallChildren := P -> PRF34_CT_Children(P[1], P[2], DFT1, IPRDFT2, IPRDFT2), \n\trule := (P,C) -> let(N:=P[1], k:=P[2], m:=Rows(C[1]),\n\t IPRF34_CT_Rule(N, k, C, Diag(BHD(m,1,-1)), j->RC(Diag(fPrecompute(Twid(N,m,k,1/2,0,j)))))))\n));\n\nRulesFor(PDHT4, rec(\n PDHT4_Base2 := BaseRule(PDHT4, [2, @]),\n PDHT4_CT := rec(\n\tisApplicable := P -> not IsPrime(P[1]),\n\tallChildren := P -> PRF34_CT_Children(P[1], P[2], DFT2, PDHT3, PDHT4), \n\trule := (P,C) -> let(N:=P[1], k:=P[2], m:=Rows(C[1]),\n\t PRF34_CT_Rule(N, k, C, TopHalf(m, -J(2)), \n\t\t j -> RCDiag(RCData(fPrecompute(Twid(N,m,-k,1/2,1/2,j))), -J(2))))),\n PDHT4_Trig := rec(\n\tisApplicable := P -> P[1] > 2 and IsEvenInt(P[1]) and P[2]=1,\n\tallChildren := P -> [[ DCT4(P[1]/2), DST4(P[1]/2) ]],\n\trule := (P, C) -> let(n:=P[1]/2, \n\t Tensor(I(n), F(2)) * L(2n,n) DirectSum(C[1], C[2]) * SymSplit4(n)))\n));\n\nRulesFor(PDHT3, rec(\n PDHT3_Base2 := rec(\n\tisApplicable := P -> P[1]=2,\n\trule := (P, C) -> Cond(\n\t P[2] mod 4 = 1, F(2), \n\t P[2] mod 4 = 3, J(2)F(2),\n\t Error(\"Bad second parameter for PRDFT3(n,k), gcd(n,k)=1 does not hold\"))\n ),\n\n PDHT3_CT := rec(\n\tisApplicable := P -> not IsPrime(P[1]),\n\tallChildren := P -> PRF34_CT_Children(P[1], P[2], DFT1, PDHT3, PDHT3), \n\trule := (P,C) -> let(N:=P[1], k:=P[2], m:=Rows(C[1]),\n\t PRF34_CT_Rule(N, k, C, TopHalf(m, J(2)), \n\t\t j -> RCDiag(RCData(fPrecompute(Twid(N,m,-k,1/2,0,j))), J(2))))),\n PDHT3_Trig := rec(\n\tisApplicable := P -> P[1] > 2 and IsEvenInt(P[1]) and P[2]=1,\n\tallChildren := P -> [[ DCT3(P[1]/2), DST3(P[1]/2) ]],\n\trule := (P, C) -> let(n:=P[1]/2, \n\t Tensor(I(n), F(2)) L(2n,n) DirectSum(C[1], C[2]) * SymSplit3(n)))\n\n));\n", "meta": {"hexsha": "169e1d54c628f7887740d51f9158deed08e58bb1", "size": 5622, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/realdft/prf34.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], 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	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nRulesFor(DCT4, rec(\n\n #F DCT4_Base2: DCT4_2 = (1,2) * R_13/8\n #F\n DCT4_Base2 := rec(\n\tinfo := \"DCT4_2 -> R_13/8\",\n\tforTransposition := false,\n\tisApplicable := P -> P[1] = 2, \n\trule := (P, C) -> J(2) * Rot(13/8)\n ),\n\n #F DCT4_Base3: (base case for size 3)\n #F\n #F DCT4_2 = (2,3) * (F_2 dirsum 1) * (a dirsum M) * (F_2 dirsum 1) * (2,3)\n #F\n #F derived by hand starting with AREP's decomposition by mon-mon symmetry.\n #F\n DCT4_Base3 := rec (\n\tinfo := \"DCT4_3 -> F_2, M, F_2\",\n\tforTransposition := false,\n\tisApplicable := P -> P[1] = 3, \n\trule := (P, C) -> \n\t Perm((2,3), 3) * \n\t DirectSum(F(2), I(1)) \n\t DirectSum(Diag(Sqrt(3/8)), Sqrt(1/2)Mat([[1/2, 1], [1, -1]])) \n\t DirectSum(F(2), I(1)) \n\t Perm((2,3), 3)\n ),\n\n #F DCT4_DCT2: DCT4_n = sums * DCT2_n * diag\n #F\n #F inverse - transpose of RuleDCT4_2\n #F\n DCT4_DCT2 := rec (\n\tinfo := \"DCT4_n --> DCT2'_n\",\n\tisApplicable := P -> P[1] > 2,\n\tallChildren := P -> [[ DCT2(P[1]) ]],\n\trule := (P, C) -> \n\t sums1(P[1]) \n\t C[1] \n\t Diag(List([0..P[1]-1], i -> 1/(2CosPi((2i+1)/(4P[1])))))\n ),\n\n #F DCT4_DCT2t: 1985, DCT4_n = sums DCT2_n * diag\n #F\n #F Chan: \n #F Direct Methods for computing discrete sinusoidal transforms\n #F IEE Proceedings, Vol. 137, 1990, pp. 433--442\n #F\n # switched off since critical path too long (sums6)\n # also there seems to be one mult too much\n DCT4_DCT2t := rec (\n\tinfo := \"DCT4_n --> DCT2'_n\",\n\tswitch := false,\n\tisApplicable := P -> P[1] > 2,\n\tallChildren := P -> [[ DCT2(P[1]) ]],\n\trule := ( P, C ) -> \n\t sums6(P[1]) \n\t C[1] \n\t Diag(List([0..P[1] - 1], i -> 2 * CosPi((2i + 1)/(4P[1]))))\n ),\n\n #F DCT4_DCT2andDST2: 1985\n #F\n #F DCT4_n = blocks * perm * (DCT2_n/2 dirsum DST2_n/2) * rotations\n #F\n #F Wang: (transposed)\n #F On Computing the Discrete Fourier ans Cosine Transforms,\n #F IEEE Trans. on Signal Proc., 1985, pp. 1341--1344\n #F\n DCT4_DCT2andDST2 := rec (\n\tinfo := \"DCT4_n --> DCT2'_n/2, DST2'_n/2\",\n\tisApplicable := P -> IsInt(P[1]) and P[1] > 2 and P[1] mod 2 = 0, \n\tallChildren := P -> [[ DCT2(P[1]/2), DST2(P[1]/2) ]],\n\trule := (P, C) -> \n\t DirectSum(I(1), \n\t\t Tensor(I(P[1]/2-1), F(2)J(2)),\n\t\t I(1)) \n\t DirectSum(C[1], C[2]) ^ L(P[1], 2) \n\t DirectSum(List([0..P[1]/2-1], i -> J(2)Rot(2-(2P[1]-2i-1)/(4P[1])))) \n\t LIJ(P[1])\n\n\t # LIJ(P[1]) * \n\t # DirectSum(C[1], C[2] ^ J(P[1]/2)) \n\t # DirectSum(List([0..P[1]/2-1], i -> J(2)Rot(2-(2P[1]-2i-1)/(4P[1])))) \n\t # ^ LIJ(P[1])\n ),\n\n #F DCT4_DST4andDST2: 1988\n #F\n #F DCT4_n = diag sums * perm * (DST4_n/2 dirsum DST2_n/2) * sign \n #F (DFT_2 tensor I_n/2) diag * perm\n #F\n #F Rao/Yip:\n #F The Decimation-in-Frequency Algorithms for a family of \n #F Discrete Sine and Cosine Algorithms.\n #F Circuits, Systems, and Signal Processing, 1988, pp. 3--19\n #F\n DCT4_DST4andDST2 := rec (\n\tinfo := \"DCT4_n --> DST4_n/2, DST2_n/2\",\n\tswitch := false,\n\tisApplicable := P -> IsInt(P[1]) and P[1] > 2 and P[1] mod 2 = 0,\n\n\tallChildren := P -> [[ DST4(P[1]/2), DST2(P[1]/2) ]],\n\n\trule := (P, C) -> \n\t Diag(List([0..P[1] - 1], i -> (-1)^i)) \n\t sums1(P[1]).transpose() \n\t L(P[1], P[1]/2) \n\t DirectSum(C[1], C[2] (-1)) \n\t Tensor(F(2), I(P[1]/2)) \n\t Diag(Concat(List([1..P[1]/2], i -> 1/(2SinPi((2i - 1)/(4P[1])))),\n\t\t List([1..P[1]/2], i -> 1/(2CosPi((2i - 1)/(4P[1])))))) \n\t IJ(P[1], P[1]/2)\n ),\n\n #F DCT4_Iterative: 1985, DCT4_n = iterative\n #F\n #F Chen/Smith/Fralick: \n #F A Fast Computational Algorithm for the Discrete Cosine Transform,\n #F IEEE Trans. on Comm., 1977, pp. 1004--1009\n #F corrected in:\n #F Wang: \n #F Reconsideration of --above--, IEEE Trans. on Comm., 1983, pp. 121--123\n #F Wang: \n #F Fast Algorithms for the Discrete W Transform and the\n #F Discrete Fourier Transform.\n #F IEEE Trans. on ASSP, 1984, pp. 803--814\n #F\n DCT4_Iterative := rec (\n\tinfo := \"DCT4_n iterative\",\n\tisApplicable := P -> P[1] > 2 and Is2Power(P[1]),\n\trule := (P, C) -> \n\t LIJ(P[1]) L(P[1], 2) \n\t DirectSum(List([1..P[1]/2], i -> Rot(1/2-(4i-3)/(4P[1])) J(2))) \n\n\t Compose(List([1..Log2Int(P[1])-1], j -> let(jj := 2^j,\n\t\t Tensor(I(jj/2), F(2), I(P[1]/jj)) \n\t\t Tensor(I(jj/2), \n\t\t\tDirectSum(I(P[1]/jj), List([1..P[1]/jj/2], \n\t\t\t i -> Rot(1/2-(4i-3)/(2P[1]/jj)) * J(2))))))) *\n\t perm6(P[1])\n )\n));\n\n", "meta": {"hexsha": "a6c24574f1645ce22363e06a1115de62f1b0b169", "size": 4777, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/dct_dst/dct4rules.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/transforms/dct_dst/dct4rules.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/transforms/dct_dst/dct4rules.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 31.6357615894, "max_line_length": 81, "alphanum_fraction": 0.4925685577, "num_tokens": 1989, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. 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	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nRulesFor(DFT, rec(\n DFT_CT_Inplace := rec(\n\tinfo := \"DFT(mn,k) -> DFT(m, k%m), DFT(n, k%n)\",\n\tmaxCodeletSize := 16,\n\n\tisApplicable := (self, P) >> P[1] > 2 and not IsPrime(P[1]),\n\n\tallChildren := (self, P) >> Map2( \n\t Filtered(DivisorPairs(P[1]), d -> d[1] <= self.maxCodeletSize), \n\t (m,n) -> [ \n\t\tDFT(m, P[2] mod m), \n\t\tDFT(n, P[2] mod n) ]),\n \n\trule := (self,P,C) >> let(mn := P[1], m := Rows(C[1]), n := Rows(C[2]), \n di := fPrecompute(Tw1(mn, n, P[2])),\n\n\t When(mn > self.maxCodeletSize, # why BB?\n\t\tInplace(Tensor(C[1], I(n)) * Diag(di)), \n\t\t Tensor(C[1], I(n)) * Diag(di)) \n\t Tensor(I(m), C[2]) \n\t L(mn, m))\n ),\n\n DFT_SplitRadix_Inplace := rec(\n\tinfo := \"DFT_n -> DFT_n/2, DFT_n/4, DFT_n/4\",\n\tforTransposition := true,\n\tmaxSize := 64, \n\n\tisApplicable := (self, P) >> let(N := P[1],\n\t N >= 8 and N mod 4 = 0 and N <= self.maxSize),\n\n\tallChildren := P -> let(N := P[1], w := P[2], \n\t [[ DFT(N/2, w), DFT(N/4, w) ]]),\n\n\trule := (P, C) -> let(N := P[1], w := P[2], \n\t Inplace(Tensor(F(2), I(N/2))) \n\t DirectSum( \n\t\tC[1], \n\t\tInplace(BB(\n\t\t\tTensor(Diag(1, E(4)^w) F(2), I(N/4)) \n\t\t\tDiag(Concat(List([0..N/4-1], i->E(N)^(wi))), \n\t\t\t List([0..N/4-1], i->E(N)^(3wi))))) \n\t Tensor(I(2), C[2])L(N/2,2)\n\t ) *\n\t L(N, 2))\n ),\n\n));\n", "meta": {"hexsha": "ceea58e898a6dd1df0db6d7fe7e796cda9ce0ed1", "size": 1427, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/dft/inplace.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/transforms/dft/inplace.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/transforms/dft/inplace.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 26.4259259259, "max_line_length": 73, "alphanum_fraction": 0.4723195515, "num_tokens": 578, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8723473680407889, "lm_q2_score": 0.5851011542032312, "lm_q1q2_score": 0.5104114519068165}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nTrPRDFT1 := arg -> let(x:=ApplyFunc(PRDFT1, arg).transpose(), Chain(PrintLine(x, \" \", x.dimensions), x));\nTrPRDFT2 := arg -> ApplyFunc(PRDFT2, arg).transpose();\nTrPRDFT3 := arg -> ApplyFunc(PRDFT3, arg).transpose();\nTrPRDFT4 := arg -> ApplyFunc(PRDFT4, arg).transpose();\n\nDFTSymmetries := rec( #n-even, #n-odd\n DFT := [\n\t[Real , [CE0_R2Cpx(W_RFT, 1), [PRDFT1, PRDFT1], 1]],\n\t[CE0_R2Cpx(W_URFTT, 1), [Real, [TrPRDFT1, TrPRDFT1], 1]],\n\t[Even0, [Even0, [DCT1, DCT5], 1]],\n\t[Odd00, [Odd00, [DST1, DST5], E(4)]] # j\n ],\n\n DFT2 := [\n\t[Real , [CO0_R2Cpx(W_RFT, -E(4)), [PRDFT2, PRDFT2], 1]],\n\t[CE1_R2Cpx(W_URFTT, 1), [Real, [TrPRDFT3, TrPRDFT3], 1]],\n\t[Even1, [Odd0, [DCT2, DCT6], 1]], \n\t[Odd1 , [Even00, [DST2, DST6], E(4)]]\n ],\n\n DFT3 := [\n\t[Real , [CE1_R2Cpx(W_RFT, 1), [PRDFT3, PRDFT3], 1]],\n\t[CO1_R2Cpx(W_URFTT, E(4)), [Real, [TrPRDFT2, TrPRDFT2], 1]],\n\t[Real , [CE1_R2Cpx(W_RFT, 1), [PRDFT3, PRDFT3], 1]],\n\t[Odd0 , [Even1, [DCT3, DCT7], 1]],\n\t[Even00,[Odd1, [DST3, DST7], E(4)]]\n ],\n\n DFT4 := [\n\t[Real , [CO1_R2Cpx(W_RFT, -E(4)), [PRDFT4, PRDFT4], 1]],\n\t[CO1_R2Cpx(W_URFTT, E(4)), [Real, [TrPRDFT4, TrPRDFT4], 1]],\n\t[Odd1 , [Odd1, [DCT4, DCT8], 1]],\n\t[Even1, [Even1, [DST4, DST8], E(4)]] \n ]\n);\n\n_dftSym := function(nt, sym) \n local pos, entry, dftsym;\n if not IsBound(DFTSymmetries.(nt.name)) \n\tthen return false; fi;\n\n dftsym := DFTSymmetries.(nt.name);\n pos := PositionProperty(dftsym, x->x[1]=sym);\n if pos = false then \n\treturn false; fi;\n\n entry := dftsym[pos][2];\n if IsEvenInt(Rows(nt)) then return [entry[1], entry[2][1], entry[3]];\n else return [entry[1], entry[2][2], entry[3]];\n fi;\nend;\n\n\n# let Q := JDFTp_Reconstruct(n), p = 1..4 (DFT type)\n# Q is defined to be the matrix that satisfies\n# Q DFTp(n) = DFTp(n) * J(n)\n# Q = J(n) ^ (DFTp(n)^-1)\n#\n#spiral> PrintMat( MatSPL(J(8))^(MatSPL(DFT(8))^-1) );\n\nClass(JRecTwid1, DiagFunc, rec(\n def := n -> rec(size:=n),\n range := self >> TComplex,\n lambda := self >> let(n:=self.params[1], i:=Ind(n), \n\tLambda(i, omega(n, -i)))\n));\n\nClass(JRecTwid3, DiagFunc, rec(\n def := n -> rec(size:=n),\n range := self >> TComplex,\n lambda := self >> let(n:=self.params[1], i:=Ind(n), \n\tLambda(i, omega(2n, (-2i + n - 1))))\n));\n\nmk_InvDFT_Reconstruct := dft -> (let(n:=dft.params[1], Cond(\n ObjId(dft) = DFT1, DirectSum(I(1), J(n-1)),\n ObjId(dft) = DFT2, DirectSum(I(1), -J(n-1)),\n ObjId(dft) = DFT3, J(n),\n ObjId(dft) = DFT4, -J(n),\n Error(\"<dft> must be a non-terminal DFT1, DFT2, DFT3, or DFT4\"))));\n\nmk_JInvDFT_Reconstruct := dft -> (let(n:=dft.params[1], Cond(\n ObjId(dft) = DFT1, Diag(JRecTwid1(n)),\n ObjId(dft) = DFT2, I(n), \n ObjId(dft) = DFT3, Diag(JRecTwid3(n)),\n ObjId(dft) = DFT4, -I(n), \n Error(\"<dft> must be a non-terminal DFT1, DFT2, DFT3, or DFT4\"))));\n\nmk_JDFT_Reconstruct := dft -> (let(n:=dft.params[1], Cond(\n ObjId(dft) = DFT1, Diag(JRecTwid1(n)) * mk_InvDFT_Reconstruct(dft),\n ObjId(dft) = DFT2, mk_InvDFT_Reconstruct(dft),\n ObjId(dft) = DFT3, Diag(JRecTwid3(n)) * mk_InvDFT_Reconstruct(dft),\n ObjId(dft) = DFT4, -mk_InvDFT_Reconstruct(dft),\n Error(\"<dft> must be a non-terminal DFT1, DFT2, DFT3, or DFT4\"))));\n\nverify_JInvDFT_Reconstruct := dft -> let(T:=ObjId(dft), n:=dft.params[1], k:=dft.params[2], \n MatSPL(dft * J(n)) - MatSPL(mk_JInvDFT_Reconstruct(dft) * T(n, -k))\n);\nverify_JDFT_Reconstruct := dft -> let(T:=ObjId(dft), n:=dft.params[1], k:=dft.params[2], \n MatSPL(dft * J(n)) - MatSPL(mk_JDFT_Reconstruct(dft) * dft)\n);\n\n\n\nClass(RulesDFTSymmetry, RuleSet);\nRewriteRules(RulesDFTSymmetry, rec(\n\n DFT1_upgrade := ARule(Compose, [@(1,DFT), [@(2,GathExtend), @, @(3).cond(e->e in [Even1, Odd1])]], \n\t e -> let(n := Cols(@(1).val), [ Diag(Twid(n,n,-1,1/2,0,0)), DFT2(n), @(2).val])),\n\n DFT3_upgrade := ARule(Compose, [@(1,DFT3), [@(2,GathExtend), @, @(3).cond(e->e in [Even1, Odd1])]], \n\t e -> let(n := Cols(@(1).val), [ Diag(Twid(n,n,-1,1/2,1/2,0)), DFT4(n), @(2).val])),\n\n DFT1_upgradeCE := ARule(Compose, [@(1,DFT), [@(2,GathExtend), @, @(3, [CE1_R2Cpx, CO1_R2Cpx])]], \n\t e -> let(n := Cols(@(1).val), [ Diag(Twid(n,n,-1,1/2,0,0)), DFT2(n), @(2).val])),\n\n DFT3_upgradeCE := ARule(Compose, [@(1,DFT3), [@(2,GathExtend), @, @(3, [CE1_R2Cpx, CO1_R2Cpx])]], \n\t e -> let(n := Cols(@(1).val), [ Diag(Twid(n,n,-1,1/2,1/2,0)), DFT4(n), @(2).val])),\n\n DFT_EO_Symmetry := ARule(Compose,\n\t [ @(1,[DFT,DFT2,DFT3,DFT4]), \n\t [ @(2, GathExtend), @, @(3).cond(e->_dftSym(@(1).val, e)<>false)] ], \n\t e -> \n\t let(sym := _dftSym(@(1).val, @(3).val), \n\t\t out := sym[1],\n\t\t transf := sym[2],\n\t\t n := When(@(3).val.tsize = \"cols\", Cols(@(2).val), Rows(@(2).val)),\n\t\t scale := sym[3],\n\t\t [PushL(GathExtendU(Rows(@(1).val), out)), scaletransf(n)])),\n\n L_Real := ARule(Compose, [[L, @(1), @(2)], [@(3,GathExtend), @, Real]], \n\t e -> let(N:=@(1).val, k:=@(2).val, \n\t [ GathExtend(N, Real), L(N, k) ])),\n\n L_Conj0_R2Cpx := ARule(Compose, [[L, @(1), @(2)], [@(3,GathExtend), @, @(4, [CE0_R2Cpx, CO0_R2Cpx])]], \n\t e -> let(N:=@(1).val, k:=@(2).val, m:=N/k, nn:=Cols(@(3).val)/2, \n\t sym := @(4).val, \n\t sym1 := When(ObjId(sym)=CE0_R2Cpx, CE1_R2Cpx(sym.w, sym.j), CO1_R2Cpx(sym.w, sym.j)), \n\t\t diag := When(ObjId(sym)=CE0_R2Cpx, Diag(BHD(m, 1, -1)), Diag(BHD(m, -1, 1))),\n\t [ DirectSum(GathExtend(m, sym), GathExtend(N-m, sym1)),\n\t DirectSum(I(Int(m+1+_even(m))), Tensor(I(Int((k-1)/2)), diag), I(_even(k)(m+_odd(m)))),\n\t RC(VStack(Gath(Refl(nn, N, Int((m+2)/2), L(N,k))), \n\t\t Gath(Refl(nn, N, nn-Int((m+2)/2), fCompose(L(N,k), fAdd(N, N-m, m)))))) ])), \n\n L_Conj1_R2Cpx := ARule(Compose, [[L, @(1), @(2)], [@(3,GathExtend), @, @(4, [CE1_R2Cpx, CO1_R2Cpx])]], \n\t e -> let(N:=@(1).val, k:=@(2).val, m:=N/k, nn:=Cols(@(3).val)/2,\n\t sym := @(4).val, \n\t\t diag := When(sym=CE1_R2Cpx, Diag(BHD(m, 1, -1)), Diag(BHD(m, -1, 1))),\n\t [ GathExtend(N, sym), \n\t DirectSum(Tensor(I(Int(k/2)), diag), When(IsOddInt(k), I(m+_odd(m)), [])),\n\t RC(Gath(Refl(nn, N-1, nn, L(N,k)))) ])), \n\n L_Even0 := ARule(Compose, [[L, @(1), @(2)], [@(3,GathExtend), @, Even0]], \n\t e -> let(N:=@(1).val, k:=@(2).val, m:=N/k, nn:=Cols(@(3).val),\n\t [ DirectSum(GathExtend(m, Even0), GathExtend(N-m, Even1)),\n\t VStack(Gath(Refl(nn, N, Int((m+2)/2), L(N,k))), \n\t\t Gath(Refl(nn, N, nn-Int((m+2)/2), fCompose(L(N,k), fAdd(N, N-m, m))))) ])), \n\n L_Even00 := ARule(Compose, [[L, @(1), @(2)], [@(3,GathExtend), @, Even00]], \n\t e -> let(N:=@(1).val, k:=@(2).val, m:=N/k, nn:=Cols(@(3).val),\n\t [ DirectSum(GathExtend(m, Even00), GathExtend(N-m, Even1)),\n\t VStack(Gath(Refl(nn, N-2, Int(m/2), fCompose(fAdd(N,N,-1), L(N,k), fAdd(N, N-1, 1)))), \n\t\t Gath(Refl(nn, N-2, nn-Int(m/2), fCompose(fAdd(N,N,-1), L(N,k), fAdd(N, N-m, m))))) ])), \n\n L_Odd0 := ARule(Compose, [[L, @(1), @(2)], [@(3,GathExtend), @, Odd0]], \n\t e -> let(N:=@(1).val, k:=@(2).val, m:=N/k, nn:=Cols(@(3).val),\n\t [ DirectSum(GathExtend(m, Odd0), GathExtend(m(k-1), Odd1)),\n\t DirectSum(I(Int((m+1)/2)), Tensor(I(Int((k-1)/2)), Diag(BHN(m))), When(IsEvenInt(k), I(Int(m/2)), [])),\n\t VStack(Gath(Refl(nn, N, Int((m+1)/2), L(N,k))), \n\t\t Gath(Refl(nn, N, nn-Int((m+1)/2), fCompose(L(N,k), fAdd(N, N-m, m))))) ])), \n\n L_Odd00 := ARule(Compose, [[L, @(1), @(2)], [@(3,GathExtend), @, Odd00]], \n\t e -> let(N:=@(1).val, k:=@(2).val, m:=N/k, nn:=Cols(@(3).val),\n\t [ DirectSum(GathExtend(m, Odd00), GathExtend(m(k-1), Odd1)),\n\t DirectSum(I(Int((m-1)/2)), Tensor(I(Int((k-1)/2)), Diag(BHN(m))), When(IsEvenInt(k), I(Int(m/2)), [])),\n\t VStack(Gath(Refl(nn, N-2, Int((m-1)/2), fCompose(fAdd(N,N,-1), L(N,k), fAdd(N, N-1, 1)))), \n\t\t Gath(Refl(nn, N-2, nn-Int((m-1)/2), fCompose(fAdd(N,N,-1), L(N,k), fAdd(N, N-m, m))))) ])), \n\n L_Even1 := ARule(Compose, [[L, @(1), @(2)], [@(3,GathExtend), @, Even1]], \n\t e -> let(N:=@(1).val, k:=@(2).val, m:=N/k, nn:=Cols(@(3).val),\n\t [ GathExtend(N, Even1), \n\t Gath(Refl(nn, N-1, nn, L(N,k))) ])), \n\n L_Odd1 := ARule(Compose, [[L, @(1), @(2)], [@(3,GathExtend), @, Odd1]], \n\t e -> let(N:=@(1).val, k:=@(2).val, m:=N/k, nn:=Cols(@(3).val),\n\t [ GathExtend(N, Odd1), \n\t DirectSum(Tensor(I(Int(k/2)), Diag(BHN(m))), When(IsOddInt(k), I(Int(m/2)), [])),\n\t Gath(Refl(nn, N-1, nn, L(N,k))) ])), \n\n CRT_Even1 := ARule(Compose, [@(1, CRT), [@(2,GathExtend), @, Even1]], \n\t e -> let(N:=Rows(@(2).val), nn:=Cols(@(2).val),\n\t [ GathExtend(N, Even1), \n\t Gath(Refl(nn, N-1, nn, @(1).val)) ])), \n\n Tensor_Dirsum_split := ARule(Compose, \n\t [[Tensor, [I, @(1)], @(2)], [DirectSum, @(3).cond(e->Rows(e)=Cols(@(2).val)), @(4)]],\n\t e -> [ DirectSum(@(2).val * @(3).val, Tensor(I(@(1).val-1), @(2).val) * @(4).val) ]),\n\n IxDFT_EO1 := ARule(Compose,\n\t [[Tensor, [I, @(1)], [@(2,[DFT,DFT2,DFT3,DFT4]), @, 1, ...]], [@(3,GathExtend), @, @(4).cond(e->e in [Even1, Odd1])]],\n\t e -> let(k:=@(1).val, n:=Cols(@(2).val), transf:=@(2).val, sign := When(@(4).val=Odd1, -1, 1),\n\t When(k mod 2 = 0,\n\t [ # Below is actually a scaled type 1 extension! exploit this for final rewriting phase\n PushL(DirectSum(I(nk/2), Tensor(I(k/2), mk_JDFT_Reconstruct(transf)J(n))) * \n @(3).val) * \n\t\t Tensor(I(k/2), transf) ],\n\n # again, a scaled type 1 extension!\n\t\t [ PushL(VStack(I(n(k+1)/2),\n\t\t\t Tensor(J((k-1)/2), sign mk_JDFT_Reconstruct(transf)) \n\t\t\t\t * Gath(fAdd(n(k+1)/2, n(k-1)/2, 0)))), \n\t\t DirectSum(Tensor(I((k-1)/2), 1/2transf), \n\t\t\t transf GathExtend(n, @(4).val))]))),\n\n # IxDFT_EO1 := ARule(Compose,\n# \t [[Tensor, [I, @(1)], [@(2,[DFT,DFT2,DFT3,DFT4]), @, 1, ...]], [GathExtend, @(3), @(4).cond(e->e in [Even1, Odd1])]],\n# \t e -> let(k:=@(1).val, n:=Cols(@(2).val), transf:=@(2).val, sign := When(@(4).val=Odd1, -1, 1),\n# \t When(k mod 2 = 0,\n# \t [ # Below is actually a scaled type 1 extension! exploit this for final rewriting phase\n# PushL(VStack(I(nk/2), Tensor(J(k/2), sign mk_JDFT_Reconstruct(transf)))), \n# \t\t Tensor(I(k/2), 1/2transf) ],\n\n# # again, a scaled type 1 extension!\n# \t\t [ PushL(VStack(I(n(k+1)/2),\n# \t\t\t Tensor(J((k-1)/2), sign * mk_JDFT_Reconstruct(transf)) \n# \t\t\t\t * Gath(fAdd(n(k+1)/2, n(k-1)/2, 0)))), \n# \t\t DirectSum(Tensor(I((k-1)/2), 1/2transf), \n# \t\t\t transf GathExtend(n, @(4).val))]))),\n\n IxDFT_CEO1_RFTT_DHT := ARule(Compose,\n\t [[Tensor, [I, @(1)], @(2,[DFT,DFT2,DFT3,DFT4])], \n\t [GathExtend, @(3), @(4,[CE1_R2Cpx, CO1_R2Cpx],e->e.w in [W_RFTT, W_URFTT, W_DHT, W_DHT])]], \n\n\t e -> let(k:=@(1).val, n:=Cols(@(2).val), \n\t transf := @(2).val, sign := When(ObjId(@(4).val)=CO1_R2Cpx, -1, 1),\n\t newtransf := RC(ObjId(transf)(transf.params[1], -transf.params[2])), \n\t\t winv := @(4).val.w^-1,\n\t\t pack1 := Mat([winv[1]]),\n\t\t pack2 := Mat([winv[2]]),\n\n\t When(k mod 2 = 0,\n\t [ PushL(VStack(Tensor(I(nk/2), pack1), \n\t\t\t Tensor(J(k/2), sign Tensor(I(n), pack2)\n\t\t\t\t RC(mk_JInvDFT_Reconstruct(transf))))), \n\t\t Tensor(I(k/2), newtransf) ],\n\n\t\t [ PushL(VStack(DirectSum(Tensor(I(n(k-1)/2), pack1), I(n)),\n\t\t\t Tensor(J((k-1)/2), sign * Tensor(I(n), pack2) \n\t\t\t\t RC(mk_JInvDFT_Reconstruct(transf))) Gath(fAdd(nk, n(k-1), 0)))), \n\t\t DirectSum(Tensor(I((k-1)/2), newtransf), \n\t\t\t transf * GathExtend(n, @(4).val))]))),\n\n IxDFT_Real := ARule(Compose,\n\t [[Tensor, [I, @(1)], [@(2,[DFT,DFT2,DFT3,DFT4]), @, 1, ...]], [GathExtend, @(3), Real]],\n\t e -> [ Tensor(I(@(1).val), @(2).val * GathExtend(Cols(@(2).val), Real)) ]),\n\n DFTxI_Ext := ARule(Compose,\n\t [[@(1,Tensor), [@(2,[DFT,DFT2,DFT3,DFT4]), @, 1, ...], I], @(4, GathExtend)],\n\t e -> [ @(1).val.parallelForm() * @(4).val]),\n\n Tensor_J1 := Rule([Tensor, [J, 1], @(1)], e -> @(1).val), \n Tensor_I1 := Rule([Tensor, [I, 1], @(1)], e -> @(1).val),\n Tensor_I0 := Rule([Tensor, ..., [I, 0], ...], e -> I(0)),\n Compose_I := ARule(Compose, [I], e -> []),\n DirectSum_I0 := ARule(DirectSum, [[I, 0]], e -> []),\n DirectSum_Assoc := ARule(DirectSum, [@(1,DirectSum)], e -> [@(1).val.children()]),\n DirectSum_Single := Rule([DirectSum, @(1)], e -> @(1).val),\n Compose_Assoc := ARule(Compose, [@(1,Compose)], e -> [@(1).val.children()]),\n Compose_Single := Rule([Compose, @(1)], e -> @(1).val),\n J_J := ARule(Compose, [@(1,J), @(2,J)], e -> [ I(@(1).val.params[1]) ]),\n\n # ===============\n # Diags\n # ================\n Diag_Diag := ARule(Compose, [[Diag, @(1)], [Diag, @(2)]], e -> \n [ Diag(diagMul(@(1).val, @(2).val)) ]),\n\n Diag_L_Diag := ARule(Compose, [[Diag, @(1)], @(2, L), [Diag, @(3)]], e -> \n [ Diag(diagMul(@(1).val, fCompose(@(3).val, @(2).val))) * @(2).val ]),\n\n Tensor_Diag := Rule([Tensor, [I, @(1)], [Diag, @(2)]], \n e -> Diag(diagTensor(fConst(@(1).val, 1), @(2).val))),\n DirectSum_Diag := Rule([DirectSum, [I, @(1)], [Diag, @(2)]], \n e -> Diag(diagDirsum(fConst(@(1).val, 1), @(2).val))),\n \n E1_Diag_E1 := ARule(Compose, [[@(1,GathExtend,e->e.transposed), @, Odd1], \n [Diag, @(2)], \n [@(1,GathExtend,e->not e.transposed), @, Odd1]],\n e -> let(n:=@(2).val.domain(), f := @(2).val, \n [Diag(diagMul(fConst(n/2, 1/4), \n diagAdd(fCompose(f, fTensor(fBase(2, 0), fId(n/2))),\n fCompose(f, fTensor(fBase(2, 1), J(n/2))))))])),\n\n Scale_Scale := Rule([Scale, @(1), [Scale, @(2), @(3)]], e->Scale(@(1).val * @(2).val, @(3))),\n Scale_1 := Rule([Scale, @(1).cond(e->e=1), @(2)], e->@(2).val),\n\n # =============\n # PushL/PushR\n # =============\n PushL_within_PushL := Rule(@@(1,PushL, (e,cx)->IsBound(cx.PushL) and cx.PushL<>[]), e -> e.child(1)),\n\n Compose_PushL_PushL := ARule(Compose, [[PushL, @(1)], [PushL, @(2)]], e -> [ PushL(@(1).val * @(2).val) ]),\n Compose_PushR_PushL := ARule(Compose, [[PushR, @(1)], [PushL, @(2)]], e -> [ PushR(@(1).val * @(2).val) ]),\n XXX_PushL := ARule(Compose, [@(1, [Diag, L]), [PushL, @(2)]], e -> [PushL(@(1).val * @(2).val)]),\n \n Tensor_PushL := Rule([Tensor, @(1, I), [Compose, @(2, PushL), @(3)]], \n\t e -> PushL(Tensor(@(1).val, @(2).val.child(1))) * Tensor(@(1).val, @(3).val)),\n\n DirectSum_PushL := Rule(@(1, DirectSum, \n\t e -> ForAny(e.children(), \n\t\t c -> ObjId(c)=PushL or (ObjId(c)=Compose and ObjId(c.child(1)) = PushL))),\n\n\t e -> let(ch := @(1).val.children(),\n\t split := List(ch, e -> Cond(ObjId(e) = PushL, \n\t\t\t [e, I(Cols(e))], \n\t\t\t ObjId(e) = Compose and ObjId(e.child(1))=PushL, \n\t\t\t\t\t [e.child(1).child(1), Drop(e.children(), 1)], \n\t\t\t\t\t [I(Rows(e)), e])),\n\t\t PushL(DirectSum(List(split, x->x[1]))) * DirectSum(List(split, x->x[2]))))\n));\n\nRewriteRules(RulesDFTSymmetry, rec(\n BRDFT3_ExtendOdd0 := ARule(Compose, [[BRDFT3, @(1).cond(e->IsEvenInt(e)), 1/4], [GathExtend, @, Odd0]], \n\t e -> let(k:=@(1).val,\n\t [ GathExtend(k,Upsample0),SkewDTT(DCT3(k/2),1/2)])),\n\n Odd1_split := ARule(Compose, [[Tensor, [I,@(1)],@(2)],[GathExtend, @, Odd1]],\n\t e -> let(n:=@(1).val,A:=@(2).val,k:=When(IsEvenInt(n),n/2, (n-1)/2),When(IsEvenInt(n),\n\t [VStack(Tensor(I(k),A)(1/2),Tensor(J(k),AJ(Cols(A))(-1/2)))],\n\t [VStack(DirectSum(Tensor(I(k),A)(1/2),AGathExtend(Cols(A),Odd1)),Tensor(J(k),AJ(Cols(A))(-1/2)))]))),\n\n ReduceUpsample0_RC := ARule(Compose, [[ScatReduce, @(1), Upsample0],[RC, @(2)]], \n\t e -> [@(2).valScatReduce(@(1).val,Upsample0)]),\n\n Push_ScatReduceWithinSum := ARule(Compose, [[ScatReduce, @, Upsample0],[@(1,IterDirectSum).cond(e->IsEvenInt(e.domain)),@(2)]],\n\t e -> [IterDirectSum(@(1).val.var,@(1).val.domain,ScatReduce(Rows(@(2).val),Upsample0)@(2).val)]\n),\n\n Cut_SkewPRDFT := ARule(Compose, [[ScatReduce, @, Upsample0],[BSkewPRDFT,@(1),@(2)]],\n\t e -> let(n:=@(1).val,a:=@(2).val,f:=2cospi(2a),\n\t [SkewDTT(DCT3(n/2),2a)When(IsEvenInt(n/2),\n\t\t HStack(I(n/2),DirectSum(Mat([[f/2]]),Tensor(I(((n/2)-2)/2),Mat([[f,-1],[-1,f]])),Mat([[f-1]]))^M((n)/2,n/4)),\n\t\t HStack(I(n/2),DirectSum(Mat([[f/2]]),Conjugate(Tensor(I((n/2-1)/2),Mat([[f,-1],[-1,f]])),M(n/2-1,(n/2-1)/2)))))])),\n\n SplitIterDirectSum := Rule([@(1,IterDirectSum), [Compose,@(2,SkewDTT),@(3,HStack)]],\n\t e->let(i:=@(1).val.var,IterDirectSum(@(1).val.var,@(1).val.domain,@(2).val)IterDirectSum(@(1).val.var,@(1).val.domain,@(3).val))),\n\n BRDFT3_ExtendOdd1 := ARule(Compose, [[BRDFT3, @(1).cond(e->IsEvenInt(e)), 1/4], [GathExtend, @, Odd1]],\n e -> let(k:=@(1).val,i:=Ind(),\n\t [IterDirectSum(i,k/2,Mat([[1/2+cospi((2i+1)/k)],[-1/2]]))PolyDTT(DCT4(k/2))])),\n \n BRDFT3_J := ARule(Compose, [[BRDFT3, @(1).cond(e->IsEvenInt(e)), 1/4], [J, @]],\n e -> let(k:=@(1).val,i:=Ind(),\n [IterDirectSum(i,k/2,Mat([[-2cospi((2i+1)/k),-1-2cospi((2i+1)/(k/2))],[1,-2cospi((2((k/2)-i)-1)/k)]]))BRDFT3(k)]))\n));\n\n \n#z := L(15,3) GathExtend(15, Odd0);; zz := RulesDFTSymmetry(z);; PrintMat(MatSPL(z)-MatSPL(zz));\n#z := L(16,4) * GathExtend(16, Odd0);; zz := RulesDFTSymmetry(z);; PrintMat(MatSPL(z)-MatSPL(zz));\n\n#z := L(15,3) * GathExtend(15, Even00);; zz := RulesDFTSymmetry(z);; PrintMat(MatSPL(z)-MatSPL(zz));\n#z := L(16,4) * GathExtend(16, Odd1);; zz := RulesDFTSymmetry(z);; PrintMat(MatSPL(z)-MatSPL(zz));\n\n#RulesDFTSymmetry(Tensor(I(3), DFT(5))L(15,3)GathExtend(15, Even0));\n#RulesDFTSymmetry(Tensor(I(2), DFT3(8))L(16,2)GathExtend(16, Even0));\n\n\ndft1 := (N, k) -> Tensor(DFT1(k), I(N/k)) * Diag(Tw1(N, N/k, 1)) * Tensor(I(k), DFT1(N/k)) * L(N, k);\ndft2 := (N, k) -> Tensor(DFT2(k), I(N/k)) * Diag(Tw2(N, N/k, 1)) * Tensor(I(k), DFT1(N/k)) * L(N, k);\ndft3 := (N, k) -> Tensor(DFT1(k), I(N/k)) * Diag(Tw3(N, N/k, 1)) * Tensor(I(k), DFT3(N/k)) * L(N, k);\ndft4 := (N, k) -> Tensor(DFT2(k), I(N/k)) * Diag(Tw4(N, N/k, 1)) * Tensor(I(k), DFT3(N/k)) * L(N, k);\n\npdft1 := (N, k, lsym, rsym) -> GathExtend(N, lsym).transpose() * dft1(N, k) * GathExtend(N, rsym);\npdft2 := (N, k, lsym, rsym) -> GathExtend(N, lsym).transpose() * dft2(N, k) * GathExtend(N, rsym);\npdft3 := (N, k, lsym, rsym) -> GathExtend(N, lsym).transpose() * dft3(N, k) * GathExtend(N, rsym);\npdft4 := (N, k, lsym, rsym) -> GathExtend(N, lsym).transpose() * dft4(N, k) * GathExtend(N, rsym);\n\n# DCT6(8)\nf := L(15, 3) * Tensor(I(5), DFT2(3, 1)) * L(15, 5) * \n Diag(Tw2(15, 5, 1)) * \n Tensor(I(3), DFT(5, 1)) * L(15, 3);\nff := GathExtend(Rows(f), Odd0).transpose() * f * GathExtend(Cols(f), Even1);\n\n# f := L(16,4) * Tensor(I(4), DFT(4)) * L(16,4) * Diag(Tw1(16,4,1)) * Tensor(I(4), DFT(4)) * L(16,4);\n# ff := GathExtend(Rows(f), Odd00).transpose() * f * GathExtend(Cols(f), Odd00);\n\n# DCT2/DCT6\n# f := L(16,4) * Tensor(I(4), DFT2(4)) * L(16,4) * Diag(Tw2(16,4)) * Tensor(I(4), DFT(4)) * L(16,4);\n#ff := GathExtend(Rows(f), Odd0).transpose() * f * GathExtend(Cols(f), Even1);\n\n# f4 := L(16,4) * Tensor(I(4), DFT2(4)) * L(16,4) * Diag(Tw4(16,4)) * Tensor(I(4), DFT3(4)) * L(16,4);\n# ff := GathExtend(Rows(f), Odd1).transpose() * f4 * GathExtend(Cols(f), Odd1);\n\n# fo := L(21,3) * Tensor(I(7), DFT2(3)) * L(21,7) * Diag(Tw4(21,7)) * Tensor(I(3), DFT3(7)) * L(21,3);\n# ffo := GathExtend(Rows(fo), Odd1).transpose() * fo * GathExtend(Cols(fo), Odd1);\n\n# fr1 := GathExtend(16, CE0_R2Cpx(W_RFT, 1).invertW()).transpose() * f * GathExtend(16, Real);\n\n fr2 := GathExtend(21, CE0_R2Cpx(W_RFT, 1).invertW()).transpose() * \n L(21,3) * Tensor(I(7), DFT(3)) * L(21,7) * Diag(Tw1(21,7,1)) * Tensor(I(3), DFT(7)) * L(21,3) \n\tGathExtend(21, Real);\n\n fr4 := GathExtend(21, CO1_R2Cpx(W_RFT, -E(4)).invertW()).transpose() \n L(21,3) * Tensor(I(7), DFT2(3)) * L(21,7) * Diag(Tw4(21,7,1)) * Tensor(I(3), DFT3(7)) * L(21,3) \n\tGathExtend(21, Real);\n\n# fr4 := GathExtend(16, CO1_R2Cpx).transpose() L(16,4) * Tensor(I(4), DFT2(4)) * L(16,4) * Diag(Tw4(16,4)) * Tensor(I(4), DFT3(4)) * L(16,4) * GathExtend(16, Real);\n\n#p := Mat(1/2[[1, E(4)]]);\n#pp := Mat(1/2[[1, -E(4)]]);\n\n#them := MatSPL(DFT(4) * Tensor(I(4), 2pp));;\n#me := MatSPL(Tensor(I(4), 2pp) * RC(DFT(4,1)));;\n\n# y = DFT x* = (DFT* x)* ?\n#\n# C IxP = IxP' RC(C) \n# IxP' = C IxP RC(C)^-1\n\n# C IxP =IxP' C Ix(1,j)\n\ndftproj := function(f)\n f := 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	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n#############################\n# General Case Cooley-Tukey\n#############################\n\n# R1 -> (R1, C1, R3) (R1)\n# R2 -> (R2, C2, R4) (R1)\nPRF12_CT_Children := (N,k,PRFt,DFTt,PRFtp,PRF1) -> Map2(DivisorPairs(N),\n (m,n) -> When(IsEvenInt(n),\n\t[ PRFt(m,k), DFTt(m,k), PRF1(n,k), PRFtp(m,k) ],\n\t[ PRFt(m,k), DFTt(m,k), PRF1(n,k) ] )\n);\n\nPRF12_CT_Rule := (N,k,C,Conj,Tw) -> let(m:=Cols(C[1]), n:=Cols(C[3]), Nf:=Int(N/2),\n nf:=Int(n/2), nc:=Int((n+1)/2), mf:=Int(m/2), mc:=Int((m+1)/2), j:=Ind(nc-1),\n\n SUM(\n\tRC(Scat(H(Nf+1,mf+1,0,n))) * C[1] * Gath(H(2(nf+1)m, m, 0, 2(nf+1))),\n\n\tWhen(nc=1, [], \n\tISum(j, \n\t RC(Scat(BH(Nf+1,N,m,j+1,n))) \n\t Conj * RC(C[2]) * Tw(j) \n\t RC(Gath(H((nf+1)m, m, j+1, nf+1))))),\n\n\tWhen(IsOddInt(n), [],\n\tRC(Scat(H(Nf+1,mc,nf,n))) * C[4] * Gath(H(2(nf+1)m, m, 2nf, 2(nf+1))))\n ) * \n Tensor(I(m), C[3]) * L(N,m)\n);\n\n\nIPRF12_CT_Rule := (N,k,C,Conj,Tw) -> let(m:=Rows(C[1]), n:=Rows(C[3]), Nf:=Int(N/2),\n nf:=Int(n/2), nc:=Int((n+1)/2), mf:=Int(m/2), mc:=Int((m+1)/2), j:=Ind(nc-1),\n\n L(N,n) * Tensor(I(m), C[3]) * \n SUM(\n\tScat(H(2(nf+1)m, m, 0, 2(nf+1))) C[1] * RC(Gath(H(Nf+1,mf+1,0,n))),\n\n\tWhen(nc=1, [], \n\tISum(j, \n\t RC(Scat(H((nf+1)m, m, j+1, nf+1))) \n\t Tw(j) \n\t RC(C[2]) \n\t Conj * \n\t RC(Gath(BH(Nf+1,N,m,j+1,n))))),\n\n\tWhen(IsOddInt(n), [],\n\tScat(H(2(nf+1)m, m, 2nf, 2(nf+1))) * C[4] * RC(Gath(H(Nf+1,mc,nf,n))))\n )\n );\n\n####################\n# Prime Factor \n####################\n\nPRF12_PF_Children := (N,k,PRFt,DFTt,PRF1) -> Map2(DivisorPairsRP(N),\n (m,n) -> When(IsEvenInt(n),\n\t[ PRFt(m,kn), DFTt(m,kn), PRF1(n,km), PRF1(m,kn) ],\n\t[ PRFt(m,kn), DFTt(m,kn), PRF1(n,km) ] )\n);\n\n RC.toAMat := self >> AMatMat(RCMatCyc( MatSPL(self.child(1)) ));\n\nPRF12_PF_Rule := (N,k,C) -> let(m:=Cols(C[1]), n:=Cols(C[3]), Nf:=Int(N/2), Nc:=Int((N+1)/2), \n nf:=Int(n/2), nc:=Int((n+1)/2), mf:=Int(m/2), mc:=Int((m+1)/2), j:=Ind(nc-1),\n alpha := (1/n) mod m,\n beta := (1/m) mod n,\n jj:=Ind(m), q := Ind(2m), \n\n SUM(\n\tRC(Scat(H(Nf+1,mf+1,0,n))) * C[1] * Gath(H(2(nf+1)m, m, 0, 2(nf+1))),\n\n\tWhen(nc=1, [], \n\tISum(j, \n\t RC(Scat(Refl(Nf+1, N, m, HZ(N, m, (j+1)m, n)))) \n\t # conjugate those values which indices will be reflected by the scatter Refl\n\t # NOTE: Unless 1.0 is used below, vector code will break due to TVect(TInt, ...)\n\t Diag(Lambda(q, cond(neq(imod(q, 2),0), cond(leq(imod(nidiv(q, 2) + (j+1)m, N), Nc-1), 1.0, -1.0), 1.0))) \n\t RC(C[2]) * \n\t RC(Gath(H((nf+1)m, m, j+1, nf+1))))),\n\n\tWhen(IsOddInt(n), [],\n\t let(inds := HZ(N, mc, ncm, n).tolist(),\n\t\t conj := ConcatList(inds{[1..mc]}, i -> When(i.v > Nf, [1.0,-1.0], [1.0,1.0])),\n\n\t\t RC(Scat(Refl(Nf+1, N, mc, HZ(N, mc, ncm, n)))) \n\t\t #RC(Scat(H(Nf+1, mc, nf, n))) \n\t\t Diag(conj) C[4] * \n\t\t Gath(H(2(nf+1)m, m, 2nf, 2(nf+1)))\n\t ))\n ) * \n Tensor(I(m), C[3]) * CRT(m,n,1,1)\n);\n\n# s := PRF12_PF_Rule(6,1,PRF12_PF_Children(6,1,PRDFT1, DFT1, PRDFT1)[1]);\n# Print(s);\n# me := MatSPL(s);\n# them := MatSPL(PRDFT(6));\n\n###########\n# RDFT #\n###########\n\nDeclare(PRDFT1_PF);\n\nRulesFor(PRDFT1, rec(\n PRDFT1_Base1 := BaseRule(PRDFT1, [1, @]),\n PRDFT1_Base2 := BaseRule(PRDFT1, [2, @]),\n\n #F PRDFT1_CT: projection of DFT_CT \n PRDFT1_CT := rec(\n\tforcePrimeFactor := false,\n\tisApplicable := (self, P) >> not IsPrime(P[1]) and \n\t When(self.forcePrimeFactor, not PRDFT1_PF.isApplicable(P), true),\n\n\tallChildren := P -> PRF12_CT_Children(P[1], P[2], PRDFT1, DFT1, PRDFT3, PRDFT1), \n\trule := (P,C) -> let(N:=P[1], k:=P[2], m:=Cols(C[1]),\n\t PRF12_CT_Rule(N, k, C, Diag(BHD(m,1,-1)), j->RC(Diag(fPrecompute(Twid(N,m,k,0,0,j+1))))))),\n\n #F PRDFT1_Complex: computes PRDFT using half of the outputs of complex DFT\n #F this rule can be successfully pruned by the compiler, and thus\n #F works for all sizes, including primes\n PRDFT1_Complex := rec(\n\tswitch := false,\n\tisApplicable := P -> not Is2Power(P[1]),\n\tallChildren := P -> [[ DFT(P[1], P[2]) ]],\n\tforTransposition := false,\n\trule := (P,C) -> let(n := P[1], nn:=Int(n/2)+1, \n\t Buf(Gath(H(2n,2nn, 0, 1))) * \n\t Diag(diagDirsum(fConst(2nn,1), fConst(2n-2nn,0))) \n\t RC(C[1]) \n\t Tensor(I(n), Diag(1,0)) \n\t Buf(Scat(H(2n,n,0,2)))\n\t)\n ),\n\n # transpose of RC(DFT(n)) is RC(DFT(n,-1)), since correct transposition is not implemented, \n # we need a separate rule\n PRDFT1_Complex_T := rec(\n\tswitch := false,\n\tisApplicable := P -> not Is2Power(P[1]),\n\tallChildren := P -> [[ DFT(P[1], -P[2]) ]],\n\tforTransposition := false,\n\ttransposed := true,\n\trule := (P,C) -> let(n := P[1], nn:=Int(n/2)+1, \n\t Buf(Gath(H(2n,n,0,2))) \n\t Tensor(I(n), Diag(1,0)) \n\t RC(C[1]) \n\t Diag(diagDirsum(fConst(2nn,1), fConst(2n-2nn,0))) * \n\t Buf(Scat(H(2n,2nn, 0, 1)))\n\t)\n ),\n\n #F PRDFT1_Trig: PRDFT1_n -> P (DCT1_(n/2+1) dirsum DST1_(n/2-1)) A\n #F\n PRDFT1_Trig := rec(\n\tisApplicable := P -> P[1] > 2 and IsEvenInt(P[1]) and (P[2] mod P[1]) in [1,-1 mod P[1]],\n\tallChildren := P -> [[ DCT1(P[1]/2+1), DST1(P[1]/2-1) ]],\n\trule := (P, C) -> let(n:=P[1]/2, \n\t Z(2n+2,2) \n\t DirectSum(Mat([[1,0],[0,0],[0,1],[0,0]]), L(2n-2,n-1)) \n\t DirectSum(Z(n+1,-1)C[1], Scale(P[2],C[2])) SymSplit1(n))),\n\n PRDFT1_PF := rec(\n\tmaxSize := false, \n \tisApplicable := (self, P) >> (self.maxSize=false or P[1]<=self.maxSize) and not IsPrime(P[1]) and DivisorPairsRP(P[1])<>[],\n \tallChildren := P -> PRF12_PF_Children(P[1], P[2], PRDFT1, DFT1, PRDFT1), \n \trule := (P,C) -> let(N:=P[1], k:=P[2], m:=Cols(C[1]),\n \t PRF12_PF_Rule(N, k, C)))\n));\n\nRulesFor(IPRDFT1, rec(\n IPRDFT1_Base1 := BaseRule(IPRDFT1, [1, @]),\n IPRDFT1_Base2 := BaseRule(IPRDFT1, [2, @]),\n\n IPRDFT1_CT := rec(\n\tisApplicable := P -> not IsPrime(P[1]),\n\tallChildren := P -> PRF12_CT_Children(P[1], P[2], IPRDFT1, DFT1, IPRDFT2, IPRDFT1), \n\trule := (P,C) -> let(N:=P[1], k:=P[2], m:=Rows(C[1]),\n\t IPRF12_CT_Rule(N, k, C, Diag(BHD(m,1,-1)), j->RC(Diag(fPrecompute(Twid(N,m,k,0,0,j+1))))))),\n\n IPRDFT1_Complex := rec(\n \tswitch := false,\n \tisApplicable := P -> IsPrime(P[1]),\n \tallChildren := P -> [[ DFT(P[1], P[2]) ]],\n\tforTransposition := false,\n\trule := (P,C) -> let(n := P[1], nn:=Int(n/2)+1, \n\t Mat(MatSPL(Gath(H(2n,n,0,2)))) \n\t #Tensor(I(n), Diag(1,0)) \n\t RC(C[1]) \n\t Mat(MatSPL(Scat(H(2n,2nn, 0, 1)))) \n\t)\n )\n));\n\nRulesFor(PRDFT2, rec(\n PRDFT2_Base1 := BaseRule(PRDFT2, [1, @]),\n PRDFT2_Base2 := BaseRule(PRDFT2, [2, @]),\n\n #F PRDFT2_CT: projection of DFT2_CT \n PRDFT2_CT := rec(\n\tisApplicable := P -> not IsPrime(P[1]),\n\tallChildren := P -> PRF12_CT_Children(P[1], P[2], PRDFT2, DFT2, PRDFT4, PRDFT1), \n\trule := (P,C) -> let(N:=P[1], k:=P[2], m:=Cols(C[1]),\n\t PRF12_CT_Rule(N, k, C, Diag(BHD(m,-1,1)), j->RC(Diag(fPrecompute(Twid(N,m,k,0,1/2,j+1)))))))\n));\n\nRulesFor(IPRDFT3, rec(\n IPRDFT3_Base1 := BaseRule(IPRDFT3, [1, @]),\n IPRDFT3_Base2 := BaseRule(IPRDFT3, [2, @]),\n\n IPRDFT3_CT := rec(\n\tisApplicable := P -> not IsPrime(P[1]),\n\tallChildren := P -> PRF12_CT_Children(P[1], P[2], IPRDFT3, DFT3, IPRDFT4, IPRDFT1), \n\trule := (P,C) -> let(N:=P[1], k:=P[2], m:=Rows(C[1]),\n\t IPRF12_CT_Rule(N, k, C, Diag(BHD(m,-1,1)), j->RC(Diag(fPrecompute(Twid(N,m,k,0,1/2,j+1)))))))\n));\n\n###########\n# Hartley #\n###########\n\nRulesFor(PDHT1, rec(\n PDHT1_Base2 := rec(\n\tisApplicable := P -> P[1]=2,\n\trule := (P, C) -> Tensor(I(2), Mat([[1],[1]])) * F(2)\n ),\n \n PDHT1_CT := rec(\n\tisApplicable := P -> not IsPrime(P[1]),\n\tallChildren := P -> PRF12_CT_Children(P[1], P[2], PDHT1, DFT1, PDHT3, PDHT1), \n\trule := (P,C) -> let(N:=P[1], k:=P[2], m:=Cols(C[1]),\n\t PRF12_CT_Rule(N, k, C, TopHalf(m, J(2)), j->HTwid(N,m,k,0,0,j+1,J(2)).obj)))\n));\n\nRulesFor(PDHT2, rec(\n PDHT2_Base2 := rec(\n\tisApplicable := P -> P[1]=2,\n\trule := (P, C) -> DirectSum(Mat([[1],[1]]), Mat([[1],[-1]])) * Mat(MatSPL(PRDFT2(P[1], P[2])){[1,4]})\n ),\n PDHT2_CT := rec(\n\tisApplicable := P -> not IsPrime(P[1]),\n\tallChildren := P -> PRF12_CT_Children(P[1], P[2], PDHT2, DFT2, PDHT4, PDHT1), \n\trule := (P,C) -> let(N:=P[1], k:=P[2], m:=Cols(C[1]),\n\t PRF12_CT_Rule(N, k, C, TopHalf(m, -J(2)), j->HTwid(N,m,k,0,1/2,j+1,-J(2)).obj)))\n));\n", "meta": {"hexsha": "082f04e9d3cbbd7bdfecbcfb8aa6843497cef9a1", "size": 8400, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/realdft/prf12.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/transforms/realdft/prf12.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/transforms/realdft/prf12.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 33.3333333333, "max_line_length": 128, "alphanum_fraction": 0.5135714286, "num_tokens": 3679, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8006920116079209, "lm_q2_score": 0.6370308082623217, "lm_q1q2_score": 0.5100654793237781}}
	{"text": "# Examples/Tests for ANATPH\n\n# Jack Button's Group\n# -------------------\n#\n# With presentation <a,b,t \| a^t = ab, b^t = ba>\n#\n# Alan Logan says this is hyperbolic, but noone wants to publish\n# this result alone.\n#\n# Tester now proves this to be hyperbolic, after corrected\n# relation. Bug reported by email by Chris Chalk <chalk235@gmail.com>\n#\nInstallGlobalFunction(\"JackButtonGroup\",\nfunction()\n local pg;\n\n pg := PregroupOfFreeGroup(3);\n SetPregroupElementNames(pg, \"1aAbBtT\");\n return NewPregroupPresentation(pg, [ pg_word( pg, [7,2,6,5,3])\n , pg_word( pg, [7,4,6,3,5]) ]);\nend);\n\n# Triangle Groups\n# ---------------\n# As demonstrated in Proposition 9.4 of anatph, for l > 2 (and hence n > 3 if the\n# group is supposed to be hyperbolic) there are no instantiable green places, and if\n# l = 2 then there are exactly two instantiable green places.\nInstallGlobalFunction(\"TriangleGroup\",\nfunction(l,m,n)\n local pg;\n pg := PregroupOfFreeProduct( CyclicGroup( IsPermGroup, l)\n , CyclicGroup( IsPermGroup, m) );\n\n # This is a bit icky, we can't tell which element of pg is the one of the\n # second cyclic group\n return NewPregroupPresentation(pg, [ pg_word( pg, Repeat(n, [2, l + 1]))]);\nend);\n\n# Example from Theorem 9.5, triangle-like: quotient of 2-3-m triangle group\n# our choice of pregroup is the free product of cyclic groups of order 2 and 3\n#T see what happens if we present this group as\n#T <x,y,z \| x^2, y^3, z^m, (zxY)^n > ?\n#T we push a parameter into the pregroup\nInstallGlobalFunction(TriangleCommutatorQuotient,\nfunction(m,n)\n local pg;\n pg := PregroupOfFreeProduct( CyclicGroup(IsPermGroup, 2)\n , CyclicGroup(IsPermGroup, 3) );\n # Do this to have slightly nicer display. Maybe we need to give the user\n # a way to label generators\n pg!.enams := \"1xyY\";\n return NewPregroupPresentation(pg,\n [ pg_word(pg, Repeat(m, [2,3])),\n pg_word(pg, Repeat(n, [2,3,2,4]))\n ]);\nend);\n\nInstallGlobalFunction(RandomTriangleQuotient,\nfunction(p,q,r,len)\n local pg;\n pg := PregroupOfFreeProduct( CyclicGroup(IsPermGroup, p)\n , CyclicGroup(IsPermGroup, q) );\n # Do this to have slightly nicer display. Maybe we need to give the user\n # a way to label generators\n pg!.enams := \"1xyY\";\n return NewPregroupPresentation(pg,\n [ pg_word(pg, Repeat(r, [2,3])),\n RandomPregroupWord(pg, len)\n ]);\nend);\n\nInstallGlobalFunction(RandomPregroupWord,\nfunction(pg, len)\n local i, lett, rel;\n\n rel := [];\n\n rel[1] := Random([2..Size(pg)]);\n for i in [2..len-1] do\n rel[i] := Random(Difference( [2..Size(pg)]\n , [__ID(PregroupInverse(pg[rel[i-1]]))]));\n od;\n rel[len] := Random(Difference([2..Size(pg)]\n , [ __ID(PregroupInverse(pg[rel[len - 1]]))\n , __ID(PregroupInverse(pg[rel[1]]))\n ] ));\n return pg_word(pg, rel);\nend);\n\n# Given a pregroup make a random presentation with nrel relators\n# of length lrel\nInstallGlobalFunction(RandomPregroupPresentation,\nfunction(pg, nrel, lrel)\n local rels;\n\n rels := List([1..nrel], i -> RandomPregroupWord(pg, lrel));\n return NewPregroupPresentation(pg, rels);\nend);\n\n\nBindGlobal(\"CreateRandomExample\",\nfunction(path, pg, nrel, lrel)\n local pgp;\n\n if not IsDirectoryPath(path) then\n Error(\"path does not exist or is not a directory\");\n return;\n fi;\n pgp := RandomPregroupPresentation(pg, nrel, lrel);\n\n # Write the pregroup presentation to file\n PregroupPresentationToFile(Concatenation(path, \"/presentation-gap\"), pgp);\n PregroupPresentationToSimpleFile(Concatenation(path, \"/presentation-simple\"), pgp);\n\n if WALRUS_kbmag_available then\n # Also create a KBMAG input file, if RSymTest succeeds on this presentation,\n # we can try computing an automatic structure and run gpgeowa on the result\n # to check whether the group is hyperbolic.\n WriteRWS(KBMAGRewritingSystem(PregroupPresentationToFpGroup(pgp)),\n Concatenation(path, \"/presentation-kbmag\"));\n fi;\nend);\n\n# Create a series of examples\nBindGlobal(\"CreateRandomSeries\",\nfunction(pg, nrels, lrels, nexs, prf, basepath)\n local path, path2, i, pgp, lrel, nrel;\n\n if not IsDirectoryPath(basepath) then\n Error(\"path does not exist or is not a directory\");\n return;\n fi;\n path := basepath;\n\n for lrel in lrels do\n CreateDir(Concatenation(path, \"/\", String(lrel)));\n for nrel in nrels do\n CreateDir(Concatenation(path, \"/\", String(lrel), \"/\", String(nrel)));\n for i in [1..nexs] do\n path2 := Concatenation(path, \"/\", String(lrel), \"/\", String(nrel), \"/\", String(i));\n prf(\"creating example nr \", i, \" in \", path2, \" \\c\");\n\n CreateDir(path2);\n CreateRandomExample(path2, pg, nrel, lrel);\n prf(\"\\n\");\n od;\n od;\n od;\nend);\n\nBindGlobal(\"CreateRandomSeriesOverSmallPregroups\",\nfunction(basepath)\n local i, n, sizes, path;\n\n if not IsDirectoryPath(basepath) then\n Error(\"path does not exist or is not a directory\");\n return;\n fi;\n\n # at the moment we only have pregroups\n # of size 6\n sizes := [6];\n for n in sizes do\n CreateDir(Concatenation(basepath, \"/\", String(n)));\n for i in [1..NrSmallPregroups(n)] do\n path := Concatenation(basepath, \"/\", String(n), \"/\", String(i));\n CreateDir(path);\n CreateRandomSeries( SmallPregroup(n, i)\n , [1,2,4,8,10]\n , [5,10,15,20,25,30,35,40,45,50]\n , 20\n , Print\n , path);\n od;\n od;\nend);\n\nBindGlobal(\"CreateRandomSeriesOverFreeGroup\",\nfunction(basepath)\n local i, n, sizes, path;\n\n if not IsDirectoryPath(basepath) then\n Error(\"path does not exist or is not a directory\");\n return;\n fi;\n\n # ranks of free group\n sizes := [2,4,8,16,32,64];\n for n in sizes do\n path := Concatenation(basepath, \"/\", String(n));\n CreateDir(path);\n CreateRandomSeries( PregroupOfFreeGroup(n)\n , [1,2,4,8,10]\n , [5,10,15,20,25,30,35,40,45,50]\n , 20\n , Print\n , path);\n od;\nend);\n\nBindGlobal(\"CreateRandomSeriesOverTrianglePregroup\",\nfunction(eps, p, q, nrel, lrel, nexs, prf, path)\n local pg;\n pg := PregroupOfFreeProduct( CyclicGroup( IsPermGroup, p)\n , CyclicGroup( IsPermGroup, q) );\n pg!.enams := \"1xyY\";\n CreateRandomSeries( pg\n , [1]\n , [5,10,15,20,25,30,35,40,45,50]\n , 20\n , Print\n , path );\nend);\n\nBindGlobal(\"CreateRandomSeriesOverTriangleGroup\",\n function(eps, p, q, nrel, lrel, nexs, prf, path)\n local pg;\n pg := PregroupOfFreeProduct( CyclicGroup( IsPermGroup, p)\n , CyclicGroup( IsPermGroup, q) );\n pg!.enams := \"1xyY\";\n CreateRandomSeries( pg\n , [1]\n , [5,10,15,20,25,30,35,40,45,50]\n , 20\n , Print\n , path );\n end);\n\n\n\nBindGlobal(\"BenchmarkRandomPresentation\",\nfunction(pg, eps, nrel, lrel, nexs, prf, path)\n local i, pgp, start, stop, estart, estop, n, nfail, res, runt, fid, stream;\n\n n := 0;\n runt := [];\n\n start := NanosecondsSinceEpoch();\n for i in [1..nexs] do\n prf(\"creating example nr \", i, \", \\c\");\n pgp := RandomPregroupPresentation(pg, nrel, lrel);\n prf(\"starting RSymTest, \\c\");\n estart := NanosecondsSinceEpoch();\n res := RSymTest(pgp, eps);\n estop := NanosecondsSinceEpoch();\n if res = true then\n prf(\"succeeded after \\c\");\n else\n prf(\"failed \\c\");\n fi;\n# LogPregroupPresentation(path, pgp, res);\n prf(Float((estop - estart) / 1000000000), \" seconds\\n\");\n Add(runt, [pgp, res, estop - estart]);\n od;\n stop := NanosecondsSinceEpoch();\n return rec( runtime := (stop - start) / 1000000000,\n samples := runt );\nend);\n\nBindGlobal(\"RandomPregroupFromSmallGroups\",\nfunction()\n local n, i, g1, g2;\n\n n := Random([1..64]);\n i := Random([1..NrSmallGroups(n)]);\n g1 := SmallGroup(n,i);\n\n n := Random([1..64]);\n i := Random([1..NrSmallGroups(n)]);\n g2 := SmallGroup(n,i);\n\n return PregroupOfFreeProduct(g1, g2);\nend);\n\nBindGlobal(\"BenchmarkRandom_TriPregroup\",\nfunction(eps, nrel, lrel, nexs, prf, path)\n local pg;\n pg := PregroupOfFreeProduct( CyclicGroup( IsPermGroup, 2)\n , CyclicGroup( IsPermGroup, 3) );\n pg!.enams := \"1xyY\";\n return BenchmarkRandomPresentation(pg, eps, nrel, lrel, nexs, prf, path);\nend);\n\nBindGlobal(\"BenchmarkRandom_FreeGroupPregroup\",\nfunction(eps, ngen, nrel, lrel, nexs, prf, path)\n local pg;\n pg := PregroupOfFreeGroup(ngen);\n return BenchmarkRandomPresentation(pg, eps, nrel, lrel, nexs, prf, path);\nend);\n\nBindGlobal(\"BenchmarkRandom_OverSmallPregroup\",\nfunction(eps, nrel, lrel, nexs, prf, path)\n local pg, res;\n\n res := [];\n # FIXME: We only have pregroups of size 6 at the moment\n for pg in ANATPH_small_pregroups[6] do\n pg := PregroupByTable([1,'a','b','c','d', 'e'], pg);\n Add(res, BenchmarkRandomPresentation(pg, eps, nrel, lrel, nexs, prf, path));\n od;\n return res;\nend);\n\nBindGlobal(\"_VARIANCE\",\nfunction(v)\n local q, avg;\n if Length(v) = 1 then\n q := 1;\n else\n q := Length(v) - 1;\n fi;\n avg := Average(v);\n return Sum(List(v, x -> (x - avg)^2)) / (q);\nend);\n\nBindGlobal(\"AnalyseBenchmarkResult\",\nfunction(res)\n local r, succed, failed;\n\n r := rec();\n\n r.n := Length(res.samples);\n r.rt_avg := Average(List(res.samples, x->x[3]));\n r.rt_std := Sqrt(Float(_VARIANCE(List(res.samples, x->x[3]))));\n\n succed := Filtered(res.samples, x -> not IsList(x[2]));\n r.succed_n := Length(succed);\n if r.succed_n > 0 then\n r.succed_rt_avg := Average(List(succed, x->x[3]));\n r.succed_rt_std := Sqrt(Float(_VARIANCE(List(succed, x->x[3]))));\n fi;\n\n failed := Filtered(res.samples, x -> IsList(x[2]));\n r.failed_n := Length(failed);\n if r.failed_n > 0 then\n r.failed_rt_avg := Average(List(failed, x->x[3]));\n r.failed_rt_std := Sqrt(Float(_VARIANCE(List(failed, x->x[3]))));\n fi;\n\n return r;\nend);\n\nBindGlobal(\"StringBenchResult\",\nfunction(r)\n local res;\n \n res := STRINGIFY(\"n: \", r.n, \", s: \", r.succed_n, \" f: \", r.failed_n, \" (\", Float(r.succed_n) / r.n, \")\\n\",\n \" (\", Float(r.rt_avg), \",\", r.rt_std, \")\\n\");\n Append(res, STRINGIFY(\" success: \", r.succed_n));\n if r.succed_n > 0 then\n Append(res, STRINGIFY(\" \", Float(r.succed_rt_avg), \",\", r.succed_rt_std, \"\\n\"));\n fi;\n Append(res, STRINGIFY(\" failure: \", r.failed_n));\n if r.failed_n > 0 then\n Append(res, STRINGIFY(\" \", Float(r.failed_rt_avg), \",\", r.failed_rt_std, \"\\n\"));\n fi;\n if res[Length(res)] <> '\\n' then\n Add(res, '\\n');\n fi;\n return res;\nend);\n \nBindGlobal(\"StandardBenchmarks\",\nfunction(nsamples, prn)\n local d, ngens, rlen, nrels, r, path;\n\n path := DirectoryTemporary(); \n prn(\"running standard benchmarks for anatph, \", nsamples, \" each\\n\");\n\n prn(\"= = = = = = =\\n\");\n prn(\" Quotients of free group pregroup\\n\");\n prn(\"= = = = = = =\\n\");\n for ngens in [2,4,8,16] do\n for nrels in [1,2,3,4] do\n for rlen in [10,20,30,40,50] do\n prn(\"running \"\n , ngens, \" generators, \"\n , nrels, \" relators \"\n , \"of length \", rlen, \"\\n\");\n r := BenchmarkRandom_FreeGroupPregroup(\n 1/12\n , ngens\n , nrels\n , rlen\n , nsamples\n , prn\n , path\n );\n prn(StringBenchResult(AnalyseBenchmarkResult(r)));\n od;\n od;\n od;\n\n prn(\"= = = = = = =\\n\");\n prn(\" Quotients of 2-3-triangle group pregroup\\n\");\n prn(\"= = = = = = =\\n\");\n for nrels in [1,2,3,4] do\n for rlen in [10,20,30,40,50] do\n prn(\"running \", nrels, \"relators of length \", rlen, \"\\n\");\n r := BenchmarkRandom_TriPregroup(\n 1/12\n , nrels\n , rlen\n , nsamples\n , prn\n , path\n );\n prn(StringBenchResult(AnalyseBenchmarkResult(r)));\n od;\n od;\n\nend);\n\nBenchmarkSinglePres := function(eps, pg, nrel, len)\n local r,t,res;\n r := RandomPregroupPresentation(pg, nrel, len);\n t := NanosecondsSinceEpoch();\n res := RSymTest(r, eps);\n t := NanosecondsSinceEpoch() - t;\n return [r, res, t / 1000000000.];\nend;\n\nif IsBound(OutputAnnotatedCodeCoverageFiles) then\n ProfileSinglePresentation := function(eps, pg, nrel, len)\n local t, dir, fn;\n\n dir := DirectoryTemporary();\n fn := Filename(dir, \"anatph.gz\");\n\n Print(\"Profiling presentation to \", fn, \"\\n\");\n ProfileLineByLine(fn);\n t := BenchmarkSinglePres(eps, pg, nrel, len);\n UnprofileLineByLine();\n\n Print(\"Writing annotated code coverage to \", Filename(dir, \"\"), \"\\n\");\n OutputAnnotatedCodeCoverageFiles(fn, Filename(dir, \"\"));\n\n return t;\nend;\n\nelse\n Print(\"profiling package is not available, disabling ProfileSinglePresentation\\n\");\nfi;\n\n# Benchmark the RSym tester with a presentation given <A>density</A>\n# and <A>length</A>\nBenchmarkGromovDensity := function(eps, ngens, length, density)\n local pg, nrels;\n\n pg := PregroupOfFreeGroup(ngens);\n nrels := Int( (2 * ngens - 1)^Float(density * length ) );\n Print(\"number of relators: \", nrels, \"\\n\");\n return BenchmarkSinglePres(eps\n , pg\n , nrels\n , length );\nend;\n\n\n\n\n\n", "meta": {"hexsha": "04e581d76fdff0eeb3f776176aee3ae669d861d5", "size": 15065, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "gap/examples.gi", "max_stars_repo_name": "RussWoodroofe/walrus", "max_stars_repo_head_hexsha": "f7a4e3597f288c6d9518aaa39091826dadc864b8", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-10-02T14:55:52.000Z", "max_stars_repo_stars_event_max_datetime": "2021-10-02T14:55:52.000Z", "max_issues_repo_path": "gap/examples.gi", "max_issues_repo_name": "RussWoodroofe/walrus", "max_issues_repo_head_hexsha": "f7a4e3597f288c6d9518aaa39091826dadc864b8", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 26, "max_issues_repo_issues_event_min_datetime": "2018-11-22T11:15:07.000Z", "max_issues_repo_issues_event_max_datetime": "2022-02-21T13:31:01.000Z", "max_forks_repo_path": "gap/examples.gi", "max_forks_repo_name": "RussWoodroofe/walrus", "max_forks_repo_head_hexsha": "f7a4e3597f288c6d9518aaa39091826dadc864b8", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 4, "max_forks_repo_forks_event_min_datetime": "2019-02-11T14:47:47.000Z", "max_forks_repo_forks_event_max_datetime": "2021-05-20T10:22:09.000Z", "avg_line_length": 32.4676724138, "max_line_length": 111, "alphanum_fraction": 0.5382011284, "num_tokens": 4052, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7956581000631542, "lm_q2_score": 0.640635854839898, "lm_q1q2_score": 0.509727107094248}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nunpacklo := (l1,l2,n,k) -> Flat(List([1..n/(2k)], i-> [\n List([1..k], j->l1[(i-1)k+j]),\n List([1..k], j->l2[(i-1)k+j])\n]));\n\nunpackhi := (l1,l2,n,k) -> Flat(List([1..n/(2k)], i -> [\n List([1..k], j->l1[n/2+(i-1)k+j]),\n List([1..k], j->l2[n/2+(i-1)k+j])\n]));\n\n# saturation in pack_semantic is not taken into account\npack_semantic := (l1, l2, n) -> Flat(List( [1..n], i -> [l1[i], l2[i]]));\n\nsparams := (l,n) -> List([1..l], i->[1..n]);\n\nshuffle := (in1, in2, p, n, k) -> Flat([\n List([1..n/(2k)], i->List([1..k], j->in1[(p[i]-1)k+j])),\n List([n/(2k)+1..n/k], i->List([1..k], j->in2[(p[i]-1)k+j]))\n]);\n\ninverse_ushuffle := (inp, p, n) -> List([1..n], i->inp[p[i]]);\n\nshufflehi := (in1, p, n, k) -> Concat(\n Sublist(in1, [1..n/2]),\n let(l := Sublist(in1, [n/2+1..n]), shuffle(l, l, p, n/2, k)));\n\nshufflelo := (in1, p, n, k) -> Concat(\n let(l := Sublist(in1, [1..n/2]), shuffle(l, l, p, n/2, k)),\n Sublist(in1, [n/2+1..n]));\n\niclshuffle := p -> Print(\"_MM_SHUFFLE\", When(Length(p)=2, \"2\", \"\"), \"(\", PrintCS(Reversed(p-1)), \")\");\n\niclprintop := self >> Print(self.icl, \"(\", _vcprintcs(self.args), \")\");\n\niperm4 := self >> Filtered(Cartesian(self.params()), i->i[1]<>i[2] and i[3] <> i[4]);\n\nvtakehi := (v) -> Checked(IsValue(v) and IsVecT(v.t) and v.t.size>1, TakeLast(v.v, Length(v.v)/2));\nvtakelo := (v) -> Checked(IsValue(v) and IsVecT(v.t) and v.t.size>1, Take(v.v, Length(v.v)/2));\n\n", "meta": {"hexsha": "5bbc5dca30ee4569ffb78c3ccd229ef47f63ca28", "size": 1529, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/platforms/sse/misc.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/platforms/sse/misc.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/platforms/sse/misc.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 33.9777777778, "max_line_length": 102, "alphanum_fraction": 0.5075212557, "num_tokens": 624, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7248702761768249, "lm_q2_score": 0.7025300698514777, "lm_q1q2_score": 0.5092431657557647}}
	{"text": "################################################################################\n##\n#W DwG_data.gi GroupTheoretical Package\n##\n#W Paul Bruillard, Cesar Galindo, Siu-Hung Ng, Julia Plavnik, Eric Rowell, \n#W Zhenghan Wang\n##\n## Installation file for DwG_data functions of the GroupTheoretical Package\n##\n#Y Copyright (C) 2016, Battelle Memorial Institute\n##\n################################################################################\n\n################################################################################\n##\n#F DwG_simples(<group>,<int>,<function>) . . . . . compute simples in D^w(G)\n##\nInstallGlobalFunction( DwG_simples, function(G,n,w)\n local x,Zx,wx,CC,SimpleObjects,projective_characters,chi;\n CC:=List(ConjugacyClasses(G),Representative);;\n SimpleObjects:=[];\n for x in CC do\n Zx:=Centralizer(G,x);\n wx:=function(g,h) return w(g,h,x)w(x,g,h)(w(g,x,h)^-1); end;;\n projective_characters:=projective_reps(Zx,wx,n);\n if not(Sum(List(projective_characters,chi->chi[1]^2))=Order(Zx)) then\n Display(\"ERROR\");\n fi;\n for chi in projective_characters do\n Append(SimpleObjects,[[x,chi,ConjugacyClass(G,x),wx,Zx]]);\n od;\n od;\n return SimpleObjects;\nend );\n\n################################################################################\n##\n#F DwG_S_and_T(<list>,<group>) . . . . . . . . . .compute S and T for D^w(G)\n##\nInstallGlobalFunction(DwG_S_and_T, function(Simples,G)\n local r,S,T,i,simple1,x,chi,Kx,betax,Zx,x_idx,Zx_Transversal,j,simple2,y,chi_prime,Ky,betay,Zy,Zy_Transversal,a,g,Zg,b,g_prime,h_prime,h,h_idx,h_prime_idx;\n\n r:=Length(Simples);\n S:=NullMat(r,r);;\n T:=List([1..r],i->0);\n for i in [1..r] do\n simple1:=Simples[i];\n x:=simple1[1];\n chi:=simple1[2];\n Kx:=simple1[3];\n betax:=simple1[4];\n Zx:=simple1[5];\n #x_idx:=Position(GSet,x);\n x_idx:=Position(AsSet(Zx),x);\n T[i]:=chi[x_idx]/chi[Position(AsSet(Zx),Identity(Zx))];\n Zx_Transversal:=RightTransversal(G,Zx);\n for j in [i..r] do\n simple2:=Simples[j];\n y:=simple2[1];\n chi_prime:=simple2[2];\n Ky:=simple2[3];\n betay:=simple2[4];\n Zy:=simple2[5];\n #y_idx:=Position(GSet,y);\n Zy_Transversal:=RightTransversal(G,Zy);\n for a in Zx_Transversal do\n g:=(a^-1)xa;\n if not(g in Kx) then\n continue;\n fi;\n Zg:=Centralizer(G,g);\n for b in Zy_Transversal do\n g_prime:=(b^-1)yb;\n if not((g_prime in Ky) and (g_prime in Zg)) then\n continue;\n fi;\n h_prime:=bg(b^-1);\n h:=ag_prime(a^-1);\n h_idx:=Position(AsSet(Zx),h);\n h_prime_idx:=Position(AsSet(Zy),h_prime);\n S[i][j]:=S[i][j]+betax(a,g_prime)betax(ag_prime,a^-1)betay(b,g)betay(bg,b^-1)(betax(a,a^-1)^-1)(betay(b,b^-1)^-1)chi[h_idx]*chi_prime[h_prime_idx];\n od;\n od;\n S[j][i]:=S[i][j];\n od;\n od;\n\n return [S,T];\nend);\n\n################################################################################\n##\n#F DwG_data(<group>,<function>,<int>) . . . . . compute data of D^w(G)\nInstallGlobalFunction(DwG_data,function(G,w,n)\n local Simples, S_and_T, pseudounitary_data, S, T, N, FPdimC, FPdim,sorted_data;\n Simples := DwG_simples(G,n,w);;\n S_and_T := DwG_S_and_T(Simples,G);;\n S := S_and_T[1];\n T := S_and_T[2];\n pseudounitary_data := pseudounitary_sort(S,T,Simples);\n Simples := pseudounitary_data[1];\n S := pseudounitary_data[2];\n T := pseudounitary_data[3];\n FPdim := pseudounitary_data[4];\n FPdimC := pseudounitary_data[5];\n sorted_data := dimension_sort(S,T,Simples,FPdim);\n Simples := sorted_data[1];\n S := sorted_data[2];\n T := sorted_data[3];\n FPdim := sorted_data[4];\n N:=compute_fusion_rules(S,FPdimC);;\n return [Simples, S, T, N, FPdim, FPdimC];;\nend);\n\n#E DwG_data.gi . . . . . . . . . . . . . . . . . . . . . . . . . . . . ends here\n", "meta": {"hexsha": "f109434edba9de23abb2ae616b8ab0106c39ab1a", "size": 3879, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "lib/DwG_data.gi", "max_stars_repo_name": "pnnl/GroupTheoretical", "max_stars_repo_head_hexsha": "d60aaec27d2ca98ec55b12b78213538a346eef27", 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"num_tokens": 1214, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8080672320414786, "lm_q2_score": 0.6297746143530797, "lm_q1q2_score": 0.5089002294302827}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n#D TL.withTags := (self, tags) >> CopyFields(self, rec(params := [self.params[1], self.params[2], self.params[3], self.params[4], tags]));\n#D TL.getTags := self >> self.params[self.tagpos];\n\nDoubleDivisorPairs:=function(n,m)\n local a,b,l;\n l:=[];\n for a in DivisorPairs(n) do\n Append(l,[Concatenation(a,[1,m]),Concatenation(a,[m,1])]);\n for b in DivisorPairs(m) do\n Append(l,[Concatenation(a,b)]);\n od;\n od;\n for b in DivisorPairs(m) do\n Append(l,[Concatenation([n,1],b),Concatenation([1,n],b)]);\n od;\n return l;\nend;\n\nVectorDivisible:=function(m,c,k,b,v)\n#not yet taken into account : b or c =1\n local leftpart,rightpart;\n leftpart := v in DivisorsInt(c) or m=1 or (b=1 and k=1);\n rightpart:= v in DivisorsInt(b) or c=1 or k=1;\n return leftpart and rightpart;\nend;\n\nDoubleDivisorPairsVector:=function(n,m,v)\n return Filtered(DoubleDivisorPairs(n,m) , a -> VectorDivisible(a[1],a[2],a[3],a[4],v));\nend;\n\nBlocking:=function(m,c,k,b,v)\n local t, nv, PageSize, CacheLineSize;\n t:=128/v;\n PageSize:=410248(2);\n nv:=mckbt;\n if (nv>PageSize) then\n return When((PageSize/8<=bct)and(bct<=PageSize),true,false);\n\n #CacheLineSize:=648(4);\n #else\n #if (nv>CacheLineSize) then\n #return When((CacheLineSize/8<=bct)and(bct<=CacheLineSize),true,false);\n #fi;\n fi;\n return true;\nend;\n\nDoubleDivisorPairsVectorBlocking:=function(n,m,v)\n return Filtered(DoubleDivisorPairsVector(n,m,v), a->Blocking(a[1],a[2],a[3],a[4],v));\nend;\n\nNewRulesFor(TL,rec(\n L_cx_real := rec(\n switch:=false,\n forTransposition := false,\n applicable := t -> t.isTag(1, AVecRegCx) and let(P := t.params, P[1] = P[2]^2), #FF: NOTE!! can only terminate symmetrical ones...\n children := nt -> let(P:=nt.params, [[TL(P[1], P[2], P[3], P[4]2).withTags([AVecReg(nt.getTags()[1].isa)])]]),\n apply := (t, C, Nonterms) -> CR(When(t.params[1]=t.params[2]^2, SymSPL(C[1]), C[1]))\n ),\n\n L_base_vec := rec(\n switch:=false,\n forTransposition := false,\n applicable := t -> t.isTag(1, AVecReg) or t.isTag(1, AVecRegCx),\n apply := (t, C, Nonterms) -> let(\n C1:=When(t.params[3]=1, [], [I(t.params[3])]),\n C2:=When(t.params[4]=1, [], [I(t.params[4])]),\n Tensor(Concat(C1, [L(t.params[1], t.params[2])], C2))\n )\n#D applicable := (self, t) >> FirstTagEq(t, AVecReg) or FirstTagEq(t, AVecRegCx),\n#D apply := (t, C, Nonterms) -> let(C1:=When(t.params[3]=1, [], [I(t.params[3])]), \n#D C2:=When(t.params[4]=1, [], [I(t.params[4])]), Tensor(Concat(C1, [L(t.params[1], t.params[2])], C2)))),\n ),\n\n\n #L^mn_m -> (L^mn/v_m x I_v)(I_mn/v2 x L^v2_v)(I_n/v x L^m_m/v x I_v)\n L_mn_m_vec := rec(\n forTransposition := false,\n freedoms := (self, t) >> [],\n applicable := t ->\n t.params[3] = 1\n and t.params[4] = 1\n and (t.isTag(1, AVecReg) or t.isTag(1, AVecRegCx))\n and let(\n v := t.firstTag().v,\n m := t.params[2],\n n := t.params[1] / m,\n IsInt(m/v)\n and IsInt(n/v)\n and not (\n t.params[1] = vv\n and t.params[2] = v\n )\n ),\n child := (nt,freedoms) -> let (v := nt.firstTag().v, [ TL(vv, v, 1, 1).withTags(nt.getTags()) ] ),\n\n apply := (nt, C, cnt) -> let(\n v := nt.firstTag().v,\n v2 := vv,\n m := nt.params[2],\n n := nt.params[1]/m,\n VTensor(L(mn/v, m), v)\n * SymSPL(BlockVPerm(mn/v2, v, C[1], L(v^2,v)))\n VTensor(Tensor(I(n/v), L(m,m/v)), v)\n )\n\n#D applicable := (self, t) >> t.params[3] = 1 and t.params[4] = 1 and FirstTagEq(t, AVecReg) and\n#D let (v := GetFirstTag(t).v, m:=t.params[2], n:= t.params[1]/m,\n#D IsInt(m/v) and IsInt(n/v) and not(t.params[1]=vv and t.params[2]=v)) ,\n#D\n#D child := (nt,freedoms) -> let (v := GetFirstTag(nt).v, [TL(vv, v, 1, 1, GetTags(nt))]),\n#D\n#D apply := (nt,C,cnt) -> let(v:=GetFirstTag(nt).v, v2:=vv, m:=nt.params[2], n:= nt.params[1]/m,\n#D VTensor(L(mn/v, m), v) \n#D SymSPL(BlockVPerm(mn/v2, v, C[1], L(v^2,v))) \n#D VTensor(Tensor(I(n/v), L(m,m/v)), v))),\n ),\n\n#SymSPL-BlockVPerm can be replaced by Tensor(I(mn/v2), C[1])\n\n#L^mn_m could probably also be splitted like that:\n\n# #L^mn_m -> (L^mn/v_m x I_v)(I_mn/v2 x L^v2_v)(I_n/v x L^m_m/v x I_v)\n# L_mn_m_vec := rec(\n# forTransposition := false,\n# applicable := (self, t) >> t.params[3] = 1 and t.params[4] = 1 and FirstTagEq(t, AVecReg) and\n# let (v := GetFirstTag(t).v, m:=t.params[2], n:= t.params[1]/m,\n# IsInt(m/v) and IsInt(n/v)),\n\n# freedoms := (self, t) >> [],\n# child := (nt,freedoms) -> let (v := GetFirstTag(nt).v, m:=nt.params[2], n:= nt.params[1]/m,\n# [TL(mn/v, m, 1, v, GetTags(nt)),\n# TL(vv, v, mn/(vv), 1, GetTags(nt)),\n# TL(m,m/v,n/v, v, GetTags(nt))]),\n# apply := (nt,C,cnt) -> let(v:=GetFirstTag(nt).v, v2:=vv, m:=nt.params[2], n:= nt.params[1]/m, C[1] C[2] * C[3])),\n\n# #I x L -> BlockVPerm\n# IxLxI_BlockVPerm := rec(\n# forTransposition := false,\n# applicable := (self, t) >> FirstTagEq(t, AVecReg) and (t.params[4]=1)\n# and let (v := GetFirstTag(t).v, (t.params[1]=vv) and (t.params[2]=v)),\n# freedoms := (self, t) >> [],\n# child := (nt,freedoms) -> let (v := GetFirstTag(nt).v,[TL(vv, v, 1, 1, GetTags(nt))]),\n# apply := (t, C, cnt) -> let(v:=GetFirstTag(t).v,\n#SymSPL(BlockVPerm(t.params[3], v, C[1], DropTag(cnt[1]))))),\n\n\n #A x I_v -> VTensor\n IxLxI_vtensor := rec(\n forTransposition := false,\n applicable := t ->\n (\n t.isTag(1, AVecReg)\n or t.isTag(1, AVecRegCx)\n )\n and IsPosInt(t.params[4] / t.firstTag().v),\n apply := (t, C, Nonterms) -> let(\n v:=t.firstTag().v,\n l1 := When(t.params[3] > 1, [I(t.params[3])], []),\n l2 := When(t.params[4]/v > 1, [I(t.params[4]/v)], []),\n VTensor(Tensor(Concat(l1, [L(t.params[1], t.params[2])], l2)), v)\n )\n#D applicable := (self, t) >> (FirstTagEq(t, AVecReg) or FirstTagEq(t, AVecRegCx)) and\n#D let(v:=GetFirstTag(t).v, IsPosInt(t.params[4]/v)),\n#D apply := (t, C, Nonterms) -> let(v:=GetFirstTag(t).v, l1:= When(t.params[3] > 1, [I(t.params[3])], []), l2:=When(t.params[4]/v > 1, [I(t.params[4]/v)], []) , VTensor(Tensor(Concat(l1, [L(t.params[1], t.params[2])], l2)), v))),\n ),\n\n#GV1 shouldn't be enabled for stuff that are not strides!\n#It is highly disruptive because it doesn't respect the VTensor VPerm nomenclatura\n#F L_GV1: TL(kmbc,kb,r,s) = I_r tensor ((L(kbm,bk) tensor I_c) * (I_m tensor TL(bc,b,k,1)) * (I_m tensor L(kc,k) tensor I_b)) tensor I_s\n L_GV1 := rec(\n switch:=false,\n forTransposition := false,\n freedoms := nt -> [\n MapN(\n DoubleDivisorPairsVector(nt.params[1] / nt.params[2], nt.params[2], nt.firstTag().v),\n (m,c,k,b) -> [b,c]\n )\n ],\n child := (nt,freedoms) -> let(b:=freedoms[1][1],c:=freedoms[1][2], [TL(bc,b,1,1).withTags(nt.getTags())]),\n apply := (nt,C,cnt) -> let(\n n:=nt.params[1],\n b:=cnt[1].params[2],\n c:=cnt[1].params[1]/b,\n k:=nt.params[2]/b,\n m:=nt.params[1]/(kbc),\n r:=nt.params[3],\n s:=nt.params[4],\n Tensor(\n I(r),\n Tensor(\n Tensor(L(kbm,bk),I(c))\n * Tensor(I(m),Tensor(I(k),C[1]))\n * Tensor(Tensor(I(m),L(kc,k)),I(b)),\n I(s))\n )\n )\n#D freedoms := nt -> [MapN(DoubleDivisorPairsVector(nt.params[1]/nt.params[2],nt.params[2],GetFirstTag(nt).v),(m,c,k,b) -> [b,c])],\n#D child := (nt,freedoms) -> let(b:=freedoms[1][1],c:=freedoms[1][2], [TL(bc,b,1,1,GetTags(nt))]),\n#D apply := (nt,C,cnt) -> let(\n#D n:=nt.params[1],b:=cnt[1].params[2],c:=cnt[1].params[1]/b,k:=nt.params[2]/b,m:=nt.params[1]/(kbc),r:=nt.params[3],s:=nt.params[4],\n#D Tensor(I(r),(Tensor(\n#D Tensor(L(kbm,bk),I(c))\n#D Tensor(I(m),Tensor(I(k),C[1]))\n#D Tensor(Tensor(I(m),L(kc,k)),I(b))\n#D , I(s)))))),\n ),\n\n\n L_GV1_vtensor := rec(\n switch:=false,\n forTransposition := false,\n applicable := nt -> let(p := nt.params,\n nt.isTag(1, AVecReg)\n and p[1] <> p[2]\n and p[2] <> 1\n and Length(\n DoubleDivisorPairsVectorBlocking(p[1] / p[2], p[2], nt.firstTag().v)\n ) > 0\n ),\n freedoms := nt -> let(p := nt.params, [\n MapN(\n DoubleDivisorPairsVectorBlocking(p[1] / p[2], p[2], nt.firstTag().v),\n (m,c,k,b) -> [b,c]\n )\n ]),\n child := (nt, freedoms) -> let(\n b:=freedoms[1][1],\n c:=freedoms[1][2],\n [ TL(bc,b,1,1).withTags(nt.getTags()) ]\n ),\n apply := (nt,C,cnt) -> let(\n n := nt.params[1],\n b := cnt[1].params[2],\n c := cnt[1].params[1]/b,\n k := nt.params[2]/b,\n m := nt.params[1]/(kbc),\n r := nt.params[3],\n s := nt.params[4],\n v := nt.firstTag().v,\n# garbage:=fPrint([\"n:\",n,\" b:\",b,\" c:\",c,\" k:\",k,\" m:\",m,\" r:\",r,\" s:\",s, \" v:\",v,\"\\n\"]),\n prefactor := When(r = 1, [], [I(r)]),\n firstfactor := When(m = 1 or (b = 1 and k = 1),\n [],\n [When(c=1,L(kbm,bk), VTensor(Tensor(L(kbm,bk),I(c/v)),v))]\n ),\n middlefactor := [ Tensor(I(m), Tensor(I(k), C[1])) ],\n# middlefactor:=When(k>1 and bc<1024,[Tensor(I(m),I(k/2),BB(Tensor(I(2),C[1])))],[Tensor(I(m),Tensor(I(k),C[1]))]),\n thirdfactor := When(c=1 or k=1,\n [],\n [\n When(b=1,\n Tensor(I(m),L(kc,k)),\n VTensor(Tensor(I(m),L(kc,k),I(b/v)),v)\n )\n ]\n ),\n postfactor := When(r=s, [], [I(s)]),\n\n Tensor(Concat(\n prefactor,\n [Compose(Concat(\n firstfactor,\n middlefactor,\n thirdfactor\n ))],\n postfactor\n ))\n )\n#D applicable := (self, nt)>> FirstTagEq(nt, AVecReg) and (nt.params[1]<>nt.params[2]) and (nt.params[2]<>1) and\n#D (Length(DoubleDivisorPairsVectorBlocking(nt.params[1]/nt.params[2],nt.params[2],GetFirstTag(nt).v))>0),\n#D freedoms := nt -> [MapN(DoubleDivisorPairsVectorBlocking(nt.params[1]/nt.params[2],nt.params[2],GetFirstTag(nt).v),(m,c,k,b) -> [b,c])],\n#D child := (nt,freedoms) -> let(b:=freedoms[1][1],c:=freedoms[1][2], [TL(bc,b,1,1,GetTags(nt))]),\n#D apply := (nt,C,cnt) -> let(\n#D n:=nt.params[1],b:=cnt[1].params[2],c:=cnt[1].params[1]/b,k:=nt.params[2]/b,m:=nt.params[1]/(kbc),r:=nt.params[3],s:=nt.params[4],v:=GetFirstTag(nt).v,\n#D# garbage:=fPrint([\"n:\",n,\" b:\",b,\" c:\",c,\" k:\",k,\" m:\",m,\" r:\",r,\" s:\",s, \" v:\",v,\"\\n\"]),\n#D prefactor :=When(r=1, [], [I(r)]),\n#D firstfactor:=When(m=1 or (b=1 and k=1), [],[When(c=1,L(kbm,bk), VTensor(Tensor(L(kbm,bk),I(c/v)),v))]),\n#D middlefactor:=[Tensor(I(m),Tensor(I(k),C[1]))],\n#D# middlefactor:=When(k>1 and bc<1024,[Tensor(I(m),I(k/2),BB(Tensor(I(2),C[1])))],[Tensor(I(m),Tensor(I(k),C[1]))]),\n#D thirdfactor:=When(c=1 or k=1, [], [When(b=1,Tensor(I(m),L(kc,k)), VTensor(Tensor(I(m),L(kc,k),I(b/v)),v))]),\n#D postfactor :=When(r=s, [], [I(s)]),\n#D Tensor(Concat(\n#D prefactor,\n#D [Compose(Concat(\n#D firstfactor,\n#D middlefactor,\n#D thirdfactor))\n#D ],\n#D postfactor))))\n )\n));\n\n\n\n\n\n\n######################################################################\n# OBSOLETE RULES\n######################################################################\n\nNewRulesFor(TL,rec(\n\n # L^nv_n -> (I_n/v x L^v2_v)(L^n_n/v x I_v)\n # superseeded by L_mn_m_vec with n=v\n L_nv_n_vec := rec(\n switch := false,\n forTransposition := false,\n applicable := t ->\n t.params[3] = 1\n and t.params[4] = 1\n and (t.isTag(1, AVecReg) or t.isTag(1, AVecRegCx))\n and let (v := t.firstTag().v,\n t.params[1] = t.params[2] * v\n and t.params[2] <> v\n and IsInt(t.params[2]/v)\n ),\n freedoms := (self, t) >> [],\n child := (nt,freedoms) -> let(\n v := nt.firstTag().v,\n [ TL(vv, v, 1, 1).withTags(nt.getTags()) ]\n ),\n apply := (nt, C, cnt) -> let (\n v := nt.firstTag().v,\n n := nt.params[2],\n SymSPL(\n BlockVPerm(n/v, v, C[1], L(v^2,v))\n ) VTensor(L(n, n/v), v)\n )\n#D applicable := (self, t) >> t.params[3] = 1 and t.params[4] = 1 and FirstTagEq(t, AVecReg) and\n#D let (v := GetFirstTag(t).v, t.params[1] = t.params[2] * v and t.params[2] <> v and IsInt(t.params[2]/v)),\n#D freedoms := (self, t) >> [],\n#D child := (nt,freedoms) -> let (v := GetFirstTag(nt).v, [TL(vv, v, 1, 1, GetTags(nt))]),\n#D apply := (nt,C,cnt) -> let (v := GetFirstTag(nt).v, n:= nt.params[2], SymSPL(BlockVPerm(n/v, v, C[1], L(v^2,v))) VTensor(L(n, n/v), v))),\n #SymSPL-BlockVPerm can be replaced by Tensor(I(n/v), C[1])\n ),\n\n\n\n #L^nv_v -> (L^n_v x I_v)(I_n/v x L^v2_v)\n # superseeded by L_mn_m_vec with m=v\n L_nv_v_vec := rec(\n switch := false,\n forTransposition := false,\n applicable := t ->\n t.params[3] = 1\n and t.params[4] = 1\n and (t.isTag(1, AVecReg) or t.isTag(1, AVecRegCx))\n and let(v := t.firstTag().v,\n t.params[2] = v\n and t.params[1] <> v * v\n and IsInt(t.params[1]/(vv))\n ),\n freedoms := (self, t) >> [],\n child := (nt, freedoms) -> let(v := nt.firstTag().v, [ TL(vv, v, 1, 1).withTags(nt.getTags()) ]),\n apply := (nt, C, cnt) -> let(\n v := nt.firstTag().v,\n n:= nt.params[1]/v,\n VTensor(L(n, v), v)\n * SymSPL(BlockVPerm(n/v, v, C[1], L(v^2,v)))\n )\n#D applicable := (self, t) >> t.params[3] = 1 and t.params[4] = 1 and FirstTagEq(t, AVecReg) and\n#D let (v := GetFirstTag(t).v, t.params[2] = v and t.params[1] <> v * v and IsInt(t.params[1]/(vv))),\n#D freedoms := (self, t) >> [],\n#D child := (nt,freedoms) -> let (v := GetFirstTag(nt).v, [TL(vv, v, 1, 1, GetTags(nt))]),\n#D apply := (nt,C,cnt) -> let (v := GetFirstTag(nt).v, n:= nt.params[1]/v, VTensor(L(n, v), v) * SymSPL(BlockVPerm(n/v, v, C[1], L(v^2,v))))),\n #SymSPL-BlockVPerm can be replaced by Tensor(I(n/v), C[1])))\n )\n\n));\n", "meta": {"hexsha": "cb4ed63170949666cb18313f65c2960282a64c40", "size": 15597, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/vector/breakdown/tl_rec.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/paradigms/vector/breakdown/tl_rec.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", 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	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n#F Perm_CCS(<n>) - SPL objects for CCS -> Perm IPP data format conversion\n#F \n#F Returns an SPL object that converts the result of an RDFT in CCS format into\n#F Perm format. Both of these formats are defined in the IPP manual. \n#F IPP manual does not define Perm format for odd RDFT size, so in this case\n#F we defined it to coincide with CCS.\n#F\n#F The output of SPIRAL's PRDFT transform is equivalent to IPP CCS format. \n#F Suggested uses are:\n#F Perm_CCS(n) * PRDFT(n) \n#F IPRDFT(n) * Perm_CCS(n).transpose()\n#F \nPerm_CCS := n -> When(IsEvenInt(n), \n Gath(H(n+2,n,0,1))Perm((2,n+1),n+2),\n DirectSum(Mat([[1,0]]), I(n-1))\n);\n\n\n#F Pack_CCS(<n>) - SPL objects for CCS -> Pack IPP data format conversion of RDFT of type 1\n#F \n#F Returns an SPL object that converts the result of an RDFT in CCS format into\n#F Pack format. Both of these formats are defined in the IPP manual. \n#F\n#F The output of SPIRAL's PRDFT transform is equivalent to IPP CCS format. \n#F Suggested uses are:\n#F Pack_CCS(n) PRDFT(n) \n#F IPRDFT(n) * Pack_CCS(n).transpose()\n#F \nPack_CCS := n -> When(IsEvenInt(n), \n DirectSum(Mat([[1,0]]), When(n=2, [], I(n-2)), Mat([[1,0]])),\n DirectSum(Mat([[1,0]]), I(n-1))\n);\n\n#F Pack_CCS(<n>) - SPL objects for CCS -> Pack IPP data format conversion of RDFT of type 3\n#F\n#F [ note that IPP does not have RDFT of type 3, we just use their format terminology ]\n#F Returns an SPL object that converts the result of an RDFT in CCS format into\n#F Pack format. Both of these formats are defined in the IPP manual. \n#F Perm format does not make sense for PRDFT3.\n#F\n#F The output of SPIRAL's PRDFT3 transform is equivalent to IPP CCS format. \n#F Suggested uses are:\n#F Pack_CCS3(n) * PRDFT3(n) \n#F PRDFT3(n).inverse() * Pack_CCS3(n).transpose()\n#F \nPack_CCS3 := n -> When(IsEvenInt(n), \n I(n), \n DirectSum(I(n-1), Mat([[1,0]]))\n);\n", "meta": {"hexsha": "b472c296f6f80a9e6ef3a469520c24b9dd61bf1f", "size": 1960, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/realdft/formats.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/transforms/realdft/formats.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/transforms/realdft/formats.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 35.6363636364, "max_line_length": 91, "alphanum_fraction": 0.6775510204, "num_tokens": 627, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.800692021119887, "lm_q2_score": 0.6334102705979902, "lm_q1q2_score": 0.5071665497631993}}
	{"text": "############################################################################\n##\n## primitive.gi IRREDSOL Burkhard Höfling\n##\n## Copyright © 2003–2016 Burkhard Höfling\n##\n\n\n############################################################################\n##\n#F PcGroupExtensionByMatrixAction(<pcgs>, <hom>)\n##\n## Let <G> be a finite soluble group with pcgs <pcgs>, and let <hom> be a \n## group hom. $<hom>\\colon G \\to GL(n, p)$, where $p$ is a prime. Let $E$ \n## denote the split\n## extension of $G$ by $V = \\F_p$, where <G> acts on <V> via <hom>.\n## This function returns a record with the following components.\n## ext: the group $E$ as a new pc group\n## V: the subgroup $V$ of $E$ corresponding to the vector space\n## C: a complement of $V$ in $E$ isomorphic with $G$\n## embed: a group homomorphism $G \\to E$ with image $C$\n## proj: a group homomorphism $E \\to G$ with kernel $V$\n## pcgsV: an induced pcgs of V (wrt. FamilyPcgs(E)) whose elements \n## correspond to the natural basis elements\n## of the vector space V\n## pcgsC: an induced pcgs of C (wrt. FamilyPcgs(E)) whose elements \n## correspond to the images of pcgs under embed; \n## the elements of pcgsC act on pcgsV as the images of pcgs\n## under hom act on the natural basis of V\n## \nInstallGlobalFunction(PcGroupExtensionByMatrixAction,\n function(pcgs, hom)\n local p, d, ros, f, coll, exp, mat, i, j, r, E, pcgsC, pcgsV;\n \n p := Size(FieldOfMatrixGroup(Range(hom)));\n d := DegreeOfMatrixGroup(Range(hom));\n if not IsPrimeInt(p) then\n Error(\"Range(hom) must be over a prime field \");\n fi;\n \n ros := RelativeOrders(pcgs);\n \n f := FreeGroup(Length(pcgs) + d);\n coll := SingleCollector(f,\n Concatenation(ros, \n ListWithIdenticalEntries(d, p)));\n \n # relations for complement - same as for those for G \n exp := []; \n exp{[1,3..2Length(pcgs)-1]} := [1..Length(pcgs)];\n for i in [1..Length(pcgs)] do\n exp{[2,4..2Length(pcgs)]} := ExponentsOfPcElement(pcgs, pcgs[i]^ros[i]);\n # Print(\"power relation \", i,\": \", exp, \"\\n\");\n SetPower(coll, i, ObjByExtRep(FamilyObj(f.1), exp));\n for j in [i+1..Length(pcgs)] do\n exp{[2,4..2Length(pcgs)]} := ExponentsOfPcElement(pcgs, pcgs[j]^pcgs[i]);\n # Print(\"conj. relation \", j, \"^\", i,\": \", exp, \"\\n\");\n SetConjugate(coll, j, i, ObjByExtRep(FamilyObj(f.1), exp));\n od;\n od;\n \n # relations for socle\n for j in [1..d] do\n SetPower(coll, j+Length(pcgs), One(f));\n od;\n \n exp := [];\n exp{[1,3..2d-1]} := \n [Length(pcgs) + 1..Length(pcgs) + d];\n \n for i in [1..Length(pcgs)] do\n mat := ImageElm(hom, pcgs[i]);\n for j in [1..d] do\n exp{[2,4..2d]} := List(mat[j], IntFFE);\n # Print(\"conj. relation \", j+ Length(pcgs), \"^\", i,\": \", exp, \"\\n\");\n SetConjugate(coll, j + Length(pcgs), i, ObjByExtRep(FamilyObj(f.1), exp));\n od;\n od;\n \n E := GroupByRwsNC(coll);\n SetSize(E, Product(ros) p^d);\n pcgsV := InducedPcgsByPcSequenceNC(FamilyPcgs(E),\n FamilyPcgs(E){[Length(pcgs) + 1..Length(FamilyPcgs(E))]});\n\n # the following sets attributes/properties which are defined \n # in the CRISP packages\n \n pcgsC := InducedPcgsByPcSequenceNC(FamilyPcgs(E),\n FamilyPcgs(E){[1..Length(pcgs)]});\n\n r := rec(\n E := E, \n V := GroupOfPcgs(pcgsV), \n C := GroupOfPcgs(pcgsC),\n pcgsV := pcgsV,\n pcgsC := pcgsC); \n r.embed := GroupHomomorphismByImagesNC(GroupOfPcgs(pcgs), E, pcgs, pcgsC);\n SetIsInjective(r.embed, true);\n SetImagesSource(r.embed, r.C);\n r.proj := GroupHomomorphismByImagesNC(E, GroupOfPcgs(pcgs), \n Concatenation(pcgsC, pcgsV), \n Concatenation(pcgs, ListWithIdenticalEntries(d, OneOfPcgs(pcgs))));\n SetIsSurjective(r.proj, true);\n SetKernelOfMultiplicativeGeneralMapping(r.proj, r.V);\n return r;\n end);\n\n \n############################################################################\n##\n#F PrimitivePcGroupIrreducibleMatrixGroup(<G>)\n##\n## see IRREDSOL documentation\n## \nInstallGlobalFunction(PrimitivePcGroupIrreducibleMatrixGroup,\n function(G)\n \n if not IsMatrixGroup(G) or not IsFinite(FieldOfMatrixGroup(G))\n or not IsPrimeInt(Size(FieldOfMatrixGroup(G)))\n or not IsIrreducibleMatrixGroup(G) then\n Error(\"G must be an irreducible matrix group over a prime field\");\n fi;\n\n return PrimitivePcGroupIrreducibleMatrixGroupNC(G);\n end);\n \n \n############################################################################\n##\n#F PrimitivePcGroupIrreducibleMatrixGroupNC(<G>)\n##\n## see IRREDSOL documentation\n##\n## it is important that the map from Pcgs(Source(RepresentationIsomorphism(G)))\n## \nInstallGlobalFunction(PrimitivePcGroupIrreducibleMatrixGroupNC,\n function(G)\n \n local rep, ext;\n \n rep := RepresentationIsomorphism(G);\n ext := PcGroupExtensionByMatrixAction(Pcgs(Source(rep)), rep);\n SetSocle(ext.E, ext.V);\n SetSocleComplement(ext.E, ext.C);\n SetFittingSubgroup(ext.E, ext.V);\n\n # the following sets attributes/properties which are defined \n # in the CRISP packages\n \n if IsBoundGlobal(\"SetIsPrimitiveSoluble\") then\n ValueGlobal(\"SetIsPrimitiveSoluble\")(ext.E, true);\n fi;\n return ext.E;\n \n end);\n \n\n \n\n############################################################################\n##\n#F PrimitivePcGroup(<n>,<p>,<d>,<k>)\n##\n## see IRREDSOL documentation\n## \nInstallGlobalFunction(PrimitivePcGroup,\n function(n, p, d, k)\n \n local q, desc, G, mat, bas, hom, ext, o, pcgs, pcgsC, pcgsV, H;\n \n if not IsPosInt(n) or not IsPosInt(d) or not IsPosInt(p) or not IsPrimeInt(p) or n mod d <> 0 then\n Error(\"n, p, and d must be positive integers, \",\n \"p must be a prime, and d must divide n\");\n elif not k in IndicesIrreducibleSolubleMatrixGroups(n, p, d) then\n Error(\"k must be in IndicesIrreducibleSolubleMatrixGroups(n, p, d)\");\n else \n n := n /d;\n q := p^d;\n LoadAbsolutelyIrreducibleSolubleGroupData(n, q);\n if n > 1 then\n desc := IRREDSOL_DATA.GROUPS[n][q][k];\n fi;\n if not IsBound(IRREDSOL_DATA.PRIM_GUARDIANS[n]) then\n IRREDSOL_DATA.PRIM_GUARDIANS[n] := [];\n fi;\n if not IsBound(IRREDSOL_DATA.PRIM_GUARDIANS[n][q]) then\n if n = 1 then\n G := IRREDSOL_DATA.GUARDIANS[1][q][1];\n mat := [[Z(q)]];\n hom := GroupHomomorphismByImagesNC(G, Group(mat), \n MinimalGeneratingSet(G), [mat]);\n SetIsBijective(hom, true);\n else\n hom := IRREDSOL_DATA.GUARDIANS[n][q][desc[1]][3];\n G := Source(hom);\n fi;\n if d > 1 then\n bas := CanonicalBasis(AsVectorSpace(GF(p), GF(q)));\n mat := List(InducedPcgsWrtFamilyPcgs(G), \n g -> BlownUpMat(bas, ImageElm(hom, g)));\n hom := GroupHomomorphismByImagesNC(G, Group(mat), \n InducedPcgsWrtFamilyPcgs(G), mat);\n fi;\n \n IRREDSOL_DATA.PRIM_GUARDIANS[n][q] := \n PcGroupExtensionByMatrixAction(InducedPcgsWrtFamilyPcgs(G), hom);\n\n fi;\n ext := IRREDSOL_DATA.PRIM_GUARDIANS[n][q];\n if n = 1 then\n Assert(1, Length(MinimalGeneratingSet(ext.C)) = 1);\n o := IRREDSOL_DATA.GROUPS_DIM1[q][k][1];\n pcgsC := InducedPcgsByGenerators(FamilyPcgs(ext.E),\n [MinimalGeneratingSet(ext.C)[1]^((q-1)/o)]);\n else\n pcgsC := CanonicalPcgsByNumber(ext.pcgsC, desc[2]);\n fi;\n pcgs := InducedPcgsByPcSequenceNC(FamilyPcgs(ext.E), Concatenation(pcgsC, ext.pcgsV));\n H := GroupOfPcgs(pcgs);\n SetIdPrimitiveSolubleGroup(H, [nd,p,d,k]);\n SetSocle(H, ext.V);\n SetFittingSubgroup(H, ext.V);\n SetSocleComplement(H, GroupOfPcgs(pcgsC));\n\n # the following sets attributes/properties which are defined \n # in the CRISP packages\n \n if IsBoundGlobal(\"SetIsPrimitiveSoluble\") then\n ValueGlobal(\"SetIsPrimitiveSoluble\")(H, true);\n fi;\n return H;\n fi;\n end);\n \n \n############################################################################\n##\n#F IrreducibleMatrixGroupPrimitiveSolubleGroup(<G>)\n##\n## see IRREDSOL documentation\n## \nInstallGlobalFunction(IrreducibleMatrixGroupPrimitiveSolubleGroup,\n function(G)\n\n local F, p, matgrp, compl;\n\n if not IsFinite(G) or not IsSolvableGroup(G) then\n Error(\"G must be finite and soluble\");\n \n # test if primitive - use the CRISP method if it is available \n elif IsBoundGlobal(\"IsPrimitiveSoluble\") \n and ValueGlobal(\"IsPrimitiveSoluble\")(G) then\n return IrreducibleMatrixGroupPrimitiveSolubleGroupNC(G);\n \n else # test for primitivity\n F := FittingSubgroup(G);\n \n if not IsPGroup(F) or not IsAbelian(F) then\n Error(\"G must be primitive\");\n else\n p := PrimePGroup(F);\n\n if ForAny(GeneratorsOfGroup(F), x -> x^p <> One(G)) then\n Error(\"G must be primitive\");\n else\n matgrp := IrreducibleMatrixGroupPrimitiveSolubleGroupNC(G);\n if not IsIrreducibleMatrixGroup(matgrp, GF(p)) then\n Error(\"G must be primitive\");\n else\n compl := ComplementClassesRepresentatives(G, F);\n if Length(compl) <> 1 then\n Error(\"G must be primitive\");\n fi;\n SetSocle(G, F);\n return matgrp;\n fi;\n fi;\n fi;\n fi;\n end);\n \n \n############################################################################\n##\n#F IrreducibleMatrixGroupPrimitiveSolubleGroupNC(<G>)\n##\n## see IRREDSOL documentation\n## \nInstallGlobalFunction(IrreducibleMatrixGroupPrimitiveSolubleGroupNC,\n function(G)\n \n local N, p, F, pcgsN, pcgsGmodN, GmodN, one, mat, mats, g, h, i, H, hom;\n \n N := FittingSubgroup(G);\n \n pcgsN := Pcgs(N);\n p := RelativeOrders(pcgsN)[1];\n F := GF(p);\n one := One(F);\n \n mats := [];\n \n pcgsGmodN := ModuloPcgs(G, N);\n for g in pcgsGmodN do\n mat := [];\n for i in [1..Length(pcgsN)] do\n mat[i] := ExponentsOfPcElement(pcgsN, pcgsN[i]^g)one;\n od;\n Add(mats, ImmutableMatrix(F, mat));\n od;\n H := Group(mats);\n SetSize(H, Size(G)/Size(N));\n GmodN := PcGroupWithPcgs(pcgsGmodN);\n hom := GroupGeneralMappingByImagesNC(GmodN, H, FamilyPcgs(GmodN), mats);\n SetIsGroupHomomorphism(hom, true);\n SetIsBijective(hom, true);\n SetRepresentationIsomorphism(H, hom);\n return H;\n end);\n \n\n############################################################################\n##\n#F DoIteratorPrimitiveSolubleGroups(<convert_func>, <arg_list>)\n##\n## generic constructor function for an iterator of all primitive soluble groups\n## which can construct permutation groups or pc groups (or other types of groups),\n## depending on convert_func\n## \nInstallGlobalFunction(DoIteratorPrimitiveSolubleGroups, \n function(convert_func, arg_list)\n\n local r, iter;\n \n r := CheckAndExtractArguments([\n [[Degree, NrMovedPoints, LargestMovedPoint], IsPosInt],\n [[Order, Size], IsPosInt]],\n arg_list, \n \"IteratorPrimitivePcGroups\");\n if ForAny(r.specialvalues, v -> IsEmpty(v)) then\n return Iterator([]);\n fi;\n\n iter := rec(convert_func := convert_func);\n\n if not IsBound(r.specialvalues[1]) then \n Error(\"IteratorPrimitivePcGroupsIterator: You must specify the degree(s) of the desired primitive groups\");\n else\n iter.degs := Filtered(r.specialvalues[1], IsPPowerInt);\n fi; \n \n iter.degind := 0;\n \n if IsBound(r.specialvalues[2]) then\n iter.orders := r.specialvalues[2];\n else\n iter.orders := fail;\n fi;\n \n iter.iteratormatgrp := Iterator([]);\n\n iter.IsDoneIterator := function(iterator)\n\n local d, p, n, orders, o;\n \n if iterator!.degind > Length(iterator!.degs) then\n Error(\"isDoneIterator called after it returned true\");\n fi;\n \n while IsDoneIterator(iterator!.iteratormatgrp) do\n iterator!.degind := iterator!.degind + 1;\n if iterator!.degind > Length(iterator!.degs) then\n return true;\n fi;\n d := iterator!.degs[iterator!.degind];\n p := SmallestRootInt(d);\n n := LogInt(d, p);\n if IsAvailableIrreducibleSolubleGroupData(n, p) then \n if iterator!.orders <> fail then\n orders := [];\n for o in iterator!.orders do\n if o mod d = 0 then\n Add(orders, o/d);\n fi;\n od;\n iterator!.iteratormatgrp := IteratorIrreducibleSolubleMatrixGroups(\n Degree, n, Field, GF(p), Order, orders);\n else\n iterator!.iteratormatgrp := IteratorIrreducibleSolubleMatrixGroups(\n Degree, n, Field, GF(p));\n\n fi;\n else\n Error(\"groups of degree \", d, \" are beyond the scope of the IRREDSOL library\");\n iterator!.iteratormatgrp := Iterator([]);\n fi;\n od;\n return false;\n end;\n\n iter.NextIterator := function(iterator)\n \n local G;\n \n G := NextIterator(iterator!.iteratormatgrp);\n return iterator!.convert_func(G);\n end;\n \n iter.ShallowCopy := function(iterator)\n return rec(\n orders := iterator!.orders,\n degs := iterator!.degs,\n degind := iterator!.degind,\n convert_func := iterator!.convert_func,\n iteratormatgrp := ShallowCopy(iterator!.iteratormatgrp),\n IsDoneIterator := iterator!.IsDoneIterator,\n NextIterator := iterator!.NextIterator,\n ShallowCopy := iterator!.ShallowCopy);\n end;\n return IteratorByFunctions(iter);\n end);\n \n \n############################################################################\n##\n#F IteratorPrimitivePcGroups(<func_1>, <val_1>, ...)\n##\n## see the IRREDSOL manual\n## \nInstallGlobalFunction(IteratorPrimitivePcGroups,\n function(arg)\n return DoIteratorPrimitiveSolubleGroups(\n PrimitivePcGroupIrreducibleMatrixGroupNC,\n arg);\n end);\n \n\n###########################################################################\n##\n#F AllPrimitivePcGroups(<arg>)\n##\n## see IRREDSOL documentation\n## \nInstallGlobalFunction(AllPrimitivePcGroups,\n function(arg)\n \n local iter, l, G;\n \n iter := CallFuncList(IteratorPrimitivePcGroups, arg);\n \n l := [];\n for G in iter do\n Add(l, G);\n od;\n return l;\n end);\n\n\n###########################################################################\n##\n#F OnePrimitivePcGroup(<arg>)\n##\n## see IRREDSOL documentation\n## \nInstallGlobalFunction(OnePrimitivePcGroup,\n function(arg)\n \n local iter;\n \n iter := CallFuncList(IteratorPrimitivePcGroups, arg);\n if IsDoneIterator(iter) then\n return fail;\n else \n return NextIterator(iter);\n fi;\n end);\n\n\n############################################################################\n##\n#F PrimitivePermGroupIrreducibleMatrixGroup(<G>)\n##\n## see IRREDSOL documentation\n## \nInstallGlobalFunction(PrimitivePermGroupIrreducibleMatrixGroup,\n function(G)\n \n if not IsMatrixGroup(G) or not IsFinite(FieldOfMatrixGroup(G))\n or not IsPrimeInt(Size(FieldOfMatrixGroup(G)))\n or not IsIrreducibleMatrixGroup(G) then\n Error(\"G must be an irreducible matrix group over a prime field\");\n fi;\n\n return PrimitivePermGroupIrreducibleMatrixGroupNC(G);\n end);\n \n \n############################################################################\n##\n#F PrimitivePermGroupIrreducibleMatrixGroupNC(<G>)\n##\n## see IRREDSOL documentation\n## \nInstallGlobalFunction(PrimitivePermGroupIrreducibleMatrixGroupNC, \n function( M )\n local gensc, genss, V, bas, enum, G;\n V := FieldOfMatrixGroup( M ) ^ DimensionOfMatrixGroup( M );\n bas := CanonicalBasis(V);\n enum := EnumeratorByBasis(bas);\n gensc := List(GeneratorsOfGroup(M), x -> Permutation(x, enum));\n genss := List( bas, x -> Permutation( x, enum, \\+));\n G := GroupByGenerators(Concatenation(genss, gensc));\n SetSize( G, Size( M ) * Size( V ) );\n SetSocle(G, Subgroup(G, genss));\n SetSocleComplement(G, Subgroup(G, gensc));\n \n # the following sets attributes/properties which are defined \n # in the CRISP packages\n\n if IsBoundGlobal(\"SetIsPrimitiveSoluble\") then\n ValueGlobal(\"SetIsPrimitiveSoluble\")(G, true);\n fi;\n return G;\n end);\n\n\n############################################################################\n##\n#F PrimitiveSolublePermGroup(<n>,<p>,<d>,<k>)\n##\n## see IRREDSOL documentation\n## \nInstallGlobalFunction(PrimitiveSolublePermGroup,\n function(n, p, d, k)\n\n local G;\n if not IsPosInt(n) or not IsPosInt(d) or not IsPosInt(p) or not IsPrimeInt(p) then\n Error(\"n, p, and d must be positive integers, \",\n \"p must be a prime, and d must divide n\");\n elif not k in IndicesIrreducibleSolubleMatrixGroups(n, p, d) then\n Error(\"k must be in IndicesIrreducibleSolubleMatrixGroups(n, p, d)\");\n else\n G := PrimitivePermGroupIrreducibleMatrixGroupNC(\n IrreducibleSolubleMatrixGroup(n, p, d, k));\n SetIdPrimitiveSolubleGroup(G, [n,p,d,k]);\n fi;\n return G;\n end);\n \n \n############################################################################\n##\n#F IteratorPrimitiveSolublePermGroups(<func_1>, <val_1>, ...)\n##\n## see the IRREDSOL manual\n## \nInstallGlobalFunction(IteratorPrimitiveSolublePermGroups,\n function(arg)\n return DoIteratorPrimitiveSolubleGroups(\n PrimitivePermGroupIrreducibleMatrixGroupNC,\n arg);\n end);\n \n\n###########################################################################\n##\n#F AllPrimitiveSolublePermGroups(<arg>)\n##\n## see IRREDSOL documentation\n## \nInstallGlobalFunction(AllPrimitiveSolublePermGroups,\n function(arg)\n \n local iter, l, G;\n \n iter := CallFuncList(IteratorPrimitiveSolublePermGroups, arg);\n \n l := [];\n for G in iter do\n Add(l, G);\n od;\n return l;\n end);\n\n\n###########################################################################\n##\n#F OnePrimitiveSolublePermGroup(<arg>)\n##\n## see IRREDSOL documentation\n## \nInstallGlobalFunction(OnePrimitiveSolublePermGroup,\n function(arg)\n \n local iter;\n \n iter := CallFuncList(IteratorPrimitiveSolublePermGroups, arg);\n if IsDoneIterator(iter) then\n return fail;\n else \n return NextIterator(iter);\n fi;\n end);\n\n\n############################################################################\n##\n#E\n##\n \n \n \n\n \n", "meta": {"hexsha": "a6312c0eaacdf858709da9e0c35e07d6ca2c21f2", "size": 21072, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "lib/primitive.gi", "max_stars_repo_name": "fingolfin/irredsol", "max_stars_repo_head_hexsha": "c7ab06f5123650049142a5ae3a1c1e05a38d2151", "max_stars_repo_licenses": ["BSD-2-Clause"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2017-09-01T16:53:11.000Z", "max_stars_repo_stars_event_max_datetime": "2017-09-01T16:53:11.000Z", "max_issues_repo_path": "lib/primitive.gi", "max_issues_repo_name": "fingolfin/irredsol", "max_issues_repo_head_hexsha": "c7ab06f5123650049142a5ae3a1c1e05a38d2151", "max_issues_repo_licenses": ["BSD-2-Clause"], "max_issues_count": 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	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n#F Circulant(<n>, <filt-func>, <valuation>) -- n x n circulant matrix non-terminal\n#F\n#F The circulant matrix with coefficients of the first row given by\n#F the filter function <filt-func>.\n#F\n#F <valuation> is the offset, default = 0, meaning no offset.\n#F\n#F Examples:\n#F\n#F spiral> PrintMat(MatSPL( Circulant(5, FList(TInt, [1..3]), 0)));\n#F [ [ 1, 2, 3, , ], \n#F [ , 1, 2, 3, ], \n#F [ , , 1, 2, 3 ], \n#F [ 3, , , 1, 2 ], \n#F [ 2, 3, , , 1 ] ]\n#F spiral> PrintMat(MatSPL( Circulant(5, FList(TInt, [1..3]), -1)));\n#F [ [ 2, 3, , , 1 ], \n#F [ 1, 2, 3, , ], \n#F [ , 1, 2, 3, ], \n#F [ , , 1, 2, 3 ], \n#F [ 3, , , 1, 2 ] ]\n\nClass(Circulant, NonTerminal, rec(\n _short_print := true,\n\n abbrevs := [ \n (L) -> [ toSize(L), toFunc(L), toValuation(L) ],\n (n,L) -> [ Checked(IsPosInt(n), n), toFunc(L), toValuation(L) ],\n (n,L,v) -> [ Checked(IsPosInt(n), n), toFunc(L), Checked(IsInt(v), v) ], \n ], \n\n dims := self >> Replicate(2, self.params[1]), \n\n setData := meth(self, newdata) self.params[2] := newdata; return self; end,\n\n column := self >> let(\n\tcoeffs := List(self.params[2].tolist(), x->x.ev()),\n\tvaluation := self.params[3],\n\tCircularWrap([coeffs, valuation], self.params[1])),\n\n terminate := meth(self)\n local i, j, n, L, Ls, mat;\n L := self.column();\n n := Length(L);\n mat := [ ];\n for i in [0..n-1] do\n Ls := Replicate(n, 0);\n\t for j in [0..n-1] do Ls[(i-j) mod n + 1] := L[j+1]; od;\n\t Add(mat,Ls);\n od;\n return Mat(mat); \n end,\n\n filtlen := self >> self.params[2].domain(),\n\n transpose := self >> Circulant(\n\tself.params[1],\n\tfCompose(self.params[2], J(self.filtlen())),\n\t-self.params[3]-self.filtlen()+1),\n \n isReal := self >> not IsComplexT(self.params[2].range()),\n\n hashAs := self >> let(\n\tt := ObjId(self)(\n\t self.params[1], fUnk(self.params[2].range(), self.params[2].domain()), self.params[3]),\n\tWhen(self.transposed, t.transpose(), t)),\n\n SmallRandom := () -> let(n := Random([2..16]),\n\tList([1..n], i -> Float(Random([-2^10..2^10]), Random([-20..10])))),\n\n LargeRandom := () -> let(n := Random([16, 32, 64]),\n\tList([1..n], i -> Float(Random([-2^10..2^10]), Random([-20..10]))))\n));\n\n## \n## Rules\n##\nRulesFor(Circulant, rec(\n ###################################################################\n ## Time domain methods\n ###################################################################\n\n #F Circulant_Base: (base case)\n #F\n Circulant_Base := rec (\n\tinfo := \"Circulant -> Mat\",\n\tforTransposition := false,\n\tisApplicable := P -> P[1] <= 32, \n\tallChildren := P -> [[ ]],\n\trule := (P, C) -> ApplyFunc(Circulant, P).terminate()\n ),\n\n# Circulant_toFilt := rec (\n# \tinfo := \"Circulant -> VStack(.., Filt, ...)\",\n# \tforTransposition := false,\n# \tisApplicable := P -> P[1] > 2 and (P[1]-P[2].domain()) > 2 and P[2].domain() <= 32 and P[3] <= 0, \n# \tallChildren := P -> let(\n# \t n := P[1], l := -P[3], r := P[3] + P[2].domain() - 1,\n# \t [[ Filt(n-l-r, Poly(List(P[2].tolist(),EvalScalar), P[3])) ]]),\n\n# \trule := (P, C) -> let(\n# \t coeffs := P[2], nc := coeffs.domain(), n := P[1], l := -P[3], \n# \t r := -l + nc - 1, \n# \t j := Ind(l), k := Ind(r), v := Ind(nc),\n# \t VStack(\n# \t\tBB(ISum(j, j.range, \n# \t\t Scat(fBase(j)) * \n# \t\t RowVec(fCompose(coeffs, Lambda(v, cond(leq(v,r+j), v-j+l, v-j+l-nc))))) \n# \t\t Gath(n, nc,\tLambda(v, cond(leq(v,r+j), v, v+(n-l-r)-1 )))),\n# \t\tC[1],\n# \t\tBB(ISum(k, k.range, \n# \t\t Scat(fBase(k)) \n# \t\t RowVec(fCompose(coeffs, Lambda(v, cond(leq(v,k), v-k+(nc-1), v-k-1)))) \n# \t\t Gath(n, nc, Lambda(v, cond(leq(v,k), v, v+(n-l-r)-1 )))))))\n# ),\n\n #F Circulant_Blocking\n #F \n #F Circulant -> Blocks (Toeplitzes)\n #F\n #F Circulant is partitioned into square blocks of sizes \n #F given by all proper divisors of the input size.\n #F \n #F NOTE: this rule is invalid, Circulant_BlockingDense seems valid\n #F whats the difference between the two ???\n Circulant_Blocking := rec(\n\tinfo := \"Circulant -> Toeplitz\",\n\tforTransposition := false,\n\tisApplicable := P -> let(n := P[1],\n\t n > 2 and not IsPrime(n)), # and n <= 2Length(P[2])),\n\n\tallChildren := P -> let(\n\t divs := DivisorPairs(P[1]),\n\t ratio := P[2].domain() / P[1], \n\t List(divs, d -> [ Toeplitz(FUnk(2d[1]-1), 0, CeilingRat(ratio (2d[1]-1))) ])\n\t),\n\n prepData := (self, L, b, nc) >> let(\n\t n := Length(L),\n\t Concatenation(\n\t\tList([1..nc], k -> \n\t\t List([1..2b-1], j -> L[((n-kb+j) mod n) + 1])))),\n\n\trule := (self,P,C,Nonterms) >> let(\n\t n := P[1],\n\t b := Rows(C[1]), \n\t nc := n/b,\n\t new_data := FData(self.prepData(ApplyFunc(Circulant, P).column(), b, nc)),\n\t i := Ind(nc),\n\t k := Ind(nc),\n\t ofs := DataInd(TInt, nc (2b-1)).setAttr(\"live_out\"),\n\t bnum := DataInd(TInt, nc).setAttr(\"live_out\"),\n\t gfunc := fCompose(new_data, fAdd(nc(2b-1), 2b-1, ofs)),\n\n\t len := P[2].domain(),\n\t val := P[3] mod n,\n\t btoep_len := 2b-1,\n\n\t left := val,\n\t right := When(len+b >= n, val-1, (val + (len-1) + (b-1)) mod n), \n\t exact_right := (val + (len-1)) mod n,\n\n\t # we \"quantize\" the condition to tell us which block #s (ofs) are 0\n\t lblock := btoep_len Int(left/b),\n\t rblock := btoep_len * Int(right/b),\n\n\t rproj := bbnum + (b - 1 - left),\n\t lproj := bbnum + (b - 1 - exact_right), \n\t nt := Nonterms[1].setData(gfunc)\n\t .setNonZero(lproj, rproj),\n\n\t open := leq(rblock+1, lblock), \n\t A := leq(lblock, ofs), \n\t B := leq(ofs, rblock),\n\t isNonZero := logic_or(logic_and(A, B), logic_and(open, logic_or(A, B))),\n\n\t ISum(i, i.range, \n\t\tScat(fTensor(fBase(i), fId(b))) * \n\t\tISumAcc(k, k.range, \n\t\t Data(bnum, imod(nc+k-i, nc), \n\t\t\tData(ofs, (2b-1)bnum, \n\t\t\t COND(isNonZero, C[1], O(b)))) * \n\t\t Gath(fTensor(fBase(k), fId(b)))))\n )\n # RowDirectSum( ncb, List([1..nc], i-> \n # ColDirectSum( b, List([1..nc], k-> C[((k-i) mod nc) + 1]))))\n ),\n\n #F Circulant_BlockingDense\n #F \n #F Circulant -> Blocks (Toeplitzes)\n #F\n #F Circulant is partitioned into square blocks of sizes \n #F given by all proper divisors of the input size.\n #F \n Circulant_BlockingDense := rec(\n\tinfo := \"Circulant -> Toeplitz\",\n\tforTransposition := false,\n\tisApplicable := P -> let(n := P[1],\n\t n > 2 and not IsPrime(n) and n <= 2P[2].domain()),\n\n\tallChildren := P -> let(\n\t divs := DivisorPairs(P[1]),\n\t ratio := P[2].domain() / P[1], \n\t List(divs, d -> [ Toeplitz(FUnk(2d[1]-1), 0, CeilingRat(ratio (2d[1]-1))) ])\n\t),\n\n prepData := (self, L, b, nc) >> let(\n\t n := Length(L),\n\t Concatenation(\n\t\tList([1..nc], k -> \n\t\t List([1..2b-1], j -> L[((n-kb+j) mod n) + 1])))),\n\n\trule := (self,P,C,Nonterms) >> let(\n\t n := P[1],\n\t b := Rows(C[1]), \n\t nc := n/b,\n\t new_data := FData(self.prepData(ApplyFunc(Circulant, P).column(), b, nc)),\n\t i := Ind(nc),\n\t k := Ind(nc),\n\t ofs := DataInd(TInt, nc (2b-1)).setAttr(\"live_out\"),\n\t bnum := DataInd(TInt, nc).setAttr(\"live_out\"),\n\n\t gfunc := fCompose(new_data, fAdd(nc(2b-1), 2b-1, ofs)),\n\n\t len := P[2].domain(),\n\t val := P[3] mod n,\n\t left := val,\n\t exact_right := (val + (len-1)) mod n,\n\n\t rproj := bbnum + (b - 1 - left),\n\t lproj := bbnum + (b - 1 - exact_right), \n\t nt := Nonterms[1].setData(gfunc)\n\t .setNonZero(lproj, rproj),\n\n\t ISum(i, i.range, \n\t\tScat(fTensor(fBase(i), fId(b))) * \n\t\tISumAcc(k, k.range, \n\t\t Data(bnum, imod(nc+k-i, nc), \n\t\t\tData(ofs, (2b-1)bnum, \n\t\t\t C[1])) \n\t\t Gath(fTensor(fBase(k), fId(b)))))\n )\n # RowDirectSum( ncb, List([1..nc], i-> \n # ColDirectSum( b, List([1..nc], k-> C[((k-i) mod nc) + 1]))))\n ),\n\n #F Circulant_DiagonalizeStep\n #F\n #F Circulant_n -> (F2 tensor I2) \n #F (Circulant_n/2 dirsum Toeplitz_n/2) \n #F (F2 tensor I2)\n #F \n #F Computes circulant matrix through DFT.\n #F h is the first column of the circulant \n #F (params of Circulant nonterminal).\n #F\n Circulant_DiagonalizeStep := rec(\n\tinfo := \"Circulant_n -> Circulant_n/2 dirsum Toeplitz_n/2\",\n\tforTransposition := false,\n\tisApplicable := P -> let(n := P[1],\n\t n > 2 and n mod 2 = 0 and n<=16),\n\n\tallChildren := P -> let(n := P[1], \n\t [[ Circulant(FUnk(n/2)), Toeplitz(FUnk(n-1)) ]]),\n\n\tprepData := function(L)\n\t local l, L1, L2, circ, toep; \n\t l := Length(L);\n\t L1 := L{[1 .. l/2]}; # first half\n\t L2 := L{[l/2+1 .. l ]}; # second half\n\n\t circ := 1/2 * (L1 + L2);\n\t toep := 1/2 * Concat(Drop(L2,1) - Drop(L1,1), \n\t\t L1 - L2);\n\t return [circ, toep];\n\tend,\n\n\trule := (self, P, C, Nonterms) >> let(\n\t n := P[1], \n\t data := self.prepData(ApplyFunc(Circulant,P).column()),\n\t circ := Nonterms[1].setData(FData(data[1])),\n\t toep := Nonterms[2].setData(FData(data[2])),\n\n\t Tensor(F(2), I(n/2)) \n\t DirectSum(C[1], C[2]) \n\t Tensor(F(2), I(n/2))\n\t)\n ),\n\n ###################################################################\n ## Frequency domain methods\n ###################################################################\n\n #F Circulant_DFT\n #F\n #F Circulant -> invDFT * diag(DFT(h)) * DFT\n #F \n #F Computes circulant matrix through DFT.\n #F h is the first column of the circulant \n #F (params of Circulant nonterminal).\n #F\n Circulant_DFT := rec(\n\tinfo := \"Circulant -> invDFT * diag(DFT(h)) * DFT\",\n\tforTransposition := false,\n\tswitch := false,\n\tisApplicable := P -> P[1] > 1,\n\tallChildren := P -> [[ transforms.DFT(P[1], -1), transforms.DFT(P[1], 1) ]],\n\n\trule := function(P, C)\n local l, coef, L;\n\t L := ApplyFunc(Circulant, P).column();\n\t l := Length(L);\n\t coef := List([1..l], i -> ComplexAny(L[i]));\n\t coef := 1/l * ComplexFFT(coef);\n\t return C[1] * Diag(FData(coef)) * C[2];\n\tend\n ),\n\n #F Circulant_RDFT\n #F\n #F Circulant -> invRDFT * block(RDFT(h)) * RDFT\n #F \n #F Computes circulant matrix through the Real DFT.\n #F h is the first column of the circulant \n #F (params of nonterminal Circulant).\n #F\n Circulant_RDFT := rec(\n\tinfo := \"Circulant -> invRDFT * block(RDFT(h)) * RDFT\",\n\tforTransposition := false,\n\tswitch := false,\n\n\tisApplicable := P -> let(n := P[1],\n\t n > 2 and n <= 64 and (n mod 2 = 0) and\n\t ForAll(Factors(n), f -> f in [2, 3])),\n\n\tallChildren := P -> let(n := P[1],\n\t [[ RDFT(n).transpose(), RDFT(n) ]]),\n\n\trule := function( P, C )\n \t local i, L, M, X, l, coef, ccoef;\n\n\t L := ApplyFunc(Circulant, P).column();\n\t l := Length(L);\n\t ccoef := List([1..l], i -> ComplexAny(L[i]));\n\t ccoef := ComplexFFT(ccoef); \n\t coef := List([1..Int(l/2)+1], i -> 2/l * ReComplex(ccoef[i]));\n\t Append(coef, List([Int(l/2)+2..l], i -> 2/l * (-ImComplex(ccoef[i])) ));\n\n\t X := Diag([ 1/2 * coef[1]]);\n\t for i in [2..Int(l/2)] do\n\t M := Mat([[coef[i], coef[l-i+2]], \n\t\t\t [-coef[l-i+2], coef[i]]]);\n\t\tX := DirectSum(X, M);\n\t od;\n\t if (l mod 2 = 0) then \n\t\tX := DirectSum(X, Diag( [1/2 * coef[l/2+1]] ));\n\t fi;\n\t X := X^perm4(l);\n\t return C[1] * X * C[2];\n\tend\n ),\n\n #F Circulant_PRDFT\n #F\n #F Circulant -> IPRDFT * diag(PRDFT(h)) * PRDFT\n #F \n #F Computes circulant matrix through the Packed Real DFT.\n #F h is the first column of the circulant \n #F (params of nonterminal Circulant).\n #F\n Circulant_PRDFT := rec(\n\tinfo := \" Circulant -> IPRDFT * diag(PRDFT(h)) * PRDFT\",\n\tforTransposition := false,\n\tswitch := false,\n\n\tisApplicable := P -> true,\n\n\tallChildren := P -> let(n := P[1],\n\t [[ IPRDFT(n), PRDFT(n) ]]),\n\n\trule := function( P, C )\n \t local i, n, L, l, coef, D;\n\t n := Cols(C[1]);\n\t L := ApplyFunc(Circulant, P).column();\n\t l := Length(L);\n\t coef := List(L, EvalScalar);\n\t coef := 1/l * ComplexFFT(coef);\n\t D:=Diag(FData(coef{[1..n/2]}));\n\t return C[1] * RC(D) * C[2]; \n\tend\n ), \n\n #F Circulant_DHT\n #F\n #F Circulant -> DHT * block(DHT(h)) * DHT\n #F \n #F Computes circulant matrix through the Discrete Hartley transform.\n #F h is the first column of the circulant \n #F (params of nonterminal Circulant).\n #F\n Circulant_DHT := rec(\n\tinfo := \"Circulant -> DHT * block(DHT(h)) * DHT\",\n\tforTransposition := false,\n\tswitch := false, \n\tisApplicable := P -> let(n := P[1], n > 1 and Is2Power(n)),\n\n\tallChildren := P -> let(n := P[1], [[ DHT(n) ]]),\n\n\trule := function(P, C)\n\t local i,M,X,l,L,coef,ccoef, rcoef, icoef;\n\t L := ApplyFunc(Circulant, P).column();\n\t l := Length(L);\n\t ccoef := List([1..l], i -> ComplexAny(L[i]));\n\t ccoef := ComplexFFT(ccoef); \n\t rcoef := List([1..l/2+1], i -> 1/l * ReComplex(ccoef[i]));\n\t icoef := List([2..l/2], i -> 1/l * ImComplex(ccoef[i]));\n\t X := Diag([rcoef[1]]);\n\t for i in [2..Int(l/2)] do\n\t M := Mat([[rcoef[i], -icoef[i-1]], \n\t\t\t [icoef[i-1], rcoef[i]]]);\n\t\tX := DirectSum(X,M);\n\t od;\n\t X := DirectSum(X, Diag( [rcoef[l/2+1]] ));\n\t X := X^perm4(l);\n\t return C[1] * X * C[1];\n\tend\n )\n));\n", "meta": {"hexsha": "cdd313d33420205c34f764a7d527cb1e5ac58861", "size": 13479, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/filtering/circulant.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/transforms/filtering/circulant.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": 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	{"text": "# In reality we only need a list indexed by triples, so we\n# will quite probably end up with a tree where the leaves have\n# weights as labels.\nInstallGlobalFunction(CyclicSubList,\nfunction(l, pos, len)\n local r, i, j, llen;\n\n llen := Length(l);\n r := [];\n i := pos; j := 1;\n while j <= len do\n r[j] := l[i];\n i := i + 1; j := j + 1;\n if i > llen then\n i := 1;\n fi;\n od;\n\n return r;\nend);\n\nInstallGlobalFunction( EnterAllSubwords,\nfunction(idx, word, value)\n local i, v, pos, ww;\n pos := [1..Length(word)];\n ww := List(word, x -> __ID(x));\n for i in pos do\n v := idx[ ww{ CyclicSubList(pos, i, 3) } ];\n if value < v then\n idx[ ww{ CyclicSubList(pos, i, 3) } ] := value;\n fi;\n od;\nend);\n\n\n#\nInstallGlobalFunction( DigraphDijkstraST,\nfunction(graph, s, t)\n local vertices, dist, prev, queue, u, v, alt;\n\n dist := [];\n prev := [];\n queue := BinaryHeap({x,y} -> x[1] < y[1]);\n\n for v in DigraphVertices(graph) do\n dist[v] := infinity;\n prev[v] := -1;\n od;\n\n dist[s] := 0;\n Push(queue, [0, s]);\n\n while not IsEmpty(queue) do\n u := Pop(queue);\n u := u[2];\n if u = t then\n return [ dist, prev ];\n fi;\n for v in OutNeighbours(graph)[u] do\n alt := dist[u] + DigraphEdgeLabel(graph, u, v);\n if alt < dist[v] then\n dist[v] := alt;\n prev[v] := u;\n Push(queue, [dist[v], v]);\n fi;\n od;\n od;\n return infinity;\nend);\n\nInstallGlobalFunction( DigraphDijkstraS,\nfunction(graph, s)\n local vertices, dist, prev, queue, u, v, alt;\n\n dist := [];\n prev := [];\n queue := BinaryHeap({x,y} -> x[1] < y[1]);\n\n for v in DigraphVertices(graph) do\n dist[v] := infinity;\n prev[v] := -1;\n od;\n\n dist[s] := 0;\n Push(queue, [0, s]);\n\n while not IsEmpty(queue) do\n u := Pop(queue);\n u := u[2];\n for v in OutNeighbours(graph)[u] do\n alt := dist[u] + DigraphEdgeLabel(graph, u, v);\n if alt < dist[v] then\n dist[v] := alt;\n prev[v] := u;\n Push(queue, [dist[v], v]);\n fi;\n od;\n od;\n\n return [ dist, prev ];\nend);\n\n\n", "meta": {"hexsha": "0a1a2802abc5255775926f99b06e7e2ef91943be", "size": 2313, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "gap/anadata.gi", "max_stars_repo_name": "RussWoodroofe/walrus", "max_stars_repo_head_hexsha": "f7a4e3597f288c6d9518aaa39091826dadc864b8", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-10-02T14:55:52.000Z", "max_stars_repo_stars_event_max_datetime": "2021-10-02T14:55:52.000Z", "max_issues_repo_path": "gap/anadata.gi", "max_issues_repo_name": "RussWoodroofe/walrus", "max_issues_repo_head_hexsha": "f7a4e3597f288c6d9518aaa39091826dadc864b8", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 26, "max_issues_repo_issues_event_min_datetime": "2018-11-22T11:15:07.000Z", "max_issues_repo_issues_event_max_datetime": "2022-02-21T13:31:01.000Z", "max_forks_repo_path": "gap/anadata.gi", "max_forks_repo_name": "RussWoodroofe/walrus", "max_forks_repo_head_hexsha": "f7a4e3597f288c6d9518aaa39091826dadc864b8", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 4, "max_forks_repo_forks_event_min_datetime": "2019-02-11T14:47:47.000Z", "max_forks_repo_forks_event_max_datetime": "2021-05-20T10:22:09.000Z", "avg_line_length": 22.2403846154, "max_line_length": 62, "alphanum_fraction": 0.4807609166, "num_tokens": 675, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7185943805178138, "lm_q2_score": 0.7025300573952054, "lm_q1q2_score": 0.5048341513890517}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\nClass(InterpolateSegmentDFT, TaggedNonTerminal, rec(\n abbrevs := [ (numseg, outsize, insize, overlap, dsfunc,usfunc) -> [numseg, outsize, insize, overlap, dsfunc, usfunc] ],\n\n dims := self >> [self.params[2], self.params[3]],\n\n terminate := self >> let(\n numseg := self.params[1], \n rowlength := self.params[2],\n insize := self.params[3], \n j := Ind(numseg),\n overlap := self.params[4], \n downsample := self.params[5].at(j), \n upsample := self.params[6],\n n := upsample.domain(), \n N := downsample.range(), \n substrec := i -> rec((j.id):=V(i)),\n \n kernel := Mat(MatAMat(RowDirectSum(\n overlap,\n List([1..numseg], i -> \n Downsample(SubstVars(Copy(downsample), substrec(i-1))).terminate() \n DFT(N, 1).terminate() \n Upsample(upsample).terminate() \n Scale(1/n, DFT(n, -1).terminate())\n )).toAMat() \n Scat(fAdd(nnumseg-(numseg-1)overlap, insize, 0)).toAMat()\n )),\n When(Rows(kernel) = rowlength, kernel, VStack(kernel, O(rowlength-Rows(kernel), Cols(kernel)))) \n ),\n isReal := False,\n normalizedArithCost := self >> let(numseg := self.params[1], n:=self.params[6].domain(), N := self.params[6].range(), \n numseg * (n + IntDouble(5 * n * d_log(n) / d_log(2)) + IntDouble(5 * N * d_log(N) / d_log(2)))),\n TType := T_Complex(T_Real(64)),\n\n HashId := self >> let(h := [ self.params[1], self.params[2], self.params[3], self.params[4], self.params[5].domain(), self.params[5].range()],\n When(IsBound(self.tags), Concatenation(h, self.tags), h)),\n doNotMeasure := true\n));\n\n\n_sumSegDims := function(numsegs, seglen)\n local l, lfact, lsum, divsum, ssum;\n\n l := List([0..numsegs-1], i->seglen.at(i).domain());\n \n # check to pull out the mul\n if ForAll(l, i->ObjId(i) = mul and IsValue(i.args[1]) and i.args[1].v = l[1].args[1].v) then\n lfact := l[1].args[1];\n lsum := List(l, i -> i.args[2]);\n # we may need to create a table, but not sure yet...\n divsum := ApplyFunc(add, lsum);\n ssum := mul(lfact, divsum);\n else\n ssum := ApplyFunc(add, l);\n fi;\n \n return ssum;\nend;\n\nNewRulesFor(InterpolateSegmentDFT, rec(\n InterpolateSegmentDFT_base := rec(\n switch := false,\n applicable := (self, nt) >> not nt.hasTags() and ObjId(nt.params[6]) = fZeroPadMiddle,\n children := nt -> let(numseg := nt.params[1], j := Ind(numseg), downsample := nt.params[5].at(j), upsample := nt.params[6],\n insize := nt.params[3], overlap := nt.params[4], n:=upsample.domain(), N := downsample.range(), \n us := N/n, blk := n/2, \n inp := n + (numseg-1)(n-overlap), over := inp - insize, l := n - over,\n [[ \n Downsample(downsample),\n DFT(N, 1), \n Upsample(upsample),\n DFT(n, -1),\n Upsample(fAdd(n, l, 0)),\n InfoNt(j)\n ]]),\n apply := (nt, C, cnt) -> let(numseg := nt.params[1], _j := cnt[6].params[1], j := Ind(_j.range-1), downsample := nt.params[5].at(j), upsample := nt.params[6], \n outsize := nt.params[2], insize := nt.params[2], overlap := nt.params[4], n:=upsample.domain(), N := downsample.range(), \n ids_rows := _sumSegDims(numseg-1, nt.params[5]),\n RowDirectSum(overlap,[\n IRowDirSum(j, numseg-1, overlap, \n SubstVars(Copy(C[1]), rec((_j.id) := j)) C[2] * C[3] * Scale(1/n, C[4])).overrideDims([ids_rows, insize - C[4].dims()[2] + overlap]),\n SubstVars(Copy(C[1]), rec((_j.id) := V(numseg-1))) * C[2] * C[3] * Scale(1/n, C[4] * C[5]) \n ]).overrideDims([nt.params[2], nt.params[3]])\n )\n ),\n InterpolateSegmentDFT_PrunedDFT := rec(\n applicable := (self, nt) >> not nt.hasTags() and ObjId(nt.params[6]) = fZeroPadMiddle,\n children := nt -> let(numseg := nt.params[1], j := Ind(numseg), downsample := nt.params[5].at(j), upsample := nt.params[6], \n insize := nt.params[3], overlap := nt.params[4], n:=upsample.domain(), N := downsample.range(), \n us := N/n, blk := n/2, \n inp := n + (numseg-1)(n-overlap), over := inp - insize, l := n - over, g := Gcd(n, l), \n [[ \n Downsample(downsample),\n PrunedDFT(N, 1, blk, [0, 2us-1]), \n DFT(n, -1),\n PrunedDFT(n, -1, g, [0..l/g-1]),\n InfoNt(j) \n ]]),\n apply := (nt, C, cnt) -> let(numseg := nt.params[1], _j := cnt[5].params[1], j := Ind(_j.range-1), downsample := nt.params[5].at(j), upsample := nt.params[6],\n outsize := nt.params[2], insize := nt.params[3], overlap := nt.params[4], n := upsample.domain(), N := downsample.range(), \n ids_rows := _sumSegDims(numseg-1, nt.params[5]),\n RowDirectSum(overlap,[\n IRowDirSum(j, numseg-1, overlap, \n SubstVars(Copy(C[1]), rec((_j.id) := j)) * C[2] * Diag(fConst(n, 1/n)) * C[3]).overrideDims([ids_rows, insize - C[4].dims()[2] + overlap]),\n SubstVars(Copy(C[1]), rec((_j.id) := V(numseg-1))) * C[2] * Diag(fConst(n, 1/n)) * C[4]\n ]).overrideDims([nt.params[2], nt.params[3]])\n )\n )\n));\n", "meta": {"hexsha": "425f2c8248522229f048d63c135564a15e69587b", "size": 5711, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/interpolate/segmentdft.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/transforms/interpolate/segmentdft.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/transforms/interpolate/segmentdft.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 50.0964912281, "max_line_length": 167, "alphanum_fraction": 0.4995622483, "num_tokens": 1687, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.831143031127974, "lm_q2_score": 0.6039318337259584, "lm_q1q2_score": 0.5019537348776687}}
	{"text": "# The incidence graph of a Desarguesian projective plane.\nBindGlobal(\"DesarguesianPlaneIncidenceGraph\", function(q)\n local G, V, dp;\n V := GF(q)^3;\n dp := DirectProduct(GL(3, q), SymmetricGroup(2));\n G := Graph(dp, Union(List([1,2], d -> Subspaces(V, d))),\n OnProjectivePlane(V, dp), function(x, y)\n return x <> y and Intersection(x, y) in [x, y];\n end, true);\n G.halfDuality := Sum;\n G.halfPrimality := Intersection;\n return G;\nend);\n\n# The incidence graph of a Hall plane.\nBindGlobal(\"HallPlaneIncidenceGraph\", function(q)\n local c, p, G, H, L, P, dp, mul;\n H := GF(q)^2;\n p := DefiningPolynomial(GF(GF(q), 2));\n c := CoefficientsOfUnivariatePolynomial(p);\n mul := HallMultiplication(p);\n P := Union([[]], List(H, x -> [x]), Cartesian(H, H));\n L := Union([Union([[]], List(H, z -> [z]))],\n List(H, x -> Union([[]], List(H, z -> [x, z]))),\n List(Cartesian(H, H), w -> Union([[w[1]]],\n List(H, z -> [z, mul(z, w[1]) + w[2]]))));\n dp := DirectProduct(Concatenation(ListWithIdenticalEntries(5,\n FieldAdditionPermutationGroup(q)),\n [FieldMultiplicationPermutationGroup(q),\n Group([[c[2], Z(q)^0], [-c[1], 0Z(q)]])]));\n G := Graph(dp, Union(P, L), OnHallPlane(q, dp),\n PointLineIncidence, true);\n G.halfDuality := DefaultDualityFunction;\n G.halfPrimality := DefaultPrimalityFunction;\n return G;\nend);\n\n# The incidence graph of a Hughes plane. If the second parameter n is zero or\n# unspecified, a Dickson semifield of order q^2 is used and the first parameter\n# q must be an odd prime power. Otherwise, an exceptional near-field of order\n# q^2 is used, so q must be 5, 7, 11, 23, 29, or 59. As there are two\n# exceptional near-fields of order 11^2, setting n to 1 or 2 chooses one of\n# these semifields when q = 11.\nBindGlobal(\"HughesPlaneIncidenceGraph\", function(arg)\n local c, n, q, A, B, F, G, H, P, df, dp, th, mul, rdiv, gens, orth;\n if Length(arg) < 1 then\n Error(\"at least one argument expected\");\n return fail;\n fi;\n q := arg[1];\n if Length(arg) > 1 then\n n := arg[2];\n else\n n := 0;\n fi;\n th := Z(q^2)^((q+1)/2);\n B := Basis(GF(q^2), [Z(q)^0, th]);\n if n = 0 then\n mul := DicksonMultiplication(q);\n rdiv := DicksonRightDivision(q);\n else\n gens := [[[0, -1], [1, 0]]];\n if q = 5 then\n gens[2] := [[1, -2], [-1, -2]];\n elif q = 7 then\n gens[2] := [[1, 3], [-1, -2]];\n elif q = 11 and n = 1 then\n gens[2] := [[1, 5], [-5, -2]];\n gens[3] := [[4, 0], [0, 4]];\n elif q = 11 and n = 2 then\n gens[2] := [[2, 4], [1, -3]];\n elif q = 23 then\n gens[2] := [[1, -6], [12, -2]];\n gens[3] := [[2, 0], [0, 2]];\n elif q = 29 then\n gens[2] := [[1, -7], [-12, -2]];\n gens[3] := [[16, 0], [0, 16]];\n elif q = 59 then\n gens[2] := [[9, 15], [-10, -10]];\n gens[3] := [[4, 0], [0, 4]];\n else\n Error(\"the specified exceptional near-field does not exist\");\n return fail;\n fi;\n G := Group(gens Z(q)^0);\n F := Union([NullMat(2, 2, GF(q))], Elements(G));\n SortBy(F, x -> IntVecFFE(x[1]));\n mul := ExceptionalMultiplication(q, F, B);\n rdiv := ExceptionalRightDivision(q, F, B);\n fi;\n c := CoefficientsOfUnivariatePolynomial(DefiningPolynomial(GF(GF(q), 3)));\n A := [[-c[3], Z(q)^0, 0Z(q)],\n [-c[2], 0Z(q), Z(q)^0],\n [-c[1], 0Z(q), 0Z(q)]];\n P := Filtered(GF(q^2)^3,\n x -> not IsZero(x) and IsOne(First(x, y -> not IsZero(y))));\n dp := DirectProduct(Group(A), SymmetricGroup(2));\n orth := function(x, y)\n local z;\n z := TransposedMat(List(y, w -> Coefficients(B, w)));\n return IsZero(xz[1] + mul(th, xz[2]));\n end;\n H := Graph(dp, Cartesian([1, 2], P), OnHughesPlane(q, rdiv, dp),\n function(x, y)\n return x[1] <> y[1] and orth(x[2], y[2]);\n end, true);\n df := x -> [x[1][1]^(1, 2),\n Intersection(List(x,\n y -> Filtered(P, z -> orth(y[2], z))))[1]];\n H.halfDuality := df;\n H.halfPrimality := df;\n return H;\nend);\n\n# The collinearity graph of the generalized quadrangle Q(d, q)\n# of order (q, q^{d-3}).\nBindGlobal(\"GeneralizedQuadrangleQ\", function(d, q)\n return PolarGraphO(4-d, d+1, q);\nend);\n\n# The collinearity graph of the generalized quadrangle H(d, r^2)\n# of order (r^2, r^{d-5/2}).\nBindGlobal(\"GeneralizedQuadrangleH\", function(d, r)\n return PolarGraphU(d+1, r);\nend);\n\n# The collinearity graph of the generalized quadrangle W(q) of order (q, q).\nBindGlobal(\"GeneralizedQuadrangleW\", q -> PolarGraphSp(4, q));\n\n# The collinearity graph of the generalized quadrangle T_d(O) of order\n# (q, q^{d-1}) derived from the projective space PG(d+1, q) containing the\n# oval or ovoid O in a hyperplane.\nBindGlobal(\"GeneralizedQuadrangleT\", function(arg)\n local d, o, q, G, H, O, V, gr;\n if Length(arg) < 1 then\n Error(\"at least one argument expected\");\n return fail;\n elif Length(arg) < 3 then\n d := arg[1].d;\n q := arg[1].q;\n o := arg[1].points;\n G := arg[1].group;\n else\n d := arg[1];\n q := arg[2];\n o := arg[3];\n if Length(arg) > 3 then\n G := arg[4];\n else\n G := Group(IdentityMat(d+1, GF(q)));\n fi;\n fi;\n V := GF(q)^(d+2);\n H := Subspace(V, BasisVectors(CanonicalBasis(V)){[2..d+2]}, \"basis\");\n O := List(o, x -> Subspace(V,\n [Concatenation([0Z(q)], BasisVectors(Basis(x))[1])], \"basis\"));\n gr := Graph(Group(List(GeneratorsOfGroup(G),\n g -> Concatenation([Concatenation([Z(q)^0],\n ListWithIdenticalEntries(d+1, 0Z(q)))],\n List(g, l -> Concatenation([0Z(q)], l))))),\n Union(Filtered(Subspaces(V, 1), x -> not IsSubset(H, x)),\n Filtered(Subspaces(V, d+1),\n x -> Length(Filtered(O, y -> IsSubset(x, y))) = 1), [V]),\n OnSubspaces(V), function(x, y)\n local dx, dy, xy, yx;\n dx := Dimension(x);\n dy := Dimension(y);\n xy := x+y;\n yx := Intersection(x, y);\n return (dx = d+2 and dy = d+1) or (dx = d+1 and dy = d+2) or\n (dx = 1 and dy = 1 and ForAny(O, z -> IsSubset(xy, z))) or\n (dx = 1 and dy = d+1 and ForAny(O, z -> IsSubset(y, x+z))) or\n (dx = d+1 and dy = 1 and ForAny(O, z -> IsSubset(x, y+z))) or\n (dx = d+1 and dy = d+1 and x <> y and\n ForAny(O, z -> IsSubset(yx, z)));\n end, true);\n gr.duality := function(x)\n if V in x then\n return First(O, y -> IsSubset(Intersection(x), y));\n else\n return Sum(Filtered(x, y -> Dimension(y) = 1));\n fi;\n end;\n gr.primality := function(x)\n if ForAll(x, y -> Dimension(y) = 1) then\n return V;\n elif ForAll(x, y -> Dimension(y) = 2) then\n return Intersection(x);\n else\n return Sum(x);\n fi;\n end;\n return gr;\nend);\n\n# The collinearity graph of the generalized quadrangle T(O) of order\n# (2^h-1, 2^h+1) derived from the projective space PG(3, 2^h) containing the\n# hyperoval O in a hyperplane.\nBindGlobal(\"GeneralizedQuadrangleTstar\", function(arg)\n local o, q, G, H, O, V, gr;\n if Length(arg) < 1 then\n Error(\"at least one argument expected\");\n return fail;\n elif Length(arg) < 3 then\n q := arg[1].q;\n o := arg[1].points;\n G := arg[1].group;\n else\n q := 2^arg[1];\n o := arg[2];\n if Length(arg) > 2 then\n G := arg[3];\n else\n G := Group(IdentityMat(3, GF(q)));\n fi;\n fi;\n V := GF(q)^4;\n H := Subspace(V, BasisVectors(CanonicalBasis(V)){[2..4]}, \"basis\");\n O := List(o, x -> Subspace(V,\n [Concatenation([0Z(q)], BasisVectors(Basis(x))[1])], \"basis\"));\n gr := Graph(Group(List(GeneratorsOfGroup(G),\n g -> Concatenation([Concatenation([Z(q)^0],\n ListWithIdenticalEntries(3, 0Z(q)))],\n List(g, l -> Concatenation([0Z(q)], l))))),\n Filtered(Subspaces(V, 1), x -> not IsSubset(H, x)),\n OnSubspaces(V), function(x, y)\n local xy;\n xy := x+y;\n return not IsSubset(H, xy)\n and ForAny(O, z -> IsSubset(xy, z));\n end, true);\n gr.duality := Sum;\n gr.primality := Intersection;\n return gr;\nend);\n\n# The collinearity graph of the generalized quadrangle P(G, z) of\n# order (s-1, s+1) derived by removing the neighbourhood of a regular point z\n# of a generalized quadrangle G of order (s, s).\nBindGlobal(\"GeneralizedQuadrangleP\", function(Q, z)\n local H, P;\n H := Graph(Stabilizer(Q.group, z), DistanceSet(Q, 2, z), OnPoints,\n function(x, y)\n local c;\n c := Intersection(Adjacency(Q, x), Adjacency(Q, y));\n return not z in c and (y in Adjacency(Q, x)\n or ForAll(c, w -> z in Adjacency(Q, w)));\n end, true);\n AssignVertexNames(H, Q.names{H.names});\n CheckDualityFunctions(Q);\n H.duality := function(x)\n local p;\n p := List(x, u -> Position(Q.names, u));\n if ForAny(Cartesian(p, p), w -> Distance(Q, w[1], w[2]) = 2) then\n return [2, Set(x)];\n else\n return [1, Q.duality(Union(x,\n Q.names{Intersection(List(p, v -> Adjacency(Q, v)))}))];\n fi;\n end;\n H.primality := x -> Q.primality(List(Filtered(x, y -> y[1] = 1),\n w -> w[2]));\n return H;\nend);\n\n# The collinearity graph of the generalized quadrangle AS(q)\n# of order (q-1, q+1).\nBindGlobal(\"GeneralizedQuadrangleAS\",\n q -> GeneralizedQuadrangleP(GeneralizedQuadrangleW(q), 1));\n\n# The incidence graph of a projective plane read from a file as on\n# http://www.uwyo.edu/moorhouse/pub/planes/ or\n# http://www.uwyo.edu/moorhouse/pub/genpoly/\n# The optional second parameter is a file containing generators of the\n# automorphism group.\nBindGlobal(\"IncidenceGraphFromFile\", function(arg)\n local l, m, n, G, L, fst, lst, lns;\n if Length(arg) < 1 then\n Error(\"at least one argument expected\");\n return fail;\n fi;\n lns := ReadLines(arg[1]);\n n := Length(lns);\n L := List(lns, l -> List(SplitString(l, \" \"), x -> Int(x)+n+1));\n if Length(arg) > 1 then\n lns := ReadLines(arg[2]);\n m := Length(lns);\n fst := Filtered([1..m], i -> IntChar(lns[i][1]) <> 32);\n l := Length(fst);\n lst := List(fst{[2..l]}, i -> i-1);\n Add(lst, m);\n G := Group(List([1..l], i -> PermList(List(SplitString(\n JoinStringsWithSeparator(lns{[fst[i]..lst[i]]}, \"\"),\n \" \"), x -> Int(x)+1))));\n else\n G := Group(());\n fi;\n return Graph(G, [1..2n], OnPoints, function(x, y)\n return (x <= n and y in L[x]) or (y <= n and x in L[y]);\n end, true);\nend);\n\n# The collinearity graph of a projective plane read from a file as on\n# http://www.uwyo.edu/moorhouse/pub/genpoly/\n# The optional second parameter is a file containing generators of the\n# automorphism group.\nBindGlobal(\"CollinearityGraphFromFile\", function(arg)\n local l, m, n, G, L, fst, lst, lns;\n if Length(arg) < 1 then\n Error(\"at least one argument expected\");\n return fail;\n fi;\n lns := ReadLines(arg[1]);\n n := Length(lns);\n L := List(lns, l -> List(SplitString(l, \" \"), x -> Int(x)));\n if Length(arg) > 1 then\n lns := ReadLines(arg[2]);\n m := Length(lns);\n fst := Filtered([1..m], i -> IntChar(lns[i][1]) <> 32);\n l := Length(fst);\n lst := List(fst{[2..l]}, i -> i-1);\n Add(lst, m);\n G := Group(List([1..l], i -> PermList(Filtered(List(SplitString(\n JoinStringsWithSeparator(lns{[fst[i]..lst[i]]}, \"\"),\n \" \"), x -> Int(x)+1), y -> y <= n))));\n else\n G := Group(());\n fi;\n return Graph(G, [1..n], OnPoints, function(x, y)\n return Length(Intersection(L[x], L[y])) = 1;\n end, true);\nend);\n", "meta": {"hexsha": "6911997d7f639d632a09bbbf72ad187ad0f874a4", "size": 12730, "ext": "gap", "lang": "GAP", "max_stars_repo_path": "lib/GeometryGraphs.gap", "max_stars_repo_name": "jaanos/gap-graphs", "max_stars_repo_head_hexsha": "18dd56c9b90a12a717a0cc893fdd72c6343ee79b", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2015-10-27T15:54:29.000Z", "max_stars_repo_stars_event_max_datetime": "2016-11-07T14:09:44.000Z", "max_issues_repo_path": "lib/GeometryGraphs.gap", "max_issues_repo_name": "jaanos/gap-graphs", "max_issues_repo_head_hexsha": "18dd56c9b90a12a717a0cc893fdd72c6343ee79b", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": 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	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nDeclare(VTensor, RCVTensor, VTensorInd);\n\n# A x I_v\nClass(VTensor, Tensor, rec(\n new := (self, L) >> SPL(WithBases(self, rec(\n _children := [L[1]],\n dimensions := When(IsBound(L[1].dims), L[1].dims(), L[1].dimensions) * L[2],\n vlen := L[2]))),\n # NOTE: vlen not exposed to rChildren\n from_rChildren := (self, rch) >> ObjId(self)(rch[1], self.vlen),\n\n normalizedArithCost := (self) >> self.vlen * self.child(1).normalizedArithCost(),\n print := (self,i,is) >> Print(self.name, \"(\",\n self.child(1).print(i+is,is), \", \", self.vlen, \")\"),\n toAMat := self >> Tensor(self.child(1), I(self.vlen)).toAMat(),\n sums := self >> Inherit(self, rec(_children := [self.child(1).sums()])),\n isPermutation := False,\n dims := self >> self.child(1).dims() * self.vlen,\n needInterleavedLeft := False,\n needInterleavedRight := False,\n transpose := self >> VTensor(self.child(1).transpose(), self.vlen),\n # for BlockSums\n isBlockTransitive := true,\n area := self >> self.child(1).area() * self.vlen,\n #NOTE: check if these two should be set to true or false\n cannotChangeDataFormat := False,\n totallyCannotChangeDataFormat := False\n));\n\n\n# RC(A x I_v)\nClass(RCVTensor, Tensor, rec(\n new := (self, L) >> SPL(WithBases(self, rec(\n _children := [L[1]],\n dimensions := 2 * L[1].dimensions * L[2],\n vlen := L[2]))),\n # NOTE: vlen not exposed to rChildren\n from_rChildren := (self, rch) >> ObjId(self)(rch[1], self.vlen),\n print := (self,i,is) >> Print(self.name, \"(\",\n self.child(1).print(i+is,is), \", \", self.vlen, \")\"),\n toAMat := self >> RC(Tensor(self.child(1), I(self.vlen)).toAMat()),\n sums := self >> Inherit(self, rec(_children := [self.child(1).sums()])),\n isPermutation := False,\n dims := self >> self.child(1).dims() * self.vlen * 2,\n needInterleavedLeft := True,\n needInterleavedRight := True,\n transpose := self >> RCVTensor(self.child(1).transpose(), self.vlen),\n # for BlockSums\n isBlockTransitive := true\n));\n\n\nClass(VTensorInd, Tensor, rec(\n new := (self, L) >> SPL(WithBases(self, rec(\n _children := [L[1]],\n dimensions := When(IsBound(L[1].dims), L[1].dims(), L[1].dimensions) * L[2].range,\n vlen := L[2]))),\n from_rChildren := (self, rch) >> ObjId(self)(rch[1], self.vlen),\n\n rChildren := self >> [self._children[1], self.vlen],\n\n rSetChild := meth ( self, n, what )\n if n=1 then\n self._children[1] := what;\n elif n=2 then\n self.vlen := what;\n else\n Error(\"VTensorInd only has 2 rChildren\");\n fi;\n end,\n# from_rChildren := (self, rch) >> ObjId(self)(rch[1], rch[2]),\n\n print := (self,i,is) >> Print(self.name, \"(\",\n self.child(1).print(i+is,is), \", \", self.vlen, \")\"),\n toAMat := self >> let(d := self.child(1).dims(), v := self.vlen.range, L(d[1]v, d[1]).toAMat() IDirSum(self.vlen, self.child(1)).toAMat() * L(d[2]v, v).toAMat()),\n sums := self >> Inherit(self, rec(_children := [self.child(1).sums()])),\n isPermutation := False,\n dims := self >> self.child(1).dims() self.vlen.range,\n needInterleavedLeft := False,\n needInterleavedRight := False,\n transpose := self >> VTensorInd(self.child(1).transpose(), self.vlen),\n # for BlockSums\n isBlockTransitive := true,\n area := self >> self.child(1).area() * self.vlen.range,\n free := meth(self)\n local fvar;\n fvar := self.child(1).free();\n SubtractSet(fvar, Set([self.vlen]));\n return fvar;\n end\n));\n", "meta": {"hexsha": "93fe07cea6f2a16ed7075cb18ff2f6a9f7cc5277", "size": 3677, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/vector/sigmaspl/vtensor.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/paradigms/vector/sigmaspl/vtensor.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/paradigms/vector/sigmaspl/vtensor.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 37.9072164948, "max_line_length": 170, "alphanum_fraction": 0.5765569758, "num_tokens": 1124, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. 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	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nDeclare(DFT_Rader, DFT_GoodThomas);\n\n_accurate_dft := vec -> List(TransposedMat(MatSPL(transforms.DFT(Length(vec)))TransposedMat([vec]))[1], ComplexCyc);\n\nClass(fdft, FuncExp, rec(\n computeType := self >> self.args[1].t\n));\n\nClass(fDFT, DiagFunc, rec(\n abbrevs := [ func -> Checked(IsFunction(func), [func]) ],\n range := self >> TComplex, \n domain := self >> self.params[1].domain(), \n\n lambda := self >> fdft(self.params[1].lambda()),\n\n tolist := self >> let(\n\telts := List(self.params[1].tolist(), x->Complex(EvalScalar(x))),\n\tComplexFFT(elts))\n));\n\nNewRulesFor(DFT, rec(\n #F DFT_Base: DFT_2 = F_2\n #F\n DFT_Base := rec(\n info := \"DFT_2 -> F_2\",\n forTransposition := false,\n applicable := nt -> nt.params[1] = 2 and not nt.hasTags(),\n apply := (nt, C, cnt) -> F(2)\n ),\n\n DFT_Base1 := rec(\n info := \"DFT_1 -> I(1)\",\n forTransposition := false,\n applicable := nt -> nt.params[1] = 1 and not nt.hasTags(),\n apply := (nt, C, cnt) -> I(1)\n ),\n\n #F DFT_Canonize: DFT_n_k = perm DFT_n\n #F\n DFT_Canonize := rec(\n switch := false,\n info := \"DFT_n_k -> perm * DFT_n\",\n forTransposition := false,\n applicable := nt -> nt.params[1] > 2 and nt.params[2] <> 1 and not nt.hasTags(),\n children := nt -> [[ DFT(nt.params[1], 1) ]],\n apply := (nt, C, cnt) -> OddStride(nt.params[1], nt.params[2]) * C[1]\n ),\n\n #F DFT_CT: 1965\n #F General Cooley-Tukey Rule\n #F DFT_n = (DFT_n/d tensor I_d) * diag * (I_n/d tensor F_d) * perm\n #F\n #F Cooley/Tukey:\n #F An Algorithm for the Machine Calculation of Complex Fourier Series.\n #F Mathematics of Computation, Vol. 19, 1965, pp. 297--301.\n #F\n DFT_CT := rec(\n info := \"DFT(mn,k) -> DFT(m, k%m), DFT(n, k%n)\",\n\n maxSize := false,\n forcePrimeFactor := false,\n\n applicable := (self, nt) >> nt.params[1] > 2\n and not nt.hasTags()\n and (self.maxSize=false or nt.params[1] <= self.maxSize)\n and not IsPrime(nt.params[1])\n and When(self.forcePrimeFactor, not DFT_GoodThomas.applicable(nt), true),\n\n children := nt -> Map2(DivisorPairs(nt.params[1]),\n (m,n) -> [ DFT(m, nt.params[2] mod m), DFT(n, nt.params[2] mod n) ]\n ),\n\n apply := (nt, C, cnt) -> let(mn := nt.params[1], m := Rows(C[1]), n := Rows(C[2]),\n Tensor(C[1], I(n)) \n Diag(fPrecompute(Tw1(mn, n, nt.params[2]))) \n Tensor(I(m), C[2]) \n L(mn, m)\n )\n ),\n\n DFT_CT_Mincost := rec(\n maxSize := false,\n applicable := (self, nt) >> let(N := nt.params[1],\n\t N > 2 and not nt.hasTags() and IsEvenInt(N) and\n (self.maxSize = false or nt.params[1] <= self.maxSize)),\n\n children := nt -> let(N := nt.params[1], k := nt.params[2], Map2( \n\t Filtered(DivisorPairs(N), divpair -> IsEvenInt(divpair[2])),\n (m,n) -> [ DFT(m, k mod m), DFT3(m, k mod (2m)), DFT(n, k mod n) ])),\n\n apply := (nt, C, cnt) -> let(\n\t N := nt.params[1], m := Rows(C[1]), n := Rows(C[3]), k := nt.params[2],\n hf := (n-2)/2, i := Ind(hf), j := Ind(hf),\n\n SUM( _hhi(N, m, 0, n, C[1]), # first iteration has no twiddles\n When(hf=0, [],\n\t\tISum(i, _hhi(N, m, i+1, n, C[1] * Diag(fPrecompute(Twid(N,m,k,0,0,i+1)))))),\n _hhi(N, m, hf+1, n, C[2]), # middle is a DFT3\n\t When(hf=0, [],\n\t\tISum(j, _hhi(N, m, j+hf+2, n, C[1] * Diag(fPrecompute(Twid(N,m,k,0,0,j+2+hf))))))\n ) \n Tensor(I(m), C[3]) \n Tr(n, m)\n )\n ),\n\n #F DFT_CosSinSplit:\n #F\n #F DFT_n = CosDFT_n + i * SinDFT_n\n #F\n #F This rule has been restricted in applicability to small size\n #F (see config.g), Connects to Vetterli rules for CosDFT/SinDFT.\n #F\n DFT_CosSinSplit := rec(\n info := \"DFT_n -> CosDFT_n, SinDFT_n\",\n forTransposition := false,\n maxSize := 64,\n\n applicable := (self, nt) >> let(N:=nt.params[1], rot:=nt.params[2],\n N > 2 and N <= self.maxSize and Is2Power(N) and AbsInt(rot)=1 \n\t and not nt.hasTags()),\n\n children := nt -> [[ CosDFT(nt.params[1]), SinDFT(nt.params[1]) ]],\n\n apply := (nt, C, cnt) -> let(N := nt.params[1], rot := nt.params[2],\n\t Tensor(Mat([[1,1]]), I(N)) * \n VStack(C[1], (E(4)^rot) * C[2])\n\t)\n ),\n\n #F DFT_Rader: Rader's Algorithm for Prime size DFT\n #F\n #F DFT(p) -> P(g)' * (1 dirsum DFT(p-1)) * Tp * (1 dirsum DFT(p-1)) * P(g)\",\n #F P(g) = perm\n #F Tp = [[1,1],[1,-1/(p-1)]] dirsum diag\n #F\n DFT_Rader := rec(\n info := \"DFT(p) -> P(g)' * DFT(p-1) * Tp \",\n forTransposition := false,\n minSize := 3,\n maxSize := 64,\n accurate := true,\n\n raderDiag := (self, N, k, root) >> let(\n\t dft := When(self.accurate, _accurate_dft, vec->ComplexFFT(List(vec,ComplexCyc))),\n SubList(dft(List([0..N-2], x -> E(N)^(kroot^x mod N))), 2) / (N-1)),\n\n raderMid := (self, N, k, root) >>\n DirectSum(Mat([[1, 1], [1, -1/(N-1)]]),\n Diag(FData(self.raderDiag(N, k, root)))),\n\n applicable := (self, nt) >> let(n:=nt.params[1],\n n >= self.minSize and n <= self.maxSize and IsPrime(EvalScalar(n)) \n\t and not nt.hasTags()),\n\n children := nt -> [[ DFT(nt.params[1]-1, -1), DFT(nt.params[1]-1, -1) ]],\n\n apply := (self, nt, C, cnt) >> let(\n\t N := EvalScalar(nt.params[1]), k := EvalScalar(nt.params[2]), root := PrimitiveRootMod(N),\n RR(N, 1, root).transpose() \n DirectSum(I(1), C[1]) \n self.raderMid(N,k,root) \n DirectSum(I(1), C[2]) \n RR(N, 1, root)\n )\n ),\n\n DFT_RealRader := CopyFields(~.DFT_Rader, rec(\n children := nt -> [[ PRDFT1(nt.params[1]-1).transpose(), PRDFT1(nt.params[1]-1) ]],\n\n realRaderDiag := (self, N, k, root) >> let(cdiag := self.raderDiag(N, k, root),\n # cdiag is of length N-2.\n # cdiag = sublist( DFT_{N-1} omega_vector, [2..N-1])\n # now we want to obtain\n # rdiag = sublist( RDFT_N * omega_vector, [2..N-1]), we can do this using\n # the property RDFT = (1 dirsum (I tensor [[1, 1], [-j, j]]) dirsum 1) * LIJ * DFT\n # which means that rdiag = (1 dirsum (I tensor [[1, 1], [-j, j]]) dirsum 1) * LIJ * cdiag\n # the code below does this ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ plus pads a zero (for PRDFT)\n # and also the following trick.\n\n # The expected rdiag steady state is [[a, b], [b, -a]], we convert this to rotations (=RCDiag)\n # by applying J(2), ie we get [[b, -a], [a, b]], which would be a rotation by b + E(4)a,\n # but in this case both a and b are complex, so its not. We still use RCDiag though.\n #\n Concatenation(\n ConcatList([1..(N-3)/2], i -> Reversed([cdiag[i]+cdiag[N-1-i], -E(4)(cdiag[i]-cdiag[N-1-i])])), # DFT->RDFT\n [0, cdiag[(N-3)/2+1]])),\n\n raderMid := (self, N, k, root) >>\n DirectSum(Mat([[1, 1, 0], [1, -1/(N-1), 0], [0, 0, 0]]), # zero padding for PRDFT\n Tensor(I((N-1)/2), J(2))\n RCDiag(FData(self.realRaderDiag(N, k, root))).toloop()), \n # RCDiag with complex entries, max weird :) !\n # .toloop() is used because in vector code RCDiag is \n # converted to VRCDiag which is confused by complex entries AFAIK\n apply := (self,nt,C,cnt) >> let(\n N := EvalScalar(nt.params[1]), k := EvalScalar(nt.params[2]), root := PrimitiveRootMod(N),\n RR(N, 1, root).transpose() \n DirectSum(I(1), C[1]) \n self.raderMid(N,k,root) \n DirectSum(I(1), C[2]) \n RR(N, 1, root))\n )),\n\n #F DFT_Bluestein : Convert FFT to Toeplitz matrix, then embed in a larger Circulant\n #F\n #F DFT_n -> diag Toeplitz * diag\n #F\n # DFT on inputs, some of which are 0:\n #\n DFT_Bluestein := rec(\n info := \"DFT_n -> diag * Toeplitz * diag\",\n forTransposition := false,\n minSize := 3,\n maxSize := false,\n switch := false,\n\n # Applicable only for non-powers of 2 to prevent cycles\n applicable := (self, nt) >> let(N := nt.params[1],\n IsSymbolic(N) or \n\t (N >= self.minSize and When(IsInt(self.maxSize), N <= self.maxSize, true) and not Is2Power(N)\n\t\tand not nt.hasTags())),\n\n\t# NOTE: extend this to be a true degree of freedom\n\tfreedoms := t -> let(min := 2t.params[1]+1,\n\t [ integersBetween(min, 4 pow(2, floor(log(t.params[1])/log(2)))) ]),\n\n child := (t, fr) -> let(\n\t N := t.params[1], Ncirc := fr[1], \n [ DFT(Ncirc, -1).withTags(t.getTags()), DFT(Ncirc, 1).withTags(t.getTags()) ]),\n\n diag := (N, k) -> let(i:=Ind(N), Lambda(i, omegapi(fdiv(i^2 * k, N)))),\n\n\tcirc := (N, k, circsize) -> let(\n\t j1 := Ind(N),\n\t j2 := Ind(N-1),\n\t diagDirsum(\n\t\tLambda(j1, fdiv(omegapi(fdiv(-j1^2k, N)), circsize)),\n\t\tfConst(TReal, circsize-2N+1, 0),\n\t\tLambda(j2, fdiv(omegapi(fdiv(-(N-j2-1)^2k, N)), circsize)))),\n\n apply := (self, nt, C, cnt) >> let(\n N := nt.params[1],\n k := nt.params[2],\n Ncirc := Rows(C[1]),\n diag := fPrecompute(self.diag(N,k)),\n\t pad := spiral.paradigms.common.TRDiag(Ncirc, N, diag).withTags(nt.getTags()),\n\n\t #Diag(diag) Gath(fCompose(fAdd(Ncirc, N, 0))).toloop(1) * \n\t pad.transpose() * \n\t Inplace(Grp(C[1] * Diag(fPrecompute(fDFT(self.circ(N, k, Ncirc)))))) \n\t Inplace(C[2]) \n\t pad\n\t #Scat(fAdd(Ncirc, N, 0)).toloop(1) * Diag(diag) ##, O(Ncirc-N, N))\n\t)\n ),\n\n #F DFT_GoodThomas : Prime Factor FFT\n #F\n #F DFT_nk -> perm (DFT_n_a tensor DFT_k_b) * perm\n #F when gcd(n,k) = 1\n #F\n DFT_GoodThomas := rec(\n info := \"DFT_nk -> perm (DFT_n_a tensor DFT_k_b) * perm\",\n forTransposition := false,\n applicable := (self, nt) >> let(N := nt.params[1],\n\t N > 2 and DivisorPairsRP(N) <> [] and N <= self.maxSize and\n\t not nt.hasTags()),\n\n maxSize := 64,\n\n children := nt -> let(mn := nt.params[1], k:= nt.params[2], Map2(DivisorPairsRP(mn),\n (m,n) -> [ DFT(m, kn mod m), DFT(n, km mod n) ])),\n\n apply := (nt, C, cnt) -> let(\n r := Rows(C[1]),\n s := Rows(C[2]),\n alpha := 1 / s mod r,\n beta := 1 / r mod s,\n CRT(r,s,1,1).transpose() * Tensor(C[1], C[2]) * CRT(r,s,1,1)\n )\n ),\n\n #F DFT_PFA_SUMS : Prime Factor FFT using Sigma-SPL and cyclic shifts\n #F\n #F DFT_nk -> perm (DFT_n_a tensor DFT_k_b) * perm\n #F when gcd(n,k) = 1\n #F\n DFT_PFA_SUMS := CopyFields(~.DFT_GoodThomas, rec(\n apply := (nt, C, cnt) -> let(\n\t r := Rows(C[1]), s := Rows(C[2]),\n\t j := Ind(s), k := Ind(r),\n\t alpha := (1/s) mod r, beta := (1/r) mod s,\n\t ISum(j,\n Scat(fTensor(fId(r), fBase(j))) \n (C[1] ^ Z(r, -alphaj)) \n Gath(fTensor(fId(r), fBase(j)))) \n\t ISum(k,\n Scat(fTensor(fId(s), fBase(k))) \n (C[2] ^ Z(s, -betak)) \n Gath(fTensor(fId(s), fBase(k))))\n\t)\n )),\n\n DFT_PFA_RaderComb := rec(\n forTransposition := false,\n applicable := nt -> let(N := nt.params[1], divs := DivisorPairsRP(N),\n N > 2 and Length(divs)=2 and N mod 2 = 1 and\n IsPrime(divs[1][1]) and IsPrime(divs[1][2]) \n\t and not nt.hasTags()),\n\n children := nt -> let(\n\t N:=nt.params[1], k:=nt.params[2], divs := DivisorPairsRP(nt.params[1]),\n r := divs[1][1], s := divs[1][2],\n [ [DFT(r-1,-1), DFT(r-1,-1), DFT(s-1,-1), DFT(s-1,-1)],\n\t\t [DFT(s-1,-1), DFT(s-1,-1), DFT(r-1,-1), DFT(r-1,-1)] ]),\n\t\n apply := (nt, C, cnt) -> let(\n r := Rows(C[1])+1,\n s := Rows(C[3])+1,\n er := ChineseRem([r,s], [1,0]),\n es := ChineseRem([r,s], [0,1]),\n dr := DFT_Rader.raderMid(r, nt.params[2]s), # * er/s mod r),\n ds := DFT_Rader.raderMid(s, nt.params[2]r), # es/r mod s),\n\n CRT(r,s,1,1).transpose() \n Tensor(RR(r).transpose(), RR(s).transpose()) \n Tensor(\n DirectSum(I(1), C[1]) * dr * DirectSum(I(1), C[2]),\n DirectSum(I(1), C[3]) * ds * DirectSum(I(1), C[4])\n ) \n Tensor(RR(r), RR(s)) \n CRT(r,s,1,1)\n )\n ),\n\n #F DFT_SplitRadix: 1984\n #F\n #F DFT_n = B * (DFT_n/2 dirsum DFT_n/4 dirsum DFT_n/4) * perm\n #F\n #F B = (DFT_2 tensor I_n/2) * S * diag\n #F S = (I_n/2 dirsum (diag([1,E(4)] tensor I_n/4))\n #F\n #F Duhamel, Pierre:\n #F Split Radix FFT Algorithm, Electronics Letters, Vol. 20, No. 1,\n #F pp. 14--16, 1984\n #F\n DFT_SplitRadix := rec(\n info := \"DFT_n -> DFT_n/2, DFT_n/4, DFT_n/4\",\n forTransposition := true,\n maxSize := 64,\n\n applicable := (self, nt) >> let(N := nt.params[1],\n N >= 8 and N mod 4 = 0 and N <= self.maxSize and not nt.hasTags()\n ),\n\n children := nt -> let(N := nt.params[1], w := nt.params[2],\n [[ DFT(N/2, w), DFT(N/4, w) ]]\n ),\n\n apply := (nt, C, cnt) -> let(N := nt.params[1], w := nt.params[2],\n Tensor(F(2), I(N/2)) \n DirectSum(\n C[1],\n Tensor(Diag([1, E(4)^w]) F(2), I(N/4)) \n Diag(fPrecompute(fCompose(Tw3(N/2, 2, w), L(N/2, 2)))) \n Tensor(I(2), C[2])L(N/2,2)\n ) \n L(N, 2)\n )\n ),\n\n #F DFT_DCT1andDST1: 1984\n #F\n #F DFT_n = blocks * (DCT1_(n/2+1) dirsum DST1_(n/2-1)) * blocks\n #F\n #F Wang:\n #F Fast Algorithms for the Discrete W Transform and the\n #F Discrete Fourier Transform.\n #F IEEE Trans. on ASSP, 1984, pp. 803--814\n #F Britanak/Rao:\n #F The fast generalized discrete Fourier transforms: A unified\n #F approach to the discrete sinusoidal transforms computation.\n #F Signal Processing 79, 1999, pp. 135--150\n #F\n DFT_DCT1andDST1 := rec(\n info := \"DFT_n -> DCT1_(n/2+1), DST1_(n/2-1)\",\n maxSize := 64,\n\n applicable := (self, nt) >> let(N:=nt.params[1], k:=nt.params[2],\n N > 2 and N <= self.maxSize and Is2Power(N) and AbsInt(k)=1) and not nt.hasTags(),\n\n children := nt -> \n\t [[ DCT1( nt.params[1]/2 + 1 ), DST1( nt.params[1]/2 - 1 ) ]],\n\n apply := (nt, C, cnt) -> let(N:=nt.params[1], w:=nt.params[2],\n DirectSum(I(1), blocks4(N - 1, w)) \n DirectSum(C[1], C[2] ^ J(N/2 - 1)) \n DirectSum(I(1), blocks1(N - 1))\n )\n )\n));\n", "meta": {"hexsha": "82016fa0f99087cfa0769e5c46054dfc2445a24c", "size": 15239, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/dft/dft_rules.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/transforms/dft/dft_rules.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/transforms/dft/dft_rules.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 37.3504901961, "max_line_length": 124, "alphanum_fraction": 0.4860555155, "num_tokens": 5155, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. 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	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n#P SPL Parametrized Symbols\n#P ========================\n#P\n#P This package contains parametrized symbols - shortcut notation for common\n#P idiomatic constructs.\n#P\n\n#F -----------------------------------------------------------------------------\n#F I(N) : NxN identity matrix\n#F -----------------------------------------------------------------------------\nClass(I, Sym, rec(\n abbrevs := [ (x,y) -> Checked(x=y, IsPosInt0Sym(x), x),\n (n) -> Checked(IsPosInt0Sym(n), n) ],\n def := n -> Perm((), n),\n transpose := self >> self,\n conjTranspose := self >> self,\n inverse := self >> self,\n isIdentity := True,\n isSymmetric := True,\n doNotMeasure := true,\n printlatex := self >> Print(\" \\\\one_{\",self.params[1],\"} \"),\n area := self >> self.params[1],\n normalizedArithCost := self >> 0,\n));\n\n#F -----------------------------------------------------------------------------\n#F O(M,N) : MxN matrix of zeros\n#F -----------------------------------------------------------------------------\nClass(O, BaseMat, rec(\n abbrevs := [ n -> Checked(IsPosInt(n), [n,n]) ],\n\n new := (self, r, c) >> SPL(WithBases(self, rec(\n params := [r, c], dimensions := [r, c]))),\n\n isReal := True,\n isPermutation := False,\n arithmeticCost := (self, costMul, costAddMul) >> costMul(0) - costMul(0),\n\n transpose := self >> ObjId(self)(self.params[2], self.params[1]), \n conjTranspose := self >> ObjId(self)(self.params[2], self.params[1]), \n\n area := self >> Maximum(self.dimensions),\n\n toAMat := self >> AMatMat(NullMat(\n\tEvalScalar(self.params[1]), EvalScalar(self.params[2]))),\n\n print := Sym.print,\n dims := self >> [ self.params[1], self.params[2] ],\n rChildren := Sym.rChildren,\n rSetChild := Sym.rSetChild\n));\n\n#F -----------------------------------------------------------------------------\n#F RI(M,N) : MxN rectangular identity\n#F MIN(M,N) x MIN(M,N) identity padded with 0s\n#F -----------------------------------------------------------------------------\nClass(RI, Sym, rec(\n def := (r, c) -> Checked(IsPosInt(r), IsPosInt(c),\n Cond(r = c, I(r),\n r < c, Gath(fAdd(c,r,0)),\n Scat(fAdd(r,c,0)))),\n\n transpose := self >> ApplyFunc(self.__bases__[1], Reversed(self.params)),\n conjTranspose := self >> ApplyFunc(self.__bases__[1], Reversed(self.params)),\n));\n\n#F -----------------------------------------------------------------------------\n#F F(N) - NxN Discrete Fourier Transform matrix\n#F -----------------------------------------------------------------------------\nClass(F, Sym, rec(\n def := size -> Checked(IsPosInt(size),\n Cond(size = 1, Mat([[1]]),\n size = 2, Mat([[1,1], [1,-1]]),\n Mat(Global.DFT(size)))),\n\n isReal := self >> self.params[1] <= 2,\n isPermutation := False,\n transpose := self >> self,\n conjTranspose := self >> self,\n inverse := self >> let(n:=self.params[1], Cond(n=1, self, n=2, 1/2F(2), Error(\"Inverse not supported\"))),\n toAMat := self >> DFTAMat(self.params[1]),\n printlatex := (self) >> Print(\" F_{\", self.params[1], \"} \")\n));\n\n#F -----------------------------------------------------------------------------\n#F R(a) : 2x2 rotation matrix with angle api, namely\n#F\n#F cos(a) sin(a)\n#F -sin(a) cos(a)\n#F\n#F alternatively:\n#F\n#F R(c,s) : specified by a pair such as c^2 + s^2 = 1\n#F <c> <s>\n#F -<s> <c>\n#F\n#F -----------------------------------------------------------------------------\nClass(Rot, Sym, rec(\n abbrevs := [ (a) -> [cospi(a), sinpi(a)] ],\n\n def := (a,b) ->\n Mat( [[a, b], [-b, a]] ),\n\n transpose := self >>\n self.__bases__[1](self.params[1], -self.params[2]),\n\n conjTranspose := self >> self.transpose(),\n inverse := self >> self.transpose(),\n\n toAMat := self >> let(a := self.params[1], b := self.params[2],\n When(IsScalar(a) and IsScalar(b) and ScalarIsCos(a) and ScalarIsSin(b),\n RotationAMat(EvalScalar(ScalarCosArg(a))),\n AMatMat([[EvalScalar(a), EvalScalar(b)],\n [EvalScalar(-b), EvalScalar(a)]]))),\n\n #-----------------------------------------------------------------------\n # Expansions\n expandLifting := self >>\n let(c := self.params[1],\n s := self.params[2],\n ev := (not IsScalar(c) or CanBeFullyEvaluated(c.val)) and\n (not IsScalar(s) or CanBeFullyEvaluated(s.val)),\n Cond(ev and c = s, c * F(2) * Perm((1,2), 2),\n ev and c = -s, c * Perm((1,2), 2) * F(2),\n Mat([[1,1,0], [0,-1,1]]) \n Diag([c-s, s, c+s]) \n Mat([[1,0], [1,1], [0,1]]))),\n\n expandWinograd:= self >>\n let(c := self.params[1],\n s := self.params[2],\n ev := (not IsScalar(c) or CanBeFullyEvaluated(c.val)) and\n (not IsScalar(s) or CanBeFullyEvaluated(s.val)),\n Cond(ev and c = s, c * F(2) * Perm((1,2), 2),\n ev and c = -s, c * Perm((1,2), 2) * F(2),\n Mat([[1, (1-c)/s], [0, 1]]) \n Mat([[1, 0], [-s, 1]]) \n Mat([[1, (1-c)/s], [0, 1]]))),\n\n expandDef := self >> self.obj,\n));\n\n\nDeclare(toeplitz);\n\n#F -----------------------------------------------------------------------------\n#F toeplitz(elements) : toeplitz matrix given by elements of the first row and\n#F column, starting from the upper right corner\n#F -----------------------------------------------------------------------------\n#F NOTE: use generating function not list (see 'Toeplitz')\nClass(toeplitz, Sym, rec(\n abbrevs := [ arg -> When(Length(arg) > 1 or not IsList(arg[1]), [arg], arg) ],\n\n def := function(elements)\n local n;\n Constraint(IsList(elements) and Length(elements) > 0);\n Constraint(IsOddInt(Length(elements)));\n DoForAll(elements, x->Constraint(IsScalarOrNum(x)));\n n := (Length(elements) + 1) / 2;\n return Mat(ToeplitzMat(elements));\n end,\n\n transpose := self >> toeplitz(Reversed(self.params[1])),\n conjTranspose := self >> toeplitz(List(Reversed(self.params[1]), x->Global.Conjugate(x))),\n isReal := True,\n isPermutation := False,\n area := self >> Product(self.dimensions)\n));\n", "meta": {"hexsha": "45ccd2d376b88be494d53750fb01fb67aff72075", "size": 6354, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/spl/symbols.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/spl/symbols.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/spl/symbols.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 36.5172413793, "max_line_length": 110, "alphanum_fraction": 0.4557758892, "num_tokens": 1660, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. 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	{"text": "# Copyright (c) 2018-2020, Carnegie Mellon University\n# See LICENSE for details\n#\n# n-qubit Z transforms\n#\n\n\n#F qZT( n ) - Z Gate non-terminal\n#F Definition: (2^n x 2^n)-matrix that applies an n-point Z Transform to the target qubits\n#F Note: qZT(1) denotes the matrix[[1, 0], [0, -1]],\n#F qZT(_) is symmetric.\n#F\n#F qZT( n ) -> an n-qubit Z transform\nClass(qZT, TaggedNonTerminal, rec(\n abbrevs := [ n -> Checked(IsPosInt(n), [n]) ],\n dims := self >> let(size := 2^self.params[1], [size, size]),\n terminate := self >> Tensor(Replicate(self.params[1], qZ())),\n isReal := self >> true,\n groups := self >> [Replicate(self.params[1], 1)],\n rChildren := self >> self.params,\n from_rChildren := (self, rch) >> self.__bases__[1](rch[1]),\n recursive_def := (self, arch) >> self.__bases__[1](self.params[1]),\n SmallRandom := () -> Random([2..5]),\n LargeRandom := () -> Random([6..15]),\n normalizedArithCost := self >> Error(\"ArithCost not implemented\"),\n TType := T_Complex(64)\n));\n\n\nNewRulesFor(qZT, rec(\n\n # qZT_BinSplit rule\n # qzT_BinSplit qZT_(k) -> (qZT_(k1) tensor I) (I tensor qZT_(k2))\n # k1 + k2 = k\n qZT_BinSplit := rec (\n forTransposition := false,\n minSize := 2, \n applicable := (self, nt) >> nt.params[1] > 1,\n children := nt -> List( [1..nt.params[1] - 1], i -> [ Tensor(qZT(i), qZT(nt.params[1]-i)).withTags(nt.getTags()) ] ), \n apply := (nt, c, cnt) -> c[1],\n switch := true,\n ),\n\n #F qZT_Base: qZT(1) = qZ() SPL object\n #F Directly represent as an implementable gate\n qZT_Base := rec(\n info := \"qZT_(1) -> qZ()\",\n forTransposition := false,\n applicable := (self, nt) >> nt.params[1]=1,\n apply := (nt, c, cnt) -> qZ(),\n )\n\n));", "meta": {"hexsha": "bd38528ff429045a6363e2cfe516287711ca231b", "size": 1841, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "qzt.gi", "max_stars_repo_name": "spiral-software/spiral-package-quantum", "max_stars_repo_head_hexsha": "dd2323983495adbbc6261c0cdf840320d19d099d", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "qzt.gi", "max_issues_repo_name": "spiral-software/spiral-package-quantum", "max_issues_repo_head_hexsha": "dd2323983495adbbc6261c0cdf840320d19d099d", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "qzt.gi", "max_forks_repo_name": "spiral-software/spiral-package-quantum", "max_forks_repo_head_hexsha": "dd2323983495adbbc6261c0cdf840320d19d099d", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 34.7358490566, "max_line_length": 136, "alphanum_fraction": 0.5486148832, "num_tokens": 608, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8333246118695629, "lm_q2_score": 0.6548947290421275, "lm_q1q2_score": 0.5457398958944535}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n# ==========================================================================\n# RowTensor\n# ==========================================================================\nClass(RowTensor, BaseOverlap, rec(\n #-----------------------------------------------------------------------\n dims := self >> let(D := self._children[1].dimensions, \n [ self.isize * D[1],\n\t D[2] + AbsInt((D[2] - self.overlap) * (self.isize - 1)) ]),\n #-----------------------------------------------------------------------\n toAMat := self >> let(n := EvalScalar(self.isize),\n TensorProductAMat(AMatSPL(I(n)), AMatSPL(self._children[1])) \n\tAMatSPL(Sparse(\n\t\tself._rowoverlap(\n\t\t List([1..n], i-> EvalScalar(Cols(self._children[1]))),\n\t\t EvalScalar(self.overlap)\n\t\t)))\n ),\n #-----------------------------------------------------------------------\n arithmeticCost := (self, costMul, costAddMul) >>\n self.isize self._children[1].arithmeticCost(costMul, costAddMul)\n));\n\n# ==========================================================================\n# ColTensor\n# ==========================================================================\nClass(ColTensor, BaseOverlap, rec(\n #-----------------------------------------------------------------------\n dims := self >> let(D := self._children[1].dimensions,\n [ D[1] + AbsInt((D[1] - self.overlap) * (self.isize - 1)),\n\t self.isize * D[2] ]),\n #-----------------------------------------------------------------------\n toAMat := self >> let(n := _unwrap(self.isize),\n AMatSPL(Sparse(\n\t\tself._coloverlap(\n\t\t List([1..n], i->self._children[1].dimensions[1]),\n\t\t self.overlap\n\t\t))) * \n\tTensorProductAMat(AMatSPL(I(n)), AMatSPL(self._children[1]))\n )\n));\n\nColTensor._transpose_class := RowTensor;\nRowTensor._transpose_class := ColTensor;\n", "meta": {"hexsha": "997cb8c53fb77caf7b7e68f7047fa4f4f64f607b", "size": 1909, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/spl/RowColTensor.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/spl/RowColTensor.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/spl/RowColTensor.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 38.9591836735, "max_line_length": 76, "alphanum_fraction": 0.3986380304, "num_tokens": 418, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8333245787544824, "lm_q2_score": 0.6548947290421275, "lm_q1q2_score": 0.5457398742075619}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nRulesFor(DFT, rec(\n #F DFT_DFT1and3 : DFT1_2n -> L (DFT1_n dirsum DFT3_n) L (I2 tensor F2) L\n #F Derived using polynomial factorization:\n #F x^2n -> (x^n-1) (x^n+1)\n #F\n DFT_DFT1and3 := rec(\n isApplicable := P -> P[1] > 2 and P[1] mod 2 = 0,\n allChildren := P -> [[ DFT1(P[1]/2, P[2]), DFT3(P[1]/2, P[2]) ]],\n rule := (P,C) -> let(n := P[1]/2, \n L(2n, n) DirectSum(C[1], C[2]) * L(2n, 2) \n Tensor(I(n), F(2)) \n L(2n, n))\n )\n));\n\nlperm := p -> Z(p, (p-1)/2); \nrperm := p -> Z(p, (p+1)/2);\npdiag := (p,k) -> When(IsEvenInt(k), \n I(p),\n Diag(List([0..p-1], i -> (-1)^i)));\n\nRulesFor(DFT2, rec(\n DFT2_CT := Inherit(DFT_CT, rec(\n\tswitch := false,\n\tallChildren := P -> Map2(DivisorPairs(P[1]), \n\t (m,n) -> [ DFT2(m, P[2]), DFT(n, P[2]) ]),\n \n\trule := (P,C) -> let(mn := P[1], m := Rows(C[1]), n := Rows(C[2]), \n\t Tensor(C[1], I(n)) * Diag(fPrecompute(Tw2(mn, n, P[2]))) \n\t Tensor(I(m), C[2]) L(mn, m))\n )),\n));\n\nNewRulesFor(DFT2, rec(\n DFT2_PF := rec(\n \tinfo := \"DFT2_nk -> diag perm * (DFT2_n_a tensor DFT2_k_b) * perm\",\n \tforTransposition := true,\n \tapplicable := nt -> nt.params[1] > 2 and DivisorPairsRP(nt.params[1]) <> [] and not nt.hasTags(),\n \tallChildren := nt -> let(N := nt.params[1], k:= nt.params[2], Map2(DivisorPairsRP(N), \n \t\t(r,s) -> [ DFT2(r, 1/s mod r), DFT2(s, 1/r mod s) ])),\n \t\n apply := (nt, C, cnt) -> let(\n \t N := nt.params[1],\n \t r := Rows(C[1]), \n \t s := Rows(C[2]),\n \t alpha := 1 / s mod r,\n \t beta := 1 / r mod s,\n \t i := Ind(rs),\n \n \t CRT(r,s).transpose() \n \t Diag(Lambda(i, -sign(imod(salphaidiv(i,s) + rbetaimod(i,s), 2N) - N))) \n \t Tensor(C[1], C[2]) * CRT(r,s)\n \t)\n#D \tisApplicable := P -> P[1] > 2 and DivisorPairsRP(P[1]) <> [] and Length(P[3]) = 0,\n#D \tallChildren := P -> let(N := P[1], k:= P[2], Map2(DivisorPairsRP(N), \n#D \t\t(r,s) -> [ DFT2(r, 1/s mod r), DFT2(s, 1/r mod s) ])),\n#D \t\n#D \trule := (P,C) -> let(\n#D \t N := P[1],\n#D \t r := Rows(C[1]), \n#D \t s := Rows(C[2]),\n#D \t alpha := 1 / s mod r,\n#D \t beta := 1 / r mod s,\n#D \t i := Ind(rs),\n#D \n#D \t CRT(r,s).transpose() \n#D \t Diag(Lambda(i, -sign(imod(salphaidiv(i,s) + rbetaimod(i,s), 2N) - N))) \n#D \t Tensor(C[1], C[2]) * CRT(r,s)\n#D \t)\n )\n));\n\nRulesFor(DFT3, rec(\n DFT3_Base := BaseRule(DFT3, [2, ...]),\n\n DFT3_CT := Inherit(DFT_CT, rec(\n\tswitch := false,\n\tallChildren := P -> Map2(DivisorPairs(P[1]), \n\t (m,n) -> [ DFT(m, P[2]), DFT3(n, P[2]) ]),\n \n\trule := (P,C) -> let(mn := P[1], m := Rows(C[1]), n := Rows(C[2]), \n\t Tensor(C[1], I(n)) * Diag(fPrecompute(Tw3(mn, n, P[2]))) \n\t Tensor(I(m), C[2]) L(mn, m))\n )),\n\n DFT3_CT_Radix2 := rec(\n\tisApplicable := P -> P[1] > 2 and (P[1] mod 2) = 0,\n\tallChildren := P -> [[ DFT(P[1]/2, P[2]) ]], \n\trule := (P,C) -> let(n := P[1]/2,\n\t Tensor(C[1], I(2)) * Diag(fPrecompute(Tw3(2n, 2, P[2]))) \n\t Tensor(I(n), F(2)Diag(1,E(4)^P[2])) L(2n, n))\n ),\n\n DFT3_OddToDFT1 := rec(\n\tisApplicable := P -> IsOddInt(P[1]),\n\tallChildren := P -> [[ DFT(P[1], P[2]) ]],\n\trule := (P, C) -> rperm(P[1]) C[1] * pdiag(P[1], P[2])\n ),\n\n DFT3_2xOddToDFT1 := rec(\n\tisApplicable := P -> P[1] mod 4 = 2 and P[1] > 2,\n\tallChildren := P -> [[ DFT(P[1], P[2]) ]],\n\trule := (P, C) -> let(n:=P[1], k:=P[2],\n\t Z(n,-(n-2)/4) * C[1] * Diag(List([0..n-1], x->E(4)^(kx))))\n )\n\n));\n\nRulesFor(DFT4, rec(\t\n DFT4_Base := rec(\n\tisApplicable := P -> P[1]=2,\n\tforTransposition := false,\n\trule := (P,C) -> E(8)Mat((1/E(8))MatSPL(ApplyFunc(DFT4, P)))\n ),\n\n DFT4_CT := Inherit(DFT_CT, rec(\n\tallChildren := P -> Map2(DivisorPairs(P[1]), \n\t (m,n) -> [ DFT2(m, P[2]), DFT3(n, P[2]) ]),\n \n\trule := (P,C) -> let(mn := P[1], m := Rows(C[1]), n := Rows(C[2]), \n\t Tensor(C[1], I(n)) Diag(fPrecompute(Tw4(mn, n, P[2]))) \n\t Tensor(I(m), C[2]) L(mn, m))\n )),\n));\n\nNewRulesFor(DFT4, rec(\n DFT4_PF := rec(\n \tinfo := \"DFT4_nk -> diag perm * (DFT4_n_a tensor DFT4_k_b) * perm\",\n \tforTransposition := true,\n \tapplicable := nt -> nt.params[1] > 2 and DivisorPairsRP(nt.params[1]) <> [] and not nt.hasTags(),\n children := nt -> let(N := nt.params[1], k:= nt.params[2], Map2(DivisorPairsRP(N), \n \t\t(r,s) -> [ DFT4(r, 1/s mod r), DFT4(s, 1/r mod s) ])),\n \t\n apply := (nt, C, cnt) -> let(\n \t N := nt.params[1],\n \t r := Rows(C[1]), \n \t s := Rows(C[2]),\n \t alpha := 1 / s mod r,\n \t beta := 1 / r mod s,\n \t i := Ind(rs),\n \t d := Diag(Lambda(i, -sign(imod(salphaidiv(i,s) + rbetaimod(i,s), 2N) - N))),\n \t CRT(r,s).transpose() * \n \t d * (-E(4))\n \t Tensor(C[1], C[2]) \n \t d \n \t CRT(r,s)\n \t)\n#D \tisApplicable := P -> P[1] > 2 and DivisorPairsRP(P[1]) <> [] and Length(P[3]) = 0,\n#D \tallChildren := P -> let(N := P[1], k:= P[2], Map2(DivisorPairsRP(N), \n#D \t\t(r,s) -> [ DFT4(r, 1/s mod r), DFT4(s, 1/r mod s) ])),\n#D \t\n#D \trule := (P,C) -> let(\n#D \t N := P[1],\n#D \t r := Rows(C[1]), \n#D \t s := Rows(C[2]),\n#D \t alpha := 1 / s mod r,\n#D \t beta := 1 / r mod s,\n#D \t i := Ind(rs),\n#D \t d := Diag(Lambda(i, -sign(imod(salphaidiv(i,s) + rbetaimod(i,s), 2N) - N))),\n#D \t CRT(r,s).transpose() \n#D \t d * (-E(4))\n#D \t Tensor(C[1], C[2]) \n#D \t d *\n#D \t CRT(r,s)\n#D \t)\n )\n));\n\n", "meta": {"hexsha": "4e01c26420d3d8f474a10afc1e1f3171714b9f0c", "size": 5673, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/dft/dft234.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/transforms/dft/dft234.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/transforms/dft/dft234.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 32.6034482759, "max_line_length": 106, "alphanum_fraction": 0.4465009695, "num_tokens": 2287, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8376199633332891, "lm_q2_score": 0.6513548714339144, "lm_q1q2_score": 0.5455878435274346}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n# Here I define the new layer of \"index-free\" Sigma-SPL. I will use\n# this for library generation. The goal of index-free formulas is to\n# eliminate loop indices completely. In such formulas objects may\n# still depend on the loop indices, because gather/scatter/diagonal\n# functions become multivariate (vs. univariate) functions, taking\n# loop indices + point index as arguments. \n#\n# See \"Generalized Problem Spec\" write-up.\n#\n\nClass(GTIndexFunction, FuncClass, rec(\n isGTIndexFunction := true,\n\n # .upRank (=lift in spl.maude) is is the inverse of reduction .downRank, \n # it adds implicit dependency on the (new) inner loop, this happens when, eg.\n # gather is pulled into a loop: Gath(f) ISum(s) => ISum(Gath(f.upRank()) * s)\n upRank := self >> Error(\"Not implemented\"),\n\n upRankBy := (self, n) >> Checked(IsPosInt0(n), \n FoldL([1..n], (f, i) -> f.upRank(), self)),\n\n # .downRank (=red in spl.maude) is the \"reduction\" operator for\n # index mapping functions it eliminates implicit deendencies on loops \n # by introducing explicit references to loop variables ind(..)\n #\n # Eliminates dependency on loop <loopid>, 1 denotes innermost loop\n # <ind> is a loop index\n downRank := (self, loopid, ind) >> Error(\"Not implemented\"),\n\n # returns the rank, i.e., the number of implicit nested loops\n rank := self >> Error(\"Not implemented\"),\n\n # eliminated all loop dependencies \n downRankFull := (self, inds) >> \n FoldL(Reversed([1..Length(inds)]), (f, i) -> f.downRank(i, inds[i]), self),\n\n # split a loop, increase rank by 1, \n # if a loop had n iterations, the new outer loop will have <outer_its> iterations, \n # and next inner <inner_its> iterations\n split := (self, loopid, inner_its, outer_its) >> Error(\"not implemented\"),\n\n # rotate the ranks (see Doc(frotate) for explanation)\n rotate := (self, n) >> Error(\"not implemented\"),\n\n isUnitStride := self >> false,\n vecStride := (self, rank) >> self.params[4][rank+1],\n\n));\n\nClass(GTOps, rec(\n Print := PrintOps.Print,\n \\= := (a,b) -> When(IsBound(a.equals), a.equals(b), b=a)\n));\n\nIsGTIndexFunction := o -> IsRec(o) and IsBound(o.isGTIndexFunction) and o.isGTIndexFunction;\n\n# slow implementation, Haskell would love this\n_dropTail := (lst, arg) -> Cond(Length(lst)=0,lst,Cond(Last(lst)=arg, _dropTail(DropLast(lst, 1),arg), lst));\n\nClass(HHBase, GTIndexFunction, rec(\n abbrevs := [ (N,n,b,strides) -> [toExpArg(N), toExpArg(n), toExpArg(b), \n List(_dropTail(strides, 0), toExpArg)] ],\n def := (N, n, b, strides) -> Checked(IsList(strides), ForAll(strides, IsPosInt0Sym), \n\trec(N := N, n := n)), \n\n nloops := self >> Length(self.params[4]),\n free := self >> FreeVars(self.params),\n\n toSpl := (self, inds, kernel_size) >> self.downRankFull(inds),\n rank := self >> Maximum(0, Length(self.params[4])-1), # rank = number of implicit loop dependencies\n\n domain := self >> When(IsValue(self.params[2]), self.params[2].v, self.params[2]),\n range := self >> When(IsValue(self.params[1]), self.params[1].v, self.params[1]),\n\n base := self >> self.params[3],\n strides := self >> Cond(self.params[4] = [], [0], self.params[4]),\n\n # rotate(<n>)\n # switch the order of loops (represented by ranks), by making <n>-th loop innermost\n rotate := meth(self, n)\n local params, strides, rank;\n rank := self.rank();\n if rank<=1 and n<=1 then return self; \n elif n > rank then return self.upRank(); \n fi;\n \n params := ShallowCopy(self.params);\n strides := ShallowCopy(params[4]);\n strides := [strides[1], strides[n+1]] :: strides{[2..n]} :: strides{[n+2 .. rank+1]};\n params[4] := strides;\n return self.from_rChildren(params);\n end,\n\n isUnitStride := self >> false, # redefine if unit stride is possible\n));\n\nDeclare(KH, BHH, HH, HHZ);\n\n#F HH(<N>, <n>, <b>, <strides>) - generalized stride index mapping function\n#F N - range\n#F n - domain\n#F\n#F HH represents a multivariate function (j1 .. jn are indices of enclosing loops)\n#F (i, j1, ..., jn) -> b + strides[1]i + strides[2]j1 + ... + strides[n+1]jn\n#F\n#F Observe that dependence on the loop indices exists, even though no explicit\n#F loop index is present. This is how index free representation works.\n#F\nClass(HH, HHBase, rec(\n upRank := self >> let(s:=self.strides(), \n\tHH(self.params[1], self.params[2], self.params[3], Concatenation([s[1], 0], Drop(s, 1)))),\n\n downRank := (self, loopid, ind) >> Cond(loopid > self.rank(), self, let(s:=self.strides(),\n\tHH(self.params[1], self.params[2], s[loopid+1] ind + self.params[3], ListWithout(s, loopid+1)))),\n \n split := (self, loopid, inner_its, outer_its) >> Cond(loopid > self.rank(), self, let(\n strides := self.params[4],\n vs := self.params[4][1+loopid],\n\tHH(self.params[1], \n self.params[2], \n self.params[3], \n Concatenation(strides{[1..loopid+1]}, [inner_its * vs], strides{[loopid+2..Length(strides)]})))),\n \n lambda := self >> let(\n n := self.params[2],\n b := self.params[3],\n s := self.strides(),\n ind := List([1..Length(s)], i -> When(i=1, Ind(n), var.fresh_t(\"q\", TInt))),\n Lambda(Reversed(ind), b + Sum([1..Length(s)], i -> s[i] * ind[i]))),\n\n isUnitStride := self >> self.strides()[1] = 1\n));\n\nClass(BHH, HHBase, rec(\n abbrevs := [ (N,n,b,strides,refl) -> [toExpArg(N), toExpArg(n), toExpArg(b), List(_dropTail(strides,0), toExpArg), toExpArg(refl)] ],\n def := (N, n, b, strides, refl) -> Checked(\n IsList(strides), ForAll(strides, IsPosInt0Sym), IsPosIntSym(refl), \n\trec(N := N, n := n)), \n\n upRank := self >> let(s:=self.strides(), \n\tBHH(self.params[1], self.params[2], self.params[3], Concatenation([s[1], 0], Drop(s, 1)), self.params[5])),\n\n downRank := (self, loopid, ind) >> Cond(loopid > self.rank(), self, let(s:=self.strides(),\n\tBHH(self.params[1], self.params[2], self.params[3] + s[loopid+1] * ind, \n ListWithout(s, loopid+1), self.params[5]))),\n \n split := (self, loopid, inner_its, outer_its) >> Cond(loopid > self.rank(), self, let(\n strides := self.strides(),\n vs := self.params[4][1+loopid],\n\tBHH(self.params[1], \n self.params[2], \n self.params[3], \n Concatenation(strides{[1..loopid+1]}, [inner_its * vs], strides{[loopid+2..Length(strides)]}),\n self.params[5]))),\n \n lambda := self >> let(\n n := self.params[2],\n b := self.params[3],\n s := self.strides(),\n refl := self.params[5],\n inds := List([1..Length(s)], i -> When(i=1, Ind(n), var.fresh_t(\"q\", TInt))),\n res := b + Sum([1..Length(s)], i -> s[i] * inds[i]),\n Lambda(Reversed(inds), cond(leq(inds[1], idiv(n-1,2)), res, refl-res))\n ),\n));\n\n#F KH(<N>, <n>, <b>, <strides>, <corr>) - generalized (I_m dirsum J_m dirsum I_m ...) L^mn_n thingy\n#F N - range\n#F n - domain\n#F\n#F KH represents a multivariate function (j1 .. jn are indices of enclosing loops)\n#F (i, j1, ..., jn) -> b + strides[1]i + strides[2]j1 + ... + strides[n+1]jn\n#F\n#F Observe that dependence on the loop indices exists, even though no explicit\n#F loop index is present. This is how index free representation works.\n#F\nClass(KH, HHBase, rec(\n abbrevs := [ (N,n,b,strides,corr) -> [toExpArg(N), toExpArg(n), toExpArg(b), List(_dropTail(strides,0), toExpArg), List(corr, toExpArg)] ],\n def := (N, n, b, strides, corr) -> Checked(\n IsList(strides), ForAll(strides, IsPosInt0Sym), \n IsList(corr), ForAll(corr, IsIntSym), Length(corr) = 2, \n\trec(N := N, n := n)), \n\n upRank := self >> let(s:=self.strides(), \n\tKH(self.params[1], self.params[2], self.params[3], \n Concatenation([s[1], 0], Drop(s, 1)), \n self.params[5])),\n\n downRank := (self, loopid, ind) >> Checked(loopid=1, self.rank()=1, let(\n s:=self.strides(), corr:=self.params[5], b:=self.params[3],\n\tKH(self.params[1], \n self.params[2], \n b,\n [s[1]], \n [ s[2]ind + cond(neq(imod(ind,2),0), corr[2], corr[1]), \n s[1]-s[2]-ind + cond(neq(imod(ind,2),0), corr[1], corr[2]) ]))),\n \n lambda := self >> Checked(Length(self.strides())=1, let(\n n := self.params[2], \n b := self.params[3], \n s := self.strides()[1],\n i := Ind(n),\n corr_even := self.params[5][1], corr_odd := self.params[5][2],\n Lambda(i, b + si + imod(i+1, 2)corr_even + imod(i, 2)corr_odd)))\n));\n\n#F HHZ(<N>, <n>, <b>, <strides>) - generalized stride mod N index mapping (prime-factor FFT)\n#F N - range\n#F n - domain\n#F\n#F HHZ represents a multivariate function (j1 .. jn are indices of enclosing loops)\n#F (i, j1, ..., jn) -> (b + strides[1]i + strides[2]j1 + ... + strides[n+1]jn) mod N\n#F\n#F Observe that dependence on the loop indices exists, even though no explicit\n#F loop index is present. This is same as in HH. \n#F\nClass(HHZ, HHBase, rec(\n split := (self, loopid, inner_its, outer_its) >> Cond(loopid > self.rank(), self, let(\n strides := self.params[4],\n vs := self.params[4][1+loopid],\n\tHHZ(self.params[1], \n self.params[2], \n self.params[3], \n Concatenation(strides{[1..loopid+1]}, [inner_its * vs], strides{[loopid+2..Length(strides)]})))),\n\n upRank := self >> let(s:=self.strides(), \n\tHHZ(self.params[1], self.params[2], self.params[3], Concatenation([s[1], 0], Drop(s, 1)))),\n\n downRank := (self, loopid, ind) >> Cond(loopid > self.rank(), self, let(s:=self.strides(),\n\tHHZ(self.params[1], self.params[2], self.params[3] + s[loopid+1]ind, ListWithout(s, loopid+1)))),\n\n lambda := self >> let(hlambda := ApplyFunc(HH, self.params).lambda(),\n CopyFields(hlambda, rec(expr := imod(hlambda.expr, self.params[1]))))\n));\n\nDeclare(UU);\n\n## UU(<N>,<n>,<base>,<stride>,<columns>,<leading_dim>,\n## < <vstride_cols, vstride_rows>, ... > )\n## \n## index mapping: \n## (i, j1, ..., jn) -> \n## base + stride (i / columns) + leading_dim * (i mod columns)\n## + vstride_cols[1]j1 + ... + vstride_cols[n]jn\n## + (vstride_rows[1]j1 + ... + vstride_rows[n]jn)* leading_dim\n##\n## This is roughly the equivalent of an HH function for 2D inputs.\n\nClass(UU, GTIndexFunction, rec(\n abbrevs := [ (N, n, bX, bY, s, c, ld, strides) -> [toExpArg(N), toExpArg(n), toExpArg(bX), toExpArg(bY),\n toExpArg(s), toExpArg(c), toExpArg(ld),\n List(_dropTail(strides,[0,0]), x->List(x,toExpArg))] ],\n def := (N, n, bX, bY, s, c, ld, strides) -> Checked(IsList(strides), ForAll(strides, x-> \n IsList(x) and Length(x)=2 and ForAll(x,IsPosInt0Sym)), \n rec(N := N, n := n)), \n\n nloops := self >> Length(self.params[8]),\n free := self >> FreeVars(self.params),\n\n toSpl := (self, inds, kernel_size) >> self.downRankFull(inds),\n rank := self >> Length(self.params[8]), # rank = number of implicit loop dependencies\n\n domain := self >> When(IsValue(self.params[2]), self.params[2].v, self.params[2]),\n range := self >> When(IsValue(self.params[1]), self.params[1].v, self.params[1]),\n\n upRank := self >> let(ss:=self.params[8], \n\tUU(self.params[1], self.params[2], self.params[3], self.params[4], self.params[5], self.params[6], self.params[7], \n Concatenation([[0,0]], ss))),\n\n downRank := (self, loopid, ind) >> Cond(loopid > self.rank(), self, let(ss:=self.params[8],\n\tUU(self.params[1], self.params[2], self.params[3] + ss[loopid][1] * ind, self.params[4] + ss[loopid][2] * ind * self.params[7],\n self.params[5], self.params[6], self.params[7], ListWithout(ss, loopid)))),\n\n split := (self, loopid, inner_its, outer_its) >> Cond(loopid > self.rank(), self, let(\n strides := self.params[8],\n vs := self.params[8][loopid],\n UU(self.params[1], \n self.params[2], \n self.params[3], \n self.params[4],\n self.params[5],\n self.params[6],\n self.params[7],\n Concatenation(strides{[1..loopid]}, [inner_its * vs], strides{[loopid+1..Length(strides)]})))),\n\n \n lambda := self >> let(\n n := self.params[2],\n bX := self.params[3],\n bY := self.params[4],\n s := self.params[5],\n c := self.params[6],\n ld := self.params[7],\n ss := self.params[8],\n ind := List([1..Length(ss)], i -> var.fresh_t(\"q\", TInt)),\n index := Ind(n),\n Lambda(Concatenation(Reversed(ind),[index]), (bX + imod(index,c) * s) + (bY+idiv(index,c) * ld) + Sum([1..Length(ss)], i -> ss[i][1] * ind[i]) + Sum([1..Length(ss)], i -> ss[i][2] * ind[i] * ld))),\n\n isUnitStride := self >> Error(\"isUnitStride is not supported for now with UU\"),\n));\n\nDeclare(XChain);\n\n#F XChain( <permuted [1..n]> ) - fTensor chain of fBase's and single fId.\n#F\n#F This represents a subset of functions captured by HH. Namely those\n#F functions that described tightly packed index space, i.e.,\n#F if f is an XChain in k-nested loop with dimensions in loop_dims, then\n#F\n#F domain(f) * Product(loop_dims) = range(f)\n#F\nClass(XChain, GTIndexFunction, rec(\n def := perm -> Checked(IsList(perm), ForAll(perm, IsPosInt0), \n\tSet(Copy(perm))=[0..Length(perm)-1],\n rec()),\n\n range := self >> 0,\n domain := self >> 0,\n\n equals := (self, o) >> ObjId(self)=ObjId(o) and self.params[1]=o.params[1],\n\n printFull := self >> Print(self.name, \"(\", self.params[1], \")\"),\n printShort := self >> Print(\"x(\", PrintCS(self.params[1]), \")\"),\n\n toSpl := (self, inds, kernel_size) >> let(fbases := List(inds, fBase),\n\tApplyFunc(fTensor, List(self.params[1], i -> When(i=0, fId(kernel_size), fbases[i])))),\n\n toDiag := (self, loop_dims, kernel) >> let(fconst := List(loop_dims, d->fConst(d,1)),\n\tApplyFunc(diagTensor, List(self.params[1], i -> When(i=0, kernel, fconst[i])))),\n\n without := (self, loopid) >> Checked(loopid >= 1, loopid <= Length(self.params[1])-1, let(\n\tlst := ListWithout(self.params[1], Position(self.params[1], loopid)),\n\tXChain(List(lst, x -> When(x < loopid, x, x-1))))),\n\n part := (self, loopid, ind, kernel_size, loop_dims) >> \n ApplyFunc(fTensor, List(self.params[1], i ->\n\t Cond(i=0, fId(kernel_size),\n\t\t i=loopid, fBase(ind),\n\t\t fId(loop_dims[i])))),\n \n composeWith := (self, f) >> When(ObjId(f)<>XChain, Error(\"Can only compose with another XChain\"),\n\tlet(fperm := f.params[1], \n\t myperm := self.params[1],\n\t pos := Position(myperm, 0),\n\t XChain(Concatenation(1+myperm{[1..pos-1]}, fperm, 1+myperm{[pos+1..Length(myperm)]})))),\n));\n\n\n# NOTE: toSpl -> SubstTopDown( ind -> inds[i] )\n# Normal functions retrofitted for GT\nfId.toSpl := (self, inds, ksize) >> self; \nfId.without:= (self, loopid) >> self;\nfId.part := (self, loopid, loopvar, kernel_size, loop_dims) >> self;\n#fId.toDiag := (self, loop_dims) >> fConst(TReal, self.params[1], 1);\n\nfBase.toSpl := (self, inds, ksize) >> Cond(\n ObjId(self.params[2])=ind, fBase(inds[self.params[2].n]), \n self);\n\nfBase.without := (self, loopid) >> Cond(\n self.params[2]=ind(self.params[1], loopid), fBase(self.params[1], 0),\n self);\n\nfBase.part := (self, loopid, loopvar, ksize, loop_dims) >> Cond(\n self.params[2]=ind(self.params[1], loopid), fAdd(self.params[1], self.params[1], loopvar), \n fId(self.params[1]));\n\nfTensor.part := (self, loopid, loopvar, ksize, loop_dims) >>\n ApplyFunc(fTensor, List(self.children(), c -> c.part(loopid, loopvar, ksize, loop_dims)));\n\nfTensor.without := (self, loopid) >> \n ApplyFunc(fTensor, List(self.children(), c -> c.without(loopid)));\n\nfTensor.toSpl := (self, inds, ksize) >> \n ApplyFunc(ObjId(self), List(self.children(), c -> c.toSpl(inds, ksize)));\n\nfCompose.toSpl := (self, inds, ksize) >> \n ApplyFunc(fCompose, List(self.children(), c -> c.toSpl(inds, ksize)));\n\nFuncClass.toSpl := (self, inds, ksize) >> self;\n\n#FuncClassOper.rank := self >> Maximum(List(self.children(), x->x.rank()));\n#FuncClass.rank := self >> 0;\n#DiagFunc.rank := self >> 0;\n\nFuncClassOper.isUnitStride := self >> false; \nFuncClass.isUnitStride := self >> false;\nfId.isUnitStride := self >> true;\nfTensor.isUnitStride := self >> ForAll(self._children, x->x.isUnitStride());\n#fBase.toDiag := (self, loop_dims) >> fConst(TReal, self.params[1], 1);\n#fId.part := (self, loopid, ind, kernel_size, loop_dims) >> self;\n\nListAddP := function(l1, l2, c)\n local i, lenl1, lenl2, res, maxlen, minlen;\n lenl1 := Length(l1);\n lenl2 := Length(l2);\n minlen := Minimum(lenl1, lenl2);\n maxlen := Maximum(lenl1, lenl2);\n res := Concatenation(l1, Replicate(maxlen-lenl1, c)); \n for i in [1..lenl2] do \n res[i] := res[i] + l2[i];\n od;\n return res;\nend;\n\nListAddZP := (l1, l2) -> ListAddP(l1,l2,0);\nListAddLP := (l1, l2) -> ListAddP(l1,l2,[0,0]);\n\n", "meta": {"hexsha": "1823df912da8b34df8e5c51d2afb7a1b1e626cf5", "size": 17199, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/spl/gtfuncs.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/spl/gtfuncs.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/spl/gtfuncs.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 41.5434782609, "max_line_length": 206, "alphanum_fraction": 0.5891040177, "num_tokens": 5322, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. 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	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nImportAll(spiral.formgen);\nImportAll(spiral.transforms);\nImportAll(spiral.compiler);\n\ndoScalarDft := function(arg)\n\tlocal szs, userOpts, isSingle, opts, direction, func, file, t, rt, ir, N, cycles, flops;\n\t\n\tif not (Length(arg) in [1..2]) then\n\t\tError(\"usage: doScalarDft(sizes, [userOptions])\");\n\tfi;\n\t\n\tszs := When(IsList(arg[1]), arg[1], [ arg[1] ]);\n\tuserOpts := When(IsBound(arg[2]), arg[2], rec());\n\t\n\tisSingle := IsBound(userOpts.precision) and userOpts.precision = \"single\";\n\t\n\topts := CopyFields(SpiralDefaults, rec(\n\t\t\t\tprecision := When(isSingle, \"single\", \"double\"),\n\t\t\t\tTRealCtype := When(isSingle, \"float\", \"double\"),\n\t\t\t));\n\t\n\topts.globalUnrolling := 512;\n\t\t\n\tdirection := When(IsBound(userOpts.transInverse) and userOpts.transInverse, 1, -1);\n\t\n\tfor N in szs do\n\t\tif IsBound(userOpts.functionNameRoot) then\n\t\t\tfunc := ReplaceAll(userOpts.functionNameRoot, \"%sz1\", StringInt(N));\n\t\telse\n\t\t\tfunc := When(direction=1,\"i\",\"\")::\"DFT\"::When(isSingle, \"_SC\", \"_DC\")::StringInt(N);\n\t\tfi;\n\t\t\n\t\tfile := func::\".c\";\n\t\t\n\t\tt := DFT(N, direction);\n\t\trt := RandomRuleTree(t, opts);\n\t\tir := CodeRuleTree(rt, opts);\n\t\t\n\t\tPrintTo(file, PrintCode(func, ir, opts));\n\t\t\n\t\tcycles := CMeasure(ir, opts);\n\t\tflops:= t.normalizedArithCost();\n\t\tPrintLine(t, \" \", cycles, \" [cyc] \", _compute_gflops(flops, cycles), \" [Gf/s]\");\n\tod;\n\t\n\treturn true;\nend;\n\n\ndoScalar2DDft := function(arg)\n\tlocal szs, userOpts, isSingle, opts, direction, func, file, t, rt, ir, dims, cycles, flops;\n\t\n\tif not ((Length(arg) in [1..2]) and IsList(arg[1]) and Length(arg[1]) > 0) then\n\t\tError(\"usage: doScalar2DDft(sizes, [userOptions])\");\n\tfi;\n\t\n\tszs := arg[1];\n\tif Length(szs) = 2 and IsInt(szs[1]) and IsInt(szs[2]) then\n\t\tszs := [ szs ];\n\telif not ForAll(szs, dims -> Length(dims) = 2 and IsInt(dims[1]) and IsInt(dims[2])) then\n\t\tError(\"sizes must be one or more pairs of integers\");\n\tfi;\n\t\n\tuserOpts := When(IsBound(arg[2]), arg[2], rec());\n\t\n\tisSingle := IsBound(userOpts.precision) and userOpts.precision = \"single\";\n\t\n\topts := CopyFields(SpiralDefaults, rec(\n\t\t\t\tprecision := When(isSingle, \"single\", \"double\"),\n\t\t\t\tTRealCtype := When(isSingle, \"float\", \"double\"),\n\t\t\t));\n\t\t\t\t\n\topts.globalUnrolling := 128;\n\t\n\tdirection := When(IsBound(userOpts.transInverse) and userOpts.transInverse, 1, -1);\n\t\n\tfor dims in szs do\n\t\tif IsBound(userOpts.functionNameRoot) then\n\t\t\tfunc := ReplaceAll(userOpts.functionNameRoot, \"%sz1\", StringInt(dims[1]));\n\t\t\tfunc := ReplaceAll(func, \"%sz2\", StringInt(dims[2]));\n\t\telse\n\t\t\tfunc := When(direction=1,\"i\",\"\")::\"DFT\"::When(isSingle, \"_SC\", \"_DC\")::StringInt(dims[1])::\"x\"::StringInt(dims[2]);\n\t\tfi;\n\t\t\n\t\tfile := func::\".c\";\n\t\t\n\t\tt := MDDFT(dims, direction);\n\t\trt := RandomRuleTree(t, opts);\n\t\tir := CodeRuleTree(rt, opts);\n\t\t\n\t\tPrintTo(file, PrintCode(func, ir, opts));\n\t\t\n\t\tcycles := CMeasure(ir, opts);\n\t\tflops:= t.normalizedArithCost();\n\t\tPrintLine(t, \" \", cycles, \" [cyc] \", _compute_gflops(flops, cycles), \" [Gf/s]\");\n\tod;\n\t\n\treturn true;\nend;\n\n\n\nClass(ScriptGenScalar, ScriptGenBase, rec(\n\n\t_arch := () -> \"Scalar\",\n\n\n\t_init := meth(self)\n\t\tself._setTransform(SGKEY_FFT);\n\t\tself._setType(SGKEY_SPCX);\n\t\tself._setSize(16);\n\t\tself._setFilename(\"\");\n\tend,\n\t\n\t\n\t_validTransforms := meth(arg)\n\t\treturn [SGKEY_FFT, SGKEY_IFFT, SGKEY_FFT_2D, SGKEY_IFFT_2D];\n\tend,\n\t\n\t\n\t_validSizes := meth(arg)\n\t\tlocal self, szs, xform, type;\n\t\tself := arg[1];\n\t\tszs := [];\n\t\txform := self.getSettingsValue(SGKEY_TRANSFORM);\n\t\ttype := self.getSettingsValue(SGKEY_DATATYPE);\n\t\t\n\t\tif xform in [SGKEY_FFT, SGKEY_IFFT] then\n\t\t\tszs := Filtered([2..512], i->ForAll(Factors(i), j->j<=19));\n\t\t\tAppend(szs, Filtered([513..1024], i->ForAll(Factors(i), j->j<=19) and IsInt(i/16)));\n\t\t\tAppend(szs, List([11..16], i->2^i));\n\t\telif xform in [SGKEY_FFT_2D, SGKEY_IFFT_2D] then\n\t\t\tszs := List(Filtered([2..360], i->ForAll(Factors(i), j->j<=19)), n -> [n, n]);\n\t\telif xform = SGKEY_WHT then\n\t\t\tif type = SGKEY_DPCX then\n\t\t\t\tszs := List([2..10], i->2^i);\n\t\t\telse\n\t\t\t\tszs := List([4..10], i->2^i);\n\t\t\tfi;\n\t\tfi;\n\t\t\t\t\n\t\treturn szs;\n\tend,\n\t\n\t\n\t_validTypes := meth(arg)\n\t\treturn [SGKEY_SPCX, SGKEY_DPCX];\n\tend,\n\n\t\n\tgetScriptChoices := (self) >> [SGSTR_RUNRANDOMALL], \n\t\n\t\n\t_genScript := meth(self, runType)\n\t\tlocal scrstr, xform, type, szs, tempopts, optrec, optstr, funcstr;\n\t\t\n\t\txform\t := self.getSettingsValue(SGKEY_TRANSFORM);\n\t\ttype\t := self.getSettingsValue(SGKEY_DATATYPE);\n\t\tszs := self.getSettingsValue(SGKEY_SIZE);\n\t\t\n\t\ttempopts := \"scriptOpts\";\n\t\t\n\t\toptrec\t := rec(\n\t\t\t\t\t\tprecision := When(type=SGKEY_SPCX, \"single\", \"double\"),\n\t\t\t\t\t\tsearchType := runType,\n\t\t\t\t\t);\n\t\tif IsBound(self._settings.(SGKEY_FUNCNAME)) then\n\t\t\toptrec.functionNameRoot := self._settings.(SGKEY_FUNCNAME);\n\t\tfi;\n\t\tif xform in [SGKEY_IFFT, SGKEY_IFFT_2D] then\n\t\t\toptrec.transInverse := true;\n\t\tfi;\n\t\t\t\t\n\t\tif xform in [SGKEY_FFT, SGKEY_IFFT] then\n\t\t\tfuncstr := \"doScalarDft(\"::String(szs)::\", \"::tempopts::\")\";\n\t\telif xform in [SGKEY_FFT_2D, SGKEY_IFFT_2D] then\n\t\t\tfuncstr := \"doScalar2DDft(\"::String(szs)::\", \"::tempopts::\")\";\n\t\telse\n\t\t\treturn \"\";\n\t\tfi;\n\t\t\t\t\n\t\toptstr := StringPrint(optrec);\n\t\t\n\t\tscrstr := \"Import(scriptgen);;\\n\";\n\t\tAppend(scrstr, tempopts::\" := \"::optstr::\";;\\n\");\n\t\tAppend(scrstr, funcstr::\";;\\n\");\n\t\t\t\n\t\treturn scrstr;\n\tend,\n)); # Class ScriptGenScalar\n\n\nSetScriptGenConstructor(ScriptGenScalar);\n\n", "meta": {"hexsha": "d0e22d1fc5a012fb20fda58fd1c15a4e7ebb3799", "size": 5387, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/scriptgen/scalar.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/scriptgen/scalar.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", 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YES\n2. YES\n\n", "lm_q1_score": 0.7931059414036511, "lm_q2_score": 0.6859494678483918, "lm_q1q2_score": 0.5440305984532323}}
	{"text": "#############################################################################\n##\n## This file is part of GAP, a system for computational discrete algebra.\n## This file's authors include Alexander Hulpke.\n##\n## Copyright of GAP belongs to its developers, whose names are too numerous\n## to list here. Please refer to the COPYRIGHT file for details.\n##\n## SPDX-License-Identifier: GPL-2.0-or-later\n##\n## This file contains the methods for the construction of the basic fp group\n## types.\n##\n\n\n \n#############################################################################\n##\n#M TrivialGroupCons( <IsPcGroup> )\n##\nInstallMethod( TrivialGroupCons, \"fp group\",\n [ IsFpGroup and IsTrivial ],\n filter -> FreeGroup(0));\n\n\n#############################################################################\n##\n#M AbelianGroupCons( <IsFpGroup and IsFinite>, <ints> )\n##\nInstallMethod( AbelianGroupCons, \"fp group\", true,\n [ IsFpGroup and IsAbelian, IsList ], 0,\nfunction( filter, ints )\nlocal f,g,i,j,rels,gfam,fam;\n\n if Length(ints)=0 or not ForAll( ints, x -> IsInfinity(x) or (IsInt(x) and x >= 0) ) then\n Error( \"<ints> must be a list of integers\" );\n fi;\n\n f := FreeGroup(IsSyllableWordsFamily, Length(ints));\n g := GeneratorsOfGroup(f);\n rels:=[];\n for i in [1..Length(ints)] do\n for j in [1..i-1] do\n Add(rels,Comm(g[i],g[j]));\n od;\n if IsPosInt(ints[i]) then\n Add(rels,g[i]^ints[i]);\n fi;\n od;\n\n g:=f/rels;\n\n if ForAll(ints,IsPosInt) then\n SetSize( g, Product(ints) );\n else\n SetSize( g, infinity );\n fi;\n\n fam:=FamilyObj(One(f));\n gfam:=FamilyObj(One(g));\n gfam!.redorders:=ints;\n SetFpElementNFFunction(gfam,function(x)\n local u,e,i,j,n;\n u:=UnderlyingElement(x);\n e:=ExtRepOfObj(u); # syllable form\n\n # bring in correct order and reduction\n n:=ListWithIdenticalEntries(Length(gfam!.redorders),0);\n for i in [1,3..Length(e)-1] do\n j:=e[i];\n if IsPosInt(gfam!.redorders[j]) then\n\tn[j]:=n[j]+e[i+1] mod gfam!.redorders[j];\n else\n\tn[j]:=n[j]+e[i+1];\n fi;\n od;\n\n e:=[];\n for i in [1..Length(gfam!.redorders)] do\n if n[i]<>0 then\n\tAdd(e,i);\n\tAdd(e,n[i]);\n fi;\n od;\n\n return ObjByExtRep(fam,e);\n end);\n\n SetReducedMultiplication(g);\n SetIsAbelian( g, true );\n\n return g;\nend );\n\n#############################################################################\n##\n#M CyclicGroupCons( <IsFpGroup>, <n> )\n##\nInstallOtherMethod( CyclicGroupCons, \"fp group\", true,\n [ IsFpGroup and IsCyclic, IsObject ], 0,\nfunction( filter, n )\nlocal f,g,fam,gfam;\n if n=infinity then\n return FreeGroup(\"a\");\n elif not IsPosInt(n) then\n TryNextMethod();\n fi;\n f:=FreeGroup( IsSyllableWordsFamily, \"a\" );\n g:=f/[f.1^n];\n SetSize(g,n);\n fam:=FamilyObj(One(f));\n gfam:=FamilyObj(One(g));\n SetFpElementNFFunction(gfam,function(x)\n local u,e;\n u:=UnderlyingElement(x);\n e:=ExtRepOfObj(u); # syllable form\n if Length(e)=0 or (e[2]>=0 and e[2]<n) then\n return u;\n elif e[2] mod n=0 then\n return One(f);\n else\n e:=[e[1],e[2] mod n];\n return ObjByExtRep(fam,e);\n fi;\n end);\n\n SetReducedMultiplication(g);\n return g;\nend );\n\n\n#############################################################################\n##\n#M DihedralGroupCons( <IsFpGroup and IsFinite>, <n> )\n##\nInstallMethod( DihedralGroupCons,\n \"fp group\",\n true,\n [ IsFpGroup and IsFinite,\n IsInt and IsPosRat ],\n 0,\n\nfunction( filter, n )\nlocal f,rels,g;\n\n if n mod 2 = 1 then\n TryNextMethod();\n elif n = 2 then return\n CyclicGroup( IsFpGroup, 2 );\n fi;\n f := FreeGroup( IsSyllableWordsFamily, \"r\", \"s\" );\n rels:= [f.1^(n/2),f.2^2,f.1^f.2f.1];\n g := f/rels;\n SetSize(g,n);\n SetReducedMultiplication(g);\n return g;\n\nend );\n\nInstallOtherMethod( DihedralGroupCons,\n \"fp group\",\n true,\n [ IsFpGroup and IsFinite,\n IsInfinity ],\n 0,\n\nfunction( filter, inf )\nlocal f,rels,g;\n\n f := FreeGroup( IsSyllableWordsFamily, \"r\", \"s\" );\n rels:= [f.2^2,f.1^f.2f.1];\n g := f/rels;\n SetSize(g,infinity);\n SetReducedMultiplication(g);\n return g;\n\nend );\n\n#############################################################################\n##\n#M DicyclicGroupCons( <IsFpGroup and IsFinite>, <n> )\n##\nInstallMethod( DicyclicGroupCons,\n \"fp group\",\n true,\n [ IsFpGroup and IsFinite,\n IsInt and IsPosRat ],\n 0,\nfunction( filter, n )\nlocal f,rels,g;\n if 0 <> n mod 4 then\n TryNextMethod();\n elif n = 4 then return\n CyclicGroup( IsFpGroup, 4 );\n fi;\n f := FreeGroup( IsSyllableWordsFamily, \"r\", \"s\" );\n rels:= [ f.1^2/f.2^(n/4), f.2^(n/2), f.2^f.1*f.2 ];\n g := f/rels;\n SetSize(g,n);\n if n <= 10^4 then SetReducedMultiplication(g); fi;\n return g;\nend );\n\n#############################################################################\n##\n#M ElementaryAbelianGroupCons( <IsFpGroup and IsFinite>, <n> )\n##\nInstallMethod( ElementaryAbelianGroupCons,\n \"fp group\",\n true,\n [ IsFpGroup and IsFinite and IsElementaryAbelian,\n IsInt and IsPosRat ],\n 0,\n\nfunction( filter, n )\n if n = 1 then\n return CyclicGroupCons( IsFpGroup, 1 );\n elif not IsPrimePowerInt(n) then\n Error( \"<n> must be a prime power\" );\n fi;\n n:= AbelianGroupCons( IsFpGroup, Factors(n) );\n SetIsElementaryAbelian( n, true );\n return n;\nend );\n\n\n#############################################################################\n##\n#M FreeAbelianGroupCons( <IsFpGroup>, <rank> )\n##\nInstallMethod( FreeAbelianGroupCons,\n \"fp group\",\n true,\n [ IsFpGroup and IsAbelian,\n IsInt and IsPosRat ],\n 0,\n\nfunction( filter, rank )\n return AbelianGroupCons( filter, ListWithIdenticalEntries(rank, 0) );\n # TODO: Add the following if it ever moves from Polycyclic to the GAP core:\n #SetIsFreeAbelian( G, true );\nend );\n\n", "meta": {"hexsha": "ee11009956f70afcb4fb3b8cc06d5e5979c32076", "size": 5839, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "test_files/gap.gi", "max_stars_repo_name": "pheonixo/file_info", "max_stars_repo_head_hexsha": "1585f9938e591ea92312f49d9d2d7481951d9e18", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "test_files/gap.gi", "max_issues_repo_name": "pheonixo/file_info", "max_issues_repo_head_hexsha": "1585f9938e591ea92312f49d9d2d7481951d9e18", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "test_files/gap.gi", "max_forks_repo_name": "pheonixo/file_info", "max_forks_repo_head_hexsha": "1585f9938e591ea92312f49d9d2d7481951d9e18", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 23.9303278689, "max_line_length": 92, "alphanum_fraction": 0.5521493406, "num_tokens": 1795, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. 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	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nClass(LoopGath, Gath);\nClass(LoopScat, Scat);\nClass(LoopPrm, Prm);\n\nFuncClass.gath := self >> Gath(self);\nFuncClass.scat := self >> Scat(self);\n\nfId.gath := self >> I(self.params[1]);\nfId.scat := self >> I(self.params[1]);\n\nL.scat := self >> let(m:=self.params[2], n:=self.params[1]/self.params[2], j:=Ind(m), fid := fId(n), fbase := fBase(m,j),\n gath := Gath(fTensor(fid, fbase)), scat := Scat(fTensor(fbase, fid)),\n ISum(j, m, scatgath));\n\nL.gath := self >> let(m:=self.params[2], n:=self.params[1]/self.params[2], j:=Ind(n), fid := fId(m), fbase := fBase(n,j),\n gath := Gath(fTensor(fbase, fid)), scat := Scat(fTensor(fid, fbase)),\n ISum(j, n, scatgath));\n\nfCompose.gath := self >> Compose(Reversed(List(self.children(), i->i.gath())));\nfCompose.scat := self >> Compose(List(self.children(), i->i.scat()));\n\nfTensorBuf := function(func, combine)\n local ch, n, loopvars, i, lv, newch1, newch2, res; \n ch := func.children();\n n := Length(ch);\n loopvars := List(Filtered(ch, c -> ObjId(c)=fId), c -> Ind(c.size));\n \n lv := 1; newch1 := []; newch2 := [];\n for i in [1..n] do\n if ObjId(ch[i]) <> fId then\n\t Add(newch1, ch[i]);\n\telse\n\t Add(newch1, fBase(loopvars[lv]));\n\t Add(newch2, fBase(loopvars[lv]));\n\t lv := lv+1;\n\tfi;\n od;\n\n res := combine(fTensor(newch1), fTensor(newch2));\n\n # lv here is number of loopvars + 1\n for i in Reversed([1..lv-1]) do\n res := ISum(loopvars[i], res);\n\t# unroll inner loop\n\t#if i=lv-1 then res:=BB(res); fi;\n od;\n return res;\nend;\n\n#fTensor.gath := self >> Tensor(List(self.children(), i->i.gath()));\n\nfTensor.scat := self >> fTensorBuf(self, (f1, f2) -> BB(Scat(f1) * Gath(f2)));\nfTensor.gath := self >> fTensorBuf(self, (f1, f2) -> BB(Scat(f2) * Gath(f1)));\n\n", "meta": {"hexsha": "4f89fd32e5386ba906724a93425be4250bfc5d8e", "size": 1925, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/loops/sigmaspl.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/paradigms/loops/sigmaspl.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/paradigms/loops/sigmaspl.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 32.0833333333, "max_line_length": 121, "alphanum_fraction": 0.5688311688, "num_tokens": 632, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7662936430859597, "lm_q2_score": 0.7090191214879992, "lm_q1q2_score": 0.5433168456226456}}
	{"text": "# Built-in\nA := [[1, 2], [3, 4], [5, 6], [7, 8]];\nB := [[1, 2, 3], [4, 5, 6]];\n\nPrintArray(A);\n# [ [ 1, 2 ],\n# [ 3, 4 ],\n# [ 5, 6 ],\n# [ 7, 8 ] ]\n\nPrintArray(B);\n# [ [ 1, 2, 3 ],\n# [ 4, 5, 6 ] ]\n\nPrintArray(A * B);\n# [ [ 9, 12, 15 ],\n# [ 19, 26, 33 ],\n# [ 29, 40, 51 ],\n# [ 39, 54, 69 ] ]\n", "meta": {"hexsha": "3367ffc2635a5f7bf5c19cff40d3a3b7f0f01fc8", "size": 340, "ext": "gap", "lang": "GAP", "max_stars_repo_path": "Task/Matrix-multiplication/GAP/matrix-multiplication.gap", "max_stars_repo_name": "LaudateCorpus1/RosettaCodeData", "max_stars_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_stars_repo_licenses": ["Info-ZIP"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2018-11-09T22:08:38.000Z", "max_stars_repo_stars_event_max_datetime": "2018-11-09T22:08:38.000Z", "max_issues_repo_path": "Task/Matrix-multiplication/GAP/matrix-multiplication.gap", "max_issues_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_issues_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_issues_repo_licenses": ["Info-ZIP"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Task/Matrix-multiplication/GAP/matrix-multiplication.gap", "max_forks_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_forks_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_forks_repo_licenses": ["Info-ZIP"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2018-11-09T22:08:40.000Z", "max_forks_repo_forks_event_max_datetime": "2018-11-09T22:08:40.000Z", "avg_line_length": 17.0, "max_line_length": 38, "alphanum_fraction": 0.2764705882, "num_tokens": 204, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8933094003735664, "lm_q2_score": 0.6076631698328916, "lm_q1q2_score": 0.5428312218725211}}
	{"text": "# Solving equations over Free Groups\n\nInstallGlobalFunction(FreeGroupEquationSolve,\nfunction(w,u)\n local vars, consts;\n\n vars := GeneratorsOfGroup(FreeGroupOfWord(w));\n consts := GeneratorsOfGroup(FreeGroupOfWord(u));\n\nend);\n\n\n#\tex and ey are the x- and y-exponent sums of the word w respectively.\n#\tq is the quotient of the exponent sums, e.g. if exponent sums are 3 and 7 then q=2, as 2x3+1=7\n#\taut:=[x', y'] is a list consisting of the Neilsen generating pair corresponding to the Moldovanskii rewriting.\n#\tThat is, if w' is the rewritten form of w then there exists an automorphism\n#\t\\phi of F(x, y) such that \\phi(w)=w'. In aut, x' and y' are such that\n#\t\\phi(x)=x', \\phi(y)=y'. For example, for mold:=Moldovanskii(u); where u is\n#\tsome word over x and y, then mold[1]; and MappedWord(u, [x, y], mold[2]); are\n#\tthe same word.\n# NOTE: It may be that MappedWord is better than Eliminated word\n#\tfor our purposes? As might not use syllable notation! (Section 36.3-1 of GAP\n#\tdocumentation.)\n\n# TODO: Tests: Some words to rewrite + test that applying the auotmorphism\n# stabilises them.\n# Check whether w is a commutator, and error if it is\n# Error(\"w is a commutator\");\n# Error(\"\");\n\nInstallGlobalFunction(MoldovanskiiRewritingByGenerators,\nfunction(w,x,y)\n\t local ex, ey, q, aut;\n\n\t ex := ExponentSumWord(w, x);\n\t ey := ExponentSumWord(w, y);\n\t aut := [x, y];\n\n\t while ex<>0 and ey<>0 do\n\t\t if AbsInt(ey)>=AbsInt(ex) then\n\t\t\t q := -QuoInt(ey, ex); # QuoInt is quotient of integers\n\t\t\t w := MappedWord(w, [x], [xy^q] );\n\t\t\t aut[1] := MappedWord(aut[1], [x], [xy^q] );\n\t\t\t aut[2] := MappedWord(aut[2], [x], [xy^q] );\n\t\t\t ey := ExponentSumWord(w, y);\n\t\t elif AbsInt(ex)>AbsInt(ey) then\n\t\t\t q := -QuoInt(ex, ey);\n\t\t\t w := MappedWord(w, [y], [yx^q] );\n\t\t\t aut[1] := MappedWord(aut[1], [y], [yx^q] );\n\t\t\t aut[2] := MappedWord(aut[2], [y], [yx^q] );\n\t\t\t ex := ExponentSumWord(w, x);\n\t\t fi;\n\t od;\n\t return [w, aut];\nend);\n\n# We're looking for solutions to w(x,y) = u(a,b)\n# 1. Rewrite w(x,y) as w_0(xy^-1x, y)\n# If expoent sum of x <> 0 or y <> 0 then do\n# Moldovanski rewriting to get one of htem to 0.\n# Also remember the rewriting step\n# 2. If w_0 is in <x^eps y x, y> or <y^eps x y, x >\n# (If w_0 in <y^-1xy, x> then reinterpret x->x_0, y->x_0y_0\n\n# Solves the equation w(x,y) = u(a,b) where w in F(x,y) :wq\n# There is no real reason to not use\n# list and not just 2 variables\nInstallGlobalFunction(IsSolution,\nfunction(w, u, xs, ixs)\n return MappedWord(w, xs, ixs) = u;\nend);\n\nInstallGlobalFunction(SubwordLength,\nfunction(word_string, i)\n\tlocal subword, exp, next_exp, subcount, letter, j;\n\tsubcount := 0;\n\twhile i <= Length(word_string) do\n\t\tnext_exp := 0;\n\t\tletter := word_string[i];\n\t\tif IsAlphaChar(letter) then\n\t\t\tif word_string[i+1] = '^' then\n\t\t\t\tnext_exp := Int([word_string[i+2]]);\n\t\t\t\ti := i + 3;\n\t\t\t\twhile IsDigitChar(word_string[i]) do\n\t\t\t\t\tnext_exp := 10next_exp;\n\t\t\t\t\tnext_exp := next_exp + Int([word_string[i]]);\n\t\t\t\t\ti := i + 1;\n\t\t\t\tod;\n\t\t\t\tsubcount := subcount + next_exp;\n\t\t\telse\n\t\t\t\tsubcount := subcount + 1;\n\t\t\t\ti := i + 1;\n\t\t\tfi;\n\t\telif letter = ')' then\n\t\t\treturn subcount;\n\t\telif letter = '(' then\n\t\t\tsubword := SubwordLength(word_string, i + 1);\n\t\t\tj := 0;\n\t\t\twhile word_string[i + j] <> ')' do\n\t\t\t\tj := j + 1;\n\t\t\tod;\n\t\t\ti := i + j + 1;\n\t\t\texp := 1;\n\t\t\tif i >= Length(word_string) then\n\t\t\t\treturn -1;\n\t\t\tfi;\n\t\t\tif word_string[i] = '^' then\n\t\t\t\texp := Int([word_string[i + 1]]);\n\t\t\t\ti := i + 2;\n\t\t\t\twhile IsDigitChar(word_string[i]) do\n\t\t\t\t\texp := 10exp;\n\t\t\t\t\texp := exp + Int([word_string[i]]);\n\t\t\t\t\ti := i + 1;\n\t\t\t\tod;\n\t\t\tfi;\n\t\t\tsubcount := subcount + (exp * subword);\n\t\t\tif i >= Length(word_string) then\n\t\t\t\treturn -1;\n\t\t\tfi;\n\t\telse\n\t\t\ti := i + 1;\n\t\tfi;\n\tod;\nend);\n\n# Find solutions to an equation w(x,y) = u(a,b)\n# up to length n by brute force\n# w(x, y) is a function of variables\n# u(a, b) is a function of constants\n# Trying to solve for x and y\n\nInstallGlobalFunction(ShortSolutions,\nfunction(w, u, n)\n local variables, constants, f, gens, const, consts, vars, copy, solutions, tree, c1, c2, c3, c4, nodes, word_string, letter, subcount, i, next_exp, start_consts, exps;\n\tsolutions := [];\n\ttree := rec();\n\tnodes := [1];\n\n variables := FreeGroupOfWord(w);\n\tconstants := FreeGroupOfWord(u);\n\n\tf := FreeGroup(Concatenation(List(GeneratorsOfGroup(constants), String),\n\t\t\t\t\t\t\t\t List(GeneratorsOfGroup(variables), String)));\n\tgens := GeneratorsOfGroup(f){[1 .. Length(GeneratorsOfGroup(variables))]};\n\tvars := GeneratorsOfGroup(f){[Length(GeneratorsOfGroup(variables)) + 1 ..\n\t\t\t\t\t\t\t\t Length(GeneratorsOfGroup(f))]};\n\tconsts := Concatenation(gens, List(gens, Inverse));\n\tstart_consts := Concatenation(consts, [f.1f.1^-1]);\n\ttree.children := List(start_consts, x -> rec(value := x, parent := tree));\n\ttree.value := f.1 f.1^-1;\n\tw := MappedWord(w, GeneratorsOfGroup(variables), vars);\n\tu := MappedWord(u, GeneratorsOfGroup(constants), consts);\n\n\tif u = f.1 * f.1^-1 then\n\t\tword_string := String(w);\t\t\n\t\tif IsDigitChar(word_string[Length(word_string)]) then\n\t\t\tif word_string[1] = '(' then\n\t\t\t\tsubcount := SubwordLength(word_string, 2);\n\t\t\t\tif subcount > 0 then\n\t\t\t\t\tw := Subword(w, 1, subcount);\n\t\t\t\tfi;\n\t\t\tfi;\n\t\tfi;\n\t\texps := ExponentSums(w);\n\t\tif RemInt(exps[3], exps[4]) <> 0 and RemInt(exps[4], exps[3]) <> 0 then\n\t\t\treturn [[f.1 * f.1^-1, f.1 * f.1^-1]];\n\t\tfi;\n\tfi;\n\n\tfor const in start_consts do\n\t\tcopy := MappedWord(w, [vars[1]], [const]);\n\t\tif copy = u then\n\t\t\tAdd(solutions, [const, 0]);\n\t\tfi;\n\t\tsolutions := BuildTree(const, consts, tree, copy, u, f, solutions, 0, n, nodes);\n\tod;\n\t# Print(nodes[1]);\n\t# Print(\"\\n\");\n\treturn solutions;\nend);\n\nInstallGlobalFunction(BuildTree,\nfunction(x, consts, node, copy, u, f, solutions, n, limit, nodes)\n\tlocal child, const, word, grandchild, c, child_rec;\n\tnodes[1] := nodes[1] + 1;\n\tif n > limit then\n\t\treturn solutions;\n\tfi;\n\tfor child in node.children do\n\t\tchild.children := [];\n\t\tc := MappedWord(copy, [f.4], [child.value]);\n\t\tif c = u then\n\t\t\tAdd(solutions, [x, child.value]);\n\t\tfi;\n\t\tif child.value <> (f.1f.1^-1) then\n\t\t\tfor const in consts do\n\t\t\t\tword := child.value const;\n\t\t\t\tif word = child.parent.value then\n\t\t\t\t\tcontinue;\n\t\t\t\tfi;\n\t\t\t\tchild_rec := rec();\n\t\t\t\tchild_rec.value := word;\n\t\t\t\tchild_rec.parent := child;\n\t\t\t\tAdd(child.children, child_rec);\n\t\t\tod;\n\t\tfi;\n\tod;\n\tfor child in node.children do\n\t\tBuildTree(x, consts, child, copy, u, f, solutions, n + 1, limit, nodes);\n\tod;\n\treturn solutions;\nend);\n\nInstallMethod(FreeGroupOfWord, \"for a word over the free group\",\n [IsWord], w -> FamilyObj(w)!.freeGroup);\n\nGreenTest := function(n)\n local w, u, F, U, x, y, a, b;\n\n F := FreeGroup(\"x\", \"y\");\n x := F.1; y := F.2;\n\n\n w := x * y * x;\n u := a^2 * b^2 * a^2;\n\n return ShortSolutions(w, u, n);\nend;\n\n", "meta": {"hexsha": "4acbd80dffc1495df5d70a8390b32ff854e09f74", "size": 6861, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "gap/Equations.gi", "max_stars_repo_name": "db213/GreenMachine", "max_stars_repo_head_hexsha": "fbed716dbd4332ba0deb5110eb7f5a00335b12c8", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "gap/Equations.gi", "max_issues_repo_name": "db213/GreenMachine", "max_issues_repo_head_hexsha": "fbed716dbd4332ba0deb5110eb7f5a00335b12c8", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2018-01-14T00:50:08.000Z", "max_issues_repo_issues_event_max_datetime": "2018-01-14T00:50:08.000Z", "max_forks_repo_path": "gap/Equations.gi", "max_forks_repo_name": "db213/GreenMachine", "max_forks_repo_head_hexsha": "fbed716dbd4332ba0deb5110eb7f5a00335b12c8", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 29.8304347826, "max_line_length": 171, "alphanum_fraction": 0.6152164408, "num_tokens": 2243, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7772998714925402, "lm_q2_score": 0.6959583250334526, "lm_q1q2_score": 0.5409683166126662}}
	{"text": "# De Caen, Mathon and Moorhouse's Preparata graph Pr(t, e)\nBindGlobal(\"PreparataGraph\", function(arg)\n local t, e, q, s, F, K, dp;\n if Length(arg) < 1 then\n Error(\"at least one argument expected\");\n return fail;\n fi;\n t := arg[1];\n if Length(arg) > 1 then\n e := arg[2];\n else\n e := 1;\n fi;\n q := 2^(2t-1);\n s := 2^e;\n F := GF(q);\n dp := DirectProduct(FieldMultiplicationPermutationGroup(q),\n FieldAdditionPermutationGroup(2),\n FieldAdditionPermutationGroup(q),\n FieldExponentiationPermutationGroup(q));\n return Graph(dp, Cartesian(F, GF(2), F), OnPreparata(q, s, dp),\n function(x,y)\n return x <> y\n and x[3]+y[3] = x[1]^s y[1] + x[1] * y[1]^s + (x[2]+y[2])(x[1]^(s+1) + y[1]^(s+1));\n end, true);\nend);\n\n# Quotient graph of the Preparata graph\nBindGlobal(\"PreparataQuotientGraph\", function(arg)\n local h, s, t, e, B, G, H, K, T, V;\n if Length(arg) < 2 then\n Error(\"at least two arguments expected\");\n return fail;\n fi;\n h := arg[1];\n if IsGraph(arg[2]) then\n G := arg[2];\n if IsFFE(G.names[1][3]) then\n s := 1;\n else\n s := Size(G.names[1][3]);\n fi;\n t := Log2Int(2sG.order)/4;\n else\n t := arg[2];\n if Length(arg) > 2 then\n e := arg[3];\n else\n e := 1;\n fi;\n G := PreparataGraph(t, e);\n fi;\n B := BasisVectors(Basis(GF(2^(2t-1))));\n if IsFFE(G.names[1][3]) then\n K := AdditiveGroup(B{[1..h]});\n V := List(G.names, x -> [x[1], x[2], x[3]+K]);\n else\n K := AdditiveGroup(B{[1..h+Log2Int(s)]});\n V := List(G.names, x -> [x[1], x[2], Elements(x[3])[1]+K]);\n fi;\n T := Set(List(V, x -> Positions(V, x)));\n H := Graph(Stabilizer(G.group, T, OnSetsSets), T, OnSets, function(x,y)\n return IsSubset(DistanceSet(G, 1, x), y);\n end, true);\n AssignVertexNames(H, List(T, x -> V[x[1]]));\n return H;\nend);\n\n# The coset graph of a Kasami code over an odd power extension\n# of a binary field.\nBindGlobal(\"KasamiGraph\", function(i, j, m)\n local q, s, t, dp, G;\n q := 2^i;\n s := q^(2*j+1);\n t := q^m + 1;\n G := FieldAdditionPermutationGroup(s);\n dp := DirectProduct(G, G, FieldExponentiationPermutationGroup(s));\n return Graph(dp, Elements(GF(s)^2), OnKasami(s, s, dp),\n function(x, y)\n return x <> y and x[1]+y[1] = (x[2]+y[2])^t;\n end, true);\nend);\n\n# The coset graph of an extended Kasami code over an odd power extension\n# of a binary field.\nBindGlobal(\"ExtendedKasamiGraph\", function(i, j, m)\n return ExtendedBipartiteDoubleGraph(KasamiGraph(i, j, m));\nend);\n\n# The coset graph of a Kasami code over a quadratic extension\n# of a binary field.\nBindGlobal(\"QuadraticKasamiGraph\", function(i)\n local q, s, t, dp;\n q := 2^i;\n s := q^2;\n t := q + 1;\n dp := DirectProduct(FieldAdditionPermutationGroup(q),\n FieldAdditionPermutationGroup(s),\n FieldExponentiationPermutationGroup(s));\n return Graph(dp, Cartesian(GF(q), GF(s)), OnKasami(q, s, dp),\n function(x, y)\n return x <> y and x[1]+y[1] = (x[2]+y[2])^t;\n end, true);\nend);\n\n# The coset graph of an extended Kasami code over a quadratic extension\n# of a binary field.\nBindGlobal(\"ExtendedQuadraticKasamiGraph\", function(i)\n return ExtendedBipartiteDoubleGraph(QuadraticKasamiGraph(i));\nend);\n", "meta": {"hexsha": "65dd07938c7043f00dccf9eac629de0881becf3b", "size": 3530, "ext": "gap", "lang": "GAP", "max_stars_repo_path": "lib/CodeGraphs.gap", "max_stars_repo_name": "jaanos/gap-graphs", "max_stars_repo_head_hexsha": "18dd56c9b90a12a717a0cc893fdd72c6343ee79b", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2015-10-27T15:54:29.000Z", "max_stars_repo_stars_event_max_datetime": "2016-11-07T14:09:44.000Z", "max_issues_repo_path": "lib/CodeGraphs.gap", "max_issues_repo_name": "jaanos/gap-graphs", "max_issues_repo_head_hexsha": "18dd56c9b90a12a717a0cc893fdd72c6343ee79b", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2015-04-20T23:13:11.000Z", "max_issues_repo_issues_event_max_datetime": "2015-04-20T23:13:11.000Z", "max_forks_repo_path": "lib/CodeGraphs.gap", "max_forks_repo_name": "jaanos/gap-graphs", "max_forks_repo_head_hexsha": "18dd56c9b90a12a717a0cc893fdd72c6343ee79b", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 31.8018018018, "max_line_length": 102, "alphanum_fraction": 0.5512747875, "num_tokens": 1131, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8840392756357327, "lm_q2_score": 0.6113819732941511, "lm_q1q2_score": 0.5404856768077062}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n#P Parametrized permutation classes\n#P --------------------------------\n#P\n\n## -----------------------------------------------------------------------------\n#F L(<n>, <str>) - stride permutation\n##\nClass(L, PermClass, rec(\n def := (n,str) -> Checked(IsPosIntSym(n), IsPosIntSym(str),\n (not (IsInt(n) and IsInt(str)) or n mod str = 0), rec()),\n\n domain := self >> self.params[1],\n range := self >> self.params[1],\n\n lambda := self >> let(\n n := self.params[1], str := self.params[2], i := Ind(n),\n Lambda(i, idiv(i, n/str) + str * imod(i, n/str))),\n\n transpose := self >> self.__bases__[1](self.params[1], self.params[1] / self.params[2]),\n isSymmetric := self >> (self.params[1] = self.params[2]^2) or (self.params[2] = 1) or (self.params[2] = self.params[1]),\n printlatex := self >> Print(\" \\\\stride^{\", self.params[1], \"}_{\",self.params[2],\"} \")\n\n));\n\n## -----------------------------------------------------------------------------\n#F Tr(<k>, <str>) - stride permutation L(kstr, str),\n##\n## This L equivalent is used to simplify rewriting, since k is not explicit in L,\n## and if symbolics are used, to extract it we have to do simplification tricks,\n## eg. n/f1(n) = f2(n).\n##\n## Tr stands for Transpose.\n##\nClass(Tr, PermClass, rec(\n def := (k,str) -> Checked(IsPosIntSym(k), IsPosIntSym(str), rec()),\n\n lambda := self >> let(\n k := self.params[1], str := self.params[2], i := Ind(kstr),\n Lambda(i, idiv(i, k) + str * imod(i, k))),\n\n domain := self >> self.params[1] * self.params[2],\n range := self >> self.params[1] * self.params[2],\n\n dims := self >> [self.range(), self.domain()],\n \n transpose := self >> self.__bases__[1](self.params[2], self.params[1])\n));\n\n## -----------------------------------------------------------------------------\n#F Z(N,k) : Cyclic shift by <k>, permutation {0, ..., n-1} -> {k,...,n-1, 0,...,k-1}\n##\n# if one redefines .lambda, then .transposed should be also handled in custom .lambda\nClass(Z, PermClass, rec(\n abbrevs := [ n -> [n,1] ],\n def := (n,k) -> rec(), \n domain := self >> self.params[1],\n range := self >> self.params[1],\n lambda := self >> let(n:=self.params[1], k:=self.params[2], i := Ind(n),\n Lambda(i, imod(i + k, n))),\n transpose := self >> self.__bases__[1](self.params[1], self.params[1] - self.params[2])\n));\n\n## -----------------------------------------------------------------------------\n#F J(N) : NxN reverse identity, also known as reversal permutation (1,n)(2,n-1)...\n##\nClass(J, PermClass, rec(\n def := n -> rec(), \n lambda := self >> let(i := Ind(self.params[1]), Lambda(i,self.params[1]-i-1)),\n domain := self >> self.params[1],\n range := self >> self.params[1],\n transpose := self >> self,\n isSymmetric := True\n));\n\n## -----------------------------------------------------------------------------\n#F OddStride(<n>, <str>)\n#F OS(<n>, <str>) - odd stride permutation (i -> i * str mod n)\n##\nClass(OS, PermClass, rec(\n isCyclic := true,\n def := (n,str) -> Checked(IsPosIntSym(n), IsIntSym(str), n > 0,\n AnySyms(n,str) or (Gcd(EvalScalar(n),EvalScalar(str))=1), rec()),\n domain := self >> self.params[1],\n range := self >> self.params[1],\n lambda := self >> let(i := Ind(self.params[1]),\n Lambda(i, imod(self.params[2] * i, self.params[1]))),\n transpose := self >> self.__bases__[1](self.params[1], self.params[2]^-1 mod self.params[1])\n));\nOddStride := OS;\n\nDeclare(gammaTensor);\n## -----------------------------------------------------------------------------\n#F CRT(<r>, <s>) - Chinese remainder theorem permutation function of size rs\n##\nClass(CRT, PermClass, rec(\n isCyclic := true,\n\n abbrevs := [ (r, s) -> Checked(IsPosIntSym(r), IsPosIntSym(s), AnySyms(r,s) or Gcd(r,s)=1,\n let(alpha := 1/s mod r,\n beta := 1/r mod s,\n [r, s, alpha, beta])) ],\n\n toGammaTensor := self >> gammaTensor(\n OddStride(self.params[1], self.params[3]),\n OddStride(self.params[2], self.params[4])),\n\n def := (r, s, alpha, beta) -> Checked(\n IsPosIntSym(r), IsPosIntSym(s), AnySyms(r, s) or Gcd(r,s)=1,\n rec()),\n\n domain := self >> self.params[1] self.params[2],\n range := self >> self.params[1] * self.params[2],\n\n lambda := self >> let(\n r := self.params[1], s := self.params[2], N := rs,\n alpha := self.params[3], beta := self.params[4],\n aa := (1/s/alpha) mod r, bb := (1/r/beta) mod s,\n i := Ind(N),\n When(not self.transposed,\n Lambda(i, ((salphaidiv(i, s)) + (rbetaimod(i, s))) mod N),\n Lambda(i, s(imod(iaa, r)) + (imod(ibb, s))))),\n));\n\nClass(fCond, FuncClass, rec(\n def := (cond, f1, f2) -> Checked(\n f1.range() = f2.range(),\n f1.domain() = f2.domain(),\n\trec()),\n\n domain := self >> self.params[1].domain(),\n range := self >> self.params[2].range(),\n\n lambda := self >> let(f1 := self.params[2], f2:= self.params[3], mycond := self.params[1],\n i := Ind(f1.domain()),\n Lambda(i, cond(mycond.lambda().at(i), f1.lambda().at(i), f2.lambda().at(i)))),\n\n transpose := self >> let(base := self.__bases__[1],\n base(self.params[1], self.params[2].transpose(), self.params[3].transpose()))\n));\n\n# ----------------------------------------------------------\n# Bit and Digit reversals\n# ----------------------------------------------------------\n\n# Return x as a b-bit value, formed as a vector\n_numToBits := (k, b) >> Reversed(List([1..b], i-> imod(idiv(k, 2^(i-1)), 2)));\n\n# Return number corresponding to bit vector b\n_bitsToNum := b -> let(\n l := Reversed(b),\n Sum([1..Length(l)], i -> 2^(i-1) * l[i]));\n\n# Calculate base-r digit reversed value of k, where k is between 0 and n-1\n_digitRev := function(k, n, r)\n local bitval, numbits, bitsperchunk, numchunks, res_bits, i, s; \n\n numbits := Log2Int(n);\n bitsperchunk := Log2Int(r);\n numchunks := numbits / bitsperchunk;\n\n bitval := _numToBits(k, numbits);\n \n res_bits := [];\n for i in Reversed([1..numchunks]) do\n s := bitval{([bitsperchunki-(bitsperchunk-1) .. bitsperchunk i])};\n Append(res_bits, s);\n od;\n\n return _bitsToNum(res_bits);\nend;\n\n#F DR(<k, r>) - digit reversal permutation R^k_r\n##\nClass(DR, PermClass, rec(\n def := (k, r) -> Checked(IsInt(k), Is2Power(k), (r^(LogInt(k,r)) = k), rec()),\n\n domain := self >> self.params[1],\n range := self >> self.params[1],\n # This is very slow because of how Gap evaluates functions\n # lambda := self >> let(\n # n := self.params[1], base := self.params[2], t := LogInt(n, base),\n # rev := List([1..t], i-> fTensor(fId(base^(t-i)), L(base^i, base))),\n # fCompose(Reversed(rev)).lambda()),\n\n# This is faster but a little bit uglier.\n lambda := self >> let(\n i := Ind(self.params[1]),\n Lambda(i, _digitRev(i, self.params[1], self.params[2]))),\n\n transpose := self >> self\n));\n\n#F BR(<k>) - bit reversal permutation\n##\nClass(BR, PermClass, rec(\n def := k -> Checked(IsInt(k), Is2Power(k), rec()), \n domain := self >> self.params[1],\n range := self >> self.params[1],\n lambda := self >> DR(self.params[1], 2).lambda(),\n transpose := self >> self\n));\n", "meta": {"hexsha": "b51bed1eb9909529221d07ab10fdf162020a2a5c", "size": 7353, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/spl/perms.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/spl/perms.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/spl/perms.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 35.5217391304, "max_line_length": 124, "alphanum_fraction": 0.517747858, "num_tokens": 2109, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7718434873426303, "lm_q2_score": 0.6959583187272711, "lm_q1q2_score": 0.5371708957715707}}
	{"text": "################################################################################\r\n##\r\n#W GroupTheoretical_data.gi GroupTheoretical Package\r\n##\r\n#W Paul Bruillard, Cesar Galindo, Siu-Hung Ng, Julia Plavnik, Eric Rowell,\r\n#W Zhenghan Wang\r\n##\r\n## Installation file for functions in the GroupTheoretical_data portion of the GroupTheoretical package\r\n##\r\n#Y Copyright (C) 2016, Battelle Memorial Institute\r\n##\r\n################################################################################\r\n\r\n\r\n################################################################################\r\n##\r\n#F DG_S_and_T(<group>,<bool>) Computes Simples, S, T, FPdim(Xi), FPdimC for D(G)\r\n##\r\nInstallGlobalFunction(DG_S_and_T, function(G,display)\r\n local g, elmsG, R, r, tbl, chi, Simples, x, y, S, s, T, rank, x_idx, y_idx, FPdim, FPdimC,l,pseudounitary_data,sorted_data;\r\n elmsG := Elements(G);\r\n if display then \r\n Print(\"\\nG = \", StructureDescription(G), \" \", IdGroup(G), \"\\n\");\r\n fi;\r\n\r\n # compute the simples\r\n R := List(ConjugacyClasses(G), Representative);\r\n Simples := [];\r\n for r in R do\r\n tbl := CharacterTable(Centralizer(G, r));\r\n for chi in Irr(tbl) do\r\n Add(Simples, [r, chi, ConjugacyClasses(tbl)]);\r\n od;\r\n od;\r\n rank:=Size(Simples);\r\n\r\n if display then\r\n Print(\"Rank is\\n\\n\");\r\n Display(rank);\r\n Print(\"Computing S matrix\\n\");\r\n fi;\r\n\r\n # compute the S-matrix\r\n # since s is symmetric we can half the size of the inner loop\r\n #S := NullMat(rank,rank);\r\n S:=[];\r\n# for x_idx in [1..rank] do\r\n# x:=Simples[x_idx];\r\n for x in Simples do\r\n l:=[];\r\n #for y_idx in [x_idx..rank] do\r\n# for y_idx in [1..rank] do\r\n# y:=Simples[y_idx];\r\n for y in Simples do\r\n s := 0;\r\n for g in elmsG do\r\n if x[1]gy[1]Inverse(g) = gy[1]Inverse(g)x[1] then\r\n s := s + ComplexConjugate(x[2][Position(x[3], \r\n ConjugacyClass(Centralizer(G, x[1]), gy[1]Inverse(g)))])\r\n * ComplexConjugate(y[2][Position(y[3], \r\n ConjugacyClass(Centralizer(G, y[1]), Inverse(g)x[1]g))]);\r\n fi;\r\n od;\r\n s := s * (1/(Size(Centralizer(G, x[1])) * Size(Centralizer(G, y[1])))) * Size(G);\r\n #S[x_idx][y_idx] := s;\r\n #S[y_idx][x_idx] := s;\r\n Add(l,s);\r\n od;\r\n Add(S,l);\r\n od;\r\n\r\n # compute the T-matrix\r\n T := [];\r\n for x in Simples do\r\n Add(T, x[2][Position(x[3], ConjugacyClass(Centralizer(G, x[1]), x[1]))]/x[2][1]);\r\n od;\r\n\r\n if display then\r\n Print(\"\\n The S-matrix is: \\n\\n\");\r\n Print(S);\r\n Print(\"\\n\\n The T-matrix is: \\n\\n\");\r\n Print(T);\r\n Print(\"\\n\\n\");\r\n fi;\r\n\r\n pseudounitary_data := pseudounitary_sort(S,T,Simples);\r\n Simples := pseudounitary_data[1];\r\n S := pseudounitary_data[2];\r\n T := pseudounitary_data[3];\r\n FPdim := pseudounitary_data[4];\r\n FPdimC := pseudounitary_data[5];\r\n\r\n # sort by dimensions (if two objects have the same dimension, their\r\n # relative order is unchanged).\r\n sorted_data := dimension_sort(S,T,Simples,FPdim);\r\n Simples:=sorted_data[1];\r\n S:=sorted_data[2];\r\n T:=sorted_data[3];\r\n FPdim:=sorted_data[4];\r\n\r\n return [Simples, S, T, FPdim, FPdimC];\r\nend);\r\n\r\n################################################################################\r\n##\r\n#F DG_data(<group>) . . . . . . . . . . . . . . .Computes modular data for D(G).\r\nInstallGlobalFunction(DG_data, function(G)\r\n local Simples, S, T, FPdim, FPdimC, N, data;\r\n data:=DG_S_and_T(G,false);\r\n Simples:=data[1];\r\n S:=data[2];\r\n T:=data[3];\r\n FPdim:=data[4];\r\n FPdimC:=data[5];\r\n N:=compute_fusion_rules(S,FPdimC);\r\n return [Simples,S,T,N,FPdim,FPdimC];\r\nend);\r\n\r\n#E DG_data.gi . . . . . . . . . . . . . . . . . . . . . . . . . . . . .ends here\r\n", "meta": {"hexsha": "524cdaabfc6052a2244fe094aeb5fa8890a367dd", "size": 3729, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "lib/DG_data.gi", "max_stars_repo_name": "pnnl/GroupTheoretical", "max_stars_repo_head_hexsha": "d60aaec27d2ca98ec55b12b78213538a346eef27", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "lib/DG_data.gi", "max_issues_repo_name": "pnnl/GroupTheoretical", "max_issues_repo_head_hexsha": "d60aaec27d2ca98ec55b12b78213538a346eef27", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2021-05-20T21:43:28.000Z", "max_issues_repo_issues_event_max_datetime": "2021-05-20T21:43:28.000Z", "max_forks_repo_path": "lib/DG_data.gi", "max_forks_repo_name": "pnnl/GroupTheoretical", "max_forks_repo_head_hexsha": "d60aaec27d2ca98ec55b12b78213538a346eef27", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 2, "max_forks_repo_forks_event_min_datetime": "2017-12-07T13:46:25.000Z", "max_forks_repo_forks_event_max_datetime": "2020-12-12T22:39:35.000Z", "avg_line_length": 31.075, "max_line_length": 126, "alphanum_fraction": 0.5258782515, "num_tokens": 1141, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. 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	{"text": "# Using SageMath interface for GAP\n# To start GAP inside of SageMath:\n# gap.console()\n#\n# Defining groups in GAP:\n# PSL := FreeProduct(CyclicGroup(2),CyclicGroup(3))\n#\n# Using SageMath to access GAP's\n# finitely presented groups functionality\n# https://doc.sagemath.org/html/en/reference/groups/sage/groups/finitely_presented.html\n\n# from sage.interfaces.gap import get_gap_memory_pool_size, set_gap_memory_pool_size\n# set_gap_memory_pool_size(20000000000)\n\nk := 4;\n\nF := FreeGroup(\"t_k\", \"c\", \"d\");\n\nG := F / [F.3^(-1)F.1(F.3F.2^(-1))^(-k+1)F.1(F.3F.2^(-1))^(k-1)(F.1^(-1)),\n F.2^(-1)F.1F.2F.3^(-1)(F.1)^(-1)F.3F.1F.3F.2^(-1)(F.1)^(-1)];\n\nRelatorsOfFpGroup(G);\n\nAllHomomorphismClasses(G, SymmetricGroup(3));\n# AllHomomorphisms(G, SymmetricGroup(3));\n\n", "meta": {"hexsha": "a13c755d5a4c8a81a1d5cbf91636ab811bc8cff4", "size": 777, "ext": "gap", "lang": "GAP", "max_stars_repo_path": "src/gap_tests.gap", "max_stars_repo_name": "ben300694/knot-theory", "max_stars_repo_head_hexsha": "f4d889466495da3bc42f6808c9c4a1f5940480eb", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2022-03-23T17:47:05.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-23T17:47:05.000Z", "max_issues_repo_path": "src/gap_tests.gap", "max_issues_repo_name": "ben300694/knot-theory", "max_issues_repo_head_hexsha": "f4d889466495da3bc42f6808c9c4a1f5940480eb", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "src/gap_tests.gap", "max_forks_repo_name": "ben300694/knot-theory", "max_forks_repo_head_hexsha": "f4d889466495da3bc42f6808c9c4a1f5940480eb", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 28.7777777778, "max_line_length": 87, "alphanum_fraction": 0.6692406692, "num_tokens": 286, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8128673087708699, "lm_q2_score": 0.6584175072643415, "lm_q1q2_score": 0.5352060671775899}}
	{"text": "# Constants\nBindGlobal(\"Graph6ByteInteger\", 62);\nBindGlobal(\"Graph6WordInteger\", 258047);\nBindGlobal(\"Graph6DwordInteger\", 68719476735);\nBindGlobal(\"Graph6MaxInteger\", Graph6DwordInteger);\nBindGlobal(\"Graph6BitVector\", List([0..5], i -> 2^(5-i)));\nBindGlobal(\"Graph6IntVector\", List([0..5], i -> 64^(5-i)));\n\n# graph6 integer encoding\nBindGlobal(\"Graph6EncodeInteger\", function(x)\n if not IsInt(x) or x < 0 or x >= Graph6MaxInteger then\n Error(\"not an integer in allowed range\");\n return fail;\n fi;\n if x <= Graph6ByteInteger then\n return [x+63];\n elif x <= Graph6WordInteger then\n return [63, Int(x/4096), Int(x/64), x] mod 64 + 63;\n else\n return Concatenation([126, 126],\n List(Graph6IntVector, y -> Int(x/y) mod 64 + 63));\n fi;\nend);\n\n# graph6 integer decoding\nBindGlobal(\"Graph6DecodeInteger\", function(i, s)\n if s[i] <> 126 then\n return [i+1, s[i] - 63];\n elif s[i+1] <> 126 then\n return [i+4, (s{[i+1..i+3]} - 63)Graph6IntVector{[4..6]}];\n else\n return [i+8, (s{[i+2..i+7]} - 63)Graph6IntVector];\n fi;\nend);\n\n# Convert an integer to a bitstring of length w\nBindGlobal(\"IntToBits\", function(x, w)\n return List([1..w], i -> Int(x / 2^(w-i)) mod 2);\nend);\n\n# Convert a bitstring to a list of integers given the width w\nBindGlobal(\"BitsToInt\", function(b, w)\n local out, i;\n out := [];\n i := 0;\n while i+w <= Length(b) do\n Add(out, b{[i+1..i+w]} * List([1..w], j -> 2^(w-j)));\n i := i+w;\n od;\n return out;\nend);\n\n# Convert a bitstring to a graph6 string with padding p\nBindGlobal(\"BitsToString\", function(b, p)\n local c;\n c := Concatenation(b, ListWithIdenticalEntries(-Length(b) mod 6, p));\n return List([0,6..Length(c)-6], i -> c{[i+1..i+6]}Graph6BitVector + 63);\nend);\n\n# Convert a graph6 string to a bitstring\nBindGlobal(\"StringToBits\", function(s)\n return Concatenation(List(s, x -> List(Graph6BitVector, y -> Int((x-63)/y) mod 2)));\nend);\n\n# graph6 string\nBindGlobal(\"Graph6String\", function(G)\n local A, s;\n A := CollapsedAdjacencyMat(Group(()), G);\n s := Concatenation(Graph6EncodeInteger(G.order),\n BitsToString(Concatenation(List([1..G.order], i -> A[i]{[1..i-1]})), 0));\n return List(s, CharInt);\nend);\n\n# Read graph from graph6 string\nBindGlobal(\"GraphFromGraph6String\", function(s)\n local A, b, n, i, j, t;\n s := List(s, IntChar);\n t := Graph6DecodeInteger(1, s);\n i := t[1];\n n := t[2];\n b := StringToBits(s{[i..Length(s)]});\n A := NullMat(n, n);\n i := 1;\n for j in [2..n] do\n A[j]{[1..j-1]} := b{[i..i+j-2]};\n A{[1..j-1]}[j] := b{[i..i+j-2]};\n i := i+j-1;\n od;\n return AdjFunGraph([1..n], MatrixAdjacency(A));\nend);\n\n# sparse6 string\nBindGlobal(\"Sparse6String\", function(G)\n local i, j, b, c, v, w;\n w := Log2Int(G.order-1)+1;\n b := [];\n v := 1;\n for i in [1..G.order] do\n for j in [1..i] do\n if IsVertexPairEdge(G, i, j) then\n if i = v+1 then\n c := 1;\n else\n if i > v then\n Add(b, 1);\n Append(b, IntToBits(i-1, w));\n fi;\n c := 0;\n fi;\n Add(b, c);\n Append(b, IntToBits(j-1, w));\n v := i;\n fi;\n od;\n od;\n if G.order in [2,4,8,16] and (-Length(b)) mod 6 > w\n and Length(Adjacency(G, G.order-1)) > 0\n and Length(Adjacency(G, G.order)) = 0 then\n Add(b, 0);\n fi;\n return List(Concatenation([58], Graph6EncodeInteger(G.order),\n BitsToString(b, 1)), CharInt);\nend);\n\n# Read graph from sparse6 string\nBindGlobal(\"GraphFromSparse6String\", function(s)\n local A, b, t, i, m, n, v, w, c, x, y, z;\n if s[1] = ':' then\n s := s{[2..Length(s)]};\n fi;\n s := List(s, IntChar);\n t := Graph6DecodeInteger(1, s);\n i := t[1];\n n := t[2];\n w := Log2Int(n-1)+1;\n b := StringToBits(s{[i..Length(s)]});\n A := List([1..n], j -> []);\n i := 1;\n v := 1;\n z := BitsToInt(b, w+1);\n m := 2^w;\n for y in z do\n c := Int(y/m);\n x := y mod m + 1;\n if c = 1 then\n v := v+1;\n fi;\n if v > n or x > n then\n break;\n fi;\n if x > v then\n v := x;\n else\n Add(A[x], v);\n Add(A[v], x);\n fi;\n od;\n return AdjFunGraph([1..n], ListAdjacency(A));\nend);\n\n# sparse6 string\nBindGlobal(\"IncrementalSparse6String\", function(G, H)\n local i, j, b, c, v, w;\n if G.order <> H.order then\n Error(\"graphs have different orders\");\n return fail;\n fi;\n w := Log2Int(G.order-1)+1;\n b := [];\n v := 1;\n for i in [1..G.order] do\n for j in [1..i] do\n if IsVertexPairEdge(G, i, j) <> IsVertexPairEdge(H, i, j) then\n if i = v+1 then\n c := 1;\n else\n if i > v then\n Add(b, 1);\n Append(b, IntToBits(i-1, w));\n fi;\n c := 0;\n fi;\n Add(b, c);\n Append(b, IntToBits(j-1, w));\n v := i;\n fi;\n od;\n od;\n if G.order in [2,4,8,16] and (-Length(b)) mod 6 > w\n and Adjacency(G, G.order-1) = Adjacency(H, G.order-1)\n and Adjacency(G, G.order) = Adjacency(H, G.order) then\n Add(b, 0);\n fi;\n return List(Concatenation([59], BitsToString(b, 1)), CharInt);\nend);\n\n# Read graph from incremental sparse6 string\nBindGlobal(\"GraphFromIncrementalSparse6String\", function(s, H)\n local A, B, b, i, m, v, w, c, x, y, z;\n if s[1] = ';' then\n s := s{[2..Length(s)]};\n fi;\n B := List([1..H.order], j -> Adjacency(H, j));\n A := List(B, ShallowCopy);\n s := List(s, IntChar);\n w := Log2Int(H.order-1)+1;\n b := StringToBits(s);\n i := 1;\n v := 1;\n z := BitsToInt(b, w+1);\n m := 2^w;\n for y in z do\n c := Int(y/m);\n x := y mod m + 1;\n if c = 1 then\n v := v+1;\n fi;\n if v > H.order or x > H.order then\n break;\n fi;\n if x > v then\n v := x;\n elif x in A[v] then\n Remove(A[x], Position(A[x], v));\n if x <> v then\n Remove(A[v], Position(A[v], x));\n fi;\n else\n Add(A[x], v);\n Add(A[v], x);\n fi;\n od;\n return AdjFunGraph([1..H.order], ListAdjacency(A));\nend);\n\n# auto6 string\nBindGlobal(\"Auto6String\", function(G)\n local b, g, h, i, l, p, r, s, w, x, sch;\n g := GeneratorsOfGroup(G.group);\n l := [1..Length(g)];\n i := 0;\n for p in [1..Length(g)] do\n if g[p] = () then\n i := i+1;\n else\n l[p] := l[p] - i;\n fi;\n od;\n sch := List(G.schreierVector, function(y)\n if y < 0 then\n return y;\n else\n return l[y];\n fi;\n end);\n g := Filtered(g, y -> y <> ());\n w := Log2Int(G.order-1)+1;\n r := Length(G.representatives);\n b := IntToBits(r, w);\n for i in [1..r] do\n Append(b, IntToBits(G.representatives[i]-1, w));\n Append(b, IntToBits(Length(G.adjacencies[i]), w));\n for x in G.adjacencies[i] do\n Append(b, IntToBits(x-1, w));\n od;\n od;\n for h in g do\n for i in [1..G.order] do\n Append(b, IntToBits(i^h - 1, w));\n od;\n od;\n if Length(g) > 1 then\n s := Log2Int(Length(g)) + 1;\n for i in [1..G.order] do\n if sch[i] < 0 then\n Append(b, IntToBits(0, s));\n else\n Append(b, IntToBits(sch[i], s));\n fi;\n od;\n fi;\n return List(Concatenation([33], Graph6EncodeInteger(G.order),\n Graph6EncodeInteger(Length(g)), BitsToString(b, 0)), CharInt);\nend);\n\n# Read graph from auto6 string\nBindGlobal(\"GraphFromAuto6String\", function(s)\n local G, A, R, S, a, b, d, r, t, g, i, j, k, n, v, w;\n if s[1] = '!' then\n s := s{[2..Length(s)]};\n fi;\n s := List(s, IntChar);\n t := Graph6DecodeInteger(1, s);\n i := t[1];\n n := t[2];\n w := Log2Int(n-1)+1;\n t := Graph6DecodeInteger(i, s);\n i := t[1];\n g := t[2];\n b := StringToBits(s{[i..Length(s)]});\n d := BitsToInt(b, w);\n r := d[1];\n if r = 0 then\n r := n;\n fi;\n i := 2;\n R := [];\n A := [];\n for j in [1..r] do\n Add(R, d[i]+1);\n Add(A, d{[i+2..i+d[i+1]+1]}+1);\n i := i + d[i+1] + 2;\n od;\n if g = 0 then\n G := ();\n v := List([1..n], x -> -Position(R, x));\n else\n G := [];\n for j in [1..g] do\n Add(G, PermList(d{[i..i+n-1]}+1));\n i := i+n;\n od;\n if g = 1 then\n v := List([1..n], function(x)\n local y;\n y := Position(R, x);\n if y = fail then\n return 1;\n else\n return -y;\n fi;\n end);\n else\n k := w(i-1);\n t := Log2Int(g)+1;\n v := BitsToInt(b{[k+1..k+n*t]}, t);\n for j in [1..r] do\n v[R[j]] := -j;\n od;\n fi;\n fi;\n return rec(\n isGraph := true,\n order := n,\n names := [1..n],\n representatives := Immutable(R),\n adjacencies := A,\n group := Group(G),\n schreierVector := Immutable(v)\n );\nend);\n", "meta": {"hexsha": "8cee5edc4931010811ef544fefc461f2f8a2265b", "size": 9802, "ext": "gap", "lang": "GAP", "max_stars_repo_path": "lib/Graph6.gap", "max_stars_repo_name": "jaanos/gap-graphs", "max_stars_repo_head_hexsha": "18dd56c9b90a12a717a0cc893fdd72c6343ee79b", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2015-10-27T15:54:29.000Z", "max_stars_repo_stars_event_max_datetime": "2016-11-07T14:09:44.000Z", "max_issues_repo_path": "lib/Graph6.gap", "max_issues_repo_name": "jaanos/gap-graphs", "max_issues_repo_head_hexsha": "18dd56c9b90a12a717a0cc893fdd72c6343ee79b", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2015-04-20T23:13:11.000Z", "max_issues_repo_issues_event_max_datetime": "2015-04-20T23:13:11.000Z", "max_forks_repo_path": "lib/Graph6.gap", "max_forks_repo_name": "jaanos/gap-graphs", "max_forks_repo_head_hexsha": "18dd56c9b90a12a717a0cc893fdd72c6343ee79b", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 27.8465909091, "max_line_length": 88, "alphanum_fraction": 0.4531728219, "num_tokens": 3088, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8397339596505966, "lm_q2_score": 0.6334102636778403, "lm_q1q2_score": 0.5318961088015213}}
	{"text": "# The vector product of two vectors with 3 elements.\nBindGlobal(\"VectorProduct\", function(u, v)\n return [u[2]v[3]-u[3]v[2], u[3]v[1]-u[1]v[3], u[1]v[2]-u[2]v[1]];\nend);\n\n# Multiplication in Hall algebras\nBindGlobal(\"HallMultiplication\", function(p)\n local r;\n r := CoefficientsOfUnivariatePolynomial(p)[2];\n return function(x, y)\n if IsZero(y[2]) then\n return xy[1];\n else\n return [x[1]y[1] - x[2]/y[2]Value(p, y[1]),\n x[1]y[2] - x[2](y[1] + r)];\n fi;\n end;\nend);\n\n# Multiplication in Dickson near-fields\nBindGlobal(\"DicksonMultiplication\",\n q -> function(x, y)\n if IsZero(y) then\n return 0Z(q);\n else\n return x^(q^LogFFE(y, Z(q^2))) * y;\n fi;\n end);\n\n# Right division in Dickson near-fields\nBindGlobal(\"DicksonRightDivision\",\n q -> function(x, y)\n if IsZero(x) then\n return 0Z(q);\n else\n return (x / y)^(q^LogFFE(y, Z(q^2)));\n fi;\n end);\n\n# Multiplication in exceptional near-fields\nBindGlobal(\"ExceptionalMultiplication\", function(q, F, B)\n local mat;\n mat := ToExceptionalMatrix(q, F, B);\n return function(x, y)\n local M;\n M := mat(x) mat(y);\n return M[1]B;\n end;\nend);\n\n# Right division in exceptional near-fields\nBindGlobal(\"ExceptionalRightDivision\", function(q, F, B)\n local mat;\n mat := ToExceptionalMatrix(q, F, B);\n return function(x, y)\n local M;\n M := mat(x) mat(y)^-1;\n return M[1]*B;\n end;\nend);\n\n# Normalize a vector over a semifield given the semifield right division.\nBindGlobal(\"NormalizeSemifieldVector\",\n div -> function(v)\n local n;\n n := First(v, x -> not IsZero(x));\n return List(v, x -> div(x, n));\n end);\n", "meta": {"hexsha": "8f27104f607d8e8ad8864ef6ba0c7d2a691091d0", "size": 1864, "ext": "gap", "lang": "GAP", "max_stars_repo_path": "lib/Operations.gap", "max_stars_repo_name": "jaanos/gap-graphs", "max_stars_repo_head_hexsha": "18dd56c9b90a12a717a0cc893fdd72c6343ee79b", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2015-10-27T15:54:29.000Z", "max_stars_repo_stars_event_max_datetime": "2016-11-07T14:09:44.000Z", "max_issues_repo_path": "lib/Operations.gap", "max_issues_repo_name": "jaanos/gap-graphs", "max_issues_repo_head_hexsha": "18dd56c9b90a12a717a0cc893fdd72c6343ee79b", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2015-04-20T23:13:11.000Z", "max_issues_repo_issues_event_max_datetime": "2015-04-20T23:13:11.000Z", "max_forks_repo_path": "lib/Operations.gap", "max_forks_repo_name": "jaanos/gap-graphs", "max_forks_repo_head_hexsha": "18dd56c9b90a12a717a0cc893fdd72c6343ee79b", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 27.0144927536, "max_line_length": 75, "alphanum_fraction": 0.5461373391, "num_tokens": 547, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7745833737577158, "lm_q2_score": 0.6859494550081925, "lm_q1q2_score": 0.5313250430875123}}
	{"text": "InsertionSort := function(L)\n local n, i, j, x;\n n := Length(L);\n for i in [ 2 .. n ] do\n x := L[i];\n j := i - 1;\n while j >= 1 and L[j] > x do\n L[j + 1] := L[j];\n j := j - 1;\n od;\n L[j + 1] := x;\n od;\nend;\n\ns := \"BFKRIMPOQACNESWUTXDGLVZHYJ\";\nInsertionSort(s);\ns;\n# \"ABCDEFGHIJKLMNOPQRSTUVWXYZ\"\n", "meta": {"hexsha": "8ea81dd042ef9a4b87b81fc7f45ab938d64eaa05", "size": 324, "ext": "gap", "lang": "GAP", "max_stars_repo_path": "Task/Sorting-algorithms-Insertion-sort/GAP/sorting-algorithms-insertion-sort.gap", "max_stars_repo_name": "LaudateCorpus1/RosettaCodeData", "max_stars_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_stars_repo_licenses": ["Info-ZIP"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2018-11-09T22:08:38.000Z", "max_stars_repo_stars_event_max_datetime": "2018-11-09T22:08:38.000Z", "max_issues_repo_path": "Task/Sorting-algorithms-Insertion-sort/GAP/sorting-algorithms-insertion-sort.gap", "max_issues_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_issues_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_issues_repo_licenses": ["Info-ZIP"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Task/Sorting-algorithms-Insertion-sort/GAP/sorting-algorithms-insertion-sort.gap", "max_forks_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_forks_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_forks_repo_licenses": ["Info-ZIP"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2018-11-09T22:08:40.000Z", "max_forks_repo_forks_event_max_datetime": "2018-11-09T22:08:40.000Z", "avg_line_length": 17.0526315789, "max_line_length": 34, "alphanum_fraction": 0.4845679012, "num_tokens": 130, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7690802370707281, "lm_q2_score": 0.6893056104028797, "lm_q1q2_score": 0.5301313222628298}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nvtransposelo := (l1,l2,n) -> Flat(List([1..n/2], i-> [l1[2i-1],l2[2i-1]]\n));\n\nvtransposehi := (l1,l2,n) -> Flat(List([1..n/2], i-> [l1[2i],l2[2i]]\n));\n\nvrev64 := (l1,n) -> Flat(List([1..n/2], i-> [l1[2i],l1[2i-1]]\n));\n", "meta": {"hexsha": "ccf3ee9fb0f0f51460e7d74514c0a764dd7e693e", "size": 307, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/platforms/neon/misc.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/platforms/neon/misc.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/platforms/neon/misc.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 21.9285714286, "max_line_length": 74, "alphanum_fraction": 0.5472312704, "num_tokens": 139, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.72487026428967, "lm_q2_score": 0.7279754489059774, "lm_q1q2_score": 0.5276877560448671}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n# alpha is a function of P (divisor of N)\n# m = N/P\n\n# Frequency domain, u in [0, N)\n# Per processor, total pts=2m, total useful pts=m\n# We start to see aliasing at 3m/2, m=N/P.\nW := (alpha, u) -> exp(-alpha * u^2);\n\n# Time domain, t in [0, 1]\nw := (alpha, t) -> sqrt(d_PI / alpha) * exp(-d_PI^2 * t^2 / alpha);\n\n# digits - eg. 17, number of exact (unaffected by aliasing) decimal digits\ngauss_alpha := (N, p, digits) -> let(m := N/p, 4/9 * digits * d_log(10) / m^2);\n\n# how many samples of the filter to keep in the time domain, assuming gauss_alpha(N, p, digits)\n# was used.\nedge := digits -> IntDouble(d_ceil(2/(3d_PI) d_log(10) * digits));\n\n\nClass(fPerExt, FuncClass, rec(\n def := (N, l, r) -> rec(N:=N, n:=N+l+r),\n lambda := self >> let(N := self.params[1], l:=self.params[2], r:=self.params[3],\n \tj := Ind(self.n),\n\tLambda(j, imod(j-l, N)))\n));\n\n# below we should not use HZ, since HZ assumes that n * stride = N, and if used as below\n# assumption will be violated\n#RewriteRules(RulesFuncSimp, rec(\n# fPerExt_H := ARule(fCompose, [@(1,fPerExt), @(2,H)], e -> \n#\tlet(base := @(2).val.params[3], stride := @(2).val.params[4], \n#\t[ HZ(@(1).val.N, @(2).val.n, base - @(1).val.params[2], stride) ]))\n#));\n\n\nNewRulesFor(DFT, rec(\n\n DFT_Gauss := rec(\n\tforTransposition := true,\n\tminSize := 4,\n\tmaxSize := false,\n\tp := 4,\n\tdigits := 15,\n\n\tapplicable := (self, t) >> (self.minSize<>false and Rows(t) > self.minSize) and\n\t not IsPrime(Rows(t)) and t.params[2] in [1,-1 mod Rows(t)],\n\n libApplicable := (self, t) >> eq(imod(t.params[1], self.p), 0),\n\tfreedoms := (self, t) >> [],\n\n\tchild := (self, t, freedoms) >> let(N := Rows(t), p := self.p,\n\t [ DFT(2N/p, t.params[2]), DFT(p, t.params[2]) ]), \n \n\tapply := meth(self, t,C,Nonterms) \n\t local N, m, n, rot, k, p, alpha, time_filter, freq_filter, j;\n\t N := Rows(t); \n\t n := Rows(C[2]);\n\t k := edge(self.digits);\n\t p := self.p;\n\t m := N/p;\n\t alpha := gauss_alpha(N, p, self.digits);\n\n\t time_filter := let(i:=Ind(2kp), Lambda(i, w(alpha, (i-kp)/N)).setRange(TDouble));\n\t freq_filter := let(i:=Ind(m), Lambda(i, p/(2NW(alpha, i-m/2))).setRange(TDouble)); \n\t \n\t j := Ind(p);\n\t return \n\t Grp(\n\t\tIterDirectSum(j, j.range, \n\t\t Diag(freq_filter) * \n\t\t Gath(H(2m, m, mimod(j,2), 1)).toloop(4) * C[1]\n\t\t) \n\t\t(Tr(2N/p, p))\n\t ) * \n\t RowTensor(2N/p, 2kp-p/2, \n\t\tC[2] \n\t\tlet(i:=Ind(p), Diag(Lambda(i, omega(2p, i)).setRange(TComplex))) \n\t\tTensor(RowVec(List([0..2k-1], x->(-1)^x)), I(p)) \n\t\tDiag(time_filter)\n\t ) * \n\t Gath(fPerExt(N, kp, kp-p/2));\n\tend\n\t \n )\n));\n\n# scaling by p/(2N) belongs to the time_filter, but freq_filter is shorter\n#\t time_filter := List([-kp .. kp-1], i-> w(alpha, i/N));\n#\t freq_filter := List([-m/2..m/2-1], i-> p/(2NW(alpha, i))); \n\n#\t return\n#\t Z(N, m/2) \n#\t Tensor(I(p/2), \n#\t\t DirectSum(\n#\t\t Diag(freq_filter) * Gath(fStack(H(2m, m/2, 3m/2, 1), H(2m, m/2, 0, 1))) C[1],\n#\t\t Diag(freq_filter) * Gath(H(2m, m, m/2, 1)) C[1])\n#\t ) * \n\n\ntestGauss := function(N, p, k)\n local s, me, them;\n DFT_Gauss.p := p;\n SwitchRulesByNameQuiet(DFT, [DFT_Gauss]);\n s := SPLRuleTree(ExpandSPL(DFT(N,k))[1]);\n me := MatSPL(s);\n them := MatSPL(DFT(N,k));\n VisualizeMat(me-them, \" \");\n return [s, me, them];\nend;\n\nsplGauss := function(N, p, k)\n local s, me, them;\n DFT_Gauss.p := p;\n SwitchRulesByNameQuiet(DFT, [DFT_Gauss]);\n s := SPLRuleTree(ExpandSPL(DFT(N,k))[1]);\n return s;\nend;\n\nsums := function(s, opts)\n local real;\n real := s.isReal();\n s := SumsSPL(s);\n s := SubstBottomUp(s, @.cond(IsNonTerminal), x->RecursStep(0,0,x));\n s := ApplyStrategy(s, opts.formulaStrategies.sigmaSpl, UntilDone);\n if not opts.generateComplexCode and not real then\n s := ApplyStrategy(RC(s), opts.formulaStrategies.rc, UntilDone); fi;\n return ApplyStrategy(s, opts.formulaStrategies.postProcess, UntilDone);\nend;\n\n# opts := CopyFields(SpiralDefaults, rec(generateComplexCode := true));\n# opts := CopyFields(opts, rec(unparser := CMacroUnparser));\n\n# N := 128;\n# k := edge(17);\n# p := 4;\n# alpha := alpha(N, p, 17);\n\nNewRulesFor(DFT, rec(\n\n DFT_PrunedGauss := rec(\n\tforTransposition := true,\n\tminSize := 4,\n\tmaxSize := false,\n\tp := 2,\n\tdigits := 15,\n\n\tapplicable := (self, t) >> (self.minSize<>false and Rows(t) > self.minSize) and\n\t not IsPrime(Rows(t)) and t.params[2] in [1,-1 mod Rows(t)],\n\n\tchildren := (self, t) >> let(N := Rows(t), p := self.p,\n\t [[ DFT(2N/p, t.params[2]), DFT3(p, t.params[2]) ]]), #DFT3\n \n\tapply := meth(self, t,C,Nonterms) \n\t local N, m, n, mat, rot, k, p, alpha, time_filter, freq_filter, freq_filter2;\n\t N := Rows(t); \n\t n := Rows(C[2]);\n mat := MatSPL(C[2]);\n\t k := edge(self.digits);\n\t p := self.p;\n\t m := N/p;\n\t alpha := gauss_alpha(N, p, self.digits);\n\t time_filter := List([-kp .. kp-1], i-> w(alpha, i/N).eval());\n\t freq_filter := List([-m/2..m/2-1], i-> p/(2NW(alpha, i).eval())); \n\n\t return \n\t Diag(freq_filter) Gath(H(2m, m, 0, 1)) C[1] \n\t RowTensor(2N/p, 2kp-p/2, \n\t\tRowVec(mat[1]) \n\t\tTensor(RowVec(List([0..2k-1], x->(-1)^x)), I(p)) * \n\t\tDiag(time_filter)) \n\t transforms.filtering.Ext(N, transforms.filtering.per(k p), \n\t\t transforms.filtering.per(k * p - p/2));\n\tend\n )\n));\n\n#2N/p * 2kp\n#4Nk complex fmas overhead for filter (one stripe out), k=edge(digits)\n", "meta": {"hexsha": "b87d7e2d96d04f6a0277fb3227c2fbffd2ae7205", "size": 5624, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/dft/gauss.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/transforms/dft/gauss.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/transforms/dft/gauss.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 30.5652173913, "max_line_length": 95, "alphanum_fraction": 0.5554765292, "num_tokens": 1979, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8056321843145404, "lm_q2_score": 0.6548947357776795, "lm_q1q2_score": 0.5276042764806658}}
	{"text": "# return a list of two lists :\n# first is the list of months with five weekends between years y1 and y2 (included)\n# second is the list of years without such months, in the same interval\nFiveWeekends := function(y1, y2)\n local L, yL, badL, d, m, y;\n L := [ ];\n badL := [ ];\n for y in [y1 .. y2] do\n yL := [ ];\n for m in [1, 3, 5, 7, 8, 10, 12] do\n if WeekDay([1, m, y]) = \"Fri\" then\n d := StringDate([1, m, y]);\n Add(yL, d{[4 .. 11]});\n fi;\n od;\n if Length(yL) = 0 then\n Add(badL, y);\n else\n Append(L, yL);\n fi;\n od;\n return [ L, badL ];\nend;\n\nr := FiveWeekends(1900, 2100);;\nn := Length(r[1]);\n# 201\nLength(r[2]);\n# 29\nr[1]{[1 .. 5]};\n# [ \"Mar-1901\", \"Aug-1902\", \"May-1903\", \"Jan-1904\", \"Jul-1904\" ]\nr[1]{[n-4 .. n]};\n# [ \"Mar-2097\", \"Aug-2098\", \"May-2099\", \"Jan-2100\", \"Oct-2100\" ]\n", "meta": {"hexsha": "f48e053e413dd8407e8ba9d60dc9101392fef4d9", "size": 842, "ext": "gap", "lang": "GAP", "max_stars_repo_path": "Task/Five-weekends/GAP/five-weekends.gap", "max_stars_repo_name": "mullikine/RosettaCodeData", "max_stars_repo_head_hexsha": "4f0027c6ce83daa36118ee8b67915a13cd23ab67", "max_stars_repo_licenses": ["Info-ZIP"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2018-11-09T22:08:38.000Z", "max_stars_repo_stars_event_max_datetime": "2018-11-09T22:08:38.000Z", "max_issues_repo_path": "Task/Five-weekends/GAP/five-weekends.gap", "max_issues_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_issues_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_issues_repo_licenses": ["Info-ZIP"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Task/Five-weekends/GAP/five-weekends.gap", "max_forks_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_forks_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_forks_repo_licenses": ["Info-ZIP"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2018-11-09T22:08:40.000Z", "max_forks_repo_forks_event_max_datetime": "2018-11-09T22:08:40.000Z", "avg_line_length": 24.7647058824, "max_line_length": 83, "alphanum_fraction": 0.5213776722, "num_tokens": 341, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7371581741774411, "lm_q2_score": 0.7154239957834733, "lm_q1q2_score": 0.5273806464944745}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nDeclare(DWTper);\n\n#F DWTper(<n>, <j>, [<h(z)>,<g(z)>])\n#F DWTper(<n>, <j>, <L>, <V>)\n#F returns a 2-channel <j>-stage discrete wavelet transform with periodic extensions \n#F (circulant transforms) where the \n#F low pass and the high pass analysis filters given by polynomials \n#F [<h(z)>,<g(z)>] \n#F\n#F <L> = [<Lh>,<Lg>] - coefficient lists for h and g\n#F <V> = [<vh>,<vg>] - valuation for h and g\n#F\n#F <n> - size of the output of the reconstructed sequence\n#F <j> - number of filter bank stages\nClass(DWTper, NonTerminal, rec(\n\n abbrevs := [\n function(n,j,M)\n local S,L,V, j;\n if IsList(M[1]) then\n S:=List([1,2], j->FillZeros([M[1][j],M[2][j]]));\n V:=List(S, j->j[2]);\n L:=List(S, j->j[1]);\n return [n,j,L,V];\n else \n Checked(IsPosInt(n), Checked(ForAll(M,i->IsPolynomial(i)),true));\n S:=List(M, i-> FillZeros(i));\n V:=List(S, i->i[2]);\n L:=List(S, i->i[1]);\n return [n,j,L,V];\n fi;\n end,\n function(n,j,L,V)\n local S,V,L,i,j;\n S:=List([1,2], j->FillZeros([L[j],V[j]]));\n V:=List(S, j->j[2]);\n L:=List(S, j->j[1]);\n return [n,j,L,V];\n end\n ],\n\n dims := self >> [self.params[1], self.params[1]],\n\n half1 := self >> let(\n n := self.params[1],\n l1 := self.params[3][1],\n v1 := self.params[4][1],\n DownSample(n,2,0) * Circulant(n,l1,v1).terminate() ),\n\n half2 := self >> let(\n n := self.params[1],\n l2 := self.params[3][2], \n v2 := self.params[4][2],\n DownSample(n,2,0) * Circulant(n,l2,v2).terminate() ),\n \n terminate := self >> let(\n n := self.params[1],\n j := self.params[2],\n L := self.params[3],\n V := self.params[4], \n # DWT as filter bank stage + downsampling\n res := Cond(j = 1, I(n), \n\t DirectSum(DWTper(n/2,j-1,L,V).terminate(), I(n/2))) * \n VStack(self.half1(), self.half2()),\n When(self.transposed, res.transpose(), res)\n ),\n\n LiftingScheme := self >> self.lifting(),\n\n lifting := meth(self)\n local n,j,LS,h,g,he,ho,ge,go; \n n := self.params[1]; \n j := self.params[2];\n h := DownsampleTwo([self.params[3][1],self.params[4][1]]);\n g := DownsampleTwo([self.params[3][2],self.params[4][2]]);\n # Lifting scheme does not converge for wavelets longer than 9 \n # (need to be fixed)\n if (Maximum(List(h, i-> Length(i[1])))>9 or \n Maximum(List(g, i-> Length(i[1])))>9) then return [[]];fi;\n he := Poly(h[1][1],h[1][2]); \n ho := Poly(h[2][1],h[2][2]); \n ge := Poly(g[1][1],g[1][2]); \n go := Poly(g[2][1],g[2][2]); \n LS := LiftingScheme([[he,ho],[ge,go]]);\n return LS;\n end,\n\n isReal := True,\n));\n\n\n#F RuleFilter_DWT: (base case) DWT -> Mat, \n#F Computes filter by definition\n#F\nRulesFor(DWTper, rec(\n #F RuleFilt_Mallat_2:\n #F \n #F DWTper(n,j,[h,g])->DWTper(n/2,j-1,[h,g]),DWTper(n,1,[h,g]) \n #F\n #F Mallat rule recursive (single stage DWT)\n #F The I(n/2) is inefficient because it copies the output\n #F However, this rule allows application of Lifting, POlyphase, etc. \n #F on DWTper(n,1,[h,g])\n #F \n DWTper_Mallat_2 := rec(\n\tinfo := \"DWTper(n,j,[h,g])->DWTper(n,j-1,[h,g])\",\n\tforTransposition := false,\n\tisApplicable := P -> P[1] > 2 and P[1] mod 2 =0 and P[2] > 1,\n\n\tallChildren := P -> [[ DWTper(P[1]/2,P[2]-1,P[3],P[4]), DWTper(P[1],1,P[3],P[4]) ]],\n\n\trule := (P, C) -> DirectSum(C[1],I(P[1]/2))C[2]\n ),\n\n #F DWTper_Mallat:\n #F \n #F DWTper(n,j,[h,g])->DWTper(n/2,j-1,[h,g]), DSCirculant \n #F \n DWTper_Mallat := rec(\n info := \"DWTper(n,j,[h,g])->DWTper(n/2,j-1,[h,g])\",\n forTransposition := false,\n isApplicable := P -> P[1]>2 and P[1] mod 2 = 0,\n\n allChildren := P -> let(\n\t n := P[1],\n\t dcirc1 := DSCirculant(n, P[3][1], P[4][1], 2, 0),\n\t dcirc2 := DSCirculant(n, P[3][2], P[4][2], 2, 0),\n\t When(P[2]=1, [[ dcirc1, dcirc2 ]],\n\t\t [[ dcirc1, dcirc2, DWTper(P[1]/2, P[2]-1, P[3], P[4]) ]])),\n\n rule := (P, C) -> When(P[2]=1, VStack(C[1], C[2]),\n VStack(C[3]C[1], C[2]))\n ),\n\n #F DWTper_Polyphase:\n #F \n #F DWTper(n,1,[h,g])->[ [Circulant(he), Circulant(ho)],\n #F [Circulant(ge), Circulant(go)] ]\n #F\n #F Single-stage periodic DWT into a matrix of circulants of downsampled filters \n #F \n DWTper_Polyphase := rec(\n\tinfo := \"DWTper(n,1,[h,g]) -> [[Circ(he), Circ(ho)], [Circ(ge), Circ(go)]]\",\n\tforTransposition := false,\n\tisApplicable := P -> P[1]>2 and P[1] mod 2 =0 and P[2]=1,\n\tallChildren := function(P)\n\t local n,h,g,he,ho,ge,go; \n\t n := P[1]; \n\t h := DownsampleTwo([P[3][1], P[4][1]]);\n\t g := DownsampleTwo([P[3][2], P[4][2]]);\n\t he := Circulant(n/2, h[1][1], h[1][2]); \n\t ho := Circulant(n/2, h[2][1], h[2][2]);\n\t ge := Circulant(n/2, g[1][1], g[1][2]);\n\t go := Circulant(n/2, g[2][1], g[2][2]);\n\t return [[ he, ho, ge, go ]];\n\tend,\n\trule := (P, C) -> BlockMat( [[ C[1], C[2] ],\n\t\t [ C[3], C[4] ]] ) * L(P[1],2)\n ),\n\n #F RuleDWTper_Lifting:\n #F \n DWTper_Lifting := rec(\n info := \"DWTper(n,1,[h,g]) -> Lifting steps\",\n forTransposition := false,\n isApplicable := ( L ) -> L[1]>2 and L[1] mod 2 =0 and L[2]=1,\n\n allChildren := function ( P )\n local n,j,LS,Lc,scheme,step,pol; \n n := P[1];\n LS := Copy(HashLookupWav(HashTableWavelets, [P[3],P[4]]));\n Lc := List(LS, scheme->\n List(scheme{[2..Length(scheme)]}, step->\n let(pol := FillZeros(ListPoly(step)),\n Circulant(n/2,pol[1],pol[2]))));\n\n for i in [1..Length(LS)] do \n # attach the indicator of the type of the first liftings step\n Lc[i][1].lift :=LS[i][1];\n\n # fuse in the constants/shifts in the last lifting step\n #if (LS[i][1]=0 or LS[i][1]=-2) then LS[i][4]:=LS[i][4]LS[i][3];\n #else LS[i][4]:=LS[i][4]LS[i][2];\n #fi;\n\n pol := FillZeros(ListPoly(LS[i][4]));\n Lc[i][3] := Circulant(n/2,pol[1],pol[2]);\n od;\n return Lc;\n end,\n\n rule := function ( P, C, Nonterms )\n local n, i, ind, b, l, M, first, last, ind0, ind1, lstep, last_ls;\n n := P[1]; \n b := Nonterms[1].lift;\n l:=Length(C);\n\n\t ind0 := fTensor(fBase(2,0), fId(Rows(C[3])));\n\t ind1 := fTensor(fBase(2,1), fId(Rows(C[3])));\n\t lstep := (f,b) -> When(b=0, \n\t\tLStep(Scat(ind0) * f * Gath(ind1)),\n\t\tLStep(Scat(ind1) * f * Gath(ind0)));\n\n M := When(b < 0, \n\t\tSUM(Scat(ind0)C[2]Gath(ind1), Scat(ind1)C[1]Gath(ind0)),\n\t\tSUM(Scat(ind0)C[2]Gath(ind0), Scat(ind1)C[1]Gath(ind1)));\n\n\t b := (b+2) mod 2; # make b positive\n\t for i in [1 .. l-2] do\n\t M := M * lstep(C[i+2], b);\n\t\tb := (b+1) mod 2;\n od; \n\n\t first := M.child(1);\n\t M := Inplace(Compose(Drop(M.children(),1)));\n\t return first * M * L(n,2);\n end\n )\n));\n", "meta": {"hexsha": "e92cd99a45008cdefa6116bdba6fbebc294ab217", "size": 7432, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/filtering/dwt_per.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/transforms/filtering/dwt_per.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/transforms/filtering/dwt_per.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 33.0311111111, "max_line_length": 89, "alphanum_fraction": 0.4765877287, "num_tokens": 2613, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8418256313782276, "lm_q2_score": 0.626124191181315, "lm_q1q2_score": 0.5270873925623926}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\nClass(PrunedMDDFT, TaggedNonTerminal, rec(\n abbrevs := [\n (n,k,blk,pat) -> Checked(ForAll(n, IsPosIntSym), IsIntSym(k), IsPosIntSym(blk), ForAll(pat, IsList), \n [_unwrap(n), _unwrap(k), _unwrap(blk), pat, ]),\n ],\n dims := self >> [Product(self.params[1]), self.params[3]Product(self.params[4], i->Length(i))],\n isReal := self >> false,\n normalizedArithCost := self >> let(n := self.params[1], IntDouble(5 n * d_log(n) / d_log(2))),\n TType := TComplex,\n terminate := self >> let(nlist := self.params[1],\n blk := self.params[3], pat_md := self.params[4],\n scat3d := Tensor(List(Zip2(pat_md, nlist), j->let(pat := j[1], size := j[2],\n Tensor(Mat(List(pat, i->BasisVec(size/blk, i))).transpose(), I(blk)).terminate()))),\n dft3d := MDDFT(nlist, self.params[2]),\n t := dft3d * scat3d,\n t.terminate()\n )\n \n));\n\nClass(PrunedIMDDFT, TaggedNonTerminal, rec(\n abbrevs := [\n (n,k,blk,pat) -> Checked(ForAll(n, IsPosIntSym), IsIntSym(k), IsPosIntSym(blk), ForAll(pat, IsList), \n [_unwrap(n), _unwrap(k), _unwrap(blk), pat, ]),\n ],\n dims := self >> [ self.params[3]Product(self.params[4], i->Length(i)), Product(self.params[1]) ],\n isReal := self >> false,\n normalizedArithCost := self >> let(n := self.params[1], IntDouble(5 n * d_log(n) / d_log(2))),\n TType := TComplex,\n terminate := self >> let(nlist := self.params[1],\n blk := self.params[3], pat_md := self.params[4],\n gath3d := Tensor(List(Zip2(pat_md, nlist), j->let(pat := j[1], size := j[2],\n Tensor(Mat(List(pat, i->BasisVec(size/blk, i))), I(blk)).terminate()))),\n dft3d := MDDFT(nlist, self.params[2]),\n t := gath3d * dft3d,\n t.terminate()\n )\n \n));\n\n\n\n\n\nNewRulesFor(PrunedMDDFT, rec(\n PrunedMDDFT_Base := rec(\n info := \"PrunedMDDFT -> PrunedDFT\",\n applicable := nt -> Length(nt.params[1])=1,\n children := nt -> let(P := nt.params, tags := nt.getTags(), [[ PrunedDFT(P[1][1], P[2], P[3], P[4][1]).withTags(tags) ]]),\n apply := (nt, C, Nonterms) -> C[1]\n ),\n PrunedMDDFT_RowCol := rec (\n info := \"PrunedMDDFT_n -> PrunedMDDFT_n/d, PrunedMDDFT_d\",\n applicable := nt -> Length(nt.params[1]) > 1 and not nt.hasTags(),\n\n children := nt -> let(\n dims := nt.params[1],\n len := Length(dims),\n pats := nt.params[4],\n List([1..len-1],\n i -> [ PrunedMDDFT(dims{[1..i]}, nt.params[2], nt.params[3], pats{[1..i]}), \n PrunedMDDFT(dims{[i+1..len]}, nt.params[2], nt.params[3], pats{[i+1..len]}) ])),\n\n apply := (nt, C, Nonterms) -> let(\n n1 := Cols(Nonterms[1]),\n n2 := Rows(Nonterms[2]),\n Tensor(C[1], I(n2)) \n Tensor(I(n1), C[2])\n )\n )\n));\n\nNewRulesFor(PrunedIMDDFT, rec(\n PrunedIMDDFT_Base := rec(\n info := \"PrunedIMDDFT -> PrunedIDFT\",\n applicable := nt -> Length(nt.params[1])=1,\n children := nt -> let(P := nt.params, tags := nt.getTags(), [[ PrunedIDFT(P[1][1], P[2], P[3], P[4][1]).withTags(tags) ]]),\n apply := (nt, C, Nonterms) -> C[1]\n ),\n PrunedIMDDFT_RowCol := rec (\n info := \"PrunedIMDDFT_n -> PrunedIMDDFT_n/d, PrunedIMDDFT_d\",\n applicable := nt -> Length(nt.params[1]) > 1 and not nt.hasTags(),\n\n children := nt -> let(\n dims := nt.params[1],\n len := Length(dims),\n pats := nt.params[4],\n List([1..len-1],\n i -> [ PrunedIMDDFT(dims{[1..i]}, nt.params[2], nt.params[3], pats{[1..i]}), \n PrunedIMDDFT(dims{[i+1..len]}, nt.params[2], nt.params[3], pats{[i+1..len]}) ])),\n\n apply := (nt, C, Nonterms) -> let(\n n1 := Cols(Nonterms[1]),\n n2 := Rows(Nonterms[2]),\n Tensor(C[1], I(n2)) \n Tensor(I(n1), C[2])\n )\n )\n));\n\n", "meta": {"hexsha": "f5d9699fcf8aed2d778a9f94727b4b62d7e764c0", "size": 4454, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/dft/mdprune.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, 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	{"text": "# Copyright (c) 2018-2020, Carnegie Mellon University\n# See LICENSE for details\n\n# Radix N kernel for FFTE\n\nbuildScalarKernel_a := function(n, kk, conf, opts)\n local name, suffix, filesuffix, j, k, l, m, tmp1, tmp2, tmp3, i1, i2, gf, sf, gath, scat,\n gc, sc, dft, rts, rt, opcnts, dfts, dftc, i3, twt, twf, twl, tws, twc,\n cl, cc, c, cx, lp, mp;\n\n name := DFTnameStr(n, kk);\n suffix := \"a\";\n filesuffix := \"c_\";\n# suffix := \"_j\";\n Print(\"\\n\\n// == Generating \\\"\", name, \"\\\" ==================================================\\n\\n\"); \n\n # variables\n #t := var.fresh_t(\"t\", TInt);\n j := var.fresh_t(\"j\", TInt);\n# k := var.fresh_t(\"k\", TInt);\n k := V(0);\n l := var.fresh_t(\"l\", TInt);\n # m := var.fresh_t(\"m\", TInt);\n m := V(1);\n lp := var.fresh_t(\"lp\", TPtr(TInt));\n mp := var.fresh_t(\"mp\", TPtr(TInt));\n \n # temp arrays\n tmp1 := var.fresh_t(\"R\", TArray(TReal, 2n));\n tmp2 := var.fresh_t(\"S\", TArray(TReal, 2n));\n tmp3 := var.fresh_t(\"T\", TArray(TReal, 2n));\n \n # gather and scatter\n i1 := var.fresh_t(\"i\", n);\n i2 := var.fresh_t(\"i\", n);\n gf := fTensor(Lambda(i1, k + jm + i1lm), fId(2));\n sf := fTensor(Lambda(i2, k+njm + i2m), fId(2));\n gath := Gath(gf);\n scat := Scat(sf);\n\n # generate gather and scatter code\n gc := BlockUnroll(unroll_cmd(opts.codegen(gath, tmp1, X, opts)), opts);\n sc := BlockUnroll(unroll_cmd(opts.codegen(scat, Y, tmp3, opts)), opts);\n \n # generate DFT kernel\n dft := RC(DFT(n, kk));\n rts := AllRuleTrees(dft, opts);\n opcnts := List(rts, r -> [ Length(Collect(CodeRuleTree(r, opts), @(1, [add, sub, mul], e->e.t=TReal))), r]);\n rt := Minimum(opcnts)[2];\n dfts := SumsRuleTree(rt, opts);\n dftc := BlockUnroll(opts.codegen(dfts, tmp2, tmp1, opts), opts);\n \n # twiddles as lookup table\n i3 := var.fresh_t(\"i\", 2n);\n twt := var.fresh_t(\"TW\", TPtr(TReal)); \n twf := Lambda(i3, cond(eq(i3, 0), 1, eq(i3, 1), 0, nth(twt, 2((n-1)j) + 2 * idiv(i3, 2) + (imod(i3, 2) - 2))));\n \n # debug twiddles\n twl := Map(twf.tolist(), RulesStrengthReduce);\n DoForAll([0..Length(twl)-1], _i->Unparse(assign(nth(Y, _i), twl[_i+1]), CUnparser, 0, 1));\n\n tws := RCDiag(twf);\n twc :=BlockUnroll(unroll_cmd(opts.codegen(tws, tmp3, tmp2, opts)), opts);\n \n # stitch code fragments together\n cl := func(TVoid, \"transform\", [Y, X, twt, j, k, l, m], \n decl([tmp1, tmp2, tmp3], chain(gc, dftc, twc, sc)));\n cc := Compile(cl, opts);\n \n # fixup to push decls inside (?)\n c := func(TVoid, \"transform\", [Y, X, twt, j, k, lp], \n decl(cc.vars::[l], \n chain(\n assign(l, deref(lp)),\n cc.cmd.cmds[1].cmd\n )\n )\n );\n \n # print Radix N FFTE kernel as function\n# PrintCode(name, c, opts);\n# PrintTo(name::\".c\", PrintCode(name, c, opts));\n \n # function with j and k loop in the function call\n cl := func(TVoid, \"transform\", [Y, X, twt, lp], \n decl(c.cmd.vars::c.free(), \n chain(\n assign(l, deref(lp)),\n loopn(j, l, \n c.cmd.cmd)\n )\n )\n );\n \n # print Radix N FFTE kernel as function\n PrintCode(opts.FortranIze(name::suffix), cl, opts);\n PrintTo(name::filesuffix::suffix::\".c\", PrintCode(opts.FortranIze(name::suffix), cl, opts));\nend;\n\n\n", "meta": {"hexsha": "52fa530ad06f26a8021a9c884034c208915587b9", "size": 3436, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "kernelgen/scalar_a.gi", "max_stars_repo_name": "spiral-software/spiral-package-ffte", "max_stars_repo_head_hexsha": "19f751776c117e28bdbcc3d2530c895ad554d855", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "kernelgen/scalar_a.gi", "max_issues_repo_name": "spiral-software/spiral-package-ffte", "max_issues_repo_head_hexsha": "19f751776c117e28bdbcc3d2530c895ad554d855", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "kernelgen/scalar_a.gi", "max_forks_repo_name": "spiral-software/spiral-package-ffte", "max_forks_repo_head_hexsha": "19f751776c117e28bdbcc3d2530c895ad554d855", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2021-06-15T12:41:51.000Z", "max_forks_repo_forks_event_max_datetime": "2021-06-15T12:41:51.000Z", "avg_line_length": 34.0198019802, "max_line_length": 117, "alphanum_fraction": 0.5209545984, "num_tokens": 1165, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.815232489352, "lm_q2_score": 0.6442251064863697, "lm_q1q2_score": 0.5251932372639404}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nClass(PkRDFT12_Base, PRDFT_Base, rec(\n dims := self >> [self.params[1], self.params[1]],\n terminate := self >> let(N := self.params[1], k := self.params[2], \n\trr := When(self.transposed, Cols(self), Rows(self)), \n\tmat := Cond(IsEvenInt(N), \n Mat(Concatenation(\n [List([0..N-1], c-> When(IsEvenInt(c), 1,1))],\n [List([0..N-1], c-> When(IsEvenInt(c), 1,-1))],\n List([2..rr-1], r -> When(r mod 2 = 0, \n List([0..N-1], c -> self.projRe(self.omega(N,k,Int(r/2),c))),\n List([0..N-1], c -> self.projIm(self.omega(N,k,Int(r/2),c))))))),\n Mat(Concatenation(\n [List([0..N-1], c -> 1)],\n List([2..rr], r -> When(r mod 2 = 0, \n List([0..N-1], c -> self.projRe(self.omega(N,k,Int(r/2),c))),\n List([0..N-1], c -> self.projIm(self.omega(N,k,Int(r/2),c)))))))),\n When(self.transposed, mat.transpose(), mat)),\n));\n\nClass(PkRDFT1, PkRDFT12_Base, rec(\n abbrevs := [ (n) -> Checked(IsPosInt(n), [n, 1]),\n (n,k) -> Checked(IsPosIntSym(n), IsIntSym(k), \n IsSymbolic(n) or IsSymbolic(k) or Gcd(n,k)=1, [n, k mod n]) ],\n omega := (N,k,r,c) -> E(N)^(krc)\n));\nClass(PkRDFT2, PkRDFT12_Base, rec(\n abbrevs := [ (n) -> Checked(IsPosIntSym(n), [n, 1]),\n (n,k) -> Checked(IsPosIntSym(n), IsIntSym(k), \n IsSymbolic(n) or IsSymbolic(k) or Gcd(n,k)=1, [n, k mod (2n)]) ],\n omega := (N,k,r,c) -> E(2N)^(kr(2c+1))\n));\n\nClass(PkDHT1, PkRDFT1, rec(\n terminate := self >> let(n := self.params[1], k := self.params[2], i := When(IsEvenInt(n), 2, 1),\n DirectSum(I(i), Tensor(I(Int((n-1)/2)), F(2))) \n PkRDFT1(n, k).terminate()\n )\n));\n\nClass(PkDHT2, PkRDFT2, rec(\n terminate := self >> let(n := self.params[1], k := self.params[2], i := When(IsEvenInt(n), 2, 1),\n DirectSum(I(i), Tensor(I(Int((n-1)/2)), Diag(1,-1)F(2))) \n PkRDFT2(n, k).terminate()\n )\n));\n\nClass(URealDFT_Base, NonTerminal, rec(\n abbrevs := [ (n) -> Checked(IsPosInt(n), [n, 1]),\n (n,k) -> Checked(IsPosInt(n), IsInt(k), Gcd(n,k)=1, [n, k mod n]) ],\n terminate := self >> let(N := self.params[1], k := self.params[2], \n\trr := When(self.transposed, Cols(self), Rows(self)),\n\tMat(Concatenation(\n\t [List([0..N-1], c-> When(IsEvenInt(c), 1,0))],\n\t [List([0..N-1], c-> When(IsOddInt(c), 1,0))],\n\t List([2..rr-1], r -> When(r mod 2 = 0, \n\t\t List([0..N-1], c -> self.projRe(self.omega(N,k,Int(r/2),c))),\n\t\t List([0..N-1], c -> self.projIm(self.omega(N,k,Int(r/2),c)))))))),\n isReal := True,\n SmallRandom := () -> Random([2..16]), \n LargeRandom := () -> 2 ^ Random([6..15])\n));\n\nClass(URDFT_Base, URealDFT_Base, rec(\n projRe := Re,\n projIm := Im,\n hashAs := self >> self\n));\n\nClass(URDFT, URDFT_Base, rec(\n dims := self >> let(n:=self.params[1], [ 2(Int((n+1)/2)), n ]),\n omega := (N,k,r,c) -> E(N)^(krc),\n));\n\nURDFT1:=URDFT;\n\n# Regularized Rules\n# R1 -> (R1, C1) (R1')\n# R2 -> (R2, C2) (R1')\nPRF12_CTReg_Children := (N,k,PRFt,DFTt,PRF1prime, maxRadix) -> Map2(\n Filtered(DivisorPairs(N),d->d[1] <= maxRadix/2 and d[2]<>2),\n (m,n) -> When(IsEvenInt(n),\n\t[ PRFt(2m,k), DFTt(m,k), PRF1prime(n,k) ],\n\t[ PRFt(m,k), DFTt(m,k), PRF1prime(n,k) ] )\n);\n\nPRF12_CTReg_Rule := (N,k,C,Conj,Tw) -> let(mm:=Cols(C[1]), m:=When(IsEvenInt(N), mm/2, mm),\n n:=Cols(C[3]), Nf:=Int(N/2), Nc:=Int((N+1)/2),\n nf:=Int(n/2), nc:=Int((n+1)/2), mf:=Int(m/2), mc:=Int((m+1)/2), j:=Ind(nc-1),\n\n SUM(\n\tBB(RC(Scat(H(Nc,m,0,n/2))) * C[1] * L(mm,2) * RC(Gath(H(ncm, m, 0, nc)))),\n\n\tWhen(nc=1, [], \n\tISum(j, BB(\n\t RC(Scat(BH(Nc,N,m,j+1,n))) \n\t Conj * RC(C[2]) * Tw(j) \n\t RC(Gath(H(ncm, m, j+1, nc))))))\n ) * \n Tensor(I(m), C[3]) * L(N,m)\n);\n\nPRF12_CTReg2_Rule := (N,k,C,Conj,Tw) -> let(mm:=Cols(C[1]), m:=When(IsEvenInt(N), mm/2, mm),\n n:=Cols(C[3]), Nf:=Int(N/2), Nc:=Int((N+1)/2),\n nf:=Int(n/2), nc:=Int((n+1)/2), mf:=Int(m/2), mc:=Int((m+1)/2), j:=Ind(nc-1),\n\n SUM(\n\tRC(Scat(H(Nc,m,0,n/2))) * C[1] * RC(Gath(H(ncm, m, 0, 1))),\n\n\tWhen(nc=1, [], \n\tISum(j, \n\t RC(Scat(BH(Nc,N,m,j+1,n))) \n\t Conj * RC(C[2]) * Tw(j) * L(2m, m) \n\t RC(Gath(H(ncm, m, m(j+1), 1)))))\n ) * \n Tensor(C[3], I(m)) \n);\n\nPRF12_CTReg3_Rule := (N,k,C,Conj,Tw) -> let(mm:=Cols(C[1]), m:=When(IsEvenInt(N), mm/2, mm),\n n:=Cols(C[3]), Nf:=Int(N/2), Nc:=Int((N+1)/2),\n nf:=Int(n/2), nc:=Int((n+1)/2), mf:=Int(m/2), mc:=Int((m+1)/2), j:=Ind(nc-1),\n\n SUM(\n\tRC(Scat(H(Nc,m,0,n/2))) * C[1] * L(2m, 2) Gath(H(N, 2m, 0, nc)),\n\n\tWhen(nc=1, [], \n\tISum(j, \n\t RC(Scat(BH(Nc,N,m,j+1,n))) \n\t Conj * RC(C[2]) * Tw(j) \n\t Gath(H(N, 2m, j+1, nc))))\n ) * \n Tensor(I(m), L(n,2)C[3]) L(N,m)\n);\n\nPRF12_CTReg4_Rule := (N,k,C,Conj,Tw) -> let(mm:=Cols(C[1]), m:=When(IsEvenInt(N), mm/2, mm),\n n:=Cols(C[3]), Nf:=Int(N/2), Nc:=Int((N+1)/2),\n nf:=Int(n/2), nc:=Int((n+1)/2), mf:=Int(m/2), mc:=Int((m+1)/2), j:=Ind(nc-1),\n\n RC(Tensor(I(m/2), DirectSum(I(n/2+1), J(n/2-1)))) \n RC(L(N/2, m)) \n DirectSum(\n C[1] * L(2m, 2),\n\tIterDirectSum(j, RC(M(m,m/2)) Conj * RC(C[2]) * Tw(j))\n ) * \n L(N, nc) * \n Tensor(I(m), L(n,2)C[3]) L(N,m)\n);\n\nPRF12_CTReg5_Rule := (N,k,C,Conj,Tw) -> let(mm:=Cols(C[1]), m:=When(IsEvenInt(N), mm/2, mm),\n n:=Cols(C[3]), Nf:=Int(N/2), Nc:=Int((N+1)/2),\n nf:=Int(n/2), nc:=Int((n+1)/2), mf:=Int(m/2), mc:=Int((m+1)/2), j:=Ind(nc-1),\n\n RC(Tensor(I(m/2), DirectSum(I(n/2+1), J(n/2-1)))) \n RC(L(N/2, m)) \n DirectSum(\n C[1],\n\tIterDirectSum(j, RC(M(m,m/2)) * Conj * RC(C[2]) * Tw(j) * L(2m, m))\n ) \n Tensor(C[3], I(m))\n);\n\nunrc := m -> let(r := Dimensions(m)[1], c := Dimensions(m)[2],\n MatSPL(Gath(H(r,r/2,0,2))) * m * MatSPL(Scat(H(c,c/2,0,2))));\n\nRulesFor(URDFT1, rec(\n URDFT1_Base1 := BaseRule(URDFT1, [1, @]),\n URDFT1_Base2 := BaseRule(URDFT1, [2, @]),\n URDFT1_Base4 := BaseRule(URDFT1, [4, @]),\n\n URDFT1_CT := rec(\n maxRadix := 32,\n\tisApplicable := P -> not IsPrime(P[1]) and not (IsEvenInt(P[1]) and IsPrime(P[1]/2)),\n\tallChildren := (self, P) >> PRF12_CTReg_Children(P[1], P[2], URDFT1, DFT1, URDFT1, self.maxRadix), \n\trule := (P,C) -> let(N:=P[1], k:=P[2], m:=When(IsEvenInt(N), Cols(C[1])/2, Cols(C[1])),\n\t PRF12_CTReg_Rule(N, k, C, Diag(BHD(m,1,-1)), \n j -> RC(DirectSum(I(1), Diag(fPrecompute(fCompose(Twid(N,m,k,0,0,j+1), fAdd(m, m-1, 1))))))))),\n\n # slightly different variant of same rule, \n URDFT1_CT2 := rec(\n\tisApplicable := P -> not IsPrime(P[1]) and not (IsEvenInt(P[1]) and IsPrime(P[1]/2)),\n\tallChildren := P -> PRF12_CTReg_Children(P[1], P[2], URDFT1, DFT1, URDFT1), \n\trule := (P,C) -> let(N:=P[1], k:=P[2], m:=When(IsEvenInt(N), Cols(C[1])/2, Cols(C[1])),\n\t PRF12_CTReg2_Rule(N, k, C, Diag(BHD(m,1,-1)), j->RC(Diag(fPrecompute(Twid(N,m,k,0,0,j+1))))))),\n\n URDFT1_CT3 := rec(\n\tisApplicable := P -> not IsPrime(P[1]) and not (IsEvenInt(P[1]) and IsPrime(P[1]/2)),\n\tallChildren := P -> PRF12_CTReg_Children(P[1], P[2], URDFT1, DFT1, URDFT1), \n\trule := (P,C) -> let(N:=P[1], k:=P[2], m:=When(IsEvenInt(N), Cols(C[1])/2, Cols(C[1])),\n\t PRF12_CTReg3_Rule(N, k, C, Diag(BHD(m,1,-1)), j->RC(Diag(fPrecompute(Twid(N,m,k,0,0,j+1))))))),\n\n URDFT1_CT4 := rec(\n\tisApplicable := P -> not IsPrime(P[1]) and not (IsEvenInt(P[1]) and IsPrime(P[1]/2)),\n\tallChildren := P -> PRF12_CTReg_Children(P[1], P[2], URDFT1, DFT1, URDFT1), \n\trule := (P,C) -> let(N:=P[1], k:=P[2], m:=When(IsEvenInt(N), Cols(C[1])/2, Cols(C[1])),\n\t PRF12_CTReg4_Rule(N, k, C, Diag(BHD(m,1,-1)), j->RC(Diag(fPrecompute(Twid(N,m,k,0,0,j+1))))))),\n\n URDFT1_CT5 := rec(\n\tisApplicable := P -> not IsPrime(P[1]) and not (IsEvenInt(P[1]) and IsPrime(P[1]/2)),\n\tallChildren := P -> PRF12_CTReg_Children(P[1], P[2], URDFT1, DFT1, URDFT1), \n\trule := (P,C) -> let(N:=P[1], k:=P[2], m:=When(IsEvenInt(N), Cols(C[1])/2, Cols(C[1])),\n\t PRF12_CTReg5_Rule(N, k, C, Diag(BHD(m,1,-1)), j->RC(Diag(fPrecompute(Twid(N,m,k,0,0,j+1))))))),\n\n));\n\n\n", "meta": {"hexsha": "26b9fc720d4eb4e52a5dfdb89952450231ee799b", "size": 8226, "ext": "gi", "lang": "GAP", "max_stars_repo_path": 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	{"text": "# Copyright (c) 2018-2020, Carnegie Mellon University\n# See LICENSE for details\n#\n# Contains the CNOT and SWAP non-terminals and rewrite rules\n#\n\n##\n#F qSWAPT( <qi>, <qj>, <n>,, <arch> ) Object\n##\n#F Awaps qi and qj in a system of n qubits, with architecture arch\n#F Definition: (2^n x 2^n)-matrix \n#F that swaps qubit qi and qubit qj, with the identity operation applied to all others\nClass(qSWAPT, TaggedNonTerminal, rec(\n abbrevs := [ (qi, qj, n, arch) -> Checked(IsPosInt(n), [qi, qj, n, arch]) ],\n dims := self >> let(size := 2^self.params[3], [size, size]),\n terminate := self >> GenSwapMat(self.params[1], self.params[2], self.params[3]), \n isReal := self >> true,\n rChildren := self >> self.params,\n from_rChildren := (self, rch) >> self.__bases__[1](rch[1], rch[2], rch[3], rch[4]),\n SmallRandom := () -> Random([2..5]),\n LargeRandom := () -> Random([6..15]),\n normalizedArithCost := self >> Error(\"ArithCost not implemented\"),\n TType := T_Real(64)\n));\n\n##\n#F CnotTerm( <i>, <j>, <n> )\n##\n## .terminate() function for the qCNOT Non-terminal. Expands qCNOT non-terminal into a 2^n by 2^n matrix\nCnotTerm := function (i, j, n)\n return When(i < j, Tensor(Tensor(I(2^(i)), GenCnotMat(j, 0)), I(2^(n-j))), Tensor(Tensor(I(2^(j)), GenCnotMat(i, 1)), I(2^(n-i)))); # create the intended cnot matrix\nend;\n\n##\n#F CnotSPL( <i>, <j>, <n> )\n##\n## Used for the qCNOT_Base breakdown rule. Represents a qCNOT Non-terminal as a tensor of CNOT and I SPL objects\nCnotSPL := function (i, j, n)\n return When(i < j, Tensor(Tensor(I(2^(i)), CNOT(j-i, 0)), I(2^(n-1-j))), Tensor(Tensor(I(2^(j)), CNOT(i-j, 1)), I(2^(n-1-i)))); # create the intended cnot matrix\nend;\n\n##\n#F qCNOT( <qj>, <dir>, <arch> ) Object\n##\n#F CNOT Non-terminal\n#F Definition: (2^n x 2^n)-matrix that applies a CNOT from qubit 0 to j \nClass(qCNOT, TaggedNonTerminal, rec(\n abbrevs := [ (qj, dir, arch) -> Checked([qj, dir, arch]) ],\n dims := self >> let(size := 2^(self.params[1]+1), [size, size]),\n terminate := self >> GenCnotMat(self.params[1], self.params[2]),\n isReal := self >> true,\n groups := self >> [[2]],\n recursive_def := (self, arch) >> self.__bases__[1](self.params[1], self.params[2], arch),\n rChildren := self >> self.params,\n from_rChildren := (self, rch) >> self.__bases__[1](rch[1], rch[2], rch[3]),\n connected := self >> true,\n SmallRandom := () -> Random([2..5]),\n LargeRandom := () -> Random([6..15]),\n normalizedArithCost := self >> Error(\"ArithCost not implemented\"),\n TType := T_Real(64)\n));\n\n\n##\n#F qCNOT Breakdown Rules\n## \nNewRulesFor(qCNOT, rec(\n \n #F qCNOT_Base: qCNOT(_) = CNOT() SPL object\n #F Directly represent as an implementable gate, if a proper edge exists\n qCNOT_Base := rec(\n info := \"qCNOT_(_) -> CNOT(_)\",\n forTransposition := false,\n applicable := (self, nt) >> (HasEdge(0, nt.params[1], nt.params[3]) = 1),\n apply := (nt, c, cnt) -> CNOT(nt.params[1], nt.params[2]),\n )\n\n));\n\n##\n#F CnotSPL( <i>, <j>, <n> )\n##\n## Used for the qSWAP_Base breakdown rule. Represents a qCNOT Non-terminal as a tensor of CNOT and I SPL objects\nCnotSPL := function (i, j, n)\n return When(i < j, Tensor(Tensor(I(2^(i)), CNOT(j-i, 0)), I(2^(n-1-j))), Tensor(Tensor(I(2^(j)), CNOT(i-j, 1)), I(2^(n-1-i)))); # create the intended cnot matrix\nend;\n\n##\n#F SwapGenChildren( <start>, <ending>, <n>, <arch> )\n##\n## decompose a qSWAPT transform into smaller qSWAPT transforms\nSwapGenChildren := function (start, ending, n, arch)\n local move, children;\n move := Best_Move(start, ending, arch);\n children := [];\n Add(children, [qSWAPT(start, move, n, arch) * qSWAPT(move, ending, n, arch) * qSWAPT(start, move, n, arch)]);\n return children;\nend;\n\n##\n#F qSWAPT Breakdown Rules\n## \nNewRulesFor(qSWAPT, rec(\n\n #F qSWAPT_Base: qSWAPT(_) = qCNOT() SPL objects\n #F SWAP to CNOT conversion, only if an edge exists\n #F represent a swap as a series of 3 CNOTs with the middle being an alternate direction\n qSWAPT_Base := rec(\n info := \"qSWAPT() -> CNOT * CNOT * CNOT \",\n forTransposition := false,\n applicable := (self, nt) >> ( (HasEdge(nt.params[1], nt.params[2], nt.params[4]) = 1) and (nt.params[1] <> nt.params[2])),\n children := nt -> List( [ [ (CnotSPL(nt.params[1], nt.params[2], nt.params[3]))(CnotSPL(nt.params[2], nt.params[1], nt.params[3]))(CnotSPL(nt.params[1], nt.params[2], nt.params[3])) ] , [ (CnotSPL(nt.params[2], nt.params[1], nt.params[3]))(CnotSPL(nt.params[1], nt.params[2], nt.params[3]))(CnotSPL(nt.params[2], nt.params[1], nt.params[3])) ] ] ), \n apply := (nt, c, cnt) -> c[1],\n ),\n\n\n #F qSWAPT_ID: qSWAPT(_) = I() SPL object\n #F SWAP to Identity conversion if the swap is trivial\n qSWAPT_Id := rec(\n info := \"qSWAPT() -> Identity \",\n forTransposition := false,\n applicable := (self, nt) >> (nt.params[1] = nt.params[2]),\n apply := (nt, c, cnt) -> I(2^(nt.params[3])),\n ),\n\n #F qSWAPT_Rec: qSWAPT(_) = qSWAPT(_) * qSWAPT(_) \n #F Break down an unimplementable qSWAP into an implementable swap and a swap that is 1 step closer to being implementable\n #F TODO, make this a bit more intelligent, right now SwapGenChildren just does a random walk\n qSWAPT_Rec := rec(\n info := \"qSWAPT() -> qSWAPT() * qSWAPT()\",\n forTransposition := false,\n applicable := (self, nt) >> ((nt.params[1] <> nt.params[2]) and (HasEdge(nt.params[1], nt.params[2], nt.params[4]) = 0)),\n children := nt -> SwapGenChildren(nt.params[1], nt.params[2], nt.params[3], nt.params[4]), \n apply := (nt, c, cnt) -> c[1],\n )\n\n));\n\n##\n#F ShiftMat( <swap1>, <swap2>, <arch>, <n> )\n##\n## generates a martix of SWAP operations that swap the qubit groups swap1 and swap2 in parallel\n## swap1 is the target position, and swap2 are original positions\nShiftMat := function (swap1, swap2, arch, n)\n local idx, format, backmat, targets, t, positions, e, sw1, sw2, s, i, test, already_swapped;\n idx := 1;\n format := I(2^(n));\n backmat := I(2^(n));\n positions := [];\n targets := [];\n for s in swap1 do \n Add(positions, s);\n od;\n for t in swap2 do \n Add(targets, t);\n od;\n for s in swap1 do\n if ((targets[idx] <> positions[idx])) then # just save the extra trouble, if the swap is trivial\n format := format * qSWAPT(positions[idx], targets[idx], n ,arch);\n backmat := qSWAPT(positions[idx], targets[idx], n , arch) * backmat;\n sw1 := targets[idx];\n sw2 := positions[idx];\n i := 1;\n for e in positions do \n if e = sw1 then \n positions[i] := sw2;\n fi;\n if e = sw2 then \n positions[i] := sw1;\n fi;\n i := i + 1;\n od;\n fi;\n idx := idx + 1;\n od;\n return [format, backmat];\nend;\n\n", "meta": {"hexsha": "e6e0a9e052a85ebd01190f5f8557feb2da43ee4d", "size": 7072, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "qcnot.gi", "max_stars_repo_name": "spiral-software/spiral-package-quantum", "max_stars_repo_head_hexsha": "dd2323983495adbbc6261c0cdf840320d19d099d", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "qcnot.gi", "max_issues_repo_name": "spiral-software/spiral-package-quantum", "max_issues_repo_head_hexsha": "dd2323983495adbbc6261c0cdf840320d19d099d", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "qcnot.gi", "max_forks_repo_name": "spiral-software/spiral-package-quantum", "max_forks_repo_head_hexsha": "dd2323983495adbbc6261c0cdf840320d19d099d", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 39.5083798883, "max_line_length": 370, "alphanum_fraction": 0.5764988688, "num_tokens": 2233, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.8289387998695209, "lm_q2_score": 0.6297746074044134, "lm_q1q2_score": 0.5220446072501131}}
	{"text": "#\n# cls 17: A_2\n#\nhandle17char3:=function()\n local tmp1,tmp2,o,info,rep,cent,uu;\n o:=AllClasses(orbs)[17];\n info:=infos[17];\n \n rep:=Representative(o);\n #pr[15]=[0,0,1,1,1,0]\n #pr[13]=[0,1,1,1,0,0]\n #pr[26]=[1,1,1,2,1,0]\n tmp1:=ApplyRootsReflections(rep,[15,13,26]);\n uu:=Unipotent(chevalleyAdj(rep),[[3,1]]);\n tmp1:=Conj(tmp1,uu);\n tmp1:=ConjugateByTori(tmp1,[3],[-1]);\n \n cent:=FromPositiveBorel(o,info[2]);\n tmp2:=ApplyRootsReflections(cent,[15,13,26]);\n uu:=Unipotent(chevalleyAdj(cent),[[3,1]]);\n tmp2:=Conj(tmp2,uu);\n tmp2:=ConjugateByTori(tmp2,[3],[-1]);\n\n return [tmp1,tmp2];\nend;\n\n\n#\n# cls 10: D_4(a_1)\n#\nhandle10char3:=function()\n local tmp1,tmp2,tmp3,tmp4,o,info,rep,cent,uu;\n o:=AllClasses(orbs)[10];\n info:=infos[10];\n \n rep:=Representative(o);\n #pr[4] =[0,0,0,1,0,0]\n #pr[32]=[1,1,2,2,1,1]\n #pr[33]=[1,1,1,2,2,1]\n tmp1:=ApplyRootsReflections(rep,[4,32,33]);\n uu:=Unipotent(chevalleyAdj(rep),[[3,-1],[5,1]]);\n tmp1:=Conj(tmp1,uu);\n tmp1:=ConjugateByTori(tmp1,[4,1,2,6],[-1,-1,-1,-1]);\n\n #pr[20]=[0,1,0,1,1,1]\n #pr[21]=[0,0,1,1,1,1]\n tmp3:=ApplyRootsReflections(rep,[20,21]);\n uu:=Unipotent(chevalleyAdj(rep),[[3,1],[4,1],[5,-1],[9,1],[10,-1]]);\n tmp3:=Conj(tmp3,uu);\n tmp3:=ConjugateByTori(tmp3,[2,4],[-1,-1,-1,-1]);\n \n \n cent:=FromPositiveBorel(o,info[2]);\n tmp2:=ApplyRootsReflections(cent,[4,32,33]);\n uu:=Unipotent(chevalleyAdj(cent),[[3,-1],[5,1]]);\n tmp2:=Conj(tmp2,uu);\n tmp2:=ConjugateByTori(tmp2,[4,1,2,6],[-1,-1,-1,-1]);\n\n tmp4:=ApplyRootsReflections(cent,[20,21]);\n uu:=Unipotent(chevalleyAdj(cent),[[3,1],[4,1],[5,-1],[9,1],[10,-1]]);\n tmp4:=Conj(tmp4,uu);\n tmp4:=ConjugateByTori(tmp4,[2,4],[-1,-1,-1,-1]);\n \n return [tmp1,tmp3,tmp2,tmp4];\nend;\n\n\n#\n# cls 4: E_6(a_3) [13,1,15,6,14,4] \n#\nhandle4char3:=function()\n local tmp1,tmp2,o,info,rep,cent;\n o:=AllClasses(orbs)[4];\n info:=infos[4];\n \n rep:=Representative(o);\n tmp1:=ConjugateByTorus(rep,4,-1);# h_1 --> h_4\n \n cent:=FromPositiveBorel(o,info[2]);\n tmp2:=ConjugateByTorus(cent,4,-1);# h_1 --> h_4\n \n return [tmp1,tmp2];\nend;\n", "meta": {"hexsha": "8ec938e65ac3ed44c0dfe428fd8ce78a98d62efc", "size": 2187, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "lib/components/E6char3.gi", "max_stars_repo_name": "iuliansimion/Chevalley.gap", "max_stars_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "lib/components/E6char3.gi", "max_issues_repo_name": "iuliansimion/Chevalley.gap", "max_issues_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "lib/components/E6char3.gi", "max_forks_repo_name": "iuliansimion/Chevalley.gap", "max_forks_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 26.0357142857, "max_line_length": 73, "alphanum_fraction": 0.5729309556, "num_tokens": 934, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7606506635289836, "lm_q2_score": 0.685949467848392, "lm_q1q2_score": 0.5217679178662326}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n# equality of scalars\nscalareq := (a,b) -> AbsFloat(a-b) < 1e-10;\n# equality of lists\nlseq := (a,b) -> Length(a)=Length(b) and ForAll([1..Length(a)], scalareq(a[i], b[i]));\n\nlequiv := (a,b) -> Cond(\n lseq(a,b), \"eq\", \n lseq(a, -b), \"eqneg\",\n lseq(a, Reversed(b)), \"rev\", \n lseq(a, -Reversed(b)), \"revneg\",\n \"none\");\n\ntovec := lst -> TransposedMat([lst]);\ntolst := vec -> TransposedMat(vec)[1];\nrpart := vec -> List(vec, x->ReComplex(Complex(x)));\nipart := vec -> List(vec, x->ImComplex(Complex(x)));\n\nrand := arg -> RandomList([-100..100]);\n#rand := x->x;\n\n##\n## Constructors for symmetric sequences\n##\nreal := n -> List([1..n], rand);\ncplx := (rsym, isym) -> (n -> rsym(n) + E(4)isym(n));\n\neven0 := n -> let(len := Int((n-1)/2), lst := List([2..len+1], rand),\n Flat([rand(1), lst, When(IsEvenInt(n),rand(len+2),[]), Reversed(lst)]));\n\neven00 := n -> let(len := Int((n-1)/2), lst := List([1..len], rand),\n Flat([0, lst, When(IsEvenInt(n),rand(len+1),[]), Reversed(lst)]));\nodd0 := n -> let(len := Int((n-1)/2), lst := List([2..len+1], rand),\n Flat([rand(1), lst, When(IsEvenInt(n),0,[]), -Reversed(lst)]));\nodd00 := n -> let(len := Int((n-1)/2), lst := List([1..len], rand),\n Flat([0, lst, When(IsEvenInt(n),0,[]), -Reversed(lst)]));\n\neven1 := n -> let(len := Int(n/2), lst := List([1..len], rand),\n Flat([lst, When(IsOddInt(n),rand(len+1),[]), Reversed(lst)]));\nodd1 := n -> let(len := Int(n/2), lst := List([1..len], rand),\n Flat([lst, When(IsOddInt(n),0,[]), -Reversed(lst)]));\n\njeven1 := n -> Checked(IsEvenInt(n), let(lst:=List([1..n/2], rand), Flat([lst,lst])));\njodd1 := n -> Checked(IsEvenInt(n), let(lst:=List([1..n/2], rand), Flat([lst,-lst])));\njeven0 := n -> Checked(IsOddInt(n), Concatenation([rand(0)], jeven1(n-1)));\njeven00 := n -> Checked(IsOddInt(n), Concatenation([0], jeven1(n-1)));\njodd0 := n -> Checked(IsOddInt(n), Concatenation([rand(0)], jodd1(n-1)));\njodd00 := n -> Checked(IsOddInt(n), Concatenation([0], jodd1(n-1)));\n\nce0 := cplx(even0, odd00);\nco0 := cplx(odd0, even00);\nce1 := cplx(even1, odd1);\nco1 := cplx(odd1, even1);\n\njce0 := cplx(jeven0, jodd00);\njco0 := cplx(jodd0, jeven00);\njce1 := cplx(jeven1, jodd1);\njco1 := cplx(jodd1, jeven1);\n\nraderce0 := n -> Checked(IsPrime(n+1), Drop(\n tolst(MatSPL(DFT_Rader.raderMid(n+1,1,PrimitiveRootMod(n+1))) \n\t tovec(Concat([rand(0)], ce0(n)))), 1));\n\nupsample0 := n -> Checked(IsEvenInt(n), List([1..n], i -> When(IsEvenInt(i),0,rand())));\n\nupsample1 := n -> Checked(IsEvenInt(n), List([1..n], i -> When(IsOddInt(i),0,rand())));\n\n_even := n -> ((n+1) mod 2);\n_odd := n -> (n mod 2);\n\n_minsetPoints := function(points, n)\n local uniq, cur, p;\n cur := []; uniq := Set([]);\n for p in points do\n if not (p in uniq) and p < n then \n\t Add(cur, p); \n\t AddSet(uniq, p); \n\tfi;\n od;\n return cur;\nend;\n\n_CommuteExt := function(perm, sym, refl_diff, n, drop0) \n local mat, N, ext, points, minset, pmat;\n mat:=MatSPL(Prm(perm));\n N := perm.domain();\n ext := sym.ext(N,false);\n points := List(Refl(n, N-refl_diff, N, perm).tolist(), x->x.ev());\n minset := When(not drop0, _minsetPoints(points, n), Drop(_minsetPoints(points,n), 1)-1);\n pmat := MatSPL(Scat(FList(minset).setRange(Cols(ext))));\n return \n mat * MatSPL(ext) * pmat;\nend;\n\n\n# CommuteExt(spl, sym, scaled) - find X, such that spl * sym.ext(n, scaled) = X * pspl\n# X = spl * sym.ext(n, scaled) * pspl^-1\n#\n\nCommuteExt1 := (perm, sym) -> _CommuteExt(perm, sym, -1, Cols(sym.ext(perm.domain(),false)), false);\nCommuteExt0 := (perm, sym) -> _CommuteExt(perm, sym, 0, Cols(sym.ext(perm.domain(),false)), false);\nCommuteExt00 := (perm, sym) -> _CommuteExt(perm, sym, 0, 1+Cols(sym.ext(perm.domain(),false)), true);\n\n##\n## Constructors for symmetric sequences\n##\nClass(Symmetry, rec(\n isSymmetry := true,\n __call__ := (self, n) >> self.seq(n),\n red := (self, n, scaled) >> self.ext(n, scaled).transpose(),\n verify := (self, n) >> MatSPL(self.red(n,false)self.ext(n, true))\n));\n\nIsSymmetry := x -> IsRec(x) and IsBound(x.isSymmetry) and x.isSymmetry;\n\n_gathI := (nn, top_hole, bot_hole) -> let(n:=Int(nn), Gath(fAdd(n, n-top_hole-bot_hole, top_hole)));\n_gathI2 := (nn, top_hole, bot_hole) -> let(n:=Int(nn), Gath(H(n, Int((n-top_hole-bot_hole+1)/2), top_hole, 2)));\n_gathJ := (nn, top_hole, bot_hole) -> let(n:=Int(nn), Gath(fCompose(fAdd(n, n-top_hole-bot_hole, top_hole), J(n-top_hole-bot_hole))));\n\nClass(GathExtend, Sym, rec(def := (n, symmetry) -> symmetry.ext(n, true)));\nClass(GathExtendU, Sym, rec(def := (n, symmetry) -> symmetry.ext(n, false)));\nClass(GathExtendZ, Sym, rec(def := (n, symmetry) -> DirectSum(I(1),-J(n-1))symmetry.ext(n, true)));\nClass(GathExtendZU, Sym, rec(def := (n, symmetry) -> DirectSum(I(1),-J(n-1))symmetry.ext(n, false)));\nClass(ScatReduce, Sym, rec(def := (n, symmetry) -> symmetry.red(n, true)));\nClass(ScatReduceU, Sym, rec(def := (n, symmetry) -> symmetry.red(n, false)));\n\n\nClass(EOSymmetry, Symmetry, rec(tsize := \"cols\"));\n\nClass(Upsample0, EOSymmetry, rec(\n seq:= n -> Checked(IsEvenInt(n), List([1..n], i -> When(IsEvenInt(i),0,rand()))),\n ext := (n, scaled) -> Checked(IsEvenInt(n), Tensor(I(n/2),Mat([[1],[0]]))),\n red := (n, scaled) -> Checked(IsEvenInt(n), Tensor(I(n/2),Mat([[1,0]]))),\n));\n\nClass(Upsample1, EOSymmetry, rec(\n seq:= n -> Checked(IsEvenInt(n), List([1..n], i -> When(IsEvenInt(i),0,rand()))),\n ext := (n, scaled) -> Checked(IsEvenInt(n), Tensor(I(n/2),Mat([[0],[1]]))),\n red := (n, scaled) -> Checked(IsEvenInt(n), Tensor(I(n/2),Mat([[0,1]]))),\n));\n\nClass(Even0, EOSymmetry, rec(\n seq := n -> let(len := Int((n-1)/2), lst := List([2..len+1], rand),\n\tFlat([rand(1), lst, When(IsEvenInt(n),rand(len+2),[]), Reversed(lst)])),\n ext := (n, scaled) -> let(hf := When(scaled, 1/2, 1), \n\tDirectSum(I(1), \n\t VStack(\n\t\t\tDirectSum(hfI(Int((n-1)/2)), I(_even(n))),\n\t\t\thf_gathJ(n/2, 0, _even(n))))),\n# red := n -> Gath(fAdd(n, Int((n+2)/2), 0))\n));\n\nClass(Even0star, EOSymmetry, rec(\n seq := n -> let(len := Int((n-1)/2), lst := List([2..len+1], rand),\n\tFlat([rand(1), lst, When(IsEvenInt(n),0,[]), Reversed(lst)])),\n ext := (n, scaled) -> let(hf := When(scaled, 1/2, 1), \n\tDirectSum(I(1), \n\t VStack(\n\t\t\thfI(Int((n-1)/2)), \n When(IsEvenInt(n), O(1, Int((n-1)/2)), []), \n\t\t\thfJ(Int((n-1)/2))))),\n# red := n -> Gath(fAdd(n, Int((n+2)/2), 0))\n));\n\nClass(Even00, EOSymmetry, rec(\n seq := n -> let(len := Int((n-1)/2), lst := List([2..len+1], rand),\n\tFlat([0, lst, When(IsEvenInt(n),rand(len+2),[]), Reversed(lst)])),\n ext := (n, scaled) -> let(hf := When(scaled, 1/2, 1), \n\tVStack(O(1,Int(n/2)), \n\t DirectSum(hfI(Int((n-1)/2)), I(_even(n))),\n\t hf_gathJ(n/2, 0, _even(n)))),\n# red := n -> Gath(fAdd(n, Int(n/2), 1))\n));\n\nClass(Even00star, EOSymmetry, rec(\n seq := n -> let(len := Int((n-1)/2), lst := List([2..len+1], rand),\n\tFlat([0, lst, When(IsEvenInt(n),0,[]), Reversed(lst)])),\n ext := (n, scaled) -> let(hf := When(scaled, 1/2, 1), \n\tVStack(O(1,Int(n/2)), \n\t DirectSum(hfI(Int((n-1)/2)), O(_even(n))),\n\t hf_gathJ(n/2, 0, _even(n)))),\n# red := n -> Gath(fAdd(n, Int(n/2), 1))\n));\n\nClass(Even1, EOSymmetry, rec(\n seq := n -> let(len := Int(n/2), lst := List([1..len], rand),\n\tFlat([lst, When(IsOddInt(n),rand(len+1),[]), Reversed(lst)])),\n ext := (n, scaled) -> let(hf := When(scaled, 1/2, 1), \n\tWhen(IsEvenInt(n), \n\t hf VStack(I(n/2), J(n/2)), \n\t VStack(DirectSum(hfI((n-1)/2), I(1)), hf_gathJ((n+1)/2, 0, 1))))\n# red := n -> Gath(fAdd(n, Int((n+1)/2), 0))\n));\n\n\nClass(Odd0, EOSymmetry, rec(\n seq := n -> let(len := Int((n-1)/2), lst := List([2..len+1], rand),\n\tFlat([rand(1), lst, When(IsEvenInt(n),0,[]), -Reversed(lst)])),\n ext := (n, scaled) -> let(hf := When(scaled, 1/2, 1),\n\tDirectSum(I(1), \n\t hfVStack(I(Int((n-1)/2)), \n\t\t When(IsEvenInt(n), O(1, Int((n-1)/2)), []), \n\t\t\t -J(Int((n-1)/2))))) \n# red := n -> Gath(fAdd(n, Int((n+2)/2), 0))\n));\n\nClass(Odd00, EOSymmetry, rec(\n seq := n -> let(len := Int((n-1)/2), lst := List([2..len+1], rand),\n\tFlat([0, lst, When(IsEvenInt(n),0,[]), -Reversed(lst)])),\n ext := (n, scaled) -> let(hf := When(scaled, 1/2, 1), \n\t hf VStack(O(1,Int((n-1)/2)), \n\t I(Int((n-1)/2)),\n\t\t\t When(IsEvenInt(n), O(1,Int((n-1)/2)), []), \n\t -J(Int((n-1)/2)))),\n# red := n -> Gath(fAdd(n, Int((n-1)/2), 1))\n));\n\nClass(Odd00star, EOSymmetry, rec(\n seq := n -> let(len := Int((n-1)/2), lst := List([2..len+1], rand),\n\tFlat([0, lst, When(IsEvenInt(n),rand(len+2),[]), -Reversed(lst)])),\n ext := (n, scaled) -> let(hf := When(scaled, 1/2, 1), \n\t hf * VStack(O(1,Int((n-1)/2)), \n\t I(Int((n-1)/2)),\n When(IsEvenInt(n), RowVec( Replicate(Int((n-3)/2),0)::[1] ), []), \n -J(Int((n-1)/2)))),\n# red := n -> Gath(fAdd(n, Int((n-1)/2), 1))\n));\n\n\nClass(Odd1, EOSymmetry, rec(\n seq := n -> let(len := Int(n/2), lst := List([1..len], rand),\n\tFlat([lst, When(IsOddInt(n),0,[]), -Reversed(lst)])),\n ext := (n, scaled) -> let(hf := When(scaled, 1/2, 1), \n\t hf * VStack(I(Int(n/2)), \n\t\t When(IsOddInt(n), O(1, Int(n/2)),[]), \n\t\t\t -J(Int(n/2)))),\n# red := n -> Gath(fAdd(n, Int(n/2), 0))\n));\n\n\nClass(Real, EOSymmetry, rec(\n seq := n -> List([1..n], rand),\n ext := (n, scaled) -> I(n),\n tsize := \"rows\", # does not matter, since ext is square\n));\n\n# NOTE: red != ext^T, how to handle?\n# - silently drop scaling?\n\n# DirectSum((I tensor W), j * I(1))\n#\nClass(Conj_Base, Symmetry, rec(\n __call__ := (self, w, j) >> Checked(IsMat(w), DimensionsMat(w)=[2,2], \n\tWithBases(self, rec(\n\t\tw := w, \n\t\tj := j, \n\t\toperations := PrintOps\n ))),\n tsize := \"rows\",\n print := self >> Print(self.name, \"(\", self.w, \", \", self.j, \")\"),\n W := self >> When(IsBound(self.isOdd) and self.isOdd, self.w * DiagonalMat([1, -1]), self.w),\n invertW := self >> let(base := self.__bases__[1], base(TransposedMat(self.w^-1), 1/self.j)),\n seq := (self, n) >> self.re.seq(n) + E(4) * self.im.seq(n),\n verify := (self, n) >> MatSPL(self.red(n,false)self.ext(n, false))\n));\n\nClass(Conj0_Base, Conj_Base, rec(\n P := n -> DirectSum(I(1), L_or_OS(n-1, Int(n/2)) DirectSum(I(Int(n/2)), J(Int((n-1)/2)))),\n ext := (self, n, scaled) >> self.invertW().red(n, scaled).transpose(),\n red := (self, n, scaled) >> let(\n\tW := Mat(When(scaled, self.W(), self.W())),\n self.PP(n) * DirectSum(I(1), Tensor(I(Int((n-1)/2)), W), self.j * I(_even(n))) * self.P(n)\n )\n));\n\nClass(Conj1_Base, Conj_Base, rec(\n P := n -> L_or_OS(n, Int((n+1)/2)) * DirectSum(I(Int((n+1)/2)), J(Int(n/2))),\n seq := (self, n) >> self.re.seq(n) + E(4) * self.im.seq(n),\n ext := (self, n, scaled) >> self.invertW().red(n, scaled).transpose(),\n red := (self, n, scaled) >> let(\n\tW := Mat(When(scaled, self.W(), self.W())),\n self.PP(n) * DirectSum(Tensor(I(Int(n/2)), W), self.j * I(_odd(n))) * self.P(n)\n )\n));\n\nClass(Conj0_R2R, Conj0_Base, rec(PP := (self, n) >> self.P(n).transpose()));\nClass(Conj1_R2R, Conj1_Base, rec(PP := (self, n) >> self.P(n).transpose()));\n\nClass(CE0_R2R, Conj0_R2R, rec(re := Even0, im := Odd00, isOdd := false));\nClass(CO0_R2R, Conj0_R2R, rec(re := Odd0, im := Even00, isOdd := true, j := -E(4)));\nClass(CE1_R2R, Conj1_R2R, rec(re := Even1, im := Odd1, isOdd := false));\nClass(CO1_R2R, Conj1_R2R, rec(re := Odd1, im := Even1, isOdd := true, j := -E(4)));\n\n_m := n -> When(n=1, Mat([[1], [0]]), I(0));\n_mj := n -> When(n=1, Mat([[0], [1]]), I(0));\n\nClass(Conj0_R2Cpx, Conj0_Base, rec(PP := (self, n) >> \n\tDirectSum(_m(1), I(n-1-_even(n)), _m(_even(n)))));\n\nClass(Conj1_R2Cpx, Conj1_Base, rec(PP := (self, n) >> \n\tDirectSum(I(n-_odd(n)), When(self.isOdd, _mj(_odd(n)), _m(_odd(n))))));\n\nClass(CE0_R2Cpx, Conj0_R2Cpx, rec(re := Even0, im := Odd00, isOdd := false));\nClass(CO0_R2Cpx, Conj0_R2Cpx, rec(re := Odd0, im := Even00, isOdd := true, j := -E(4)));\nClass(CE1_R2Cpx, Conj1_R2Cpx, rec(re := Even1, im := Odd1, isOdd := false));\nClass(CO1_R2Cpx, Conj1_R2Cpx, rec(re := Odd1, im := Even1, isOdd := true, j := -E(4)));\n\nW_RFT := 1/2[[1, 1], [-E(4), E(4)]];\nW_RFTT := 1/2[[1, 1], [E(4), -E(4)]];\nW_URFT := [[1, 1], [-E(4), E(4)]];\nW_URFTT := [[1, 1], [E(4), -E(4)]];\nW_DHT := 1/2[[1-E(4), 1+E(4)], [1+E(4), 1-E(4)]];\n\nrsym := function(x)\n local n, nc, nf, mid, uniq, zeros, fst_0, mid_0, fstmid;\n n := Length(x); nc := Int((n+1)/2); nf := Int(n/2); mid := nf;\n if n=0 then return \"empty\"; fi;\n\n fst_0 := scalareq(x[1], 0);\n mid_0 := scalareq(x[nf+1], 0);\n fstmid := [Cond(fst_0,0, 1), Cond(mid_0, 0, 1)];\n\n if ForAll(x, e->scalareq(e,0)) then return \"zero\";\n\n # normal symmetries\n elif ForAll([1..nc-1], i->scalareq(x[1+ i], x[1+ (n-i) mod n])) then\n fstmid[2] := Cond(IsOddInt(n), 1, fstmid[2]);\n if fstmid=[0,0] then return \"even00\"; \n\telif fstmid=[0,1] then return \"even00\"; \n elif fstmid=[1,0] then return \"even0\"; \n elif fstmid=[1,1] then return \"even0\"; \n fi;\n elif ForAll([1..nc-1], i->scalareq(x[1+ i], -x[1+ (n-i) mod n])) then\n fstmid[2] := Cond(IsOddInt(n), 0, fstmid[2]);\n if fstmid=[0,0] then return \"odd00\"; \n\telif fstmid=[0,1] then return \"odd00\"; \n elif fstmid=[1,0] then return \"odd0\"; \n elif fstmid=[1,1] then return \"odd0\"; \n fi;\n elif ForAll([0..mid-1], i->scalareq(x[1+ i], x[1+ (n-1-i)])) then \n if IsOddInt(n) and mid_0 then return \"even1\"; \n else return \"even1\";\n fi;\n elif ForAll([0..mid-1], i->scalareq(x[1+ i], -x[1+ (n-1-i)])) then \n if IsOddInt(n) and not mid_0 then return \"odd1\"; \n else return \"odd1\";\n fi;\n\n # symmetries with flipped bottom, i.e. abcabc\n elif n>2 and IsOddInt(n) and ForAll([1..nc-1], i->scalareq(x[1+ i], x[1+ mid+i])) then\n\tif fst_0 then return \"jeven00\"; else return \"jeven0\"; fi;\n elif n>2 and IsOddInt(n) and ForAll([1..nc-1], i->scalareq(x[1+ i], -x[1+ mid+i])) then\n\tif fst_0 then return \"jodd00\"; else return \"jodd0\"; fi;\n elif n>2 and ForAll([0..mid-1], i->scalareq(x[1+ i], x[1+ mid+i])) then return \"jeven1\";\n elif n>2 and ForAll([0..mid-1], i->scalareq(x[1+ i], -x[1+ mid+i])) then return \"jodd1\";\n\n # rader symmetries, similar to normal but every other sample in bottom half is negated\n elif ForAll([1..nc-1], i->scalareq(x[1+i], (-1)^i x[1+(n-i) mod n])) then\n\tif fst_0 then return \"rader_even00\"; else return \"rader_even0\"; fi;\n elif ForAll([1..nc-1], i->scalareq(x[1+i], - (-1)^i * x[1+(n-i) mod n])) then\n\tif fst_0 then return \"rader_odd00\"; else return \"rader_odd0\"; fi;\n\n # symmetries with normal shape, but elements negated in some non-recognized way\n elif ForAll([1..nc-1], i->scalareq(x[1+i], x[1+(n-i) mod n]) or scalareq(x[1+i], -x[1+(n-i) mod n])) then\n\tif fst_0 then return \"eo00\"; else return \"eo0\"; fi;\n elif ForAll([0..mid-1], i->scalareq(x[1+i], x[1+(n-1-i)]) or scalareq(x[1+i], -x[1+(n-1-i)])) then\n\treturn \"eo1\"; \n else\n\tuniq := Length(Set(List(x, e->V(AbsFloat(e)))));\n\tzeros := Length(Filtered(x, e->scalareq(e,0)));\n\tif uniq <= Int((n+2)/2) then\n # no obvious symmetry, but only approx half unique elements\n\t # so sequence is still redundant\n\t return Concat(\"red_\", String(uniq-zeros), \"/\", String(zeros), \"/\",String(Length(x))); \n\telse return \"none\";\n\tfi;\n fi;\nend;\n\nrisym := function(x)\n local rs, is, re, im;\n re := List(x, e->ReComplex(Complex(e)));\n im := List(x, e->ImComplex(Complex(e)));\n rs := rsym(re);\n is := rsym(im);\n return [rs,is];\nend;\n\ncsym := function(x)\n local s;\n s := sym(x);\n if s = [\"even0\", \"odd00\"] then return \"ce0\";\n elif s = [\"odd0\", \"even00\"] then return \"co0\";\n elif s = [\"even1\", \"odd1\"] then return \"ce1\";\n elif s = [\"odd1\", \"even1\"] then return \"co1\";\n elif s = [\"jeven1\", \"jodd1\"] then return \"jce1\";\n elif s = [\"jodd1\", \"jeven1\"] then return \"jco1\";\n elif s = [\"rader_even0\", \"rader_odd00\"] then return \"rader_ce0\";\n elif s = [\"rader_odd0\", \"rader_even00\"] then return \"rader_co0\";\n elif s = [\"none\", \"zero\"] then return \"real\";\n elif s = [\"zero\", \"none\"] then return \"imag\";\n elif s = [\"zero\", \"zero\"] then return \"zero\";\n elif s = [\"none\", \"none\"] then return \"cplx\";\n else return s;\n fi;\nend;\n\n \npart := (v, str, n) -> v{1 + [ 0 .. (Length(v) / str - 1) ] * str + n};\n \nfxi_inputs := (inp, fsize) -> let(\n m := Length(inp)/fsize, \n List([0..m-1], x->part(inp,m,x)));\n\nfxi_rsyms := (inp, fsize) -> List(fxi_inputs(inp, fsize), rsym);\nfxi_syms := (inp, fsize) -> List(fxi_inputs(inp, fsize), risym);\n\ntransf_syms := (n, transforms, syms) -> \n List(syms, s ->\n List(transforms, transform -> \n\t let(inpvec := TransposedMat([s(n)]),\n\t outvec := TransposedMat(MatSPL(transform(n))inpvec)[1],\n\t outsym := sym(outvec),\n\t Cond(outsym[2]=\"zero\", outsym[1],\n\t\t outsym[1]=\"zero\", Concat(\"j\", outsym[2]),\n\t\t \"none\"))));\n\nctransf_syms := (n, transforms, syms) -> \n List(syms, s ->\n List(transforms, transform -> \n\t let(inpvec := TransposedMat([s(n)]),\n\t outvec := TransposedMat(MatSPL(transform(n))inpvec)[1],\n\t risym(outvec))));\n\n\n# transf_syms(18, [ DFT1, DFT2, DFT3, DFT4 ], [even00, even1, odd00, odd1]);\n\n# fxi_syms(even0(36),6);\n# fxi_syms(even00(36),6);\n# fxi_syms(even1(36),6);\n# fxi_syms(odd0(36),6);\n# fxi_syms(odd00(36),6);\n# fxi_syms(odd1(36),6);\n\n\n# if rs=\"none\" and is=\"none\" then return \"none\";\n# elif rs=\"none\" and is=\"zero\" then return \"real\";\n# elif rs=\"even\" and is=\"odd\" then return \"ce\";\n# elif rs=\"even\" and is=\"odd\" then return \"ce\";\n#end;\ntwpow := (N,n) -> List([0..N-1], j -> (j mod n) Int(j / n));\n\ntw1 := (N,n) -> List([0..N-1], j -> E(4N)^((2(j mod n)) * (2Int(j / n))));\ntw2 := (N,n) -> List([0..N-1], j -> E(4N)^((2(j mod n)) (2Int(j / n)+1)));\ntw3 := (N,n) -> List([0..N-1], j -> E(4N)^((2(j mod n)+1) (2Int(j / n))));\ntw4 := (N,n) -> List([0..N-1], j -> E(4N)^((2(j mod n)+1) (2Int(j / n)+1)));\ndct2diag := N -> List([0..N-1], i->E(2N)^i);\ndct4diag := N -> List([0..N-1], i->E(4N)^(2i+1));\nidct2diag := N -> List([0..N-1], i->E(2N)^-i);\nlistmul := (l1,l2) -> List([1..Length(l1)], i->l1[i]l2[i]);\n\nComplexFFT2 := input -> TransposedMat(MatSPL(DFT2(Length(input))) * TransposedMat([input]))[1];\nComplexFFT3 := input -> TransposedMat(MatSPL(DFT3(Length(input))) * TransposedMat([input]))[1];\nComplexFFT4 := input -> TransposedMat(MatSPL(DFT4(Length(input))) * TransposedMat([input]))[1];\n\n\n# Macro Extensions\n#\nMacroExt0 := (k,a,b,c,d) -> Checked(IsSymmetry(a), IsSPL(b), IsSPL(d), b.dims()=d.dims(),\n IsOddInt(k) or IsSymmetry(c), \n Cond(IsOddInt(k),\n let(kk := (k-1)/2, n := Cols(b), \n top := DirectSum(GathExtendU(n, a), Tensor(I(kk), b)),\n VStack(top,\n Tensor(J(kk), d) * Gath(fAdd(Cols(top), kkCols(d), Cols(a.ext(n,true)))))),\n let(kk := (k-2)/2, n := Cols(b), \n top := DirectSum(GathExtendU(n, a), Tensor(I(kk), b), GathExtendU(n, c)),\n VStack(top, \n Tensor(J(kk), d) Gath(fAdd(Cols(top), kkCols(d), Cols(a.ext(n,true))))))\n ));\n\nMacroExt1 := (k,b,c,d) -> Checked(IsSPL(b), IsSPL(d), b.dims()=d.dims(),\n IsEvenInt(k) or IsSymmetry(c), \n Cond(IsOddInt(k),\n let(kk := (k-1)/2, n := Cols(b), \n top := DirectSum(Tensor(I(kk), b), GathExtendU(n, c)),\n VStack(top,\n Tensor(J(kk), d) Gath(fAdd(Cols(top), kkCols(d), 0)))),\n let(kk := k/2, \n VStack(Tensor(I(kk), b),\n Tensor(J(kk), d)))\n ));\n\nJp := x -> OS(x, -1);\n\nlistExtMat := mat -> List(mat, row -> let(n:=PositionProperty(row, x->x<>0), \n Cond(n=false, 0, \n row[n]<0, -n,\n +n)));\n\nanalyze := (stride, extmat) -> let(\n lst := listExtMat(MatSPL(extmat)),\n fsize := Length(lst)/stride,\n rec(inp := fxi_inputs(lst, fsize),\n sym := fxi_rsyms(lst, fsize)));\n\nanalyzeT := (stride, extmat, partsizes) -> let(\n fsize := Rows(extmat)/stride,\n lst := listExtMat(TransposedMat(MatSPL(L(fsizestride, stride)*extmat))),\n part := Drop(ScanL(partsizes, (p, x) -> [Last(p)+1..Last(p)+x], [0]), 1),\n rec(out := List(part, p->lst{p}))); \n\npanalyze := function(stride, extmat) \n local r, zip, i, e, sym, n, mid, j, cur, absprev, prev, sign;\n r := analyze(stride, extmat);\n zip := Zip2(r.sym, r.inp);\n n := Length(zip);\n mid := Int((n+1)/2);\n for i in [1..Length(zip)] do\n e := zip[i];\n if e[1] = \"none\" then \n sym := \"I\";\n if i > mid then\n cur := List(e[2], AbsInt);\n for j in [1..mid] do \n prev := r.inp[j];\n absprev := List(r.inp[j], AbsInt);\n if cur=Reversed(absprev) then \n prev := Reversed(prev);\n sign := Cond(e[2]=prev, \"\", e[2]=-prev, \"-\", \"#\");\n sym := sign :: \"J/\" :: StringInt(j); \n elif cur=[absprev[1]]::Reversed(Drop(absprev, 1)) then \n prev := [prev[1]]::Reversed(Drop(prev, 1)); \n sign := Cond(e[2]=prev, \"\", e[2]=-prev, \"-\", \"#\");\n sym := sign :: \"J'/\"::StringInt(j); \n fi;\n od;\n fi;\n else\n sym := YellowStr(e[1]);\n fi;\n Print(sym, \": \", e[2], \"\\n\");\n od;\nend;\n\n", "meta": {"hexsha": "ceb65da08038283bed81c7f49c2f7ac966c24a36", "size": 21670, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/sym/symmetries.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/sym/symmetries.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/sym/symmetries.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 39.4, "max_line_length": 134, "alphanum_fraction": 0.5359021689, "num_tokens": 7984, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7606506526772883, "lm_q2_score": 0.6859494485880928, "lm_q1q2_score": 0.5217678957721588}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nClass(RealDFT_Base, TaggedNonTerminal, rec(\n abbrevs := [ (n) -> Checked(IsPosInt(n), [n, 1]),\n (n,k) -> Checked(IsPosInt(n), IsInt(k), Gcd(n,k)=1, [n, k]) ],\n \n terminate := self >> let(N := self.params[1], k := self.params[2], \n\trr := When(self.transposed, Cols(self), Rows(self)),\n\tmat := Mat(List([0..rr-1], r -> When(r mod 2 = 0, \n List([0..N-1], c -> self.projRe(self.omega(N,k,Int(r/2),c))),\n List([0..N-1], c -> self.projIm(self.omega(N,k,Int(r/2),c)))))),\n When(self.transposed, mat.transpose(), mat)),\n\n toAMat := self >> self.terminate().toAMat(), \n\n isReal := True,\n SmallRandom := () -> Random([2..16]), \n LargeRandom := () -> 2 ^ Random([6..15]),\n\n normalizedArithCost := self >> let(n := self.params[1], \n floor(2.5 * n * log(n) / log(2.0))),\n\n hashAs := self >> let(t:=ObjId(self)(self.params[1], 1).withTags(self.getTags()),\n When(self.transposed, t.transpose(), t))\n\n));\n\n\nClass(PDHT13_Base, RealDFT_Base, rec(\n projRe := w -> Re(w)+Im(w),\n projIm := w -> Re(w)-Im(w)\n));\n\nClass(PDHT24_Base, RealDFT_Base, rec(\n projRe := w -> Re(w)+Im(w),\n projIm := w -> -Re(w)+Im(w)\n));\n\nClass(PRDFT_Base, RealDFT_Base, rec(\n projRe := Re,\n projIm := Im\n));\n\nClass(IPRDFT_Base, TaggedNonTerminal, rec(\n abbrevs := [ (n) -> Checked(IsPosInt(n), [n, 1]),\n\t (n,k) -> Checked(IsPosInt(n), IsInt(k), Gcd(n,k)=1, [n, k]) ],\n terminate := self >> let(n:=self.params[1], k:=self.params[2],\n\tself.rdft(n, -k).terminate().transpose() * self.diag(n)),\n isReal := True,\n SmallRandom := () -> Random([2..16]), \n LargeRandom := () -> 2 ^ Random([6..15]),\n\n diag0 := n -> When(n=2, I(4), \n Diag(diagDirsum(fConst(TReal, 2, 1), fConst(TReal, 2Int((n-1)/2), 2), \n When(IsEvenInt(n), fConst(TReal, 2, 1), [])))),\n\n diag1 := n -> Diag(diagDirsum(fConst(TReal, 2Int(n/2), 2), \n When(IsOddInt(n), fConst(TReal, 2, 1), []))),\n\n normalizedArithCost := self >> let(n := self.params[1], \n floor(2.5 * n * log(n) / log(2.0))),\n\n hashAs := self >> let(t:=ObjId(self)(self.params[1], 1).withTags(self.getTags()),\n When(self.transposed, t.transpose(), t))\n));\n\nDeclare(IPRDFT, IPRDFT1, IPRDFT2, IPRDFT3, IPRDFT4);\n\n# PRDFT(<N>, <k>) - Packed Real DFT Nonterminal\n# Is a N+2 x N real matrix. N+2 outputs correspond\n# to Floor(N/2)+1 complex outputs of complex DFT\n# the other half of complex DFT outputs are complex\n#\nClass(PRDFT, PRDFT_Base, rec(\n abbrevs := [ (n) -> Checked(IsPosInt(n), [n, 1]),\n (n,k) -> Checked(IsPosInt(n), IsInt(k), Gcd(n,k)=1, [n, k mod n]) ],\n dims := self >> let(n:=self.params[1], d := [2(Int(n/2)+1), n], When(self.transposed, Reversed(d), d)),\n omega := (N,k,r,c) -> E(N)^(krc),\n inverse := self >> IPRDFT1(self.params[1], -self.params[2]),\n inverseViaDiag := self >> self.transpose() IPRDFT.diag(self.params[1])\n));\nPRDFT1 := PRDFT;\n\nClass(PRDFT2, PRDFT_Base, rec(\n abbrevs := [ (n) -> Checked(IsPosInt(n), [n, 1]),\n (n,k) -> Checked(IsPosInt(n), IsInt(k), Gcd(n,k)=1, [n, k mod (2n)]) ],\n dims := self >> let(n:=self.params[1], d := [2(Int(n/2)+1), n], When(self.transposed, Reversed(d), d)),\n omega := (N,k,r,c) -> E(2N)^(kr(2c+1)),\n inverse := self >> IPRDFT3(self.params[1], -self.params[2])\n));\n\nClass(PRDFT3, PRDFT_Base, rec(\n abbrevs := [ (n) -> Checked(IsPosInt(n), [n, 1]),\n (n,k) -> Checked(IsPosInt(n), IsInt(k), Gcd(n,k)=1, [n, k mod (2n)]) ],\n dims := self >> let(n:=self.params[1], d := [2(Int((n+1)/2)), n], When(self.transposed, Reversed(d), d)),\n omega := (N,k,r,c) -> E(2N)^(k(2r+1)c),\n inverse := self >> IPRDFT2(self.params[1], -self.params[2])\n));\n\nClass(PRDFT4, PRDFT_Base, rec(\n abbrevs := [ (n) -> Checked(IsPosInt(n), [n, 1]),\n (n,k) -> Checked(IsPosInt(n), IsInt(k), Gcd(n,k)=1, [n, k mod (4n)]) ],\n dims := self >> let(n:=self.params[1], d := [2(Int((n+1)/2)), n], When(self.transposed, Reversed(d), d)),\n omega := (N,k,r,c) -> E(4N)^(k(2r+1)(2c+1)),\n inverse := self >> IPRDFT4(self.params[1], -self.params[2])\n));\n\n# Class(SkewRDFT3, PRDFT_Base, rec(\n# abbrevs := [ (n) -> Checked(IsPosInt(n), [n, 1, 0, 0]),\n# (n,k) -> Checked(IsPosInt(n), IsInt(k), Gcd(n,k)=1, [n, k, 0, 0]), \n# (n,k,lr,rr) -> Checked(IsPosInt(n), IsInt(k), IsRat(lr), IsRat(rr), \n# \t Gcd(n,k)=1, [n, k, lr, rr])\n# ],\n# dims := self >> let(n:=self.params[1], [ 2Int((n+1)/2), n ]),\n# omega := (self,N,k,r,c) >> let(\n# \tlnum:=Numerator(self.params[3]), lden:=Denominator(self.params[3]),\n# \trnum:=Numerator(self.params[4]), rden:=Denominator(self.params[4]),\n# \tE(2Nldenrden) ^ (k(lden(2r+1)+lnum)(rdenc+rnum)))\n# ));\n# Class(SkewRDFT4, SkewRDFT3, rec(\n# dims := self >> let(n:=self.params[1], [ 2Int((n+1)/2), n ]),\n# omega := (self,N,k,r,c) >> let(\n# \tlnum:=Numerator(self.params[3]), lden:=Denominator(self.params[3]),\n# \trnum:=Numerator(self.params[4]), rden:=Denominator(self.params[4]),\n# \tE(4Nldenrden) ^ (k(lden(2r+1)+lnum)(rden(2c+1)+rnum)))\n# ));\n\n#\n# Hartley\n#\nClass(PDHT, PDHT13_Base, rec(\n abbrevs := [ (n) -> Checked(IsPosInt(n), [n, 1]),\n (n,k) -> Checked(IsPosInt(n), IsInt(k), Gcd(n,k)=1, [n, k mod (n)]) ],\n dims := self >> let(n:=self.params[1], d := [2(Int(n/2)+1), n], When(self.transposed, Reversed(d), d)),\n omega := PRDFT.omega\n));\nPDHT1 := PDHT;\n\nClass(PDHT2, PDHT24_Base, rec(\n abbrevs := [ (n) -> Checked(IsPosInt(n), [n, 1]),\n (n,k) -> Checked(IsPosInt(n), IsInt(k), Gcd(n,k)=1, [n, k mod (2n)]) ],\n dims := self >> let(n:=self.params[1], d := [2(Int(n/2)+1), n], When(self.transposed, Reversed(d), d)),\n omega := PRDFT2.omega\n));\n\nClass(PDHT3, PDHT13_Base, rec(\n abbrevs := [ (n) -> Checked(IsPosInt(n), [n, 1]),\n (n,k) -> Checked(IsPosInt(n), IsInt(k), Gcd(n,k)=1, [n, k mod (2n)]) ],\n dims := self >> let(n:=self.params[1], d := [2(Int((n+1)/2)), n], When(self.transposed, Reversed(d), d)),\n omega := PRDFT3.omega\n));\n\nClass(PDHT4, PDHT24_Base, rec(\n abbrevs := [ (n) -> Checked(IsPosInt(n), [n, 1]),\n (n,k) -> Checked(IsPosInt(n), IsInt(k), Gcd(n,k)=1, [n, k mod (4n)]) ],\n dims := self >> let(n:=self.params[1], d := [2(Int((n+1)/2)), n], When(self.transposed, Reversed(d), d)),\n omega := PRDFT4.omega\n));\n\n\n# IPRDFT(<N>, <k>) - Inverse Packed Real DFT Nonterminal\n# Is a N x N+2 real matrix. When applied to N+2 outputs\n# of PRDFT yields the original real input.\nClass(IPRDFT, IPRDFT_Base, rec(\n abbrevs := [ (n) -> Checked(IsPosInt(n), [n, 1]),\n (n,k) -> Checked(IsPosInt(n), IsInt(k), Gcd(n,k)=1, [n, k mod (n)]) ],\n dims := self >> let(n:=self.params[1], d := [n, 2(Int(n/2)+1)], When(self.transposed, Reversed(d), d)),\n rdft := PRDFT,\n diag := IPRDFT_Base.diag0\n));\nIPRDFT1 := IPRDFT;\n\n# IPRDFT2 is inverse if PRDFT3\nClass(IPRDFT2, IPRDFT_Base, rec(\n abbrevs := [ (n) -> Checked(IsPosInt(n), [n, 1]),\n (n,k) -> Checked(IsPosInt(n), IsInt(k), Gcd(n,k)=1, [n, k mod (2n)]) ],\n dims := self >> let(n:=self.params[1], d := [n, 2(Int((n+1)/2))], When(self.transposed, Reversed(d), d)),\n rdft := PRDFT3,\n diag := IPRDFT_Base.diag1\n)); \n\n# IPRDFT3 is inverse if PRDFT2\nClass(IPRDFT3, IPRDFT_Base, rec(\n abbrevs := [ (n) -> Checked(IsPosInt(n), [n, 1]),\n (n,k) -> Checked(IsPosInt(n), IsInt(k), Gcd(n,k)=1, [n, k mod (2n)]) ],\n dims := self >> let(n:=self.params[1], d := [n, 2(Int(n/2)+1)], When(self.transposed, Reversed(d), d)),\n rdft := PRDFT2,\n diag := IPRDFT_Base.diag0\n));\n\nClass(IPRDFT4, IPRDFT_Base, rec(\n abbrevs := [ (n) -> Checked(IsPosInt(n), [n, 1]),\n (n,k) -> Checked(IsPosInt(n), IsInt(k), Gcd(n,k)=1, [n, k mod (4n)]) ],\n dims := self >> let(n:=self.params[1], d := [n, 2(Int((n+1)/2))], When(self.transposed, Reversed(d), d)),\n rdft := PRDFT4,\n diag := IPRDFT_Base.diag1\n));\n\n", "meta": {"hexsha": "c4d71d0561b9e221efd2ea1480b1e2f81d11da90", "size": 8171, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/realdft/prdft.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/transforms/realdft/prdft.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/transforms/realdft/prdft.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 40.4504950495, "max_line_length": 110, "alphanum_fraction": 0.5372659405, "num_tokens": 3006, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. 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	{"text": "# The tetrahedron with v=4, k=3, lm=2.\nBindGlobal(\"TetrahedronGraph\", CompleteGraph(SymmetricGroup(4)));\n\n# The octahedron with v=6, k=4, lm=2, mu=4.\nBindGlobal(\"OctahedronGraph\", CocktailPartyGraph(3));\n\n# The Petersen graph with v=10, k=3, lm=0, mu=1.\nBindGlobal(\"PetersenGraph\", OddGraph(2));\n\n# The Clebsch graph with v=16, k=10, lm=6, mu=6.\nBindGlobal(\"ClebschGraph\", HalvedCubeGraph(5));\n\n# The Schlaefli graph with v=27, k=16, lm=10, mu=8.\nBindGlobal(\"SchlaefliGraph\",\n Graph(DirectProduct(SymmetricGroup(6), SymmetricGroup(2)),\n [[-3,-3,1,1,1,1,1,1], [3,-1,-1,-1,-1,-1,-1,3]],\n OnRoots, RootAdjacency));\n\n# The Hoffman-Singleton graph with v=50, k=7, lm=0, mu=1.\nBindGlobal(\"HoffmanSingletonGraph\", List([function()\n local G, dp, p1, p2, p3, p4;\n G := Group((1, 2, 3, 4, 5));\n dp := DirectProduct(G, G, G, Group((1, 2)));\n p1 := Projection(dp, 1);\n p2 := Projection(dp, 2);\n p3 := Projection(dp, 3);\n p4 := Projection(dp, 4);\n return Graph(dp, Cartesian(GF(5), GF(5), [1, 2]),\n function(x, g)\n local g4, j, s, u, v;\n u := 5^Image(p2, g) * Z(5)^0;\n v := 5^Image(p3, g) * Z(5)^0;\n g4 := Image(p4, g);\n s := x[3]^2;\n j := [1, 2x[3]];\n return [1^g4(x[1]+x[2](u-sv)+s(u^2-v^2)/2)+5^Image(p1, g),\n j[1^g4](x[2]+su+v), x[3]^g4];\n end, function(x, y)\n return (x{[2,3]} = y{[2,3]} and y[1] in [x[1]-x[3], x[1]+x[3]])\n or x[3] <> y[3] and y[1] = x[1] + x[2]y[2]x[3]^2;\n end, true);\n end])[1]());\n\n# The Gewirtz graph with v=56, k=10, lm=0, mu=2.\nBindGlobal(\"GewirtzGraph\", Graph(MathieuGroup(21), [[1,2,3,7,10,20]],\n OnSets, DisjointSets));\n\n# The strongly regular Witt graph with v=77, k=16, lm=0, mu=4.\nBindGlobal(\"WittStronglyRegularGraph\", Graph(MathieuGroup(22),\n [[1,2,3,7,10,20]], OnSets, DisjointSets));\n\n# The graph with v=210, k=99, lm=48, mu=45 constructed by M. Klin\nBindGlobal(\"KlinGraph\", List([function()\n local G, H, N, V;\n H := Group([(1,2,3,4,5,6), (1,4)]);\n V := Set(List(SymmetricGroup(7), g -> Hg));\n N := Position(V, H());\n G := EdgeOrbitsGraph(Action(SymmetricGroup(7), V, OnRight),\n List([(3,4,5,6,7), (2,4,6,3,5,7), (3,5,6,7), (2,4,5,6,7,3),\n (2,3,5,6,7), (2,4,5,6), (2,3,5,6)],\n g -> [N, Position(V, Hg)]));\n AssignVertexNames(G, V);\n return G;\n end])[1]());\n\n# The cube with intersection array {3, 2, 1; 1, 2, 3}\nBindGlobal(\"CubeGraph\", HammingGraph(3, 2));\n\n# The Heawood graph with intersection array {3, 2, 2; 1, 1, 3}.\nBindGlobal(\"HeawoodGraph\", DesarguesianPlaneIncidenceGraph(2));\n\n# The icosahedron with intersection array {5, 2, 1; 1, 2, 5}.\nBindGlobal(\"IcosahedronGraph\", Graph(DirectProduct(AlternatingGroup(5),\n Group((1, 2))),\n [(1,3,5,2,4)], function(p, g)\n return (p^g)^((-1)^(6^g));\n end, function(x, y)\n return Order(x*y) = 3;\n end));\n\n# The Sylvester graph with intersection array {5, 4, 2; 1, 1, 4}\nBindGlobal(\"SylvesterGraph\", Graph(SymmetricGroup(6),\n [[1, [[[1,2], [3,4], [5,6]],\n [[1,3], [2,5], [4,6]],\n [[1,4], [2,6], [3,5]],\n [[1,5], [2,4], [3,6]],\n [[1,6], [2,3], [4,5]]]]],\n function(x, g)\n return [x[1]^g,\n Set(List(x[2], l -> OnSetsSets(l, g)))];\n end, function(x, y)\n return x[1] <> y[1] and x[2] <> y[2] and\n Set([x[1], y[1]]) in Intersection(x[2], y[2])[1];\n end));\n\n# The Perkel graph with intersection array {6, 5, 2; 1, 1, 3}.\nBindGlobal(\"PerkelGraph\", Graph(PSL(2, 19),\n Elements(Filtered(ConjugacyClassesSubgroups(PSL(2, 19)),\n x -> Size(x) = 57 and Order(x[1]) = 60)[1]),\n ConjugateGroup, function(x, y)\n return Order(Intersection(x, y)) = 10;\n end, true));\n\n\n# The Gosset graph with intersection array {27, 10, 1; 1, 10, 27}.\nBindGlobal(\"GossetGraph\",\n Graph(DirectProduct(SymmetricGroup(8), SymmetricGroup(2)),\n [[-3,-3,1,1,1,1,1,1]], OnRoots, RootAdjacency));\n\n# The truncated Witt graph with intersection array {15, 14, 12; 1, 1, 9}.\nBindGlobal(\"Witt23Graph\", Graph(MathieuGroup(23), [[1,4,8,12,13,19,21,23]],\n OnSets, DisjointSets));\n\n# The large Witt graph with intersection array {30, 28, 24; 1, 3, 15}.\nBindGlobal(\"Witt24Graph\", Graph(MathieuGroup(24), [[1,4,8,12,13,19,21,23]],\n OnSets, DisjointSets));\n\n# The bipartite graph associated to Higman's design\n# with intersection array {50, 49, 36; 1, 14, 50}.\nBindGlobal(\"HigmanGraph\", Graph(Stabilizer(MathieuGroup(24), [23, 24], OnSets),\n [[1,4,8,12,13,19,21,23]], OnSets,\n function (x, y)\n return Length(Difference(Intersection(x, y),\n [23, 24])) in [0, 4];\n end));\n\n# The Coxeter graph with intersection array {3,2,2,1; 1,1,1,2}.\nBindGlobal(\"CoxeterGraph\", PolarGraphNOorth(1, 3, 7));\n\n# The doubly truncated Witt graph with intersection array {7,6,4,4; 1,1,1,6}.\nBindGlobal(\"Witt22Graph\", Graph(MathieuGroup(22), [[1,2,3,4,5,10,18,21]],\n OnSets, DisjointSets));\n\n# The dodecahedron with intersection array {3,2,1,1,1; 1,1,1,2,3}.\nBindGlobal(\"DodecahedronGraph\", List([function()\n local G, O, act, dp, p1, p2, u, v;\n dp := DirectProduct(AlternatingGroup(5), Group((1, 2)));\n p1 := Projection(dp, 1);\n p2 := Projection(dp, 2);\n act := function(t, g)\n return OnTuples(t{Permuted([1,2], Image(p2, g))}, Image(p1, g));\n end;\n u := [1, 2];\n v := [3, 4];\n O := Arrangements([1..5], 2);\n G := EdgeOrbitsGraph(Action(dp, O, act),\n [Position(O, u), Position(O, v)]);\n AssignVertexNames(G, O);\n return G;\n end])[1]());\n\n# The Desargues graph with intersection array {3,2,2,1,1; 1,1,2,2,3}.\nBindGlobal(\"DesarguesGraph\", DoubledOddGraph(2));\n\n# The Biggs-Smith graph with intersection array {3,2,2,2,1,1,1; 1,1,1,1,1,1,3}.\nBindGlobal(\"BiggsSmithGraph\", Graph(PSL(2, 17),\n Elements(Filtered(ConjugacyClassesSubgroups(PSL(2, 17)),\n x -> Size(x) = 102 and Order(x[1]) = 24)[1]),\n ConjugateGroup, function(x, y)\n return Order(Intersection(x, y)) = 8;\n end, true));\n", "meta": {"hexsha": "7df3549810daa46886654b27cdb837f4e5b45f5e", "size": 7140, "ext": "gap", "lang": "GAP", "max_stars_repo_path": "lib/NamedGraphs.gap", "max_stars_repo_name": "jaanos/gap-graphs", "max_stars_repo_head_hexsha": "18dd56c9b90a12a717a0cc893fdd72c6343ee79b", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2015-10-27T15:54:29.000Z", "max_stars_repo_stars_event_max_datetime": "2016-11-07T14:09:44.000Z", "max_issues_repo_path": "lib/NamedGraphs.gap", "max_issues_repo_name": "jaanos/gap-graphs", "max_issues_repo_head_hexsha": "18dd56c9b90a12a717a0cc893fdd72c6343ee79b", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2015-04-20T23:13:11.000Z", "max_issues_repo_issues_event_max_datetime": "2015-04-20T23:13:11.000Z", "max_forks_repo_path": "lib/NamedGraphs.gap", "max_forks_repo_name": "jaanos/gap-graphs", "max_forks_repo_head_hexsha": "18dd56c9b90a12a717a0cc893fdd72c6343ee79b", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 44.0740740741, "max_line_length": 79, "alphanum_fraction": 0.4894957983, "num_tokens": 2344, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7879311956428946, "lm_q2_score": 0.6619228691808012, "lm_q1q2_score": 0.521549677737004}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nDeclare(ImageData, ImageVar, ImageUnk);\n\nClass(ImageUnk, SumsBase, BaseContainer, rec(\n new := (self, dims) >> Checked(IsList(dims) and Length(dims) = 2 and ForAll(dims, IsPosInt),\n SPL(WithBases(self, rec(dimensions := dims, _children := [], dims := self >> self.dimensions)))),\n print := (self, i, is) >> Print(\"ImageUnk(\", self.dims(), \")\"),\n codeletShape := self >> let(d := self.dims(), Concat(\"ImageUnk_\", StringInt(d[1]),\"x\",StringInt(d[2]))),\n fftImage := self >> ApplyFunc(O, TRDFT2D(self.dims()).dims()/self.dims()[2]),\n freqImage := self >> let(lindims := Product(TRDFT2D(self.dims()).dims())/(2Product(self.dims())),\n fPrecompute(fConst(TComplex, lindims, 1+E(4)))),\n timeImage := self >> O(self.dims()[1], self.dims()[2]),\n randomImage := (self, m, n) >> ImageUnk(m, n),\n toAMat := self >> NullAMat(self.dimensions),\n unknownImage := self >> self\n));\n\nClass(ImageData, Mat, rec(\n print := (self, i, is) >> Print(\"ImageData(\", Mat(self.element).dims(), \")\"),\n codeletShape := self >> let(d := self.dims(), Concat(\"ImageData_\", StringInt(d[1]),\"x\",StringInt(d[2]))),\n fftImage := self >> TRDFT2D(self.dims()).compute(self.element),\n freqImage := self >> let(fftRData := 1/Product(self.dims()) Flat(self.fftImage()),\n fftCxData := List([1..Length(fftRData)/2], i->Complex(fftRData[2i-1], fftRData[2i])),\n FData(List(fftCxData, i->TComplex.value(i)))),\n timeImage := self >> self.element,\n randomImage := (self, m, n) >> let(data := List([1..m], i->List([1..n], j->FloatRat(Random([1..1000]/1000)))),\n ImageData(data)),\n unknownImage := self >> ImageUnk(self.dims())\n));\n\nClass(ImageVar, SumsBase, BaseContainer, rec(\n new := (self, dims) >> Checked(IsList(dims) and Length(dims) = 2 and ForAll(dims, IsPosInt),\n SPL(WithBases(self, rec(dimensions := dims, _children := [], dims := self >> self.dimensions)))),\n print := (self, i, is) >> Print(\"ImageVar(\", self.dims(), \")\"),\n codeletShape := self >> let(d := self.dims(), Concat(\"ImageVar_\", StringInt(d[1]),\"x\",StringInt(d[2]))),\n fftImage := self >> ApplyFunc(O, TRDFT2D(self.dims()).dims()/self.dims()[2]),\n freqImage := self >> let(lindims := Product(TRDFT2D(self.dims()).dims())/(2Product(self.dims())),\n type := TArray(TComplex, lindims), d := param(type, \"freqImage\"), FDataOfs(d, lindims, 0)),\n timeImage := self >> O(self.dims()[1], self.dims()[2]),\n randomImage := (self, m, n) >> ImageVar(m, n),\n toAMat := self >> NullAMat(self.dimensions),\n unknownImage := self >> ImageUnk(self.dims())\n));\n\n\n#F TRConv2D(img)\n# For an image\n# img := [ [ 1, 2, 3, 4 ],\n# [ 5, 6, 7, 8 ],\n# [ 9, 10, 11, 12 ],\n# [ 13, 14, 15, 16 ] ];\n#\n# MatSPL(TRConv2D(RealImage(img))) =\n#\n#[ [ 1, 4, 3, 2, 13, 16, 15, 14, 9, 12, 11, 10, 5, 8, 7, 6 ],\n# [ 2, 1, 4, 3, 14, 13, 16, 15, 10, 9, 12, 11, 6, 5, 8, 7 ],\n# [ 3, 2, 1, 4, 15, 14, 13, 16, 11, 10, 9, 12, 7, 6, 5, 8 ],\n# [ 4, 3, 2, 1, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5 ],\n# [ 5, 8, 7, 6, 1, 4, 3, 2, 13, 16, 15, 14, 9, 12, 11, 10 ],\n# [ 6, 5, 8, 7, 2, 1, 4, 3, 14, 13, 16, 15, 10, 9, 12, 11 ],\n# [ 7, 6, 5, 8, 3, 2, 1, 4, 15, 14, 13, 16, 11, 10, 9, 12 ],\n# [ 8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 14, 13, 12, 11, 10, 9 ],\n# [ 9, 12, 11, 10, 5, 8, 7, 6, 1, 4, 3, 2, 13, 16, 15, 14 ],\n# [ 10, 9, 12, 11, 6, 5, 8, 7, 2, 1, 4, 3, 14, 13, 16, 15 ],\n# [ 11, 10, 9, 12, 7, 6, 5, 8, 3, 2, 1, 4, 15, 14, 13, 16 ],\n# [ 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 14, 13 ],\n# [ 13, 16, 15, 14, 9, 12, 11, 10, 5, 8, 7, 6, 1, 4, 3, 2 ],\n# [ 14, 13, 16, 15, 10, 9, 12, 11, 6, 5, 8, 7, 2, 1, 4, 3 ],\n# [ 15, 14, 13, 16, 11, 10, 9, 12, 7, 6, 5, 8, 3, 2, 1, 4 ],\n# [ 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 ] ]\n#\nClass(TRConv2D, TaggedNonTerminal, rec(\n abbrevs := [ img -> [img]],\n dims := self >> self.params[1].dims(),\n isReal := True,\n terminate := self >>\n TIRDFT2D(self.params[1].dims()).terminate() \n RCDiag(FList(TReal, 1/Product(self.params[1].dims())Flat(self.params[1].fftImage()))) \n TRDFT2D(self.params[1].dims()).terminate(),\n normalizedArithCost := (self) >>\n TRDFT2D(self.params[1].dims()).normalizedArithCost() +\n TIRDFT2D(self.params[1].dims()).normalizedArithCost() +\n 3 * Rows(TRDFT2D(self.params[1].dims())),\n symTerminate := self >> let(N := self.params[1].dims(),\n imgv := Flat(self.params[1].timeImage()),\n tf := MDDFT(N),\n ti := MDDFT(N, -1),\n d := MatSPL(tf) * imgv,\n t := ti * (1/Product(N))Diag(d) tf,\n MatSPL(t)),\n forwardTransform := self >> let(t := TRDFT2D(self.params[1].dims()), tags := self.getTags(),\n When(\n Length(tags) >= 1 and ObjId(tags[1]) = paradigms.vector.AVecReg, let(n := t.dims()[1], v := tags[1].v,\n TCompose([TPrm(fTensor(fId(n/(2v)), L(2v, 2))), t]).withTags(tags)),\n t.withTags(tags))),\n\n HashId := self >> let(conv := self.params[1].dims(), When(IsBound(self.tags), Concatenation(conv, self.tags), conv)),\n\n hashAs := meth(self)\n local conv;\n conv := Copy(self);\n conv.params[1] := self.params[1].unknownImage();\n return conv;\n end\n));\n\n\n#F 2D RConv Rule\nNewRulesFor(TRConv2D, rec(\n TRConv2D_TRDFT2D_tSPL := rec(\n switch := true,\n applicable := (self, t) >> true,\n children := (self, t) >>\n [[\n TCompose([\n TIRDFT2D(t.params[1].dims()),\n TRCDiag(fPrecompute(t.params[1].freqImage())),\n TRDFT2D(t.params[1].dims())\n ]).withTags(t.getTags())\n ]],\n apply := (self, t, C, Nonterms) >> C[1]\n )\n));\n\n\n#Class(TRCorr2D, TaggedNonTerminal, rec(\n# abbrevs := [ img -> [img]],\n# dims := self >> self.params[1].dims(),\n# isReal := True,\n# terminate := self >> let(tf := TRDFT2D(self.params[1].dims()), d := 1/Product(self.params[1].dims()) * Flat(tf.compute(self.params[1].element)),\n# TIRDFT2D(self.params[1].dims()).terminate() \n# RCDiag(FList(TReal, List([1..Length(d)], j->When(IsOddInt(j), d[j], -d[j])))) \n# tf.terminate(),\n# normalizedArithCost := (self) >>\n# TRDFT2D(self.params[1].dims()).normalizedArithCost() +\n# TIRDFT2D(self.params[1].dims()).normalizedArithCost() +\n# 3 * Rows(TRDFT2D(self.params[1].dims()))),\n# symTerminate := self >> let(N := self.params[1].dims(),\n# img := self.params[1].element,\n# rimg := Reversed(List(img, Reversed)),\n# imgv := Flat(rimg),\n# tf := MDDFT(N),\n# ti := MDDFT(N, -1),\n# d := MatSPL(tf) * imgv,\n# t := ti * (1/Product(N))Diag(d) tf,\n# MatSPL(t))\n#));\n", "meta": {"hexsha": "25841b2d60712763a5ad488f606c793f39f635aa", "size": 6851, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/common/mdconv.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": 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	{"text": "################################################################################\n##\n#W pseudounitary_sort.gi GroupTheoretical Package\n##\n#W Paul Bruillard, Cesar Galindo, Siu-Hung Ng, Julia Plavnik, Eric Rowell, \n#W Zhenghan Wang\n##\n## Installation file for pseudounitary_sort functions of the GroupTheoretical Package\n##\n#Y Copyright (C) 2016, Battelle Memorial Institute\n##\n################################################################################\n\n################################################################################\n##\n#F pseudounitary_sort(<list>,<list>,<list>) . . . . sorts S and T to give pseudo\n##. . . . . . . . . . . . . . . . . . . . . .unitary data. FPdims are computed.\n##\nInstallGlobalFunction(pseudounitary_sort, function(S,T,Simples)\n local FPdim,FPdimC,x,r,i,FPRow,FPRow_idx,j,is_real,is_pos;\n #\n # look along the diagonal for 1's and check that the corresponding row is real\n # and positive\n FPRow:=[];\n r := Size(Simples);\n for i in [1..r] do\n if S[i][i] = 1 then\n is_real := true;\n is_pos := true;\n for j in [1..r] do\n if ImaginaryPart(S[i][j]) <> 0 then\n is_real := false;\n break;\n fi;\n if S[i][j] <= 0 then\n is_pos := false;\n break;\n fi;\n od;\n if is_real and is_pos then\n Add(FPRow,ShallowCopy(S[i]));\n fi;;\n fi;\n od;\n\n # find out which row is largest\n Sort(FPRow);\n FPRow:=Reversed(FPRow);\n FPRow_idx:=Position(S,FPRow[1]);\n\n # switch 1 with FPRow_idx\n if FPRow_idx <> 1 then\n S{[1,FPRow_idx]}:=S{[FPRow_idx,1]};\n S:=TransposedMatMutable(S);\n S{[1,FPRow_idx]}:=S{[FPRow_idx,1]};\n S:=TransposedMatMutable(S);\n Simples{[1,FPRow_idx]}:=Simples{[FPRow_idx,1]};\n T{[1,FPRow_idx]}:=T{[FPRow_idx,1]};\n fi;\n\n # get the FPdimension\n FPdim:=ShallowCopy(S[1]);\n FPdimC:=Sum(List(FPdim,x->x^2));\n\n return [Simples,S,T,FPdim,FPdimC];\nend);\n\n################################################################################\n##\n#F dimension_sort(<list>,<list>,<list>,<list>) . . . . sorts data by increasing\n# dimension.\n##\nInstallGlobalFunction(dimension_sort, function(S,T,Simples,FPdim)\n local made_switch, x, r;\n made_switch := true;\n r:=Size(FPdim);\n while made_switch do\n made_switch := false;\n for x in [3..r] do\n if FPdim[x] < FPdim[x-1] then\n S{[x,x-1]} := S{[x-1,x]};\n S:=TransposedMatMutable(S);\n S{[x,x-1]} := S{[x-1,x]};\n S:=TransposedMatMutable(S);\n T{[x,x-1]} := T{[x-1,x]};\n FPdim{[x,x-1]} := FPdim{[x-1,x]};\n Simples{[x,x-1]} := Simples{[x-1,x]};\n made_switch := true;\n fi;\n od;\n od;\n return [Simples,S,T,FPdim];\nend);\n#E pseudounitary_sort.gi . . . . . . . . . . . . . . . . . . . . . . . ends here\n", "meta": {"hexsha": "7b1b9f55ddebe597bcab93a9e8fcbd83ffc770ef", "size": 2829, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "lib/pseudounitary_sort.gi", "max_stars_repo_name": "pnnl/GroupTheoretical", "max_stars_repo_head_hexsha": "d60aaec27d2ca98ec55b12b78213538a346eef27", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "lib/pseudounitary_sort.gi", "max_issues_repo_name": "pnnl/GroupTheoretical", "max_issues_repo_head_hexsha": "d60aaec27d2ca98ec55b12b78213538a346eef27", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2021-05-20T21:43:28.000Z", "max_issues_repo_issues_event_max_datetime": "2021-05-20T21:43:28.000Z", "max_forks_repo_path": "lib/pseudounitary_sort.gi", "max_forks_repo_name": "pnnl/GroupTheoretical", "max_forks_repo_head_hexsha": "d60aaec27d2ca98ec55b12b78213538a346eef27", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 2, "max_forks_repo_forks_event_min_datetime": "2017-12-07T13:46:25.000Z", "max_forks_repo_forks_event_max_datetime": "2020-12-12T22:39:35.000Z", "avg_line_length": 29.7789473684, "max_line_length": 85, "alphanum_fraction": 0.5008837045, "num_tokens": 860, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.785308580887758, "lm_q2_score": 0.66192288918838, "lm_q1q2_score": 0.5198137247656515}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nClass(PrunedDFT, TaggedNonTerminal, rec(\n abbrevs := [\n (n,blk,pat) -> Checked(IsPosIntSym(n), IsPosIntSym(blk), IsList(pat),\n AnySyms(n,blk) or (IsInt(_unwrap(n)/_unwrap(blk)) and ForAll(pat, i->IsInt(i) and i < n/blk)),\n [_unwrap(n), 1, _unwrap(blk), pat]),\n (n,k,blk,pat) -> Checked(IsPosIntSym(n), IsIntSym(k), IsPosIntSym(blk), IsList(pat),\n AnySyms(n,k) or Gcd(_unwrap(n),_unwrap(k))=1,\n AnySyms(n,blk) or (IsInt(_unwrap(n)/_unwrap(blk)) and ForAll(pat, i->IsInt(i) and i < n/blk)),\n [_unwrap(n), When(AnySyms(n,k), k, k mod _unwrap(n)), _unwrap(blk), pat])\n ],\n\n dims := self >> let(\n size := self.params[1],\n d := [size, self.params[3]Length(self.params[4])],\n When(self.transposed, [d[2], d[1]], d)\n ),\n\n terminate := self >> let(\n size := self.params[1], blk := self.params[3], pat := self.params[4],\n res := DFT(size, self.params[2]).terminate() \n Tensor(Mat(List(pat, i->BasisVec(size/blk, i))).transpose(), I(blk)).terminate(),\n When(self.transposed, res.transpose(), res)\n ),\n\n isReal := self >> false,\n normalizedArithCost := self >> let(n := self.params[1], IntDouble(5 * n * d_log(n) / d_log(2))),\n TType := T_Complex(T_Real(64))\n));\n\n\n\nClass(PrunedIDFT, TaggedNonTerminal, rec(\n abbrevs := [\n (n,blk,pat) -> Checked(IsPosIntSym(n), IsPosIntSym(blk), IsList(pat),\n AnySyms(n,blk) or (IsInt(_unwrap(n)/_unwrap(blk)) and ForAll(pat, i->IsInt(i) and i < n/blk)),\n [_unwrap(n), 1, _unwrap(blk), pat]),\n (n,k,blk,pat) -> Checked(IsPosIntSym(n), IsIntSym(k), IsPosIntSym(blk), IsList(pat),\n AnySyms(n,k) or Gcd(_unwrap(n),_unwrap(k))=1,\n AnySyms(n,blk) or (IsInt(_unwrap(n)/_unwrap(blk)) and ForAll(pat, i->IsInt(i) and i < n/blk)),\n [_unwrap(n), When(AnySyms(n,k), k, k mod _unwrap(n)), _unwrap(blk), pat])\n ],\n\n dims := self >> let(\n size := self.params[1],\n d := [size, self.params[3]Length(self.params[4])],\n When(not self.transposed, [d[2], d[1]], d)\n ),\n\n terminate := self >> let(\n size := self.params[1], blk := self.params[3], pat := self.params[4],\n res := DFT(size, self.params[2]).terminate() \n Tensor(Mat(List(pat, i->BasisVec(size/blk, i))).transpose(), I(blk)).terminate(),\n When(not self.transposed, res.transpose(), res)\n ),\n\n isReal := self >> false,\n normalizedArithCost := self >> let(n := self.params[1], IntDouble(5 * n * d_log(n) / d_log(2))),\n TType := T_Complex(T_Real(64))\n));\n\n\n_pruned_children := function(m, n, scatpat, pdft)\n local pdfts, scatpats, iterparts, uspats, uuspats, uspats, spats;\n spats := Map([0..m-1], i->List(Intersection(scatpat, i+m[0..n-1]), j->j));\n uspats := Map([0..Length(spats)-1], i->(spats[i+1]-i)/m);\n uuspats := Set(uspats);\n\n # partition iterations into unique patterns\n iterparts := List([1..Length(uuspats)], j->Filtered([1..m], i->uspats[i] = uuspats[j])-1);\n Sort(iterparts);\n\n scatpats := List(iterparts, lst->uspats[lst[1]+1]);\n pdfts := Map(scatpats, sp->pdft(n, sp));\n return pdfts;\nend;\n\n_ctpr_applicable := function(m, n, scatpat)\n local spats, gpats, strides;\n spats := Map([0..m-1], i->List(Intersection(scatpat, i+m[0..n-1]), j->j));\n gpats := Map(spats, lst->Map(lst, i->Position(scatpat, i)-1));\n strides := Set(Flat(Map(gpats, lst->Map([1..Length(lst)-1], j->lst[j+1]-lst[j]))));\n return ForAll(spats, i->i<>[]) and (Length(strides) in [0, 1]);\nend;\n\n_build_basef := lst -> When(lst = lst[1] + [0..Length(lst)-1], let(i := Ind(Length(lst)), Lambda(i, lst[1] + i)), FData(Map(lst, V)));\n\n_build_stack := function(m, n, scatpat, pdfts, NI, gsop, istck, stck, cmpse)\n local stack, isu, is, itervars, gatscats, lbds, lbdvars, itercounts, iterbasesf, iterbases, iterparts, uuspats, uspats, bases, strides, stride, spats, gpats;\n spats := Map([0..m-1], i->List(Intersection(scatpat, i+m[0..n-1]), j->j));\n gpats := Map(spats, lst->Map(lst, i->Position(scatpat, i)-1));\n #When(ForAny(spats, i->i=[]), Error(\"need at least one element per child DFT\"));\n strides := Set(Flat(Map(gpats, lst->Map([1..Length(lst)-1], j->lst[j+1]-lst[j]))));\n stride := When(Length(strides) = 1, strides[1], 1);\n bases := Map(gpats, i->i[1]);\n\n uspats := Map([0..Length(spats)-1], i->(spats[i+1]-i)/m);\n uuspats := Set(uspats);\n\n iterparts := List([1..Length(uuspats)], j->Filtered([1..m], i->uspats[i] = uuspats[j])-1);\n Sort(iterparts);\n iterbases := Map(iterparts, lst->Map(lst, i->bases[i+1]));\n iterbasesf := List(iterbases, _build_basef);\n itercounts := List(iterparts, Length);\n itervars := List(iterparts, lst->Ind(Length(lst)));\n lbdvars := List(iterparts, lst->Ind(Length(gpats[lst[1]+1])));\n lbds := List([1..Length(itervars)], i->Lambda(lbdvars[i], stridelbdvars[i]+iterbasesf[i].at(itervars[i])).setRange(NI));\n gatscats := List(lbds, i->ApplyFunc(gsop, [i]));\n\n is := List([1..Length(itervars)], i->ApplyFunc(istck, [itervars[i], cmpse(pdfts[i], gatscats[i])]));\n isu := Map([1..Length(is)], i->When(itervars[i].range=1, is[i].unroll().child(1), is[i]));\n stack := When(Length(isu) = 1, isu[1], ApplyFunc(stck, isu));\n return stack;\nend;\n\n\nNewRulesFor(PrunedDFT, rec(\n PrunedDFT_base := rec(\n forTransposition := false,\n maxSize := 256,\n applicable := (self, nt) >> not nt.hasTags() and nt.params[1] <= self.maxSize and nt.params[3] = 1,\n children := nt -> [[DFT(nt.params[1], nt.params[2])]],\n apply := (nt, C, cnt) -> let(size := nt.params[1], blk := nt.params[3], pat := nt.params[4],\n C[1] * Tensor(Mat(List(pat, i->BasisVec(size/blk, i))).transpose(), I(blk)).terminate())\n ),\n PrunedDFT_DFT := rec(\n forTransposition := true,\n applicable := (self, nt) >> nt.params[1] = nt.params[3] and nt.params[4] = [0],\n children := nt -> [[ DFT(nt.params[1], nt.params[2]).withTags(nt.getTags()) ]],\n apply := (nt, C, cnt) -> C[1]\n ),\n PrunedDFT_CT := rec(\n forTransposition := true,\n applicable := (self, nt) >> nt.params[1] > 2\n and not nt.hasTags()\n and not IsPrime(nt.params[1])\n and nt.params[3] > 1,\n children := nt -> Map2(Filtered(DivisorPairs(nt.params[1]), (l) -> IsInt(nt.params[3]/l[1])),\n (m,n) -> [ DFT(m, nt.params[2] mod m), PrunedDFT(n, nt.params[2] mod n, nt.params[3]/m, nt.params[4]) ]\n ),\n apply := (nt, C, cnt) -> let(mn := nt.params[1], m := Rows(C[1]), n := Rows(C[2]),\n Tensor(C[1], I(n)) \n Diag(fPrecompute(Tw1(mn, n, nt.params[2]))) \n L(mn, m) * Tensor(C[2], I(m))\n )),\n PrunedDFT_CT_rec_block := rec(\n forTransposition := true,\n applicable := (self, nt) >> nt.params[1] > 2\n and not nt.hasTags()\n and not IsPrime(nt.params[1])\n and nt.params[3] = 1\n and Last(nt.params[4])+1-nt.params[4][1] = Length(Set(nt.params[4]))\n and ForAny(Map2(DivisorPairs(nt.params[1]), (m,n)->_ctpr_applicable(m, n, nt.params[4])), i->i),\n children := (nt) -> Filtered(Map2(DivisorPairs(nt.params[1]), (m, n) -> [ DFT(m, nt.params[2] mod m) ]::\n _pruned_children(m, n, nt.params[4], (r, sp) -> PrunedDFT(r, nt.params[2] mod n, nt.params[3], sp))),\n lst -> ForAll(Filtered(lst, i->ObjId(i) = PrunedDFT), j->j.params[4] <> [])),\n apply := (nt, C, cnt) -> let(mn := nt.params[1], m := Rows(C[1]), n := Rows(C[2]),\n Tensor(C[1], I(n)) \n Diag(fPrecompute(Tw1(mn, n, nt.params[2]))) \n _build_stack(m, n, nt.params[4], Drop(C, 1), nt.dims()[2], Gath, IterVStack, VStack, (a,b)->ab)\n )\n )\n));\n\nNewRulesFor(PrunedIDFT, rec(\n PrunedIDFT_base := rec(\n forTransposition := false,\n maxSize :=256,\n applicable := (self, nt) >> not nt.hasTags() and nt.params[1] <= self.maxSize and nt.params[3] = 1,\n children := nt -> [[DFT(nt.params[1], nt.params[2])]],\n apply := (nt, C, cnt) -> let(size := nt.params[1], blk := nt.params[3], pat := nt.params[4],\n Tensor(Mat(List(pat, i->BasisVec(size/blk, i))) C[1], I(blk)).terminate())\n ),\n PrunedIDFT_CT_rec_block := rec(\n forTransposition := true,\n applicable := (self, nt) >> nt.params[1] > 2\n and not nt.hasTags()\n and not IsPrime(nt.params[1])\n and nt.params[3] = 1\n and Last(nt.params[4])+1-nt.params[4][1] = Length(Set(nt.params[4]))\n and ForAny(Map2(DivisorPairs(nt.params[1]), (m,n)->_ctpr_applicable(m, n, nt.params[4])), i->i),\n children := (nt) -> Filtered(Map2(DivisorPairs(nt.params[1]), (n, m) ->\n _pruned_children(m, n, nt.params[4], (r, sp) -> PrunedIDFT(r, nt.params[2] mod n, nt.params[3], sp)) ::\n [ DFT(m, nt.params[2] mod m) ]),\n lst -> ForAll(Filtered(lst, i->ObjId(i) = PrunedIDFT), j->j.params[4] <> [])),\n apply := (nt, C, cnt) -> let(mn := nt.params[1], m := Rows(Last(C)), n := Cols(C[1]),\n _build_stack(m, n, nt.params[4], DropLast(C, 1), nt.dims()[1], Scat, IterHStack1, HStack1, (a,b)->ba) \n Diag(fPrecompute(Tw1(mn, n, nt.params[2]))) \n Tensor(Last(C), I(n))\n )\n )\n));\n\n\n\nClass(IOPrunedDFT, TaggedNonTerminal, rec(\n abbrevs := [\n (n,oblk,opat,iblk,ipat) -> Checked(IsPosIntSym(n), IsPosIntSym(oblk), IsList(opat), IsPosIntSym(iblk), IsList(ipat),\n AnySyms(n,iblk,oblk) or (IsInt(_unwrap(n)/_unwrap(iblk)) and IsInt(_unwrap(n)/_unwrap(oblk)) and\n ForAll(ipat, i->IsInt(i) and i < n/iblk) and ForAll(opat, i->IsInt(i) and i < n/oblk)),\n [_unwrap(n), 1, _unwrap(oblk), opat, _unwrap(iblk), ipat]),\n\n\n (n,k,oblk,opat,iblk,ipat) -> Checked(IsPosIntSym(n), IsIntSym(k), IsPosIntSym(oblk), IsList(opat), IsPosIntSym(iblk), IsList(ipat),\n AnySyms(n,k) or Gcd(_unwrap(n),_unwrap(k))=1,\n AnySyms(n,iblk,oblk) or (IsInt(_unwrap(n)/_unwrap(iblk)) and IsInt(_unwrap(n)/_unwrap(oblk)) and\n ForAll(ipat, i->IsInt(i) and i < n/iblk) and ForAll(opat, i->IsInt(i) and i < n/oblk)),\n [_unwrap(n), When(AnySyms(n,k), k, k mod _unwrap(n)), _unwrap(oblk), opat, _unwrap(iblk), ipat])\n ],\n dims := self >> [self.params[3]Length(self.params[4]), self.params[5]Length(self.params[6])],\n terminate := self >> let(size := self.params[1],\n oblk := self.params[3], opat := self.params[4], iblk := self.params[5], ipat := self.params[6],\n Tensor(Mat(List(opat, i->BasisVec(size/oblk, i))), I(oblk)).terminate() \n DFT(size, self.params[2]).terminate() \n Tensor(Mat(List(ipat, i->BasisVec(size/iblk, i))).transpose(), I(iblk)).terminate()),\n isReal := self >> false,\n normalizedArithCost := self >> let(n := self.params[1], IntDouble(5 n * d_log(n) / d_log(2))),\n TType := T_Complex(T_Real(64))\n));\n\n\nNewRulesFor(IOPrunedDFT, rec(\n IOPrunedDFT_base := rec(\n forTransposition := true,\n maxSize := 16,\n applicable := (self, nt) >> not nt.hasTags() and nt.params[1] <= self.maxSize and nt.params[3] = 1 and nt.params[5] = 1,\n children := nt -> [[DFT(nt.params[1], nt.params[2])]],\n apply := (nt, C, cnt) -> let(size := nt.params[1], oblk := nt.params[3], opat := nt.params[4], iblk := nt.params[5], ipat := nt.params[6],\n Tensor(Mat(List(opat, i->BasisVec(size/oblk, i))), I(oblk)).terminate() \n C[1] \n Tensor(Mat(List(ipat, i->BasisVec(size/iblk, i))).transpose(), I(iblk)).terminate())\n ),\n\n IOPrunedDFT__PrunedDFT := rec(\n forTransposition := true,\n applicable := (self, nt) >> nt.params[1] = nt.params[3] and nt.params[4] = [0],\n children := nt -> [[ PrunedDFT(nt.params[1], nt.params[2], nt.params[5], nt.params[6]).withTags(nt.getTags()) ]],\n apply := (nt, C, cnt) -> C[1]\n ),\n\n IOPrunedDFT__PrunedDFT_T := rec(\n forTransposition := true,\n applicable := (self, nt) >> nt.params[1] = nt.params[5] and nt.params[6] = [0],\n children := nt -> [[ PrunedDFT(nt.params[1], nt.params[2], nt.params[3], nt.params[4]).transpose().withTags(nt.getTags()) ]],\n apply := (nt, C, cnt) -> C[1]\n ),\n\n IOPrunedDFT__Gath_PrunedDFT := rec(\n forTransposition := true,\n maxSize := 16,\n applicable := (self, nt) >> not nt.hasTags() and nt.params[1] <= self.maxSize and\n ((nt.params[3] = 1 and not (nt.params[5] = 1)) or (nt.params[3] * nt.params[5] < nt.params[1])),\n children := nt -> [[ PrunedDFT(nt.params[1], nt.params[2], nt.params[5], nt.params[6]) ]],\n apply := (nt, C, cnt) -> let(size := nt.params[1], oblk := nt.params[3], opat := nt.params[4], iblk := nt.params[5], ipat := nt.params[6],\n Tensor(Mat(List(opat, i->BasisVec(size/oblk, i))), I(oblk)).terminate() * C[1])\n ),\n\n IOPrunedDFT__PrunedDFT_T_Scat := rec(\n forTransposition := true,\n maxSize := 16,\n applicable := (self, nt) >> not nt.hasTags() and nt.params[1] <= self.maxSize and\n (((not nt.params[3] = 1) and nt.params[5] = 1) or(nt.params[3] * nt.params[5] < nt.params[1])),\n children := nt -> [[ PrunedDFT(nt.params[1], nt.params[2], nt.params[3], nt.params[4]).transpose() ]],\n apply := (nt, C, cnt) -> let(size := nt.params[1], oblk := nt.params[3], opat := nt.params[4], iblk := nt.params[5], ipat := nt.params[6],\n C[1] * Tensor(Mat(List(ipat, i->BasisVec(size/iblk, i))).transpose(), I(iblk)).terminate())\n ),\n\n IOPrunedDFT_CT := rec(\n forTransposition := true,\n applicable := (self, nt) >> nt.params[1] > 2 and nt.params[3] * nt.params[5] >= nt.params[1]\n and not nt.hasTags()\n and not IsPrime(nt.params[1])\n and nt.params[3] > 1,\n children := nt -> Map2(Filtered(DivisorPairs(nt.params[1]), (mn) -> IsInt(nt.params[3]/mn[2]) and IsInt(nt.params[5]/mn[1])),\n (m,n) -> [\n PrunedDFT(m, nt.params[2] mod m, nt.params[3]/n, nt.params[4]).transpose(),\n PrunedDFT(n, nt.params[2] mod n, nt.params[5]/m, nt.params[6]) ]\n ),\n apply := (nt, C, cnt) -> let(mn := nt.params[1], m := Cols(C[1]), n := Rows(C[2]),\n Tensor(C[1], I(n)) \n Diag(fPrecompute(Tw1(mn, n, nt.params[2]))) \n L(mn, m) * Tensor(C[2], I(m))\n ))\n));\n", "meta": {"hexsha": "f1aebeee9b72de8fa95eeb44a9afb2777742fef3", "size": 14698, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/dft/prune.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", 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YES\n2. YES", "lm_q1_score": 0.7826624789529375, "lm_q2_score": 0.6619228691808012, "lm_q1q2_score": 0.5180621936686869}}
	{"text": "\nInstallMethod(TotalDegree,\n \"TotalDegree of multivariable polynomial\",\n [IsPolynomial],\n function(poly)\n local result;\n\n result:=ExtRepPolynomialRatFun(poly);\n result:=result{2[1..Length(result)/2]-1};\n result:=Maximum(List(result,j->Sum(j{2[1..Length(j)/2]})));\n return result;\nend);\n\nInstallMethod(ValuePoly,\n \"Value of multivariable polynomial\",\n [IsPolynomial,IsList,IsList],\n function(poly,vars,vals)\n local result,ext_rep,ext_vars,\n monom,pos,i,j;\n\n ext_rep:=ExtRepPolynomialRatFun(poly);\n ext_vars:=List(vars,i->ExtRepPolynomialRatFun(i));\n ext_vars:=List(ext_vars,i->i[1][1]);\n\n result:=Zero(poly);\n for i in 2[1..Length(ext_rep)/2]-1 do\n monom:=One(poly);\n for j in 2[1..Length(ext_rep[i])/2]-1 do\n pos:=Position(ext_vars,ext_rep[i][j]);\n monom:=monomvals[pos]^ext_rep[i][j+1];\n od;\n monom:=monom((ext_rep[i+1]One(poly)));\n result:=result+monom;\n od;\n\n return result;\nend);\n\npRadical:=function(poly,avars)\n local result,\n ext_rep,ext_avars,\n p,deg,deg_max,p_div,monom,i,j;\n\n #exterior reprezentation of polynomial and variables\n ext_rep:=ExtRepPolynomialRatFun(poly);\n ext_avars:=List(avars,i->ExtRepPolynomialRatFun(i));\n ext_avars:=List(ext_avars,i->i[1][1]);\n \n # degree of variables in monomials of poly\n deg:=List(ext_rep{2[1..Length(ext_rep)/2]-1},i->i{2[1..Length(i)/2]});\n\n # Adjustment: (poly)^p ---> poly\n p:=Characteristic(poly);\n if Concatenation(deg)=[] then return poly; fi;\n deg_max:=LogInt(Maximum(Concatenation(deg)),p);\n p_div:=Gcd(p^deg_max,Gcd(Concatenation(deg)));\n if p_div>1 then\n result:=Zero(poly);\n for i in 2[1..Length(ext_rep)/2]-1 do\n monom:=One(poly);\n for j in 2[1..Length(ext_rep[i])/2]-1 do\n monom:=monomavars[Position(ext_avars,ext_rep[i][j])]^(ext_rep[i][j+1]/p_div);\n od;\n result:=result+ext_rep[i+1]monom;\n od;\n return result;\n fi;\n return poly;\nend;\n\nSolve:=function(poly,avars)\n local ext_rep,vars,ext_avars,p,\n deg,tot_deg,poz1,pozm,xpoly,xall,x,\n taboo;\n\n # Adjustment: (poly)^p ---> poly\n poly:=pRadical(poly,avars);\n \n #exterior reprezentation of polynomial and variables\n ext_rep:=ExtRepPolynomialRatFun(poly);\n ext_avars:=List(avars,i->ExtRepPolynomialRatFun(i));\n ext_avars:=List(ext_avars,i->i[1][1]);\n \n # variables of poly\n vars:=Concatenation(ext_rep{2[1..Length(ext_rep)/2]-1});\n vars:=vars{2[1..Length(vars)/2]-1};\n # degree of variables in monomials of poly\n deg:=List(ext_rep{2[1..Length(ext_rep)/2]-1},i->i{2[1..Length(i)/2]});\n tot_deg:=List(deg,i->Sum(i));\n #ignor constants\n tot_deg:=Filtered(tot_deg,i->i<>0);\n\n # Restrict: x should not be deduced from x+x^p+y\n taboo:=[];\n if Length(Set(vars))>1 then\n for x in Set(vars) do\n xall:=ext_rep{2[1..Length(ext_rep)/2]-1};\n xall:=Filtered(xall,i->x in i);\n xpoly:=Filtered(xall,i->Length(i)=2);\n if Length(xpoly)>=2 then\n # if xall=xpoly then\n # return [Position(ext_avars,x),Zero(poly),avars[Position(ext_avars,x)]];\n # fi;\n Add(taboo,Positions(vars,x));\n fi;\n od;\n taboo:=Concatenation(taboo);\n fi;\n\n p:=Characteristic(poly);\n# if Length(vars)=1 then\n# return [Position(ext_avars,vars[1]),RootsOfUPol(poly)[1],true];\n# fi;\n#Error(\"!\");\n if 1 in tot_deg then\n # x^p+P(x)^p\n if Length(Set(vars)) = 1 and Length(Set(tot_deg))>=2 then\n# Print(poly,\"\\n\");\n return [Position(ext_avars,vars[1]),Zero(poly),avars[Position(ext_avars,vars[1])]];\n# return fail;\n fi;\n \n## if Length(Set(vars)) = 1 and not Difference(tot_deg,[1])[1] mod p =0 then\n# if Length(Set(vars)) = 1 and not Set(tot_deg)=[1,p] then\n# Print(poly,\"\\n\");\n# return [Position(ext_avars,vars[1]),Zero(poly),avars[Position(ext_avars,vars[1])]];\n## return fail;\n# fi;\n \n if Length(Set(vars)) = 1 and Maximum(tot_deg)>1 then return fail; fi; # such relations produce infinite loops\n \n # position of variables among monomials of poly\n poz1:=Positions(tot_deg,1);\n poz1:=Difference(poz1,taboo);\n # if all variables are taboo return fail\n if Length(poz1)=0 then return fail; fi;\n # else choose one which is not taboo\n poz1:=poz1[1];\n # position of monomial in ext_rep\n pozm:=Position(ext_rep,[vars[poz1],1]);\n return [Position(ext_avars,vars[poz1]),avars[Position(ext_avars,vars[poz1])]-(ext_rep[pozm+1]^(-1))poly,true];\n fi;\n return fail;\nend;\n\nSolveWithTorsion:=function(poly,avars)\n local ext_rep,vars,ext_avars,\n deg,tot_deg,poz1,pozm,xpoly,x,\n taboo;\n\n # Adjustment: (poly)^p ---> poly\n poly:=pRadical(poly,avars);\n \n #exterior reprezentation of polynomial and variables\n ext_rep:=ExtRepPolynomialRatFun(poly);\n ext_avars:=List(avars,i->ExtRepPolynomialRatFun(i));\n ext_avars:=List(ext_avars,i->i[1][1]);\n \n # variables of poly\n vars:=Concatenation(ext_rep{2[1..Length(ext_rep)/2]-1});\n vars:=vars{2[1..Length(vars)/2]-1};\n # degree of variables in monomials of poly\n deg:=List(ext_rep{2[1..Length(ext_rep)/2]-1},i->i{2[1..Length(i)/2]});\n tot_deg:=List(deg,i->Sum(i));\n #ignor constants\n tot_deg:=Filtered(tot_deg,i->i<>0);\n\n # Restrict: x should not be deduced from x+x^p+y\n taboo:=[];\n if Length(Set(vars))>1 then\n for x in Set(vars) do\n xpoly:=ext_rep{2[1..Length(ext_rep)/2]-1};\n xpoly:=Filtered(xpoly,i->x in i);\n xpoly:=Filtered(xpoly,i->Length(i)=2);\n if Length(xpoly)>=2 then\n Add(taboo,Positions(vars,x));\n fi;\n od;\n taboo:=Concatenation(taboo);\n fi;\n \n# if Length(vars)=1 then\n# return [Position(ext_avars,vars[1]),RootsOfUPol(poly)[1],true];\n# fi;\n#Error(\"!\");\n if 1 in tot_deg then\n # x^p+P(x)^p\n if Length(Set(vars)) = 1 and Length(Set(tot_deg))>=2 then\n return [Position(ext_avars,vars[1]),Zero(poly),avars[Position(ext_avars,vars[1])]];\n fi;\n \n if Length(Set(vars)) = 1 and Maximum(tot_deg)>1 then return fail; fi; # such relations produce infinite loops\n \n # position of variables among monomials of poly\n poz1:=Positions(tot_deg,1);\n poz1:=Difference(poz1,taboo);\n # if all variables are taboo return fail\n if Length(poz1)=0 then return fail; fi;\n # else choose one which is not taboo\n poz1:=poz1[1];\n # position of monomial in ext_rep\n pozm:=Position(ext_rep,[vars[poz1],1]);\n return [Position(ext_avars,vars[poz1]),avars[Position(ext_avars,vars[poz1])]-(ext_rep[pozm+1]^(-1))poly,true];\n fi;\n return fail;\nend;\n\nReduceRelations:=function(relations,avars,values,APR)\n local result,#relations,\n relations_len,schimbare,Ring,torsion,GB,\n index,sol,i,modulo;\n\n result:=ShallowCopy(values);\n relations:=List(relations,i->Value(i,avars,result)One(APR));\n relations:=Filtered(relations,i->i <> Zero(APR));\n relations:=Set(relations);\n# relations:=List(coefficients(u),i->i[2]);\n relations_len:=Length(relations);\n\n# i:=1;\n# while i<relations_len do\n# modulo:=Concatenation([1..i-1],[i+1..relations_len]);\n# modulo:=relations{modulo};\n# relations:=List(relations,i->PolynomialReducedRemainder(i,relations,MonomialLexOrdering()));\n# relations:=Set(Filtered(relations,i->i <> Zero(APR)));\n# if Length(relations)<relations_len then i:=1; fi;\n# relations_len:=Length(relations);\n# od;\n# Error(\"!\");\n#Print(\"...relations: \",relations,\"\\n\");\n schimbare:=true;\n while relations<>[] and schimbare do\n #Print(\"@@@\",relations_len,\" \");\n# Print(\"..relations: \",relations,\"\\n\");\n# Print(\"--->result: \",result,\"\\n\");\n #GB:=GroebnerBasis(relations,MonomialLexOrdering()); ## ATENTIE AICI\n result:=List(result,i->PolynomialReducedRemainder(i,relations,MonomialLexOrdering()));\n #result:=List(result,i->PolynomialReducedRemainder(i,GB,MonomialLexOrdering()));\n# Print(\"fresh result:\",result,\"\\n\");\n schimbare:=false;\n #Error(\"!!\");\n #refresh relations\n #relations:=List(relations,i->Value(i,avars,result)One(APR));\n relations:=List(relations,i->ValuePoly(i,avars,result)One(APR));\n# Print(\"fresh rels:\",relations,\"\\n\");\n relations:=Filtered(relations,i->i <> Zero(APR));\n schimbare:=Length(relations)<relations_len;\n relations_len:=Length(relations);\n od;\n#Error(\"!\");\n#Print(\".relations: \",relations,\"\\n\");\n relations:=Filtered(relations,i->i <> Zero(APR));\n \n return [result,relations];\nend;\n\nSolveRelations:=function(relations,avars,values,APR)\n local result,#relations,\n relations_len,schimbare,Ring,torsion,\n index,sol,i;\n\n result:=ShallowCopy(values);\n relations:=List(relations,i->Value(i,avars,result)One(APR));\n relations:=Filtered(relations,i->i <> Zero(APR));\n \n relations:=ReduceRelations(relations,avars,result,APR);\n# #Error(\"!\");\n result:=relations[1];\n relations:=relations[2];\n# #relations:=List(coefficients(u),i->i[2]);\n relations_len:=Length(relations);\n# Print(\"...relations: \",relations,\"\\n\");\n \n Ring:=CoefficientsRing(APR);\n schimbare:=true;\n torsion:=[];\n \n #Error(\"!\");\n while relations<>[] and schimbare do\n ##Print(\"len:=\",Length(relations),\"\\n\");\n schimbare:=false;\n index:=1;\n while index<=relations_len do\n #Print(\"len===\",Length(relations),\"\\n\",\"index===\",index,\"\\n\");\n sol:=Solve(relations[index],avars);\n #Print(\"solved \",relations[index],\"\\n\");\n #Error(\"!\");\n #sol:=fail;\n if sol<>fail then\n #change result\n result[sol[1]]:=sol[2];\n for i in [1..Length(result)] do\n if not result[i] in Ring and result[i]<>avars[i] then\n result[i]:=Value(result[i],avars,result)One(APR);\n fi;\n od;\n #refresh relations\n relations:=List(relations,i->Value(i,avars,result)*One(APR));\n relations:=Filtered(relations,i->i <> Zero(APR));\n #relations:=ReduceRelations(relations,avars,result,APR);\n #result:=relations[1];\n #relations:=relations[2];\n schimbare:=Length(relations)<relations_len or sol[2]=Zero(APR);\n relations_len:=Length(relations);\n\n if Length(sol)=3 and sol[3] in avars then Add(torsion,sol[3]); fi;\n fi;\n index:=index+1;\n od;\n od;\n\n return [result,relations,torsion];\nend;\n", "meta": {"hexsha": "c1603507f48fe21a27cdc1119ca2e94b517ed09b", "size": 11077, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "lib/poly.gi", "max_stars_repo_name": "iuliansimion/Chevalley.gap", "max_stars_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "lib/poly.gi", "max_issues_repo_name": "iuliansimion/Chevalley.gap", "max_issues_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "lib/poly.gi", "max_forks_repo_name": "iuliansimion/Chevalley.gap", "max_forks_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 35.2770700637, "max_line_length": 119, "alphanum_fraction": 0.592488941, "num_tokens": 3164, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7634837635542924, "lm_q2_score": 0.6757646140788307, "lm_q1q2_score": 0.5159353108337196}}
	{"text": "RequirePackage(\"grape\");\n\nGC := function(x,y,i,j) return x[i]y[j] - x[j]y[i]; end;\n\nG2 := function(q)\n local P, Q;\n if q mod 2 = 0 then\n Q := [[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1],[0,0,0,1,0,0,0],[0,0,0,0,0,0,0],[0,0,0,0,0,0,0],[0,0,0,0,0,0,0]]Z(q)^0;;\n else\n Q := [[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1],[0,0,0,1,0,0,0],[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0]]Z(q)^0;;\n fi;\n P := Filtered(List(Subspaces(GF(q)^7, 1), y -> Elements(y)[2]), x -> xQx = 0Z(q));;\n\n return Graph(Group(()), P, function(x,y) return x; end,\n function(x,y)\n return x <> y and xQy = 0Z(q) and yQx = 0*Z(q) and \n [ GC(x,y,2,3), GC(x,y,6,5), GC(x,y,3,1), GC(x,y,7,6), GC(x,y,1,2), GC(x,y,5,7) ] =\n [ GC(x,y,4,5), GC(x,y,4,3), GC(x,y,4,6), GC(x,y,4,1), GC(x,y,4,7), GC(x,y,4,2) ];\n end, true);;\nend;\n\n", "meta": {"hexsha": "f3ae8ce35da43d4a996cba2fcaffca2c2b3a4a53", "size": 892, "ext": "gap", "lang": "GAP", "max_stars_repo_path": "lib/g2.gap", "max_stars_repo_name": "jaanos/gap-graphs", "max_stars_repo_head_hexsha": "18dd56c9b90a12a717a0cc893fdd72c6343ee79b", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2015-10-27T15:54:29.000Z", "max_stars_repo_stars_event_max_datetime": "2016-11-07T14:09:44.000Z", "max_issues_repo_path": "lib/g2.gap", "max_issues_repo_name": "jaanos/gap-graphs", "max_issues_repo_head_hexsha": "18dd56c9b90a12a717a0cc893fdd72c6343ee79b", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2015-04-20T23:13:11.000Z", "max_issues_repo_issues_event_max_datetime": "2015-04-20T23:13:11.000Z", "max_forks_repo_path": "lib/g2.gap", "max_forks_repo_name": "jaanos/gap-graphs", "max_forks_repo_head_hexsha": "18dd56c9b90a12a717a0cc893fdd72c6343ee79b", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 40.5454545455, "max_line_length": 135, "alphanum_fraction": 0.4428251121, "num_tokens": 476, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8791467738423873, "lm_q2_score": 0.5851011542032312, "lm_q1q2_score": 0.5143897920892279}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nZeroCoef := function(p)\nlocal i, L;\nL:=p.coefficients;\nfor i in [1..Length(p.coefficients)] do\n if AbsFloat(ReComplex(ComplexAny(p.coefficients[i]))) < FloatString(\"1e-4\") then\n L[i] := p.baseRing.zero;\n fi;\nod;\nreturn Polynomial(p.baseRing, L, p.valuation);\nend;\n\n\n# Recursive implementation of the long division for Laurent polynomials h(z) and g(z)\n# There are deg(h)-deg(g)+2 different schemes for division \nLaurentRemainder := function ( arg )\n\nlocal a, b, q, q1, r1, q2, r2, Ls, Lt, z, \n deghigha, deglowa, deghighb, deglowb, dega, degb, coefa, coefb, divs;\n\nif IsList(arg[1]) then arg:=arg[1];fi;\na:=arg[1];\nb:=arg[2];\n\n#Print(\"check\");\nif not (IsPolynomial(a) and IsPolynomial(a)) then\n Error(\"<a> and <b> must be polynomials\");\nelif not a.baseRing.name = b.baseRing.name then\n Error(\"Both polynomials have to be over the same field\");\nelif not IsBound(PolynomialRing(a.baseRing).isEuclideanRing) then\n Error(\"Polymonials must be constructed over a field, not over a ring\");\nfi;\n\nz:=Indeterminate(a.baseRing);\nz.name:=\"z\";\nif Length(arg)=3 then q:=arg[3]; else q:=0z^0; fi;\n\ndeglowa := a.valuation;\ndeglowb := b.valuation;\ndega := Length(a.coefficients)-1;\ndegb := Length(b.coefficients)-1;\ndeghigha := deglowa + dega;\ndeghighb := deglowb + degb;\n\n\ncoefa := a.coefficients;\ncoefb := b.coefficients; \n\nif dega<degb then return [[q,a]];fi;\n\n q1 := Polynomial(a.baseRing,[coefa[dega+1]/coefb[degb+1]],deghigha-deghighb);\n r1 := a - q1 b;\n q1 := q1 + q;\n# Print(q1);\n# Print(\"\\n\");\n# Print(r1);\n#Print(\"\\n\");\n\n# q2 := coefa[1]/coefb[1] * z^(deglowa-deglowb);\n q2 := Polynomial(a.baseRing,[coefa[1]/coefb[1]],deglowa-deglowb);\n r2 := a - q2 * b;\n q2 := q2 + q;\n Ls := [];\n for divs in [[r1,b,q1],[r2,b,q2]] do\n Lt := LaurentRemainder(divs);\n Add(Ls,Lt);\n od;\n Ls := Flat(Ls);\n Ls := List([1..Length(Ls)/2], i->[Ls[2i-1],Ls[2i]]); \n Ls := List(Collected(Ls), col->col[1]);\n if not IsList(Ls[1]) then return [Ls];\n else return Ls;\n fi; \n \n\nend;\n\n#\n# Note:\n# ! Because we now use double floats, the LiftingScheme generates more LS than\n# possible because of finite precision. There will be a bunch of the same lifting\n# schemes generated multiple times with coefficients different after 10th\n# decimal or so. This requies fixing !\n#\n\n#F LiftingScheme( <poly1>, <poly2> )\n#F returns a list of Laurent polynomials that represent \n#F primal and dual lifting steps factorization of the polyphase \n#F matrix of polynomials <poly1> and <poly2>:\n#F P(z)= [[ <poly1_even>, <poly1_odd>],\n#F [ <poly2_even>, <poly2_odd>]]\n#F In Discrete Wavelet Transform notation, <poly1> represents\n#F a low-pass filter impulse response, whereas <poly2> represents\n#F a high-pass one. \n#F \n#F The output is in the following format:\n#F [ b, l1(z), l2(z), .... , ln(z), c1, c2]\n#F \n#F b - a binary symbol that determines the type of the \n#F initial lifting step (0 - primal, 1 - dual)\n#F li(z) - polynomial representing i-th lifting step\n#F c1, c2 - scaling constants\n#F\n#F Example:\n#F \n#F P(z)= [ c1, 0 ] * [ 1, l2(z)] * [ 1 , 0 ] \n#F [ 0, c2 ] [ 0, 1 ] [ l1(z), 1 ]\n#F ---------- ----------- ------------ \n#F scaling primal l.s. dual l.s. (b=1)\n#F\n#F Note: Factorization is implemented in Laurent Polynomial\n#F ring over the base field inherited from <poly1>, <poly2>.\n#F\n\nLiftingScheme := function ( M )\n\nlocal he, ho, ge, go, hen, hon, gen, gon, b, QR, z, Le, Lo, L, Lc, Ls, ve, vo, P, factor, scheme;\n\n\n#Print(\"Recursion \\n\");\n# Check if h(z) and g(z) in fact represent a perfect reconstruction \n# filter bank -> determinant of the polyphase matrix should be\n# a monomial \nhe := M[1][1];ho := M[1][2]; ge := M[2][1]; go := M[2][2];\n if not Length(ZeroCoef(Determinant([[he, ho],[ge, go]])).coefficients) = 1 then\n Error(\"h(z) and g(z) must satisfy the perfect reconstruction condition P(z)P'(z)^(-1) = I where P and P' are analysis and synthesis polyphase matrices\");\n fi;\n\n z:=Indeterminate(he.baseRing);\n z.name:=\"z\";\n# Factoring Algorithm\n b:=0;\n\n if LaurentDegree(he) >= LaurentDegree(ho) then b:=1; fi;\n\n if (ho=0z^0 or ge=0z^0) then\n L:=[];\n if ho=0z^0 then Add(L,ZeroCoef(ge)\n Polynomial(he.baseRing,[1/ ZeroCoef(go).coefficients[1]], -go.valuation));\n else Add(L,ho/he); fi;\n Add(L, he);\n Add(L, go);\n Add(L, b);\n return [Reversed(L)];\n fi;\n if (he=0z^0 or go=0z^0) then\n L:=[];\n if he=0z^0 then Add(L,ZeroCoef(go)\n Polynomial(he.baseRing,[1/ ZeroCoef(ge).coefficients[1]], -ge.valuation));\n else Add(L,he/ho); fi;\n Add(L, ho);\n Add(L, ge);\n Add(L, b-2);\n return [Reversed(L)];\n fi;\n L:=[]; \n if b=0 then\n QR:=LaurentRemainder(ho,he);\n for factor in QR do\n hon := factor[2];\n hon := ZeroCoef(hon);\n gon := go - ge factor[1];\n gon := ZeroCoef(gon);\n\n Lc:=LiftingScheme([[he,hon],[ge,gon]]);\n for scheme in Lc do Add(scheme,factor[1]); od;\n Append(L,Lc);\n od;\n\n\n else \n QR:=LaurentRemainder(he,ho);\n for factor in QR do\n hen := factor[2];\n hen := ZeroCoef(hen);\n gen := ge - go * factor[1];\n gen := ZeroCoef(gen);\n Lc:=LiftingScheme([[hen,ho],[gen,go]]);\n for scheme in Lc do Add(scheme,factor[1]); od;\n Append(L,Lc);\n od;\n\n fi;\n\nreturn(L);\n\nend;\n\n\nLifting := function(M)\nlocal Lt, Ls, L, factor, p, normM, normDiff;\n\nL:=LiftingScheme(M,[]);\nLt:=[];\nLs:=[];\n\nfor factor in L do \n Add(Ls, factor);\n if IsInt(factor) then Add(Lt, Ls); Ls:=[];fi;\nod;\nreturn Lt;\nend;\n\n\nVerifyLiftingScheme:=function(P,L2)\n\nlocal P, M, b, i, l,z,p, normM, normDiff;\n\n z:=Indeterminate(P[1].baseRing);\n z.name:=\"z\";\n\n#P:=[[P[1],P[2]],[P[3],P[4]]];\nM:= [[1, 0],[0,1]];\n\nL2:=Reversed(L2);\nl:=Length(L2);\nb:=L2[l];\nfor i in [1 .. l-3] do\n if b=-2 then \n M:= M * [[0z^0,1z^0 ], [1z^0, L2[l-i-2]]]; b:=1;\n elif b=-1 then \n M:= M [[L2[l-i-2],1z^0 ], [1z^0, 0z^0]]; b:=0;\n elif b=0 then\n M:= M [[1z^0, L2[l-i-2]], [0z^0, 1z^0]]; b:=1;\n else \n M:= M [[1z^0, 0z^0], [L2[l-i-2], 1z^0]]; b:=0;\n fi;\nod;\nM:=[[L2[l-2], 0z^0],[0z^0, L2[l-1]]]M;\n#Print([[P[1],P[2]],[P[3],P[4]]]);\nif Same(P[1][1].baseRing, Doubles) then \n normM:=Sum(M, l->Sum(l, p->(Sum(p.coefficients,i->i^2))^1/2))^1/2;\n normDiff:=Sum(M-P, l->Sum(l, p->(Sum(p.coefficients,i->i^2))^1/2))^1/2;\n Print(\"error: \",normDiff/normM,\"\\n\");\n if (normDiff/normM > FloatString(\"1e-4\")) then return false;\n else return true;\n fi;\nelse return[M,P,M=P];\nfi;\nend;\n\nArithmeticCostLS := function(L)\nlocal step, mult, add, i;\n\nmult:=0;\nadd:=0;\nL:=Reversed(L);\nfor step in [1..Length(L)-3] do\n for i in L[step].coefficients do\n if not i = 0 then mult:=mult+1; add:=add+1;fi;\n od;\nod;\nmult:=mult+2;\nreturn [add,mult,Length(L)-3];\nend;\n\n\n#F MatPoly := function(h,g)\n#F returns a matrix formed of two filters h(z) and g(z)\n#F also returns largest and the smallest degree of the \n#F coefficients in the matrix. \n#F Format: [<mat>, q, p]\n\nMatPoly := function(h,g)\n\nlocal hc, gc, hsmall, hlarge,\n gsmall, glarge, q, p, M;\n\n # Check the degrees of the filters \n hc := h.coefficients;\n gc := g.coefficients; \n hsmall := h.valuation;\n hlarge := Length(hc) + hsmall - 1;\n gsmall := g.valuation;\n glarge := Length(gc) + gsmall - 1;\n q := Minimum([hsmall,gsmall]);\n p := Maximum([hlarge,glarge]);\n \n# Construct the 2 x l matrix of filter coefficients\n\n M := \n [\n Concat(List([1..AbsInt(q-hsmall)],i->h.baseRing.zero),\n hc, List([1..p-hlarge],i->h.baseRing.zero)\n ),\n Concat(List([1..AbsInt(q-gsmall)],i->h.baseRing.zero),\n gc, List([1..p-glarge],i->h.baseRing.zero)\n )\n ];\n\n return ([M, hsmall, hlarge, gsmall, glarge]);\nend;\n\n\nPolyphase := function(p1,p2)\n\nlocal he, ho, ge, go, z, h, g;\n\nif not (IsPolynomial(p1) and IsPolynomial(p1)) then\n Error(\"<p1> and <p2> must be polynomials\");\nelif not p1.baseRing.name = p2.baseRing.name then\n Error(\"Both polynomials have to be over the same field\");\nelif not IsBound(PolynomialRing(p1.baseRing).isEuclideanRing) then\n Error(\"Polymonials must be constructed over a field, not over a ring\");\nfi;\n\n z:=Indeterminate(p1.baseRing);\n z.name:=\"z\";\n\n h := DownsampleTwo(ListPoly(p1));\n g := DownsampleTwo(ListPoly(p2));\n he := Polynomial(p1.baseRing, h[1][1], h[1][2]); \n ho := Polynomial(p1.baseRing, h[2][1], h[2][2]); \n ge := Polynomial(p1.baseRing, g[1][1], g[1][2]); \n go := Polynomial(p1.baseRing, g[2][1], g[2][2]); \n\n# Find he(z) and ho(z)\n# Lo:=Sublist(p1.coefficients, Filtered([1..Length(p1.coefficients)],IsEvenInt));\n# Le:=Sublist(p1.coefficients, Filtered([1..Length(p1.coefficients)],IsOddInt));\n# if (p1.valuation mod 2 = 1) then L:=Le; Le:=Lo; Lo:=L; \n# ve := Int((p1.valuation + 1)/2); vo := ve;\n# else ve := Int(p1.valuation/2); vo := ve + 1;\n# fi;\n# he:=Polynomial(p1.baseRing, Le, ve);\n# ho:=Polynomial(p1.baseRing, Lo, vo); \n# \n# Find ge(z) and go(z)\n\n# Lo:=Sublist(p2.coefficients, Filtered([1..Length(p2.coefficients)],IsEvenInt));\n# Le:=Sublist(p2.coefficients, Filtered([1..Length(p2.coefficients)],IsOddInt));\n# if (p2.valuation mod 2 = 1) then L:=Le; Le:=Lo; Lo:=L; \n# ve := Int((p2.valuation + 1)/2); vo := ve;\n# else ve := Int(p2.valuation/2); vo := ve+1;\n# fi;\n# ge:=Polynomial(p2.baseRing, Le, ve);\n# go:=Polynomial(p2.baseRing, Lo, vo); \n \nreturn [[he,ho],[ge,go]];\nend;\n\n\n# PolyPolyphaseMat:=function(M)\n# Returns a list of 2 polynomials from a polyphase matrix \n\nPolyPolyphaseMat:=function(M)\n\nlocal he,ho,ge,go,h,g,z;\n\nhe:=M[1][1];\nho:=M[1][2];\nge:=M[2][1];\ngo:=M[2][2];\nz:=Indeterminate(he.baseRing);\nz.name:=\"z\";\n\nh:=Upsample(he)+z^(1)Upsample(ho);\ng:=Upsample(ge)+z^(1)Upsample(go);\n\nreturn([h,g]);\nend;\n\n\n", "meta": {"hexsha": "d4967b1029a902ab2541f146c6068cab3de8c23a", "size": 9996, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/filtering/lifting.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/transforms/filtering/lifting.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/transforms/filtering/lifting.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 27.2370572207, "max_line_length": 159, "alphanum_fraction": 0.5948379352, "num_tokens": 3532, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. 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	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n#####################\n# General Rule\n#####################\n\nPRF34_CT_Children := (N,k,DFTp,PRF3,PRFt) -> Map2(DivisorPairs(N),\n (m,n) -> When(IsEvenInt(n),\n\t[ DFTp(m, k), PRF3(n, k) ],\n\t[ DFTp(m, k), PRF3(n, k), PRFt(m, k) ])\n);\n\nPRF34_CT_Rule := (N,k,C,Conj,Tw) -> let(\n m:=Rows(C[1]), n:=Cols(C[2]), Nc:=Int((N+1)/2), \n nf:=Int(n/2), nc:=Int((n+1)/2), mf:=Int(m/2), mc:=Int((m+1)/2), j:=Ind(nf),\n \n SUM(\n\tISum(j, RC(Scat(BH(Nc, N-1, m, j, n))) \n\t Conj RC(C[1]) * Tw(j) * \n\t\tRC(Gath(H(ncm, m, j, nc)))\n\t), \n\tWhen(IsEvenInt(n), [], \n\t RC(Scat(H(Nc, mc, nf, n))) C[3] * Gath(H(2ncm, m, 2nf, 2nc)))\n ) \n Tensor(I(m), C[2]) \n L(N,m)\n);\n\nIPRF34_CT_Rule := (N,k,C,Conj,Tw) -> let(\n m:=Rows(C[1]), n:=Rows(C[2]), Nc:=Int((N+1)/2), \n nf:=Int(n/2), nc:=Int((n+1)/2), mf:=Int(m/2), mc:=Int((m+1)/2), j:=Ind(nf),\n \n L(N,n) \n Tensor(I(m), C[2]) \n SUM(\n\tISum(j, \n\t RC(Scat(H(ncm, m, j, nc))) \n\t Tw(j) * \n\t RC(C[1]) * \n\t Conj * \n\t RC(Gath(BH(Nc, N-1, m, j, n)))\n\t), \n\tWhen(IsEvenInt(n), [], \n\t Scat(H(2ncm, m, 2nf, 2nc)) * C[3] * RC(Gath(H(Nc, mc, nf, n))))\n )\n);\n\n#####################\n# Special Cases\n#####################\n\nRulesFor(PRDFT4, rec(\n PRDFT4_Base1 := BaseRule(PRDFT4, [1, @]),\n PRDFT4_Base2 := rec( \n\tisApplicable := P -> P[1]=2,\n\trule := (P, C) -> F(2) * Mat(1/2MatSPL(PDHT4(2,P[2]))) # DHT4(2) is a diagonal\n ),\n PRDFT4_CT := rec(\n\tisApplicable := P -> not IsPrime(P[1]),\n\tallChildren := P -> PRF34_CT_Children(P[1], P[2], DFT2, PRDFT3, PRDFT4), \n\trule := (P,C) -> let(N:=P[1], k:=P[2], m:=Rows(C[1]),\n\t PRF34_CT_Rule(N, k, C, Diag(BHD(m,-1,1)), j->RC(Diag(fPrecompute(Twid(N,m,k,1/2,1/2,j))))))),\n PRDFT4_Trig := rec(\n\tisApplicable := P -> P[1] > 2 and IsEvenInt(P[1]) and P[2]=1,\n\tallChildren := P -> [[ DCT4(P[1]/2), DST4(P[1]/2) ]],\n\trule := (P, C) -> let(n:=P[1]/2, \n\t L(2n, n) * DirectSum(C[1], C[2]) * SymSplit4(n)))\n));\n\nRulesFor(IPRDFT4, rec(\n IPRDFT4_Base1 := BaseRule(IPRDFT4, [1, @]),\n IPRDFT4_Base2 := rec( \n\tisApplicable := P -> P[1]=2,\n\trule := (P, C) -> Mat(1/2MatSPL(PDHT4(2,P[2]))) F(2) # DHT4(2) is a diagonal\n ),\n IPRDFT4_CT := rec(\n\tisApplicable := P -> not IsPrime(P[1]),\n\tallChildren := P -> PRF34_CT_Children(P[1], P[2], DFT3, IPRDFT2, IPRDFT4), \n\trule := (P,C) -> let(N:=P[1], k:=P[2], m:=Rows(C[1]),\n\t IPRF34_CT_Rule(N, k, C, Diag(BHD(m,-1,1)), j->RC(Diag(fPrecompute(Twid(N,m,k,1/2,1/2,j)))))))\n));\n\nRulesFor(PRDFT3, rec(\n PRDFT3_Base1 := BaseRule(PRDFT3, [1, @]),\n PRDFT3_Base2 := rec(\n\tisApplicable := P -> P[1]=2,\n\trule := (P, C) -> Cond(\n\t P[2] mod 4 = 1, I(2), \n\t P[2] mod 4 = 3, Diag(1,-1), \n\t Error(\"Bad second parameter for PRDFT3(n,k), gcd(n,k)=1 does not hold\"))\n ),\n PRDFT3_CT := rec(\n\tisApplicable := P -> not IsPrime(P[1]),\n\tallChildren := P -> PRF34_CT_Children(P[1], P[2], DFT1, PRDFT3, PRDFT3), \n\trule := (P,C) -> let(N:=P[1], k:=P[2], m:=Rows(C[1]),\n\t PRF34_CT_Rule(N, k, C, Diag(BHD(m,1,-1)), j->RC(Diag(fPrecompute(Twid(N,m,k,1/2,0,j))))))),\n PRDFT3_Trig := rec(\n\tisApplicable := P -> P[1] > 2 and IsEvenInt(P[1]) and P[2]=1,\n\tallChildren := P -> [[ DCT3(P[1]/2), DST3(P[1]/2) ]],\n\trule := (P, C) -> let(n:=P[1]/2, \n\t L(2n, n) DirectSum(C[1], C[2]) * SymSplit3(n))),\n\n PRDFT3_OddToPRDFT1 := rec(\n\tisApplicable := P -> IsOddInt(P[1]),\n\tallChildren := P -> [[ PRDFT(P[1], P[2]) ]],\n\trule := (P, C) -> rperm_ev(P[1]) * C[1] * pdiag(P[1], P[2])\n )\n));\n\nRulesFor(IPRDFT2, rec(\n IPRDFT2_Base1 := BaseRule(IPRDFT2, [1, @]),\n IPRDFT2_Base2 := rec(\n\tisApplicable := P -> P[1]=2,\n\trule := (P, C) -> Cond(\n\t P[2] mod 4 = 1, Diag(2,-2),\n\t P[2] mod 4 = 3, Diag(2,2),\n\t Error(\"Bad second parameter for IPRDFT2(n,k), gcd(n,k)=1 does not hold\"))\n ),\n IPRDFT2_CT := rec(\n\tisApplicable := P -> not IsPrime(P[1]),\n\tallChildren := P -> PRF34_CT_Children(P[1], P[2], DFT1, IPRDFT2, IPRDFT2), \n\trule := (P,C) -> let(N:=P[1], k:=P[2], m:=Rows(C[1]),\n\t IPRF34_CT_Rule(N, k, C, Diag(BHD(m,1,-1)), j->RC(Diag(fPrecompute(Twid(N,m,k,1/2,0,j)))))))\n));\n\nRulesFor(PDHT4, rec(\n PDHT4_Base2 := BaseRule(PDHT4, [2, @]),\n PDHT4_CT := rec(\n\tisApplicable := P -> not IsPrime(P[1]),\n\tallChildren := P -> PRF34_CT_Children(P[1], P[2], DFT2, PDHT3, PDHT4), \n\trule := (P,C) -> let(N:=P[1], k:=P[2], m:=Rows(C[1]),\n\t PRF34_CT_Rule(N, k, C, TopHalf(m, -J(2)), \n\t\t j -> RCDiag(RCData(fPrecompute(Twid(N,m,-k,1/2,1/2,j))), -J(2))))),\n PDHT4_Trig := rec(\n\tisApplicable := P -> P[1] > 2 and IsEvenInt(P[1]) and P[2]=1,\n\tallChildren := P -> [[ DCT4(P[1]/2), DST4(P[1]/2) ]],\n\trule := (P, C) -> let(n:=P[1]/2, \n\t Tensor(I(n), F(2)) * L(2n,n) DirectSum(C[1], C[2]) * SymSplit4(n)))\n));\n\nRulesFor(PDHT3, rec(\n PDHT3_Base2 := rec(\n\tisApplicable := P -> P[1]=2,\n\trule := (P, C) -> Cond(\n\t P[2] mod 4 = 1, F(2), \n\t P[2] mod 4 = 3, J(2)F(2),\n\t Error(\"Bad second parameter for PRDFT3(n,k), gcd(n,k)=1 does not hold\"))\n ),\n\n PDHT3_CT := rec(\n\tisApplicable := P -> not IsPrime(P[1]),\n\tallChildren := P -> PRF34_CT_Children(P[1], P[2], DFT1, PDHT3, PDHT3), \n\trule := (P,C) -> let(N:=P[1], k:=P[2], m:=Rows(C[1]),\n\t PRF34_CT_Rule(N, k, C, TopHalf(m, J(2)), \n\t\t j -> RCDiag(RCData(fPrecompute(Twid(N,m,-k,1/2,0,j))), J(2))))),\n PDHT3_Trig := rec(\n\tisApplicable := P -> P[1] > 2 and IsEvenInt(P[1]) and P[2]=1,\n\tallChildren := P -> [[ DCT3(P[1]/2), DST3(P[1]/2) ]],\n\trule := (P, C) -> let(n:=P[1]/2, \n\t Tensor(I(n), F(2)) L(2n,n) DirectSum(C[1], C[2]) * SymSplit3(n)))\n\n));\n", "meta": {"hexsha": "169e1d54c628f7887740d51f9158deed08e58bb1", "size": 5622, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/realdft/prf34.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], 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	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nRulesFor(DCT4, rec(\n\n #F DCT4_Base2: DCT4_2 = (1,2) * R_13/8\n #F\n DCT4_Base2 := rec(\n\tinfo := \"DCT4_2 -> R_13/8\",\n\tforTransposition := false,\n\tisApplicable := P -> P[1] = 2, \n\trule := (P, C) -> J(2) * Rot(13/8)\n ),\n\n #F DCT4_Base3: (base case for size 3)\n #F\n #F DCT4_2 = (2,3) * (F_2 dirsum 1) * (a dirsum M) * (F_2 dirsum 1) * (2,3)\n #F\n #F derived by hand starting with AREP's decomposition by mon-mon symmetry.\n #F\n DCT4_Base3 := rec (\n\tinfo := \"DCT4_3 -> F_2, M, F_2\",\n\tforTransposition := false,\n\tisApplicable := P -> P[1] = 3, \n\trule := (P, C) -> \n\t Perm((2,3), 3) * \n\t DirectSum(F(2), I(1)) \n\t DirectSum(Diag(Sqrt(3/8)), Sqrt(1/2)Mat([[1/2, 1], [1, -1]])) \n\t DirectSum(F(2), I(1)) \n\t Perm((2,3), 3)\n ),\n\n #F DCT4_DCT2: DCT4_n = sums * DCT2_n * diag\n #F\n #F inverse - transpose of RuleDCT4_2\n #F\n DCT4_DCT2 := rec (\n\tinfo := \"DCT4_n --> DCT2'_n\",\n\tisApplicable := P -> P[1] > 2,\n\tallChildren := P -> [[ DCT2(P[1]) ]],\n\trule := (P, C) -> \n\t sums1(P[1]) \n\t C[1] \n\t Diag(List([0..P[1]-1], i -> 1/(2CosPi((2i+1)/(4P[1])))))\n ),\n\n #F DCT4_DCT2t: 1985, DCT4_n = sums DCT2_n * diag\n #F\n #F Chan: \n #F Direct Methods for computing discrete sinusoidal transforms\n #F IEE Proceedings, Vol. 137, 1990, pp. 433--442\n #F\n # switched off since critical path too long (sums6)\n # also there seems to be one mult too much\n DCT4_DCT2t := rec (\n\tinfo := \"DCT4_n --> DCT2'_n\",\n\tswitch := false,\n\tisApplicable := P -> P[1] > 2,\n\tallChildren := P -> [[ DCT2(P[1]) ]],\n\trule := ( P, C ) -> \n\t sums6(P[1]) \n\t C[1] \n\t Diag(List([0..P[1] - 1], i -> 2 * CosPi((2i + 1)/(4P[1]))))\n ),\n\n #F DCT4_DCT2andDST2: 1985\n #F\n #F DCT4_n = blocks * perm * (DCT2_n/2 dirsum DST2_n/2) * rotations\n #F\n #F Wang: (transposed)\n #F On Computing the Discrete Fourier ans Cosine Transforms,\n #F IEEE Trans. on Signal Proc., 1985, pp. 1341--1344\n #F\n DCT4_DCT2andDST2 := rec (\n\tinfo := \"DCT4_n --> DCT2'_n/2, DST2'_n/2\",\n\tisApplicable := P -> IsInt(P[1]) and P[1] > 2 and P[1] mod 2 = 0, \n\tallChildren := P -> [[ DCT2(P[1]/2), DST2(P[1]/2) ]],\n\trule := (P, C) -> \n\t DirectSum(I(1), \n\t\t Tensor(I(P[1]/2-1), F(2)J(2)),\n\t\t I(1)) \n\t DirectSum(C[1], C[2]) ^ L(P[1], 2) \n\t DirectSum(List([0..P[1]/2-1], i -> J(2)Rot(2-(2P[1]-2i-1)/(4P[1])))) \n\t LIJ(P[1])\n\n\t # LIJ(P[1]) * \n\t # DirectSum(C[1], C[2] ^ J(P[1]/2)) \n\t # DirectSum(List([0..P[1]/2-1], i -> J(2)Rot(2-(2P[1]-2i-1)/(4P[1])))) \n\t # ^ LIJ(P[1])\n ),\n\n #F DCT4_DST4andDST2: 1988\n #F\n #F DCT4_n = diag sums * perm * (DST4_n/2 dirsum DST2_n/2) * sign \n #F (DFT_2 tensor I_n/2) diag * perm\n #F\n #F Rao/Yip:\n #F The Decimation-in-Frequency Algorithms for a family of \n #F Discrete Sine and Cosine Algorithms.\n #F Circuits, Systems, and Signal Processing, 1988, pp. 3--19\n #F\n DCT4_DST4andDST2 := rec (\n\tinfo := \"DCT4_n --> DST4_n/2, DST2_n/2\",\n\tswitch := false,\n\tisApplicable := P -> IsInt(P[1]) and P[1] > 2 and P[1] mod 2 = 0,\n\n\tallChildren := P -> [[ DST4(P[1]/2), DST2(P[1]/2) ]],\n\n\trule := (P, C) -> \n\t Diag(List([0..P[1] - 1], i -> (-1)^i)) \n\t sums1(P[1]).transpose() \n\t L(P[1], P[1]/2) \n\t DirectSum(C[1], C[2] (-1)) \n\t Tensor(F(2), I(P[1]/2)) \n\t Diag(Concat(List([1..P[1]/2], i -> 1/(2SinPi((2i - 1)/(4P[1])))),\n\t\t List([1..P[1]/2], i -> 1/(2CosPi((2i - 1)/(4P[1])))))) \n\t IJ(P[1], P[1]/2)\n ),\n\n #F DCT4_Iterative: 1985, DCT4_n = iterative\n #F\n #F Chen/Smith/Fralick: \n #F A Fast Computational Algorithm for the Discrete Cosine Transform,\n #F IEEE Trans. on Comm., 1977, pp. 1004--1009\n #F corrected in:\n #F Wang: \n #F Reconsideration of --above--, IEEE Trans. on Comm., 1983, pp. 121--123\n #F Wang: \n #F Fast Algorithms for the Discrete W Transform and the\n #F Discrete Fourier Transform.\n #F IEEE Trans. on ASSP, 1984, pp. 803--814\n #F\n DCT4_Iterative := rec (\n\tinfo := \"DCT4_n iterative\",\n\tisApplicable := P -> P[1] > 2 and Is2Power(P[1]),\n\trule := (P, C) -> \n\t LIJ(P[1]) L(P[1], 2) \n\t DirectSum(List([1..P[1]/2], i -> Rot(1/2-(4i-3)/(4P[1])) J(2))) \n\n\t Compose(List([1..Log2Int(P[1])-1], j -> let(jj := 2^j,\n\t\t Tensor(I(jj/2), F(2), I(P[1]/jj)) \n\t\t Tensor(I(jj/2), \n\t\t\tDirectSum(I(P[1]/jj), List([1..P[1]/jj/2], \n\t\t\t i -> Rot(1/2-(4i-3)/(2P[1]/jj)) * J(2))))))) *\n\t perm6(P[1])\n )\n));\n\n", "meta": {"hexsha": "a6c24574f1645ce22363e06a1115de62f1b0b169", "size": 4777, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/dct_dst/dct4rules.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/transforms/dct_dst/dct4rules.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/transforms/dct_dst/dct4rules.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 31.6357615894, "max_line_length": 81, "alphanum_fraction": 0.4925685577, "num_tokens": 1989, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. 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	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nRulesFor(DFT, rec(\n DFT_CT_Inplace := rec(\n\tinfo := \"DFT(mn,k) -> DFT(m, k%m), DFT(n, k%n)\",\n\tmaxCodeletSize := 16,\n\n\tisApplicable := (self, P) >> P[1] > 2 and not IsPrime(P[1]),\n\n\tallChildren := (self, P) >> Map2( \n\t Filtered(DivisorPairs(P[1]), d -> d[1] <= self.maxCodeletSize), \n\t (m,n) -> [ \n\t\tDFT(m, P[2] mod m), \n\t\tDFT(n, P[2] mod n) ]),\n \n\trule := (self,P,C) >> let(mn := P[1], m := Rows(C[1]), n := Rows(C[2]), \n di := fPrecompute(Tw1(mn, n, P[2])),\n\n\t When(mn > self.maxCodeletSize, # why BB?\n\t\tInplace(Tensor(C[1], I(n)) * Diag(di)), \n\t\t Tensor(C[1], I(n)) * Diag(di)) \n\t Tensor(I(m), C[2]) \n\t L(mn, m))\n ),\n\n DFT_SplitRadix_Inplace := rec(\n\tinfo := \"DFT_n -> DFT_n/2, DFT_n/4, DFT_n/4\",\n\tforTransposition := true,\n\tmaxSize := 64, \n\n\tisApplicable := (self, P) >> let(N := P[1],\n\t N >= 8 and N mod 4 = 0 and N <= self.maxSize),\n\n\tallChildren := P -> let(N := P[1], w := P[2], \n\t [[ DFT(N/2, w), DFT(N/4, w) ]]),\n\n\trule := (P, C) -> let(N := P[1], w := P[2], \n\t Inplace(Tensor(F(2), I(N/2))) \n\t DirectSum( \n\t\tC[1], \n\t\tInplace(BB(\n\t\t\tTensor(Diag(1, E(4)^w) F(2), I(N/4)) \n\t\t\tDiag(Concat(List([0..N/4-1], i->E(N)^(wi))), \n\t\t\t List([0..N/4-1], i->E(N)^(3wi))))) \n\t Tensor(I(2), C[2])L(N/2,2)\n\t ) *\n\t L(N, 2))\n ),\n\n));\n", "meta": {"hexsha": "ceea58e898a6dd1df0db6d7fe7e796cda9ce0ed1", "size": 1427, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/dft/inplace.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/transforms/dft/inplace.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/transforms/dft/inplace.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 26.4259259259, "max_line_length": 73, "alphanum_fraction": 0.4723195515, "num_tokens": 578, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8723473680407889, "lm_q2_score": 0.5851011542032312, "lm_q1q2_score": 0.5104114519068165}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nTrPRDFT1 := arg -> let(x:=ApplyFunc(PRDFT1, arg).transpose(), Chain(PrintLine(x, \" \", x.dimensions), x));\nTrPRDFT2 := arg -> ApplyFunc(PRDFT2, arg).transpose();\nTrPRDFT3 := arg -> ApplyFunc(PRDFT3, arg).transpose();\nTrPRDFT4 := arg -> ApplyFunc(PRDFT4, arg).transpose();\n\nDFTSymmetries := rec( #n-even, #n-odd\n DFT := [\n\t[Real , [CE0_R2Cpx(W_RFT, 1), [PRDFT1, PRDFT1], 1]],\n\t[CE0_R2Cpx(W_URFTT, 1), [Real, [TrPRDFT1, TrPRDFT1], 1]],\n\t[Even0, [Even0, [DCT1, DCT5], 1]],\n\t[Odd00, [Odd00, [DST1, DST5], E(4)]] # j\n ],\n\n DFT2 := [\n\t[Real , [CO0_R2Cpx(W_RFT, -E(4)), [PRDFT2, PRDFT2], 1]],\n\t[CE1_R2Cpx(W_URFTT, 1), [Real, [TrPRDFT3, TrPRDFT3], 1]],\n\t[Even1, [Odd0, [DCT2, DCT6], 1]], \n\t[Odd1 , [Even00, [DST2, DST6], E(4)]]\n ],\n\n DFT3 := [\n\t[Real , [CE1_R2Cpx(W_RFT, 1), [PRDFT3, PRDFT3], 1]],\n\t[CO1_R2Cpx(W_URFTT, E(4)), [Real, [TrPRDFT2, TrPRDFT2], 1]],\n\t[Real , [CE1_R2Cpx(W_RFT, 1), [PRDFT3, PRDFT3], 1]],\n\t[Odd0 , [Even1, [DCT3, DCT7], 1]],\n\t[Even00,[Odd1, [DST3, DST7], E(4)]]\n ],\n\n DFT4 := [\n\t[Real , [CO1_R2Cpx(W_RFT, -E(4)), [PRDFT4, PRDFT4], 1]],\n\t[CO1_R2Cpx(W_URFTT, E(4)), [Real, [TrPRDFT4, TrPRDFT4], 1]],\n\t[Odd1 , [Odd1, [DCT4, DCT8], 1]],\n\t[Even1, [Even1, [DST4, DST8], E(4)]] \n ]\n);\n\n_dftSym := function(nt, sym) \n local pos, entry, dftsym;\n if not IsBound(DFTSymmetries.(nt.name)) \n\tthen return false; fi;\n\n dftsym := DFTSymmetries.(nt.name);\n pos := PositionProperty(dftsym, x->x[1]=sym);\n if pos = false then \n\treturn false; fi;\n\n entry := dftsym[pos][2];\n if IsEvenInt(Rows(nt)) then return [entry[1], entry[2][1], entry[3]];\n else return [entry[1], entry[2][2], entry[3]];\n fi;\nend;\n\n\n# let Q := JDFTp_Reconstruct(n), p = 1..4 (DFT type)\n# Q is defined to be the matrix that satisfies\n# Q DFTp(n) = DFTp(n) * J(n)\n# Q = J(n) ^ (DFTp(n)^-1)\n#\n#spiral> PrintMat( MatSPL(J(8))^(MatSPL(DFT(8))^-1) );\n\nClass(JRecTwid1, DiagFunc, rec(\n def := n -> rec(size:=n),\n range := self >> TComplex,\n lambda := self >> let(n:=self.params[1], i:=Ind(n), \n\tLambda(i, omega(n, -i)))\n));\n\nClass(JRecTwid3, DiagFunc, rec(\n def := n -> rec(size:=n),\n range := self >> TComplex,\n lambda := self >> let(n:=self.params[1], i:=Ind(n), \n\tLambda(i, omega(2n, (-2i + n - 1))))\n));\n\nmk_InvDFT_Reconstruct := dft -> (let(n:=dft.params[1], Cond(\n ObjId(dft) = DFT1, DirectSum(I(1), J(n-1)),\n ObjId(dft) = DFT2, DirectSum(I(1), -J(n-1)),\n ObjId(dft) = DFT3, J(n),\n ObjId(dft) = DFT4, -J(n),\n Error(\"<dft> must be a non-terminal DFT1, DFT2, DFT3, or DFT4\"))));\n\nmk_JInvDFT_Reconstruct := dft -> (let(n:=dft.params[1], Cond(\n ObjId(dft) = DFT1, Diag(JRecTwid1(n)),\n ObjId(dft) = DFT2, I(n), \n ObjId(dft) = DFT3, Diag(JRecTwid3(n)),\n ObjId(dft) = DFT4, -I(n), \n Error(\"<dft> must be a non-terminal DFT1, DFT2, DFT3, or DFT4\"))));\n\nmk_JDFT_Reconstruct := dft -> (let(n:=dft.params[1], Cond(\n ObjId(dft) = DFT1, Diag(JRecTwid1(n)) * mk_InvDFT_Reconstruct(dft),\n ObjId(dft) = DFT2, mk_InvDFT_Reconstruct(dft),\n ObjId(dft) = DFT3, Diag(JRecTwid3(n)) * mk_InvDFT_Reconstruct(dft),\n ObjId(dft) = DFT4, -mk_InvDFT_Reconstruct(dft),\n Error(\"<dft> must be a non-terminal DFT1, DFT2, DFT3, or DFT4\"))));\n\nverify_JInvDFT_Reconstruct := dft -> let(T:=ObjId(dft), n:=dft.params[1], k:=dft.params[2], \n MatSPL(dft * J(n)) - MatSPL(mk_JInvDFT_Reconstruct(dft) * T(n, -k))\n);\nverify_JDFT_Reconstruct := dft -> let(T:=ObjId(dft), n:=dft.params[1], k:=dft.params[2], \n MatSPL(dft * J(n)) - MatSPL(mk_JDFT_Reconstruct(dft) * dft)\n);\n\n\n\nClass(RulesDFTSymmetry, RuleSet);\nRewriteRules(RulesDFTSymmetry, rec(\n\n DFT1_upgrade := ARule(Compose, [@(1,DFT), [@(2,GathExtend), @, @(3).cond(e->e in [Even1, Odd1])]], \n\t e -> let(n := Cols(@(1).val), [ Diag(Twid(n,n,-1,1/2,0,0)), DFT2(n), @(2).val])),\n\n DFT3_upgrade := ARule(Compose, [@(1,DFT3), [@(2,GathExtend), @, @(3).cond(e->e in [Even1, Odd1])]], \n\t e -> let(n := Cols(@(1).val), [ Diag(Twid(n,n,-1,1/2,1/2,0)), DFT4(n), @(2).val])),\n\n DFT1_upgradeCE := ARule(Compose, [@(1,DFT), [@(2,GathExtend), @, @(3, [CE1_R2Cpx, CO1_R2Cpx])]], \n\t e -> let(n := Cols(@(1).val), [ Diag(Twid(n,n,-1,1/2,0,0)), DFT2(n), @(2).val])),\n\n DFT3_upgradeCE := ARule(Compose, [@(1,DFT3), [@(2,GathExtend), @, @(3, [CE1_R2Cpx, CO1_R2Cpx])]], \n\t e -> let(n := Cols(@(1).val), [ Diag(Twid(n,n,-1,1/2,1/2,0)), DFT4(n), @(2).val])),\n\n DFT_EO_Symmetry := ARule(Compose,\n\t [ @(1,[DFT,DFT2,DFT3,DFT4]), \n\t [ @(2, GathExtend), @, @(3).cond(e->_dftSym(@(1).val, e)<>false)] ], \n\t e -> \n\t let(sym := _dftSym(@(1).val, @(3).val), \n\t\t out := sym[1],\n\t\t transf := sym[2],\n\t\t n := When(@(3).val.tsize = \"cols\", Cols(@(2).val), Rows(@(2).val)),\n\t\t scale := sym[3],\n\t\t [PushL(GathExtendU(Rows(@(1).val), out)), scaletransf(n)])),\n\n L_Real := ARule(Compose, [[L, @(1), @(2)], [@(3,GathExtend), @, Real]], \n\t e -> let(N:=@(1).val, k:=@(2).val, \n\t [ GathExtend(N, Real), L(N, k) ])),\n\n L_Conj0_R2Cpx := ARule(Compose, [[L, @(1), @(2)], [@(3,GathExtend), @, @(4, [CE0_R2Cpx, CO0_R2Cpx])]], \n\t e -> let(N:=@(1).val, k:=@(2).val, m:=N/k, nn:=Cols(@(3).val)/2, \n\t sym := @(4).val, \n\t sym1 := When(ObjId(sym)=CE0_R2Cpx, CE1_R2Cpx(sym.w, sym.j), CO1_R2Cpx(sym.w, sym.j)), \n\t\t diag := When(ObjId(sym)=CE0_R2Cpx, Diag(BHD(m, 1, -1)), Diag(BHD(m, -1, 1))),\n\t [ DirectSum(GathExtend(m, sym), GathExtend(N-m, sym1)),\n\t DirectSum(I(Int(m+1+_even(m))), Tensor(I(Int((k-1)/2)), diag), I(_even(k)(m+_odd(m)))),\n\t RC(VStack(Gath(Refl(nn, N, Int((m+2)/2), L(N,k))), \n\t\t Gath(Refl(nn, N, nn-Int((m+2)/2), fCompose(L(N,k), fAdd(N, N-m, m)))))) ])), \n\n L_Conj1_R2Cpx := ARule(Compose, [[L, @(1), @(2)], [@(3,GathExtend), @, @(4, [CE1_R2Cpx, CO1_R2Cpx])]], \n\t e -> let(N:=@(1).val, k:=@(2).val, m:=N/k, nn:=Cols(@(3).val)/2,\n\t sym := @(4).val, \n\t\t diag := When(sym=CE1_R2Cpx, Diag(BHD(m, 1, -1)), Diag(BHD(m, -1, 1))),\n\t [ GathExtend(N, sym), \n\t DirectSum(Tensor(I(Int(k/2)), diag), When(IsOddInt(k), I(m+_odd(m)), [])),\n\t RC(Gath(Refl(nn, N-1, nn, L(N,k)))) ])), \n\n L_Even0 := ARule(Compose, [[L, @(1), @(2)], [@(3,GathExtend), @, Even0]], \n\t e -> let(N:=@(1).val, k:=@(2).val, m:=N/k, nn:=Cols(@(3).val),\n\t [ DirectSum(GathExtend(m, Even0), GathExtend(N-m, Even1)),\n\t VStack(Gath(Refl(nn, N, Int((m+2)/2), L(N,k))), \n\t\t Gath(Refl(nn, N, nn-Int((m+2)/2), fCompose(L(N,k), fAdd(N, N-m, m))))) ])), \n\n L_Even00 := ARule(Compose, [[L, @(1), @(2)], [@(3,GathExtend), @, Even00]], \n\t e -> let(N:=@(1).val, k:=@(2).val, m:=N/k, nn:=Cols(@(3).val),\n\t [ DirectSum(GathExtend(m, Even00), GathExtend(N-m, Even1)),\n\t VStack(Gath(Refl(nn, N-2, Int(m/2), fCompose(fAdd(N,N,-1), L(N,k), fAdd(N, N-1, 1)))), \n\t\t Gath(Refl(nn, N-2, nn-Int(m/2), fCompose(fAdd(N,N,-1), L(N,k), fAdd(N, N-m, m))))) ])), \n\n L_Odd0 := ARule(Compose, [[L, @(1), @(2)], [@(3,GathExtend), @, Odd0]], \n\t e -> let(N:=@(1).val, k:=@(2).val, m:=N/k, nn:=Cols(@(3).val),\n\t [ DirectSum(GathExtend(m, Odd0), GathExtend(m(k-1), Odd1)),\n\t DirectSum(I(Int((m+1)/2)), Tensor(I(Int((k-1)/2)), Diag(BHN(m))), When(IsEvenInt(k), I(Int(m/2)), [])),\n\t VStack(Gath(Refl(nn, N, Int((m+1)/2), L(N,k))), \n\t\t Gath(Refl(nn, N, nn-Int((m+1)/2), fCompose(L(N,k), fAdd(N, N-m, m))))) ])), \n\n L_Odd00 := ARule(Compose, [[L, @(1), @(2)], [@(3,GathExtend), @, Odd00]], \n\t e -> let(N:=@(1).val, k:=@(2).val, m:=N/k, nn:=Cols(@(3).val),\n\t [ DirectSum(GathExtend(m, Odd00), GathExtend(m(k-1), Odd1)),\n\t DirectSum(I(Int((m-1)/2)), Tensor(I(Int((k-1)/2)), Diag(BHN(m))), When(IsEvenInt(k), I(Int(m/2)), [])),\n\t VStack(Gath(Refl(nn, N-2, Int((m-1)/2), fCompose(fAdd(N,N,-1), L(N,k), fAdd(N, N-1, 1)))), \n\t\t Gath(Refl(nn, N-2, nn-Int((m-1)/2), fCompose(fAdd(N,N,-1), L(N,k), fAdd(N, N-m, m))))) ])), \n\n L_Even1 := ARule(Compose, [[L, @(1), @(2)], [@(3,GathExtend), @, Even1]], \n\t e -> let(N:=@(1).val, k:=@(2).val, m:=N/k, nn:=Cols(@(3).val),\n\t [ GathExtend(N, Even1), \n\t Gath(Refl(nn, N-1, nn, L(N,k))) ])), \n\n L_Odd1 := ARule(Compose, [[L, @(1), @(2)], [@(3,GathExtend), @, Odd1]], \n\t e -> let(N:=@(1).val, k:=@(2).val, m:=N/k, nn:=Cols(@(3).val),\n\t [ GathExtend(N, Odd1), \n\t DirectSum(Tensor(I(Int(k/2)), Diag(BHN(m))), When(IsOddInt(k), I(Int(m/2)), [])),\n\t Gath(Refl(nn, N-1, nn, L(N,k))) ])), \n\n CRT_Even1 := ARule(Compose, [@(1, CRT), [@(2,GathExtend), @, Even1]], \n\t e -> let(N:=Rows(@(2).val), nn:=Cols(@(2).val),\n\t [ GathExtend(N, Even1), \n\t Gath(Refl(nn, N-1, nn, @(1).val)) ])), \n\n Tensor_Dirsum_split := ARule(Compose, \n\t [[Tensor, [I, @(1)], @(2)], [DirectSum, @(3).cond(e->Rows(e)=Cols(@(2).val)), @(4)]],\n\t e -> [ DirectSum(@(2).val * @(3).val, Tensor(I(@(1).val-1), @(2).val) * @(4).val) ]),\n\n IxDFT_EO1 := ARule(Compose,\n\t [[Tensor, [I, @(1)], [@(2,[DFT,DFT2,DFT3,DFT4]), @, 1, ...]], [@(3,GathExtend), @, @(4).cond(e->e in [Even1, Odd1])]],\n\t e -> let(k:=@(1).val, n:=Cols(@(2).val), transf:=@(2).val, sign := When(@(4).val=Odd1, -1, 1),\n\t When(k mod 2 = 0,\n\t [ # Below is actually a scaled type 1 extension! exploit this for final rewriting phase\n PushL(DirectSum(I(nk/2), Tensor(I(k/2), mk_JDFT_Reconstruct(transf)J(n))) * \n @(3).val) * \n\t\t Tensor(I(k/2), transf) ],\n\n # again, a scaled type 1 extension!\n\t\t [ PushL(VStack(I(n(k+1)/2),\n\t\t\t Tensor(J((k-1)/2), sign mk_JDFT_Reconstruct(transf)) \n\t\t\t\t * Gath(fAdd(n(k+1)/2, n(k-1)/2, 0)))), \n\t\t DirectSum(Tensor(I((k-1)/2), 1/2transf), \n\t\t\t transf GathExtend(n, @(4).val))]))),\n\n # IxDFT_EO1 := ARule(Compose,\n# \t [[Tensor, [I, @(1)], [@(2,[DFT,DFT2,DFT3,DFT4]), @, 1, ...]], [GathExtend, @(3), @(4).cond(e->e in [Even1, Odd1])]],\n# \t e -> let(k:=@(1).val, n:=Cols(@(2).val), transf:=@(2).val, sign := When(@(4).val=Odd1, -1, 1),\n# \t When(k mod 2 = 0,\n# \t [ # Below is actually a scaled type 1 extension! exploit this for final rewriting phase\n# PushL(VStack(I(nk/2), Tensor(J(k/2), sign mk_JDFT_Reconstruct(transf)))), \n# \t\t Tensor(I(k/2), 1/2transf) ],\n\n# # again, a scaled type 1 extension!\n# \t\t [ PushL(VStack(I(n(k+1)/2),\n# \t\t\t Tensor(J((k-1)/2), sign * mk_JDFT_Reconstruct(transf)) \n# \t\t\t\t * Gath(fAdd(n(k+1)/2, n(k-1)/2, 0)))), \n# \t\t DirectSum(Tensor(I((k-1)/2), 1/2transf), \n# \t\t\t transf GathExtend(n, @(4).val))]))),\n\n IxDFT_CEO1_RFTT_DHT := ARule(Compose,\n\t [[Tensor, [I, @(1)], @(2,[DFT,DFT2,DFT3,DFT4])], \n\t [GathExtend, @(3), @(4,[CE1_R2Cpx, CO1_R2Cpx],e->e.w in [W_RFTT, W_URFTT, W_DHT, W_DHT])]], \n\n\t e -> let(k:=@(1).val, n:=Cols(@(2).val), \n\t transf := @(2).val, sign := When(ObjId(@(4).val)=CO1_R2Cpx, -1, 1),\n\t newtransf := RC(ObjId(transf)(transf.params[1], -transf.params[2])), \n\t\t winv := @(4).val.w^-1,\n\t\t pack1 := Mat([winv[1]]),\n\t\t pack2 := Mat([winv[2]]),\n\n\t When(k mod 2 = 0,\n\t [ PushL(VStack(Tensor(I(nk/2), pack1), \n\t\t\t Tensor(J(k/2), sign Tensor(I(n), pack2)\n\t\t\t\t RC(mk_JInvDFT_Reconstruct(transf))))), \n\t\t Tensor(I(k/2), newtransf) ],\n\n\t\t [ PushL(VStack(DirectSum(Tensor(I(n(k-1)/2), pack1), I(n)),\n\t\t\t Tensor(J((k-1)/2), sign * Tensor(I(n), pack2) \n\t\t\t\t RC(mk_JInvDFT_Reconstruct(transf))) Gath(fAdd(nk, n(k-1), 0)))), \n\t\t DirectSum(Tensor(I((k-1)/2), newtransf), \n\t\t\t transf * GathExtend(n, @(4).val))]))),\n\n IxDFT_Real := ARule(Compose,\n\t [[Tensor, [I, @(1)], [@(2,[DFT,DFT2,DFT3,DFT4]), @, 1, ...]], [GathExtend, @(3), Real]],\n\t e -> [ Tensor(I(@(1).val), @(2).val * GathExtend(Cols(@(2).val), Real)) ]),\n\n DFTxI_Ext := ARule(Compose,\n\t [[@(1,Tensor), [@(2,[DFT,DFT2,DFT3,DFT4]), @, 1, ...], I], @(4, GathExtend)],\n\t e -> [ @(1).val.parallelForm() * @(4).val]),\n\n Tensor_J1 := Rule([Tensor, [J, 1], @(1)], e -> @(1).val), \n Tensor_I1 := Rule([Tensor, [I, 1], @(1)], e -> @(1).val),\n Tensor_I0 := Rule([Tensor, ..., [I, 0], ...], e -> I(0)),\n Compose_I := ARule(Compose, [I], e -> []),\n DirectSum_I0 := ARule(DirectSum, [[I, 0]], e -> []),\n DirectSum_Assoc := ARule(DirectSum, [@(1,DirectSum)], e -> [@(1).val.children()]),\n DirectSum_Single := Rule([DirectSum, @(1)], e -> @(1).val),\n Compose_Assoc := ARule(Compose, [@(1,Compose)], e -> [@(1).val.children()]),\n Compose_Single := Rule([Compose, @(1)], e -> @(1).val),\n J_J := ARule(Compose, [@(1,J), @(2,J)], e -> [ I(@(1).val.params[1]) ]),\n\n # ===============\n # Diags\n # ================\n Diag_Diag := ARule(Compose, [[Diag, @(1)], [Diag, @(2)]], e -> \n [ Diag(diagMul(@(1).val, @(2).val)) ]),\n\n Diag_L_Diag := ARule(Compose, [[Diag, @(1)], @(2, L), [Diag, @(3)]], e -> \n [ Diag(diagMul(@(1).val, fCompose(@(3).val, @(2).val))) * @(2).val ]),\n\n Tensor_Diag := Rule([Tensor, [I, @(1)], [Diag, @(2)]], \n e -> Diag(diagTensor(fConst(@(1).val, 1), @(2).val))),\n DirectSum_Diag := Rule([DirectSum, [I, @(1)], [Diag, @(2)]], \n e -> Diag(diagDirsum(fConst(@(1).val, 1), @(2).val))),\n \n E1_Diag_E1 := ARule(Compose, [[@(1,GathExtend,e->e.transposed), @, Odd1], \n [Diag, @(2)], \n [@(1,GathExtend,e->not e.transposed), @, Odd1]],\n e -> let(n:=@(2).val.domain(), f := @(2).val, \n [Diag(diagMul(fConst(n/2, 1/4), \n diagAdd(fCompose(f, fTensor(fBase(2, 0), fId(n/2))),\n fCompose(f, fTensor(fBase(2, 1), J(n/2))))))])),\n\n Scale_Scale := Rule([Scale, @(1), [Scale, @(2), @(3)]], e->Scale(@(1).val * @(2).val, @(3))),\n Scale_1 := Rule([Scale, @(1).cond(e->e=1), @(2)], e->@(2).val),\n\n # =============\n # PushL/PushR\n # =============\n PushL_within_PushL := Rule(@@(1,PushL, (e,cx)->IsBound(cx.PushL) and cx.PushL<>[]), e -> e.child(1)),\n\n Compose_PushL_PushL := ARule(Compose, [[PushL, @(1)], [PushL, @(2)]], e -> [ PushL(@(1).val * @(2).val) ]),\n Compose_PushR_PushL := ARule(Compose, [[PushR, @(1)], [PushL, @(2)]], e -> [ PushR(@(1).val * @(2).val) ]),\n XXX_PushL := ARule(Compose, [@(1, [Diag, L]), [PushL, @(2)]], e -> [PushL(@(1).val * @(2).val)]),\n \n Tensor_PushL := Rule([Tensor, @(1, I), [Compose, @(2, PushL), @(3)]], \n\t e -> PushL(Tensor(@(1).val, @(2).val.child(1))) * Tensor(@(1).val, @(3).val)),\n\n DirectSum_PushL := Rule(@(1, DirectSum, \n\t e -> ForAny(e.children(), \n\t\t c -> ObjId(c)=PushL or (ObjId(c)=Compose and ObjId(c.child(1)) = PushL))),\n\n\t e -> let(ch := @(1).val.children(),\n\t split := List(ch, e -> Cond(ObjId(e) = PushL, \n\t\t\t [e, I(Cols(e))], \n\t\t\t ObjId(e) = Compose and ObjId(e.child(1))=PushL, \n\t\t\t\t\t [e.child(1).child(1), Drop(e.children(), 1)], \n\t\t\t\t\t [I(Rows(e)), e])),\n\t\t PushL(DirectSum(List(split, x->x[1]))) * DirectSum(List(split, x->x[2]))))\n));\n\nRewriteRules(RulesDFTSymmetry, rec(\n BRDFT3_ExtendOdd0 := ARule(Compose, [[BRDFT3, @(1).cond(e->IsEvenInt(e)), 1/4], [GathExtend, @, Odd0]], \n\t e -> let(k:=@(1).val,\n\t [ GathExtend(k,Upsample0),SkewDTT(DCT3(k/2),1/2)])),\n\n Odd1_split := ARule(Compose, [[Tensor, [I,@(1)],@(2)],[GathExtend, @, Odd1]],\n\t e -> let(n:=@(1).val,A:=@(2).val,k:=When(IsEvenInt(n),n/2, (n-1)/2),When(IsEvenInt(n),\n\t [VStack(Tensor(I(k),A)(1/2),Tensor(J(k),AJ(Cols(A))(-1/2)))],\n\t [VStack(DirectSum(Tensor(I(k),A)(1/2),AGathExtend(Cols(A),Odd1)),Tensor(J(k),AJ(Cols(A))(-1/2)))]))),\n\n ReduceUpsample0_RC := ARule(Compose, [[ScatReduce, @(1), Upsample0],[RC, @(2)]], \n\t e -> [@(2).valScatReduce(@(1).val,Upsample0)]),\n\n Push_ScatReduceWithinSum := ARule(Compose, [[ScatReduce, @, Upsample0],[@(1,IterDirectSum).cond(e->IsEvenInt(e.domain)),@(2)]],\n\t e -> [IterDirectSum(@(1).val.var,@(1).val.domain,ScatReduce(Rows(@(2).val),Upsample0)@(2).val)]\n),\n\n Cut_SkewPRDFT := ARule(Compose, [[ScatReduce, @, Upsample0],[BSkewPRDFT,@(1),@(2)]],\n\t e -> let(n:=@(1).val,a:=@(2).val,f:=2cospi(2a),\n\t [SkewDTT(DCT3(n/2),2a)When(IsEvenInt(n/2),\n\t\t HStack(I(n/2),DirectSum(Mat([[f/2]]),Tensor(I(((n/2)-2)/2),Mat([[f,-1],[-1,f]])),Mat([[f-1]]))^M((n)/2,n/4)),\n\t\t HStack(I(n/2),DirectSum(Mat([[f/2]]),Conjugate(Tensor(I((n/2-1)/2),Mat([[f,-1],[-1,f]])),M(n/2-1,(n/2-1)/2)))))])),\n\n SplitIterDirectSum := Rule([@(1,IterDirectSum), [Compose,@(2,SkewDTT),@(3,HStack)]],\n\t e->let(i:=@(1).val.var,IterDirectSum(@(1).val.var,@(1).val.domain,@(2).val)IterDirectSum(@(1).val.var,@(1).val.domain,@(3).val))),\n\n BRDFT3_ExtendOdd1 := ARule(Compose, [[BRDFT3, @(1).cond(e->IsEvenInt(e)), 1/4], [GathExtend, @, Odd1]],\n e -> let(k:=@(1).val,i:=Ind(),\n\t [IterDirectSum(i,k/2,Mat([[1/2+cospi((2i+1)/k)],[-1/2]]))PolyDTT(DCT4(k/2))])),\n \n BRDFT3_J := ARule(Compose, [[BRDFT3, @(1).cond(e->IsEvenInt(e)), 1/4], [J, @]],\n e -> let(k:=@(1).val,i:=Ind(),\n [IterDirectSum(i,k/2,Mat([[-2cospi((2i+1)/k),-1-2cospi((2i+1)/(k/2))],[1,-2cospi((2((k/2)-i)-1)/k)]]))BRDFT3(k)]))\n));\n\n \n#z := L(15,3) GathExtend(15, Odd0);; zz := RulesDFTSymmetry(z);; PrintMat(MatSPL(z)-MatSPL(zz));\n#z := L(16,4) * GathExtend(16, Odd0);; zz := RulesDFTSymmetry(z);; PrintMat(MatSPL(z)-MatSPL(zz));\n\n#z := L(15,3) * GathExtend(15, Even00);; zz := RulesDFTSymmetry(z);; PrintMat(MatSPL(z)-MatSPL(zz));\n#z := L(16,4) * GathExtend(16, Odd1);; zz := RulesDFTSymmetry(z);; PrintMat(MatSPL(z)-MatSPL(zz));\n\n#RulesDFTSymmetry(Tensor(I(3), DFT(5))L(15,3)GathExtend(15, Even0));\n#RulesDFTSymmetry(Tensor(I(2), DFT3(8))L(16,2)GathExtend(16, Even0));\n\n\ndft1 := (N, k) -> Tensor(DFT1(k), I(N/k)) * Diag(Tw1(N, N/k, 1)) * Tensor(I(k), DFT1(N/k)) * L(N, k);\ndft2 := (N, k) -> Tensor(DFT2(k), I(N/k)) * Diag(Tw2(N, N/k, 1)) * Tensor(I(k), DFT1(N/k)) * L(N, k);\ndft3 := (N, k) -> Tensor(DFT1(k), I(N/k)) * Diag(Tw3(N, N/k, 1)) * Tensor(I(k), DFT3(N/k)) * L(N, k);\ndft4 := (N, k) -> Tensor(DFT2(k), I(N/k)) * Diag(Tw4(N, N/k, 1)) * Tensor(I(k), DFT3(N/k)) * L(N, k);\n\npdft1 := (N, k, lsym, rsym) -> GathExtend(N, lsym).transpose() * dft1(N, k) * GathExtend(N, rsym);\npdft2 := (N, k, lsym, rsym) -> GathExtend(N, lsym).transpose() * dft2(N, k) * GathExtend(N, rsym);\npdft3 := (N, k, lsym, rsym) -> GathExtend(N, lsym).transpose() * dft3(N, k) * GathExtend(N, rsym);\npdft4 := (N, k, lsym, rsym) -> GathExtend(N, lsym).transpose() * dft4(N, k) * GathExtend(N, rsym);\n\n# DCT6(8)\nf := L(15, 3) * Tensor(I(5), DFT2(3, 1)) * L(15, 5) * \n Diag(Tw2(15, 5, 1)) * \n Tensor(I(3), DFT(5, 1)) * L(15, 3);\nff := GathExtend(Rows(f), Odd0).transpose() * f * GathExtend(Cols(f), Even1);\n\n# f := L(16,4) * Tensor(I(4), DFT(4)) * L(16,4) * Diag(Tw1(16,4,1)) * Tensor(I(4), DFT(4)) * L(16,4);\n# ff := GathExtend(Rows(f), Odd00).transpose() * f * GathExtend(Cols(f), Odd00);\n\n# DCT2/DCT6\n# f := L(16,4) * Tensor(I(4), DFT2(4)) * L(16,4) * Diag(Tw2(16,4)) * Tensor(I(4), DFT(4)) * L(16,4);\n#ff := GathExtend(Rows(f), Odd0).transpose() * f * GathExtend(Cols(f), Even1);\n\n# f4 := L(16,4) * Tensor(I(4), DFT2(4)) * L(16,4) * Diag(Tw4(16,4)) * Tensor(I(4), DFT3(4)) * L(16,4);\n# ff := GathExtend(Rows(f), Odd1).transpose() * f4 * GathExtend(Cols(f), Odd1);\n\n# fo := L(21,3) * Tensor(I(7), DFT2(3)) * L(21,7) * Diag(Tw4(21,7)) * Tensor(I(3), DFT3(7)) * L(21,3);\n# ffo := GathExtend(Rows(fo), Odd1).transpose() * fo * GathExtend(Cols(fo), Odd1);\n\n# fr1 := GathExtend(16, CE0_R2Cpx(W_RFT, 1).invertW()).transpose() * f * GathExtend(16, Real);\n\n fr2 := GathExtend(21, CE0_R2Cpx(W_RFT, 1).invertW()).transpose() * \n L(21,3) * Tensor(I(7), DFT(3)) * L(21,7) * Diag(Tw1(21,7,1)) * Tensor(I(3), DFT(7)) * L(21,3) \n\tGathExtend(21, Real);\n\n fr4 := GathExtend(21, CO1_R2Cpx(W_RFT, -E(4)).invertW()).transpose() \n L(21,3) * Tensor(I(7), DFT2(3)) * L(21,7) * Diag(Tw4(21,7,1)) * Tensor(I(3), DFT3(7)) * L(21,3) \n\tGathExtend(21, Real);\n\n# fr4 := GathExtend(16, CO1_R2Cpx).transpose() L(16,4) * Tensor(I(4), DFT2(4)) * L(16,4) * Diag(Tw4(16,4)) * Tensor(I(4), DFT3(4)) * L(16,4) * GathExtend(16, Real);\n\n#p := Mat(1/2[[1, E(4)]]);\n#pp := Mat(1/2[[1, -E(4)]]);\n\n#them := MatSPL(DFT(4) * Tensor(I(4), 2pp));;\n#me := MatSPL(Tensor(I(4), 2pp) * RC(DFT(4,1)));;\n\n# y = DFT x* = (DFT* x)* ?\n#\n# C IxP = IxP' RC(C) \n# IxP' = C IxP RC(C)^-1\n\n# C IxP =IxP' C Ix(1,j)\n\ndftproj := function(f)\n f := 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	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n#############################\n# General Case Cooley-Tukey\n#############################\n\n# R1 -> (R1, C1, R3) (R1)\n# R2 -> (R2, C2, R4) (R1)\nPRF12_CT_Children := (N,k,PRFt,DFTt,PRFtp,PRF1) -> Map2(DivisorPairs(N),\n (m,n) -> When(IsEvenInt(n),\n\t[ PRFt(m,k), DFTt(m,k), PRF1(n,k), PRFtp(m,k) ],\n\t[ PRFt(m,k), DFTt(m,k), PRF1(n,k) ] )\n);\n\nPRF12_CT_Rule := (N,k,C,Conj,Tw) -> let(m:=Cols(C[1]), n:=Cols(C[3]), Nf:=Int(N/2),\n nf:=Int(n/2), nc:=Int((n+1)/2), mf:=Int(m/2), mc:=Int((m+1)/2), j:=Ind(nc-1),\n\n SUM(\n\tRC(Scat(H(Nf+1,mf+1,0,n))) * C[1] * Gath(H(2(nf+1)m, m, 0, 2(nf+1))),\n\n\tWhen(nc=1, [], \n\tISum(j, \n\t RC(Scat(BH(Nf+1,N,m,j+1,n))) \n\t Conj * RC(C[2]) * Tw(j) \n\t RC(Gath(H((nf+1)m, m, j+1, nf+1))))),\n\n\tWhen(IsOddInt(n), [],\n\tRC(Scat(H(Nf+1,mc,nf,n))) * C[4] * Gath(H(2(nf+1)m, m, 2nf, 2(nf+1))))\n ) * \n Tensor(I(m), C[3]) * L(N,m)\n);\n\n\nIPRF12_CT_Rule := (N,k,C,Conj,Tw) -> let(m:=Rows(C[1]), n:=Rows(C[3]), Nf:=Int(N/2),\n nf:=Int(n/2), nc:=Int((n+1)/2), mf:=Int(m/2), mc:=Int((m+1)/2), j:=Ind(nc-1),\n\n L(N,n) * Tensor(I(m), C[3]) * \n SUM(\n\tScat(H(2(nf+1)m, m, 0, 2(nf+1))) C[1] * RC(Gath(H(Nf+1,mf+1,0,n))),\n\n\tWhen(nc=1, [], \n\tISum(j, \n\t RC(Scat(H((nf+1)m, m, j+1, nf+1))) \n\t Tw(j) \n\t RC(C[2]) \n\t Conj * \n\t RC(Gath(BH(Nf+1,N,m,j+1,n))))),\n\n\tWhen(IsOddInt(n), [],\n\tScat(H(2(nf+1)m, m, 2nf, 2(nf+1))) * C[4] * RC(Gath(H(Nf+1,mc,nf,n))))\n )\n );\n\n####################\n# Prime Factor \n####################\n\nPRF12_PF_Children := (N,k,PRFt,DFTt,PRF1) -> Map2(DivisorPairsRP(N),\n (m,n) -> When(IsEvenInt(n),\n\t[ PRFt(m,kn), DFTt(m,kn), PRF1(n,km), PRF1(m,kn) ],\n\t[ PRFt(m,kn), DFTt(m,kn), PRF1(n,km) ] )\n);\n\n RC.toAMat := self >> AMatMat(RCMatCyc( MatSPL(self.child(1)) ));\n\nPRF12_PF_Rule := (N,k,C) -> let(m:=Cols(C[1]), n:=Cols(C[3]), Nf:=Int(N/2), Nc:=Int((N+1)/2), \n nf:=Int(n/2), nc:=Int((n+1)/2), mf:=Int(m/2), mc:=Int((m+1)/2), j:=Ind(nc-1),\n alpha := (1/n) mod m,\n beta := (1/m) mod n,\n jj:=Ind(m), q := Ind(2m), \n\n SUM(\n\tRC(Scat(H(Nf+1,mf+1,0,n))) * C[1] * Gath(H(2(nf+1)m, m, 0, 2(nf+1))),\n\n\tWhen(nc=1, [], \n\tISum(j, \n\t RC(Scat(Refl(Nf+1, N, m, HZ(N, m, (j+1)m, n)))) \n\t # conjugate those values which indices will be reflected by the scatter Refl\n\t # NOTE: Unless 1.0 is used below, vector code will break due to TVect(TInt, ...)\n\t Diag(Lambda(q, cond(neq(imod(q, 2),0), cond(leq(imod(nidiv(q, 2) + (j+1)m, N), Nc-1), 1.0, -1.0), 1.0))) \n\t RC(C[2]) * \n\t RC(Gath(H((nf+1)m, m, j+1, nf+1))))),\n\n\tWhen(IsOddInt(n), [],\n\t let(inds := HZ(N, mc, ncm, n).tolist(),\n\t\t conj := ConcatList(inds{[1..mc]}, i -> When(i.v > Nf, [1.0,-1.0], [1.0,1.0])),\n\n\t\t RC(Scat(Refl(Nf+1, N, mc, HZ(N, mc, ncm, n)))) \n\t\t #RC(Scat(H(Nf+1, mc, nf, n))) \n\t\t Diag(conj) C[4] * \n\t\t Gath(H(2(nf+1)m, m, 2nf, 2(nf+1)))\n\t ))\n ) * \n Tensor(I(m), C[3]) * CRT(m,n,1,1)\n);\n\n# s := PRF12_PF_Rule(6,1,PRF12_PF_Children(6,1,PRDFT1, DFT1, PRDFT1)[1]);\n# Print(s);\n# me := MatSPL(s);\n# them := MatSPL(PRDFT(6));\n\n###########\n# RDFT #\n###########\n\nDeclare(PRDFT1_PF);\n\nRulesFor(PRDFT1, rec(\n PRDFT1_Base1 := BaseRule(PRDFT1, [1, @]),\n PRDFT1_Base2 := BaseRule(PRDFT1, [2, @]),\n\n #F PRDFT1_CT: projection of DFT_CT \n PRDFT1_CT := rec(\n\tforcePrimeFactor := false,\n\tisApplicable := (self, P) >> not IsPrime(P[1]) and \n\t When(self.forcePrimeFactor, not PRDFT1_PF.isApplicable(P), true),\n\n\tallChildren := P -> PRF12_CT_Children(P[1], P[2], PRDFT1, DFT1, PRDFT3, PRDFT1), \n\trule := (P,C) -> let(N:=P[1], k:=P[2], m:=Cols(C[1]),\n\t PRF12_CT_Rule(N, k, C, Diag(BHD(m,1,-1)), j->RC(Diag(fPrecompute(Twid(N,m,k,0,0,j+1))))))),\n\n #F PRDFT1_Complex: computes PRDFT using half of the outputs of complex DFT\n #F this rule can be successfully pruned by the compiler, and thus\n #F works for all sizes, including primes\n PRDFT1_Complex := rec(\n\tswitch := false,\n\tisApplicable := P -> not Is2Power(P[1]),\n\tallChildren := P -> [[ DFT(P[1], P[2]) ]],\n\tforTransposition := false,\n\trule := (P,C) -> let(n := P[1], nn:=Int(n/2)+1, \n\t Buf(Gath(H(2n,2nn, 0, 1))) * \n\t Diag(diagDirsum(fConst(2nn,1), fConst(2n-2nn,0))) \n\t RC(C[1]) \n\t Tensor(I(n), Diag(1,0)) \n\t Buf(Scat(H(2n,n,0,2)))\n\t)\n ),\n\n # transpose of RC(DFT(n)) is RC(DFT(n,-1)), since correct transposition is not implemented, \n # we need a separate rule\n PRDFT1_Complex_T := rec(\n\tswitch := false,\n\tisApplicable := P -> not Is2Power(P[1]),\n\tallChildren := P -> [[ DFT(P[1], -P[2]) ]],\n\tforTransposition := false,\n\ttransposed := true,\n\trule := (P,C) -> let(n := P[1], nn:=Int(n/2)+1, \n\t Buf(Gath(H(2n,n,0,2))) \n\t Tensor(I(n), Diag(1,0)) \n\t RC(C[1]) \n\t Diag(diagDirsum(fConst(2nn,1), fConst(2n-2nn,0))) * \n\t Buf(Scat(H(2n,2nn, 0, 1)))\n\t)\n ),\n\n #F PRDFT1_Trig: PRDFT1_n -> P (DCT1_(n/2+1) dirsum DST1_(n/2-1)) A\n #F\n PRDFT1_Trig := rec(\n\tisApplicable := P -> P[1] > 2 and IsEvenInt(P[1]) and (P[2] mod P[1]) in [1,-1 mod P[1]],\n\tallChildren := P -> [[ DCT1(P[1]/2+1), DST1(P[1]/2-1) ]],\n\trule := (P, C) -> let(n:=P[1]/2, \n\t Z(2n+2,2) \n\t DirectSum(Mat([[1,0],[0,0],[0,1],[0,0]]), L(2n-2,n-1)) \n\t DirectSum(Z(n+1,-1)C[1], Scale(P[2],C[2])) SymSplit1(n))),\n\n PRDFT1_PF := rec(\n\tmaxSize := false, \n \tisApplicable := (self, P) >> (self.maxSize=false or P[1]<=self.maxSize) and not IsPrime(P[1]) and DivisorPairsRP(P[1])<>[],\n \tallChildren := P -> PRF12_PF_Children(P[1], P[2], PRDFT1, DFT1, PRDFT1), \n \trule := (P,C) -> let(N:=P[1], k:=P[2], m:=Cols(C[1]),\n \t PRF12_PF_Rule(N, k, C)))\n));\n\nRulesFor(IPRDFT1, rec(\n IPRDFT1_Base1 := BaseRule(IPRDFT1, [1, @]),\n IPRDFT1_Base2 := BaseRule(IPRDFT1, [2, @]),\n\n IPRDFT1_CT := rec(\n\tisApplicable := P -> not IsPrime(P[1]),\n\tallChildren := P -> PRF12_CT_Children(P[1], P[2], IPRDFT1, DFT1, IPRDFT2, IPRDFT1), \n\trule := (P,C) -> let(N:=P[1], k:=P[2], m:=Rows(C[1]),\n\t IPRF12_CT_Rule(N, k, C, Diag(BHD(m,1,-1)), j->RC(Diag(fPrecompute(Twid(N,m,k,0,0,j+1))))))),\n\n IPRDFT1_Complex := rec(\n \tswitch := false,\n \tisApplicable := P -> IsPrime(P[1]),\n \tallChildren := P -> [[ DFT(P[1], P[2]) ]],\n\tforTransposition := false,\n\trule := (P,C) -> let(n := P[1], nn:=Int(n/2)+1, \n\t Mat(MatSPL(Gath(H(2n,n,0,2)))) \n\t #Tensor(I(n), Diag(1,0)) \n\t RC(C[1]) \n\t Mat(MatSPL(Scat(H(2n,2nn, 0, 1)))) \n\t)\n )\n));\n\nRulesFor(PRDFT2, rec(\n PRDFT2_Base1 := BaseRule(PRDFT2, [1, @]),\n PRDFT2_Base2 := BaseRule(PRDFT2, [2, @]),\n\n #F PRDFT2_CT: projection of DFT2_CT \n PRDFT2_CT := rec(\n\tisApplicable := P -> not IsPrime(P[1]),\n\tallChildren := P -> PRF12_CT_Children(P[1], P[2], PRDFT2, DFT2, PRDFT4, PRDFT1), \n\trule := (P,C) -> let(N:=P[1], k:=P[2], m:=Cols(C[1]),\n\t PRF12_CT_Rule(N, k, C, Diag(BHD(m,-1,1)), j->RC(Diag(fPrecompute(Twid(N,m,k,0,1/2,j+1)))))))\n));\n\nRulesFor(IPRDFT3, rec(\n IPRDFT3_Base1 := BaseRule(IPRDFT3, [1, @]),\n IPRDFT3_Base2 := BaseRule(IPRDFT3, [2, @]),\n\n IPRDFT3_CT := rec(\n\tisApplicable := P -> not IsPrime(P[1]),\n\tallChildren := P -> PRF12_CT_Children(P[1], P[2], IPRDFT3, DFT3, IPRDFT4, IPRDFT1), \n\trule := (P,C) -> let(N:=P[1], k:=P[2], m:=Rows(C[1]),\n\t IPRF12_CT_Rule(N, k, C, Diag(BHD(m,-1,1)), j->RC(Diag(fPrecompute(Twid(N,m,k,0,1/2,j+1)))))))\n));\n\n###########\n# Hartley #\n###########\n\nRulesFor(PDHT1, rec(\n PDHT1_Base2 := rec(\n\tisApplicable := P -> P[1]=2,\n\trule := (P, C) -> Tensor(I(2), Mat([[1],[1]])) * F(2)\n ),\n \n PDHT1_CT := rec(\n\tisApplicable := P -> not IsPrime(P[1]),\n\tallChildren := P -> PRF12_CT_Children(P[1], P[2], PDHT1, DFT1, PDHT3, PDHT1), \n\trule := (P,C) -> let(N:=P[1], k:=P[2], m:=Cols(C[1]),\n\t PRF12_CT_Rule(N, k, C, TopHalf(m, J(2)), j->HTwid(N,m,k,0,0,j+1,J(2)).obj)))\n));\n\nRulesFor(PDHT2, rec(\n PDHT2_Base2 := rec(\n\tisApplicable := P -> P[1]=2,\n\trule := (P, C) -> DirectSum(Mat([[1],[1]]), Mat([[1],[-1]])) * Mat(MatSPL(PRDFT2(P[1], P[2])){[1,4]})\n ),\n PDHT2_CT := rec(\n\tisApplicable := P -> not IsPrime(P[1]),\n\tallChildren := P -> PRF12_CT_Children(P[1], P[2], PDHT2, DFT2, PDHT4, PDHT1), \n\trule := (P,C) -> let(N:=P[1], k:=P[2], m:=Cols(C[1]),\n\t PRF12_CT_Rule(N, k, C, TopHalf(m, -J(2)), j->HTwid(N,m,k,0,1/2,j+1,-J(2)).obj)))\n));\n", "meta": {"hexsha": "082f04e9d3cbbd7bdfecbcfb8aa6843497cef9a1", "size": 8400, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/realdft/prf12.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/transforms/realdft/prf12.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/transforms/realdft/prf12.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 33.3333333333, "max_line_length": 128, "alphanum_fraction": 0.5135714286, "num_tokens": 3679, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8006920116079209, "lm_q2_score": 0.6370308082623217, "lm_q1q2_score": 0.5100654793237781}}
	{"text": "# Examples/Tests for ANATPH\n\n# Jack Button's Group\n# -------------------\n#\n# With presentation <a,b,t \| a^t = ab, b^t = ba>\n#\n# Alan Logan says this is hyperbolic, but noone wants to publish\n# this result alone.\n#\n# Tester now proves this to be hyperbolic, after corrected\n# relation. Bug reported by email by Chris Chalk <chalk235@gmail.com>\n#\nInstallGlobalFunction(\"JackButtonGroup\",\nfunction()\n local pg;\n\n pg := PregroupOfFreeGroup(3);\n SetPregroupElementNames(pg, \"1aAbBtT\");\n return NewPregroupPresentation(pg, [ pg_word( pg, [7,2,6,5,3])\n , pg_word( pg, [7,4,6,3,5]) ]);\nend);\n\n# Triangle Groups\n# ---------------\n# As demonstrated in Proposition 9.4 of anatph, for l > 2 (and hence n > 3 if the\n# group is supposed to be hyperbolic) there are no instantiable green places, and if\n# l = 2 then there are exactly two instantiable green places.\nInstallGlobalFunction(\"TriangleGroup\",\nfunction(l,m,n)\n local pg;\n pg := PregroupOfFreeProduct( CyclicGroup( IsPermGroup, l)\n , CyclicGroup( IsPermGroup, m) );\n\n # This is a bit icky, we can't tell which element of pg is the one of the\n # second cyclic group\n return NewPregroupPresentation(pg, [ pg_word( pg, Repeat(n, [2, l + 1]))]);\nend);\n\n# Example from Theorem 9.5, triangle-like: quotient of 2-3-m triangle group\n# our choice of pregroup is the free product of cyclic groups of order 2 and 3\n#T see what happens if we present this group as\n#T <x,y,z \| x^2, y^3, z^m, (zxY)^n > ?\n#T we push a parameter into the pregroup\nInstallGlobalFunction(TriangleCommutatorQuotient,\nfunction(m,n)\n local pg;\n pg := PregroupOfFreeProduct( CyclicGroup(IsPermGroup, 2)\n , CyclicGroup(IsPermGroup, 3) );\n # Do this to have slightly nicer display. Maybe we need to give the user\n # a way to label generators\n pg!.enams := \"1xyY\";\n return NewPregroupPresentation(pg,\n [ pg_word(pg, Repeat(m, [2,3])),\n pg_word(pg, Repeat(n, [2,3,2,4]))\n ]);\nend);\n\nInstallGlobalFunction(RandomTriangleQuotient,\nfunction(p,q,r,len)\n local pg;\n pg := PregroupOfFreeProduct( CyclicGroup(IsPermGroup, p)\n , CyclicGroup(IsPermGroup, q) );\n # Do this to have slightly nicer display. Maybe we need to give the user\n # a way to label generators\n pg!.enams := \"1xyY\";\n return NewPregroupPresentation(pg,\n [ pg_word(pg, Repeat(r, [2,3])),\n RandomPregroupWord(pg, len)\n ]);\nend);\n\nInstallGlobalFunction(RandomPregroupWord,\nfunction(pg, len)\n local i, lett, rel;\n\n rel := [];\n\n rel[1] := Random([2..Size(pg)]);\n for i in [2..len-1] do\n rel[i] := Random(Difference( [2..Size(pg)]\n , [__ID(PregroupInverse(pg[rel[i-1]]))]));\n od;\n rel[len] := Random(Difference([2..Size(pg)]\n , [ __ID(PregroupInverse(pg[rel[len - 1]]))\n , __ID(PregroupInverse(pg[rel[1]]))\n ] ));\n return pg_word(pg, rel);\nend);\n\n# Given a pregroup make a random presentation with nrel relators\n# of length lrel\nInstallGlobalFunction(RandomPregroupPresentation,\nfunction(pg, nrel, lrel)\n local rels;\n\n rels := List([1..nrel], i -> RandomPregroupWord(pg, lrel));\n return NewPregroupPresentation(pg, rels);\nend);\n\n\nBindGlobal(\"CreateRandomExample\",\nfunction(path, pg, nrel, lrel)\n local pgp;\n\n if not IsDirectoryPath(path) then\n Error(\"path does not exist or is not a directory\");\n return;\n fi;\n pgp := RandomPregroupPresentation(pg, nrel, lrel);\n\n # Write the pregroup presentation to file\n PregroupPresentationToFile(Concatenation(path, \"/presentation-gap\"), pgp);\n PregroupPresentationToSimpleFile(Concatenation(path, \"/presentation-simple\"), pgp);\n\n if WALRUS_kbmag_available then\n # Also create a KBMAG input file, if RSymTest succeeds on this presentation,\n # we can try computing an automatic structure and run gpgeowa on the result\n # to check whether the group is hyperbolic.\n WriteRWS(KBMAGRewritingSystem(PregroupPresentationToFpGroup(pgp)),\n Concatenation(path, \"/presentation-kbmag\"));\n fi;\nend);\n\n# Create a series of examples\nBindGlobal(\"CreateRandomSeries\",\nfunction(pg, nrels, lrels, nexs, prf, basepath)\n local path, path2, i, pgp, lrel, nrel;\n\n if not IsDirectoryPath(basepath) then\n Error(\"path does not exist or is not a directory\");\n return;\n fi;\n path := basepath;\n\n for lrel in lrels do\n CreateDir(Concatenation(path, \"/\", String(lrel)));\n for nrel in nrels do\n CreateDir(Concatenation(path, \"/\", String(lrel), \"/\", String(nrel)));\n for i in [1..nexs] do\n path2 := Concatenation(path, \"/\", String(lrel), \"/\", String(nrel), \"/\", String(i));\n prf(\"creating example nr \", i, \" in \", path2, \" \\c\");\n\n CreateDir(path2);\n CreateRandomExample(path2, pg, nrel, lrel);\n prf(\"\\n\");\n od;\n od;\n od;\nend);\n\nBindGlobal(\"CreateRandomSeriesOverSmallPregroups\",\nfunction(basepath)\n local i, n, sizes, path;\n\n if not IsDirectoryPath(basepath) then\n Error(\"path does not exist or is not a directory\");\n return;\n fi;\n\n # at the moment we only have pregroups\n # of size 6\n sizes := [6];\n for n in sizes do\n CreateDir(Concatenation(basepath, \"/\", String(n)));\n for i in [1..NrSmallPregroups(n)] do\n path := Concatenation(basepath, \"/\", String(n), \"/\", String(i));\n CreateDir(path);\n CreateRandomSeries( SmallPregroup(n, i)\n , [1,2,4,8,10]\n , [5,10,15,20,25,30,35,40,45,50]\n , 20\n , Print\n , path);\n od;\n od;\nend);\n\nBindGlobal(\"CreateRandomSeriesOverFreeGroup\",\nfunction(basepath)\n local i, n, sizes, path;\n\n if not IsDirectoryPath(basepath) then\n Error(\"path does not exist or is not a directory\");\n return;\n fi;\n\n # ranks of free group\n sizes := [2,4,8,16,32,64];\n for n in sizes do\n path := Concatenation(basepath, \"/\", String(n));\n CreateDir(path);\n CreateRandomSeries( PregroupOfFreeGroup(n)\n , [1,2,4,8,10]\n , [5,10,15,20,25,30,35,40,45,50]\n , 20\n , Print\n , path);\n od;\nend);\n\nBindGlobal(\"CreateRandomSeriesOverTrianglePregroup\",\nfunction(eps, p, q, nrel, lrel, nexs, prf, path)\n local pg;\n pg := PregroupOfFreeProduct( CyclicGroup( IsPermGroup, p)\n , CyclicGroup( IsPermGroup, q) );\n pg!.enams := \"1xyY\";\n CreateRandomSeries( pg\n , [1]\n , [5,10,15,20,25,30,35,40,45,50]\n , 20\n , Print\n , path );\nend);\n\nBindGlobal(\"CreateRandomSeriesOverTriangleGroup\",\n function(eps, p, q, nrel, lrel, nexs, prf, path)\n local pg;\n pg := PregroupOfFreeProduct( CyclicGroup( IsPermGroup, p)\n , CyclicGroup( IsPermGroup, q) );\n pg!.enams := \"1xyY\";\n CreateRandomSeries( pg\n , [1]\n , [5,10,15,20,25,30,35,40,45,50]\n , 20\n , Print\n , path );\n end);\n\n\n\nBindGlobal(\"BenchmarkRandomPresentation\",\nfunction(pg, eps, nrel, lrel, nexs, prf, path)\n local i, pgp, start, stop, estart, estop, n, nfail, res, runt, fid, stream;\n\n n := 0;\n runt := [];\n\n start := NanosecondsSinceEpoch();\n for i in [1..nexs] do\n prf(\"creating example nr \", i, \", \\c\");\n pgp := RandomPregroupPresentation(pg, nrel, lrel);\n prf(\"starting RSymTest, \\c\");\n estart := NanosecondsSinceEpoch();\n res := RSymTest(pgp, eps);\n estop := NanosecondsSinceEpoch();\n if res = true then\n prf(\"succeeded after \\c\");\n else\n prf(\"failed \\c\");\n fi;\n# LogPregroupPresentation(path, pgp, res);\n prf(Float((estop - estart) / 1000000000), \" seconds\\n\");\n Add(runt, [pgp, res, estop - estart]);\n od;\n stop := NanosecondsSinceEpoch();\n return rec( runtime := (stop - start) / 1000000000,\n samples := runt );\nend);\n\nBindGlobal(\"RandomPregroupFromSmallGroups\",\nfunction()\n local n, i, g1, g2;\n\n n := Random([1..64]);\n i := Random([1..NrSmallGroups(n)]);\n g1 := SmallGroup(n,i);\n\n n := Random([1..64]);\n i := Random([1..NrSmallGroups(n)]);\n g2 := SmallGroup(n,i);\n\n return PregroupOfFreeProduct(g1, g2);\nend);\n\nBindGlobal(\"BenchmarkRandom_TriPregroup\",\nfunction(eps, nrel, lrel, nexs, prf, path)\n local pg;\n pg := PregroupOfFreeProduct( CyclicGroup( IsPermGroup, 2)\n , CyclicGroup( IsPermGroup, 3) );\n pg!.enams := \"1xyY\";\n return BenchmarkRandomPresentation(pg, eps, nrel, lrel, nexs, prf, path);\nend);\n\nBindGlobal(\"BenchmarkRandom_FreeGroupPregroup\",\nfunction(eps, ngen, nrel, lrel, nexs, prf, path)\n local pg;\n pg := PregroupOfFreeGroup(ngen);\n return BenchmarkRandomPresentation(pg, eps, nrel, lrel, nexs, prf, path);\nend);\n\nBindGlobal(\"BenchmarkRandom_OverSmallPregroup\",\nfunction(eps, nrel, lrel, nexs, prf, path)\n local pg, res;\n\n res := [];\n # FIXME: We only have pregroups of size 6 at the moment\n for pg in ANATPH_small_pregroups[6] do\n pg := PregroupByTable([1,'a','b','c','d', 'e'], pg);\n Add(res, BenchmarkRandomPresentation(pg, eps, nrel, lrel, nexs, prf, path));\n od;\n return res;\nend);\n\nBindGlobal(\"_VARIANCE\",\nfunction(v)\n local q, avg;\n if Length(v) = 1 then\n q := 1;\n else\n q := Length(v) - 1;\n fi;\n avg := Average(v);\n return Sum(List(v, x -> (x - avg)^2)) / (q);\nend);\n\nBindGlobal(\"AnalyseBenchmarkResult\",\nfunction(res)\n local r, succed, failed;\n\n r := rec();\n\n r.n := Length(res.samples);\n r.rt_avg := Average(List(res.samples, x->x[3]));\n r.rt_std := Sqrt(Float(_VARIANCE(List(res.samples, x->x[3]))));\n\n succed := Filtered(res.samples, x -> not IsList(x[2]));\n r.succed_n := Length(succed);\n if r.succed_n > 0 then\n r.succed_rt_avg := Average(List(succed, x->x[3]));\n r.succed_rt_std := Sqrt(Float(_VARIANCE(List(succed, x->x[3]))));\n fi;\n\n failed := Filtered(res.samples, x -> IsList(x[2]));\n r.failed_n := Length(failed);\n if r.failed_n > 0 then\n r.failed_rt_avg := Average(List(failed, x->x[3]));\n r.failed_rt_std := Sqrt(Float(_VARIANCE(List(failed, x->x[3]))));\n fi;\n\n return r;\nend);\n\nBindGlobal(\"StringBenchResult\",\nfunction(r)\n local res;\n \n res := STRINGIFY(\"n: \", r.n, \", s: \", r.succed_n, \" f: \", r.failed_n, \" (\", Float(r.succed_n) / r.n, \")\\n\",\n \" (\", Float(r.rt_avg), \",\", r.rt_std, \")\\n\");\n Append(res, STRINGIFY(\" success: \", r.succed_n));\n if r.succed_n > 0 then\n Append(res, STRINGIFY(\" \", Float(r.succed_rt_avg), \",\", r.succed_rt_std, \"\\n\"));\n fi;\n Append(res, STRINGIFY(\" failure: \", r.failed_n));\n if r.failed_n > 0 then\n Append(res, STRINGIFY(\" \", Float(r.failed_rt_avg), \",\", r.failed_rt_std, \"\\n\"));\n fi;\n if res[Length(res)] <> '\\n' then\n Add(res, '\\n');\n fi;\n return res;\nend);\n \nBindGlobal(\"StandardBenchmarks\",\nfunction(nsamples, prn)\n local d, ngens, rlen, nrels, r, path;\n\n path := DirectoryTemporary(); \n prn(\"running standard benchmarks for anatph, \", nsamples, \" each\\n\");\n\n prn(\"= = = = = = =\\n\");\n prn(\" Quotients of free group pregroup\\n\");\n prn(\"= = = = = = =\\n\");\n for ngens in [2,4,8,16] do\n for nrels in [1,2,3,4] do\n for rlen in [10,20,30,40,50] do\n prn(\"running \"\n , ngens, \" generators, \"\n , nrels, \" relators \"\n , \"of length \", rlen, \"\\n\");\n r := BenchmarkRandom_FreeGroupPregroup(\n 1/12\n , ngens\n , nrels\n , rlen\n , nsamples\n , prn\n , path\n );\n prn(StringBenchResult(AnalyseBenchmarkResult(r)));\n od;\n od;\n od;\n\n prn(\"= = = = = = =\\n\");\n prn(\" Quotients of 2-3-triangle group pregroup\\n\");\n prn(\"= = = = = = =\\n\");\n for nrels in [1,2,3,4] do\n for rlen in [10,20,30,40,50] do\n prn(\"running \", nrels, \"relators of length \", rlen, \"\\n\");\n r := BenchmarkRandom_TriPregroup(\n 1/12\n , nrels\n , rlen\n , nsamples\n , prn\n , path\n );\n prn(StringBenchResult(AnalyseBenchmarkResult(r)));\n od;\n od;\n\nend);\n\nBenchmarkSinglePres := function(eps, pg, nrel, len)\n local r,t,res;\n r := RandomPregroupPresentation(pg, nrel, len);\n t := NanosecondsSinceEpoch();\n res := RSymTest(r, eps);\n t := NanosecondsSinceEpoch() - t;\n return [r, res, t / 1000000000.];\nend;\n\nif IsBound(OutputAnnotatedCodeCoverageFiles) then\n ProfileSinglePresentation := function(eps, pg, nrel, len)\n local t, dir, fn;\n\n dir := DirectoryTemporary();\n fn := Filename(dir, \"anatph.gz\");\n\n Print(\"Profiling presentation to \", fn, \"\\n\");\n ProfileLineByLine(fn);\n t := BenchmarkSinglePres(eps, pg, nrel, len);\n UnprofileLineByLine();\n\n Print(\"Writing annotated code coverage to \", Filename(dir, \"\"), \"\\n\");\n OutputAnnotatedCodeCoverageFiles(fn, Filename(dir, \"\"));\n\n return t;\nend;\n\nelse\n Print(\"profiling package is not available, disabling ProfileSinglePresentation\\n\");\nfi;\n\n# Benchmark the RSym tester with a presentation given <A>density</A>\n# and <A>length</A>\nBenchmarkGromovDensity := function(eps, ngens, length, density)\n local pg, nrels;\n\n pg := PregroupOfFreeGroup(ngens);\n nrels := Int( (2 * ngens - 1)^Float(density * length ) );\n Print(\"number of relators: \", nrels, \"\\n\");\n return BenchmarkSinglePres(eps\n , pg\n , nrels\n , length );\nend;\n\n\n\n\n\n", "meta": {"hexsha": "04e581d76fdff0eeb3f776176aee3ae669d861d5", "size": 15065, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "gap/examples.gi", "max_stars_repo_name": "RussWoodroofe/walrus", "max_stars_repo_head_hexsha": "f7a4e3597f288c6d9518aaa39091826dadc864b8", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-10-02T14:55:52.000Z", "max_stars_repo_stars_event_max_datetime": "2021-10-02T14:55:52.000Z", "max_issues_repo_path": "gap/examples.gi", "max_issues_repo_name": "RussWoodroofe/walrus", "max_issues_repo_head_hexsha": "f7a4e3597f288c6d9518aaa39091826dadc864b8", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 26, "max_issues_repo_issues_event_min_datetime": "2018-11-22T11:15:07.000Z", "max_issues_repo_issues_event_max_datetime": "2022-02-21T13:31:01.000Z", "max_forks_repo_path": "gap/examples.gi", "max_forks_repo_name": "RussWoodroofe/walrus", "max_forks_repo_head_hexsha": "f7a4e3597f288c6d9518aaa39091826dadc864b8", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 4, "max_forks_repo_forks_event_min_datetime": "2019-02-11T14:47:47.000Z", "max_forks_repo_forks_event_max_datetime": "2021-05-20T10:22:09.000Z", "avg_line_length": 32.4676724138, "max_line_length": 111, "alphanum_fraction": 0.5382011284, "num_tokens": 4052, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7956581000631542, "lm_q2_score": 0.640635854839898, "lm_q1q2_score": 0.509727107094248}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nunpacklo := (l1,l2,n,k) -> Flat(List([1..n/(2k)], i-> [\n List([1..k], j->l1[(i-1)k+j]),\n List([1..k], j->l2[(i-1)k+j])\n]));\n\nunpackhi := (l1,l2,n,k) -> Flat(List([1..n/(2k)], i -> [\n List([1..k], j->l1[n/2+(i-1)k+j]),\n List([1..k], j->l2[n/2+(i-1)k+j])\n]));\n\n# saturation in pack_semantic is not taken into account\npack_semantic := (l1, l2, n) -> Flat(List( [1..n], i -> [l1[i], l2[i]]));\n\nsparams := (l,n) -> List([1..l], i->[1..n]);\n\nshuffle := (in1, in2, p, n, k) -> Flat([\n List([1..n/(2k)], i->List([1..k], j->in1[(p[i]-1)k+j])),\n List([n/(2k)+1..n/k], i->List([1..k], j->in2[(p[i]-1)k+j]))\n]);\n\ninverse_ushuffle := (inp, p, n) -> List([1..n], i->inp[p[i]]);\n\nshufflehi := (in1, p, n, k) -> Concat(\n Sublist(in1, [1..n/2]),\n let(l := Sublist(in1, [n/2+1..n]), shuffle(l, l, p, n/2, k)));\n\nshufflelo := (in1, p, n, k) -> Concat(\n let(l := Sublist(in1, [1..n/2]), shuffle(l, l, p, n/2, k)),\n Sublist(in1, [n/2+1..n]));\n\niclshuffle := p -> Print(\"_MM_SHUFFLE\", When(Length(p)=2, \"2\", \"\"), \"(\", PrintCS(Reversed(p-1)), \")\");\n\niclprintop := self >> Print(self.icl, \"(\", _vcprintcs(self.args), \")\");\n\niperm4 := self >> Filtered(Cartesian(self.params()), i->i[1]<>i[2] and i[3] <> i[4]);\n\nvtakehi := (v) -> Checked(IsValue(v) and IsVecT(v.t) and v.t.size>1, TakeLast(v.v, Length(v.v)/2));\nvtakelo := (v) -> Checked(IsValue(v) and IsVecT(v.t) and v.t.size>1, Take(v.v, Length(v.v)/2));\n\n", "meta": {"hexsha": "5bbc5dca30ee4569ffb78c3ccd229ef47f63ca28", "size": 1529, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/platforms/sse/misc.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/platforms/sse/misc.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/platforms/sse/misc.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 33.9777777778, "max_line_length": 102, "alphanum_fraction": 0.5075212557, "num_tokens": 624, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7248702761768249, "lm_q2_score": 0.7025300698514777, "lm_q1q2_score": 0.5092431657557647}}
	{"text": "################################################################################\n##\n#W DwG_data.gi GroupTheoretical Package\n##\n#W Paul Bruillard, Cesar Galindo, Siu-Hung Ng, Julia Plavnik, Eric Rowell, \n#W Zhenghan Wang\n##\n## Installation file for DwG_data functions of the GroupTheoretical Package\n##\n#Y Copyright (C) 2016, Battelle Memorial Institute\n##\n################################################################################\n\n################################################################################\n##\n#F DwG_simples(<group>,<int>,<function>) . . . . . compute simples in D^w(G)\n##\nInstallGlobalFunction( DwG_simples, function(G,n,w)\n local x,Zx,wx,CC,SimpleObjects,projective_characters,chi;\n CC:=List(ConjugacyClasses(G),Representative);;\n SimpleObjects:=[];\n for x in CC do\n Zx:=Centralizer(G,x);\n wx:=function(g,h) return w(g,h,x)w(x,g,h)(w(g,x,h)^-1); end;;\n projective_characters:=projective_reps(Zx,wx,n);\n if not(Sum(List(projective_characters,chi->chi[1]^2))=Order(Zx)) then\n Display(\"ERROR\");\n fi;\n for chi in projective_characters do\n Append(SimpleObjects,[[x,chi,ConjugacyClass(G,x),wx,Zx]]);\n od;\n od;\n return SimpleObjects;\nend );\n\n################################################################################\n##\n#F DwG_S_and_T(<list>,<group>) . . . . . . . . . .compute S and T for D^w(G)\n##\nInstallGlobalFunction(DwG_S_and_T, function(Simples,G)\n local r,S,T,i,simple1,x,chi,Kx,betax,Zx,x_idx,Zx_Transversal,j,simple2,y,chi_prime,Ky,betay,Zy,Zy_Transversal,a,g,Zg,b,g_prime,h_prime,h,h_idx,h_prime_idx;\n\n r:=Length(Simples);\n S:=NullMat(r,r);;\n T:=List([1..r],i->0);\n for i in [1..r] do\n simple1:=Simples[i];\n x:=simple1[1];\n chi:=simple1[2];\n Kx:=simple1[3];\n betax:=simple1[4];\n Zx:=simple1[5];\n #x_idx:=Position(GSet,x);\n x_idx:=Position(AsSet(Zx),x);\n T[i]:=chi[x_idx]/chi[Position(AsSet(Zx),Identity(Zx))];\n Zx_Transversal:=RightTransversal(G,Zx);\n for j in [i..r] do\n simple2:=Simples[j];\n y:=simple2[1];\n chi_prime:=simple2[2];\n Ky:=simple2[3];\n betay:=simple2[4];\n Zy:=simple2[5];\n #y_idx:=Position(GSet,y);\n Zy_Transversal:=RightTransversal(G,Zy);\n for a in Zx_Transversal do\n g:=(a^-1)xa;\n if not(g in Kx) then\n continue;\n fi;\n Zg:=Centralizer(G,g);\n for b in Zy_Transversal do\n g_prime:=(b^-1)yb;\n if not((g_prime in Ky) and (g_prime in Zg)) then\n continue;\n fi;\n h_prime:=bg(b^-1);\n h:=ag_prime(a^-1);\n h_idx:=Position(AsSet(Zx),h);\n h_prime_idx:=Position(AsSet(Zy),h_prime);\n S[i][j]:=S[i][j]+betax(a,g_prime)betax(ag_prime,a^-1)betay(b,g)betay(bg,b^-1)(betax(a,a^-1)^-1)(betay(b,b^-1)^-1)chi[h_idx]*chi_prime[h_prime_idx];\n od;\n od;\n S[j][i]:=S[i][j];\n od;\n od;\n\n return [S,T];\nend);\n\n################################################################################\n##\n#F DwG_data(<group>,<function>,<int>) . . . . . compute data of D^w(G)\nInstallGlobalFunction(DwG_data,function(G,w,n)\n local Simples, S_and_T, pseudounitary_data, S, T, N, FPdimC, FPdim,sorted_data;\n Simples := DwG_simples(G,n,w);;\n S_and_T := DwG_S_and_T(Simples,G);;\n S := S_and_T[1];\n T := S_and_T[2];\n pseudounitary_data := pseudounitary_sort(S,T,Simples);\n Simples := pseudounitary_data[1];\n S := pseudounitary_data[2];\n T := pseudounitary_data[3];\n FPdim := pseudounitary_data[4];\n FPdimC := pseudounitary_data[5];\n sorted_data := dimension_sort(S,T,Simples,FPdim);\n Simples := sorted_data[1];\n S := sorted_data[2];\n T := sorted_data[3];\n FPdim := sorted_data[4];\n N:=compute_fusion_rules(S,FPdimC);;\n return [Simples, S, T, N, FPdim, FPdimC];;\nend);\n\n#E DwG_data.gi . . . . . . . . . . . . . . . . . . . . . . . . . . . . ends here\n", "meta": {"hexsha": "f109434edba9de23abb2ae616b8ab0106c39ab1a", "size": 3879, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "lib/DwG_data.gi", "max_stars_repo_name": "pnnl/GroupTheoretical", "max_stars_repo_head_hexsha": "d60aaec27d2ca98ec55b12b78213538a346eef27", 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"num_tokens": 1214, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8080672320414786, "lm_q2_score": 0.6297746143530797, "lm_q1q2_score": 0.5089002294302827}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n#D TL.withTags := (self, tags) >> CopyFields(self, rec(params := [self.params[1], self.params[2], self.params[3], self.params[4], tags]));\n#D TL.getTags := self >> self.params[self.tagpos];\n\nDoubleDivisorPairs:=function(n,m)\n local a,b,l;\n l:=[];\n for a in DivisorPairs(n) do\n Append(l,[Concatenation(a,[1,m]),Concatenation(a,[m,1])]);\n for b in DivisorPairs(m) do\n Append(l,[Concatenation(a,b)]);\n od;\n od;\n for b in DivisorPairs(m) do\n Append(l,[Concatenation([n,1],b),Concatenation([1,n],b)]);\n od;\n return l;\nend;\n\nVectorDivisible:=function(m,c,k,b,v)\n#not yet taken into account : b or c =1\n local leftpart,rightpart;\n leftpart := v in DivisorsInt(c) or m=1 or (b=1 and k=1);\n rightpart:= v in DivisorsInt(b) or c=1 or k=1;\n return leftpart and rightpart;\nend;\n\nDoubleDivisorPairsVector:=function(n,m,v)\n return Filtered(DoubleDivisorPairs(n,m) , a -> VectorDivisible(a[1],a[2],a[3],a[4],v));\nend;\n\nBlocking:=function(m,c,k,b,v)\n local t, nv, PageSize, CacheLineSize;\n t:=128/v;\n PageSize:=410248(2);\n nv:=mckbt;\n if (nv>PageSize) then\n return When((PageSize/8<=bct)and(bct<=PageSize),true,false);\n\n #CacheLineSize:=648(4);\n #else\n #if (nv>CacheLineSize) then\n #return When((CacheLineSize/8<=bct)and(bct<=CacheLineSize),true,false);\n #fi;\n fi;\n return true;\nend;\n\nDoubleDivisorPairsVectorBlocking:=function(n,m,v)\n return Filtered(DoubleDivisorPairsVector(n,m,v), a->Blocking(a[1],a[2],a[3],a[4],v));\nend;\n\nNewRulesFor(TL,rec(\n L_cx_real := rec(\n switch:=false,\n forTransposition := false,\n applicable := t -> t.isTag(1, AVecRegCx) and let(P := t.params, P[1] = P[2]^2), #FF: NOTE!! can only terminate symmetrical ones...\n children := nt -> let(P:=nt.params, [[TL(P[1], P[2], P[3], P[4]2).withTags([AVecReg(nt.getTags()[1].isa)])]]),\n apply := (t, C, Nonterms) -> CR(When(t.params[1]=t.params[2]^2, SymSPL(C[1]), C[1]))\n ),\n\n L_base_vec := rec(\n switch:=false,\n forTransposition := false,\n applicable := t -> t.isTag(1, AVecReg) or t.isTag(1, AVecRegCx),\n apply := (t, C, Nonterms) -> let(\n C1:=When(t.params[3]=1, [], [I(t.params[3])]),\n C2:=When(t.params[4]=1, [], [I(t.params[4])]),\n Tensor(Concat(C1, [L(t.params[1], t.params[2])], C2))\n )\n#D applicable := (self, t) >> FirstTagEq(t, AVecReg) or FirstTagEq(t, AVecRegCx),\n#D apply := (t, C, Nonterms) -> let(C1:=When(t.params[3]=1, [], [I(t.params[3])]), \n#D C2:=When(t.params[4]=1, [], [I(t.params[4])]), Tensor(Concat(C1, [L(t.params[1], t.params[2])], C2)))),\n ),\n\n\n #L^mn_m -> (L^mn/v_m x I_v)(I_mn/v2 x L^v2_v)(I_n/v x L^m_m/v x I_v)\n L_mn_m_vec := rec(\n forTransposition := false,\n freedoms := (self, t) >> [],\n applicable := t ->\n t.params[3] = 1\n and t.params[4] = 1\n and (t.isTag(1, AVecReg) or t.isTag(1, AVecRegCx))\n and let(\n v := t.firstTag().v,\n m := t.params[2],\n n := t.params[1] / m,\n IsInt(m/v)\n and IsInt(n/v)\n and not (\n t.params[1] = vv\n and t.params[2] = v\n )\n ),\n child := (nt,freedoms) -> let (v := nt.firstTag().v, [ TL(vv, v, 1, 1).withTags(nt.getTags()) ] ),\n\n apply := (nt, C, cnt) -> let(\n v := nt.firstTag().v,\n v2 := vv,\n m := nt.params[2],\n n := nt.params[1]/m,\n VTensor(L(mn/v, m), v)\n * SymSPL(BlockVPerm(mn/v2, v, C[1], L(v^2,v)))\n VTensor(Tensor(I(n/v), L(m,m/v)), v)\n )\n\n#D applicable := (self, t) >> t.params[3] = 1 and t.params[4] = 1 and FirstTagEq(t, AVecReg) and\n#D let (v := GetFirstTag(t).v, m:=t.params[2], n:= t.params[1]/m,\n#D IsInt(m/v) and IsInt(n/v) and not(t.params[1]=vv and t.params[2]=v)) ,\n#D\n#D child := (nt,freedoms) -> let (v := GetFirstTag(nt).v, [TL(vv, v, 1, 1, GetTags(nt))]),\n#D\n#D apply := (nt,C,cnt) -> let(v:=GetFirstTag(nt).v, v2:=vv, m:=nt.params[2], n:= nt.params[1]/m,\n#D VTensor(L(mn/v, m), v) \n#D SymSPL(BlockVPerm(mn/v2, v, C[1], L(v^2,v))) \n#D VTensor(Tensor(I(n/v), L(m,m/v)), v))),\n ),\n\n#SymSPL-BlockVPerm can be replaced by Tensor(I(mn/v2), C[1])\n\n#L^mn_m could probably also be splitted like that:\n\n# #L^mn_m -> (L^mn/v_m x I_v)(I_mn/v2 x L^v2_v)(I_n/v x L^m_m/v x I_v)\n# L_mn_m_vec := rec(\n# forTransposition := false,\n# applicable := (self, t) >> t.params[3] = 1 and t.params[4] = 1 and FirstTagEq(t, AVecReg) and\n# let (v := GetFirstTag(t).v, m:=t.params[2], n:= t.params[1]/m,\n# IsInt(m/v) and IsInt(n/v)),\n\n# freedoms := (self, t) >> [],\n# child := (nt,freedoms) -> let (v := GetFirstTag(nt).v, m:=nt.params[2], n:= nt.params[1]/m,\n# [TL(mn/v, m, 1, v, GetTags(nt)),\n# TL(vv, v, mn/(vv), 1, GetTags(nt)),\n# TL(m,m/v,n/v, v, GetTags(nt))]),\n# apply := (nt,C,cnt) -> let(v:=GetFirstTag(nt).v, v2:=vv, m:=nt.params[2], n:= nt.params[1]/m, C[1] C[2] * C[3])),\n\n# #I x L -> BlockVPerm\n# IxLxI_BlockVPerm := rec(\n# forTransposition := false,\n# applicable := (self, t) >> FirstTagEq(t, AVecReg) and (t.params[4]=1)\n# and let (v := GetFirstTag(t).v, (t.params[1]=vv) and (t.params[2]=v)),\n# freedoms := (self, t) >> [],\n# child := (nt,freedoms) -> let (v := GetFirstTag(nt).v,[TL(vv, v, 1, 1, GetTags(nt))]),\n# apply := (t, C, cnt) -> let(v:=GetFirstTag(t).v,\n#SymSPL(BlockVPerm(t.params[3], v, C[1], DropTag(cnt[1]))))),\n\n\n #A x I_v -> VTensor\n IxLxI_vtensor := rec(\n forTransposition := false,\n applicable := t ->\n (\n t.isTag(1, AVecReg)\n or t.isTag(1, AVecRegCx)\n )\n and IsPosInt(t.params[4] / t.firstTag().v),\n apply := (t, C, Nonterms) -> let(\n v:=t.firstTag().v,\n l1 := When(t.params[3] > 1, [I(t.params[3])], []),\n l2 := When(t.params[4]/v > 1, [I(t.params[4]/v)], []),\n VTensor(Tensor(Concat(l1, [L(t.params[1], t.params[2])], l2)), v)\n )\n#D applicable := (self, t) >> (FirstTagEq(t, AVecReg) or FirstTagEq(t, AVecRegCx)) and\n#D let(v:=GetFirstTag(t).v, IsPosInt(t.params[4]/v)),\n#D apply := (t, C, Nonterms) -> let(v:=GetFirstTag(t).v, l1:= When(t.params[3] > 1, [I(t.params[3])], []), l2:=When(t.params[4]/v > 1, [I(t.params[4]/v)], []) , VTensor(Tensor(Concat(l1, [L(t.params[1], t.params[2])], l2)), v))),\n ),\n\n#GV1 shouldn't be enabled for stuff that are not strides!\n#It is highly disruptive because it doesn't respect the VTensor VPerm nomenclatura\n#F L_GV1: TL(kmbc,kb,r,s) = I_r tensor ((L(kbm,bk) tensor I_c) * (I_m tensor TL(bc,b,k,1)) * (I_m tensor L(kc,k) tensor I_b)) tensor I_s\n L_GV1 := rec(\n switch:=false,\n forTransposition := false,\n freedoms := nt -> [\n MapN(\n DoubleDivisorPairsVector(nt.params[1] / nt.params[2], nt.params[2], nt.firstTag().v),\n (m,c,k,b) -> [b,c]\n )\n ],\n child := (nt,freedoms) -> let(b:=freedoms[1][1],c:=freedoms[1][2], [TL(bc,b,1,1).withTags(nt.getTags())]),\n apply := (nt,C,cnt) -> let(\n n:=nt.params[1],\n b:=cnt[1].params[2],\n c:=cnt[1].params[1]/b,\n k:=nt.params[2]/b,\n m:=nt.params[1]/(kbc),\n r:=nt.params[3],\n s:=nt.params[4],\n Tensor(\n I(r),\n Tensor(\n Tensor(L(kbm,bk),I(c))\n * Tensor(I(m),Tensor(I(k),C[1]))\n * Tensor(Tensor(I(m),L(kc,k)),I(b)),\n I(s))\n )\n )\n#D freedoms := nt -> [MapN(DoubleDivisorPairsVector(nt.params[1]/nt.params[2],nt.params[2],GetFirstTag(nt).v),(m,c,k,b) -> [b,c])],\n#D child := (nt,freedoms) -> let(b:=freedoms[1][1],c:=freedoms[1][2], [TL(bc,b,1,1,GetTags(nt))]),\n#D apply := (nt,C,cnt) -> let(\n#D n:=nt.params[1],b:=cnt[1].params[2],c:=cnt[1].params[1]/b,k:=nt.params[2]/b,m:=nt.params[1]/(kbc),r:=nt.params[3],s:=nt.params[4],\n#D Tensor(I(r),(Tensor(\n#D Tensor(L(kbm,bk),I(c))\n#D Tensor(I(m),Tensor(I(k),C[1]))\n#D Tensor(Tensor(I(m),L(kc,k)),I(b))\n#D , I(s)))))),\n ),\n\n\n L_GV1_vtensor := rec(\n switch:=false,\n forTransposition := false,\n applicable := nt -> let(p := nt.params,\n nt.isTag(1, AVecReg)\n and p[1] <> p[2]\n and p[2] <> 1\n and Length(\n DoubleDivisorPairsVectorBlocking(p[1] / p[2], p[2], nt.firstTag().v)\n ) > 0\n ),\n freedoms := nt -> let(p := nt.params, [\n MapN(\n DoubleDivisorPairsVectorBlocking(p[1] / p[2], p[2], nt.firstTag().v),\n (m,c,k,b) -> [b,c]\n )\n ]),\n child := (nt, freedoms) -> let(\n b:=freedoms[1][1],\n c:=freedoms[1][2],\n [ TL(bc,b,1,1).withTags(nt.getTags()) ]\n ),\n apply := (nt,C,cnt) -> let(\n n := nt.params[1],\n b := cnt[1].params[2],\n c := cnt[1].params[1]/b,\n k := nt.params[2]/b,\n m := nt.params[1]/(kbc),\n r := nt.params[3],\n s := nt.params[4],\n v := nt.firstTag().v,\n# garbage:=fPrint([\"n:\",n,\" b:\",b,\" c:\",c,\" k:\",k,\" m:\",m,\" r:\",r,\" s:\",s, \" v:\",v,\"\\n\"]),\n prefactor := When(r = 1, [], [I(r)]),\n firstfactor := When(m = 1 or (b = 1 and k = 1),\n [],\n [When(c=1,L(kbm,bk), VTensor(Tensor(L(kbm,bk),I(c/v)),v))]\n ),\n middlefactor := [ Tensor(I(m), Tensor(I(k), C[1])) ],\n# middlefactor:=When(k>1 and bc<1024,[Tensor(I(m),I(k/2),BB(Tensor(I(2),C[1])))],[Tensor(I(m),Tensor(I(k),C[1]))]),\n thirdfactor := When(c=1 or k=1,\n [],\n [\n When(b=1,\n Tensor(I(m),L(kc,k)),\n VTensor(Tensor(I(m),L(kc,k),I(b/v)),v)\n )\n ]\n ),\n postfactor := When(r=s, [], [I(s)]),\n\n Tensor(Concat(\n prefactor,\n [Compose(Concat(\n firstfactor,\n middlefactor,\n thirdfactor\n ))],\n postfactor\n ))\n )\n#D applicable := (self, nt)>> FirstTagEq(nt, AVecReg) and (nt.params[1]<>nt.params[2]) and (nt.params[2]<>1) and\n#D (Length(DoubleDivisorPairsVectorBlocking(nt.params[1]/nt.params[2],nt.params[2],GetFirstTag(nt).v))>0),\n#D freedoms := nt -> [MapN(DoubleDivisorPairsVectorBlocking(nt.params[1]/nt.params[2],nt.params[2],GetFirstTag(nt).v),(m,c,k,b) -> [b,c])],\n#D child := (nt,freedoms) -> let(b:=freedoms[1][1],c:=freedoms[1][2], [TL(bc,b,1,1,GetTags(nt))]),\n#D apply := (nt,C,cnt) -> let(\n#D n:=nt.params[1],b:=cnt[1].params[2],c:=cnt[1].params[1]/b,k:=nt.params[2]/b,m:=nt.params[1]/(kbc),r:=nt.params[3],s:=nt.params[4],v:=GetFirstTag(nt).v,\n#D# garbage:=fPrint([\"n:\",n,\" b:\",b,\" c:\",c,\" k:\",k,\" m:\",m,\" r:\",r,\" s:\",s, \" v:\",v,\"\\n\"]),\n#D prefactor :=When(r=1, [], [I(r)]),\n#D firstfactor:=When(m=1 or (b=1 and k=1), [],[When(c=1,L(kbm,bk), VTensor(Tensor(L(kbm,bk),I(c/v)),v))]),\n#D middlefactor:=[Tensor(I(m),Tensor(I(k),C[1]))],\n#D# middlefactor:=When(k>1 and bc<1024,[Tensor(I(m),I(k/2),BB(Tensor(I(2),C[1])))],[Tensor(I(m),Tensor(I(k),C[1]))]),\n#D thirdfactor:=When(c=1 or k=1, [], [When(b=1,Tensor(I(m),L(kc,k)), VTensor(Tensor(I(m),L(kc,k),I(b/v)),v))]),\n#D postfactor :=When(r=s, [], [I(s)]),\n#D Tensor(Concat(\n#D prefactor,\n#D [Compose(Concat(\n#D firstfactor,\n#D middlefactor,\n#D thirdfactor))\n#D ],\n#D postfactor))))\n )\n));\n\n\n\n\n\n\n######################################################################\n# OBSOLETE RULES\n######################################################################\n\nNewRulesFor(TL,rec(\n\n # L^nv_n -> (I_n/v x L^v2_v)(L^n_n/v x I_v)\n # superseeded by L_mn_m_vec with n=v\n L_nv_n_vec := rec(\n switch := false,\n forTransposition := false,\n applicable := t ->\n t.params[3] = 1\n and t.params[4] = 1\n and (t.isTag(1, AVecReg) or t.isTag(1, AVecRegCx))\n and let (v := t.firstTag().v,\n t.params[1] = t.params[2] * v\n and t.params[2] <> v\n and IsInt(t.params[2]/v)\n ),\n freedoms := (self, t) >> [],\n child := (nt,freedoms) -> let(\n v := nt.firstTag().v,\n [ TL(vv, v, 1, 1).withTags(nt.getTags()) ]\n ),\n apply := (nt, C, cnt) -> let (\n v := nt.firstTag().v,\n n := nt.params[2],\n SymSPL(\n BlockVPerm(n/v, v, C[1], L(v^2,v))\n ) VTensor(L(n, n/v), v)\n )\n#D applicable := (self, t) >> t.params[3] = 1 and t.params[4] = 1 and FirstTagEq(t, AVecReg) and\n#D let (v := GetFirstTag(t).v, t.params[1] = t.params[2] * v and t.params[2] <> v and IsInt(t.params[2]/v)),\n#D freedoms := (self, t) >> [],\n#D child := (nt,freedoms) -> let (v := GetFirstTag(nt).v, [TL(vv, v, 1, 1, GetTags(nt))]),\n#D apply := (nt,C,cnt) -> let (v := GetFirstTag(nt).v, n:= nt.params[2], SymSPL(BlockVPerm(n/v, v, C[1], L(v^2,v))) VTensor(L(n, n/v), v))),\n #SymSPL-BlockVPerm can be replaced by Tensor(I(n/v), C[1])\n ),\n\n\n\n #L^nv_v -> (L^n_v x I_v)(I_n/v x L^v2_v)\n # superseeded by L_mn_m_vec with m=v\n L_nv_v_vec := rec(\n switch := false,\n forTransposition := false,\n applicable := t ->\n t.params[3] = 1\n and t.params[4] = 1\n and (t.isTag(1, AVecReg) or t.isTag(1, AVecRegCx))\n and let(v := t.firstTag().v,\n t.params[2] = v\n and t.params[1] <> v * v\n and IsInt(t.params[1]/(vv))\n ),\n freedoms := (self, t) >> [],\n child := (nt, freedoms) -> let(v := nt.firstTag().v, [ TL(vv, v, 1, 1).withTags(nt.getTags()) ]),\n apply := (nt, C, cnt) -> let(\n v := nt.firstTag().v,\n n:= nt.params[1]/v,\n VTensor(L(n, v), v)\n * SymSPL(BlockVPerm(n/v, v, C[1], L(v^2,v)))\n )\n#D applicable := (self, t) >> t.params[3] = 1 and t.params[4] = 1 and FirstTagEq(t, AVecReg) and\n#D let (v := GetFirstTag(t).v, t.params[2] = v and t.params[1] <> v * v and IsInt(t.params[1]/(vv))),\n#D freedoms := (self, t) >> [],\n#D child := (nt,freedoms) -> let (v := GetFirstTag(nt).v, [TL(vv, v, 1, 1, GetTags(nt))]),\n#D apply := (nt,C,cnt) -> let (v := GetFirstTag(nt).v, n:= nt.params[1]/v, VTensor(L(n, v), v) * SymSPL(BlockVPerm(n/v, v, C[1], L(v^2,v))))),\n #SymSPL-BlockVPerm can be replaced by Tensor(I(n/v), C[1])))\n )\n\n));\n", "meta": {"hexsha": "cb4ed63170949666cb18313f65c2960282a64c40", "size": 15597, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/vector/breakdown/tl_rec.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/paradigms/vector/breakdown/tl_rec.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", 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	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n#F Perm_CCS(<n>) - SPL objects for CCS -> Perm IPP data format conversion\n#F \n#F Returns an SPL object that converts the result of an RDFT in CCS format into\n#F Perm format. Both of these formats are defined in the IPP manual. \n#F IPP manual does not define Perm format for odd RDFT size, so in this case\n#F we defined it to coincide with CCS.\n#F\n#F The output of SPIRAL's PRDFT transform is equivalent to IPP CCS format. \n#F Suggested uses are:\n#F Perm_CCS(n) * PRDFT(n) \n#F IPRDFT(n) * Perm_CCS(n).transpose()\n#F \nPerm_CCS := n -> When(IsEvenInt(n), \n Gath(H(n+2,n,0,1))Perm((2,n+1),n+2),\n DirectSum(Mat([[1,0]]), I(n-1))\n);\n\n\n#F Pack_CCS(<n>) - SPL objects for CCS -> Pack IPP data format conversion of RDFT of type 1\n#F \n#F Returns an SPL object that converts the result of an RDFT in CCS format into\n#F Pack format. Both of these formats are defined in the IPP manual. \n#F\n#F The output of SPIRAL's PRDFT transform is equivalent to IPP CCS format. \n#F Suggested uses are:\n#F Pack_CCS(n) PRDFT(n) \n#F IPRDFT(n) * Pack_CCS(n).transpose()\n#F \nPack_CCS := n -> When(IsEvenInt(n), \n DirectSum(Mat([[1,0]]), When(n=2, [], I(n-2)), Mat([[1,0]])),\n DirectSum(Mat([[1,0]]), I(n-1))\n);\n\n#F Pack_CCS(<n>) - SPL objects for CCS -> Pack IPP data format conversion of RDFT of type 3\n#F\n#F [ note that IPP does not have RDFT of type 3, we just use their format terminology ]\n#F Returns an SPL object that converts the result of an RDFT in CCS format into\n#F Pack format. Both of these formats are defined in the IPP manual. \n#F Perm format does not make sense for PRDFT3.\n#F\n#F The output of SPIRAL's PRDFT3 transform is equivalent to IPP CCS format. \n#F Suggested uses are:\n#F Pack_CCS3(n) * PRDFT3(n) \n#F PRDFT3(n).inverse() * Pack_CCS3(n).transpose()\n#F \nPack_CCS3 := n -> When(IsEvenInt(n), \n I(n), \n DirectSum(I(n-1), Mat([[1,0]]))\n);\n", "meta": {"hexsha": "b472c296f6f80a9e6ef3a469520c24b9dd61bf1f", "size": 1960, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/realdft/formats.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/transforms/realdft/formats.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/transforms/realdft/formats.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 35.6363636364, "max_line_length": 91, "alphanum_fraction": 0.6775510204, "num_tokens": 627, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.800692021119887, "lm_q2_score": 0.6334102705979902, "lm_q1q2_score": 0.5071665497631993}}
	{"text": "############################################################################\n##\n## primitive.gi IRREDSOL Burkhard Höfling\n##\n## Copyright © 2003–2016 Burkhard Höfling\n##\n\n\n############################################################################\n##\n#F PcGroupExtensionByMatrixAction(<pcgs>, <hom>)\n##\n## Let <G> be a finite soluble group with pcgs <pcgs>, and let <hom> be a \n## group hom. $<hom>\\colon G \\to GL(n, p)$, where $p$ is a prime. Let $E$ \n## denote the split\n## extension of $G$ by $V = \\F_p$, where <G> acts on <V> via <hom>.\n## This function returns a record with the following components.\n## ext: the group $E$ as a new pc group\n## V: the subgroup $V$ of $E$ corresponding to the vector space\n## C: a complement of $V$ in $E$ isomorphic with $G$\n## embed: a group homomorphism $G \\to E$ with image $C$\n## proj: a group homomorphism $E \\to G$ with kernel $V$\n## pcgsV: an induced pcgs of V (wrt. FamilyPcgs(E)) whose elements \n## correspond to the natural basis elements\n## of the vector space V\n## pcgsC: an induced pcgs of C (wrt. FamilyPcgs(E)) whose elements \n## correspond to the images of pcgs under embed; \n## the elements of pcgsC act on pcgsV as the images of pcgs\n## under hom act on the natural basis of V\n## \nInstallGlobalFunction(PcGroupExtensionByMatrixAction,\n function(pcgs, hom)\n local p, d, ros, f, coll, exp, mat, i, j, r, E, pcgsC, pcgsV;\n \n p := Size(FieldOfMatrixGroup(Range(hom)));\n d := DegreeOfMatrixGroup(Range(hom));\n if not IsPrimeInt(p) then\n Error(\"Range(hom) must be over a prime field \");\n fi;\n \n ros := RelativeOrders(pcgs);\n \n f := FreeGroup(Length(pcgs) + d);\n coll := SingleCollector(f,\n Concatenation(ros, \n ListWithIdenticalEntries(d, p)));\n \n # relations for complement - same as for those for G \n exp := []; \n exp{[1,3..2Length(pcgs)-1]} := [1..Length(pcgs)];\n for i in [1..Length(pcgs)] do\n exp{[2,4..2Length(pcgs)]} := ExponentsOfPcElement(pcgs, pcgs[i]^ros[i]);\n # Print(\"power relation \", i,\": \", exp, \"\\n\");\n SetPower(coll, i, ObjByExtRep(FamilyObj(f.1), exp));\n for j in [i+1..Length(pcgs)] do\n exp{[2,4..2Length(pcgs)]} := ExponentsOfPcElement(pcgs, pcgs[j]^pcgs[i]);\n # Print(\"conj. relation \", j, \"^\", i,\": \", exp, \"\\n\");\n SetConjugate(coll, j, i, ObjByExtRep(FamilyObj(f.1), exp));\n od;\n od;\n \n # relations for socle\n for j in [1..d] do\n SetPower(coll, j+Length(pcgs), One(f));\n od;\n \n exp := [];\n exp{[1,3..2d-1]} := \n [Length(pcgs) + 1..Length(pcgs) + d];\n \n for i in [1..Length(pcgs)] do\n mat := ImageElm(hom, pcgs[i]);\n for j in [1..d] do\n exp{[2,4..2d]} := List(mat[j], IntFFE);\n # Print(\"conj. relation \", j+ Length(pcgs), \"^\", i,\": \", exp, \"\\n\");\n SetConjugate(coll, j + Length(pcgs), i, ObjByExtRep(FamilyObj(f.1), exp));\n od;\n od;\n \n E := GroupByRwsNC(coll);\n SetSize(E, Product(ros) p^d);\n pcgsV := InducedPcgsByPcSequenceNC(FamilyPcgs(E),\n FamilyPcgs(E){[Length(pcgs) + 1..Length(FamilyPcgs(E))]});\n\n # the following sets attributes/properties which are defined \n # in the CRISP packages\n \n pcgsC := InducedPcgsByPcSequenceNC(FamilyPcgs(E),\n FamilyPcgs(E){[1..Length(pcgs)]});\n\n r := rec(\n E := E, \n V := GroupOfPcgs(pcgsV), \n C := GroupOfPcgs(pcgsC),\n pcgsV := pcgsV,\n pcgsC := pcgsC); \n r.embed := GroupHomomorphismByImagesNC(GroupOfPcgs(pcgs), E, pcgs, pcgsC);\n SetIsInjective(r.embed, true);\n SetImagesSource(r.embed, r.C);\n r.proj := GroupHomomorphismByImagesNC(E, GroupOfPcgs(pcgs), \n Concatenation(pcgsC, pcgsV), \n Concatenation(pcgs, ListWithIdenticalEntries(d, OneOfPcgs(pcgs))));\n SetIsSurjective(r.proj, true);\n SetKernelOfMultiplicativeGeneralMapping(r.proj, r.V);\n return r;\n end);\n\n \n############################################################################\n##\n#F PrimitivePcGroupIrreducibleMatrixGroup(<G>)\n##\n## see IRREDSOL documentation\n## \nInstallGlobalFunction(PrimitivePcGroupIrreducibleMatrixGroup,\n function(G)\n \n if not IsMatrixGroup(G) or not IsFinite(FieldOfMatrixGroup(G))\n or not IsPrimeInt(Size(FieldOfMatrixGroup(G)))\n or not IsIrreducibleMatrixGroup(G) then\n Error(\"G must be an irreducible matrix group over a prime field\");\n fi;\n\n return PrimitivePcGroupIrreducibleMatrixGroupNC(G);\n end);\n \n \n############################################################################\n##\n#F PrimitivePcGroupIrreducibleMatrixGroupNC(<G>)\n##\n## see IRREDSOL documentation\n##\n## it is important that the map from Pcgs(Source(RepresentationIsomorphism(G)))\n## \nInstallGlobalFunction(PrimitivePcGroupIrreducibleMatrixGroupNC,\n function(G)\n \n local rep, ext;\n \n rep := RepresentationIsomorphism(G);\n ext := PcGroupExtensionByMatrixAction(Pcgs(Source(rep)), rep);\n SetSocle(ext.E, ext.V);\n SetSocleComplement(ext.E, ext.C);\n SetFittingSubgroup(ext.E, ext.V);\n\n # the following sets attributes/properties which are defined \n # in the CRISP packages\n \n if IsBoundGlobal(\"SetIsPrimitiveSoluble\") then\n ValueGlobal(\"SetIsPrimitiveSoluble\")(ext.E, true);\n fi;\n return ext.E;\n \n end);\n \n\n \n\n############################################################################\n##\n#F PrimitivePcGroup(<n>,<p>,<d>,<k>)\n##\n## see IRREDSOL documentation\n## \nInstallGlobalFunction(PrimitivePcGroup,\n function(n, p, d, k)\n \n local q, desc, G, mat, bas, hom, ext, o, pcgs, pcgsC, pcgsV, H;\n \n if not IsPosInt(n) or not IsPosInt(d) or not IsPosInt(p) or not IsPrimeInt(p) or n mod d <> 0 then\n Error(\"n, p, and d must be positive integers, \",\n \"p must be a prime, and d must divide n\");\n elif not k in IndicesIrreducibleSolubleMatrixGroups(n, p, d) then\n Error(\"k must be in IndicesIrreducibleSolubleMatrixGroups(n, p, d)\");\n else \n n := n /d;\n q := p^d;\n LoadAbsolutelyIrreducibleSolubleGroupData(n, q);\n if n > 1 then\n desc := IRREDSOL_DATA.GROUPS[n][q][k];\n fi;\n if not IsBound(IRREDSOL_DATA.PRIM_GUARDIANS[n]) then\n IRREDSOL_DATA.PRIM_GUARDIANS[n] := [];\n fi;\n if not IsBound(IRREDSOL_DATA.PRIM_GUARDIANS[n][q]) then\n if n = 1 then\n G := IRREDSOL_DATA.GUARDIANS[1][q][1];\n mat := [[Z(q)]];\n hom := GroupHomomorphismByImagesNC(G, Group(mat), \n MinimalGeneratingSet(G), [mat]);\n SetIsBijective(hom, true);\n else\n hom := IRREDSOL_DATA.GUARDIANS[n][q][desc[1]][3];\n G := Source(hom);\n fi;\n if d > 1 then\n bas := CanonicalBasis(AsVectorSpace(GF(p), GF(q)));\n mat := List(InducedPcgsWrtFamilyPcgs(G), \n g -> BlownUpMat(bas, ImageElm(hom, g)));\n hom := GroupHomomorphismByImagesNC(G, Group(mat), \n InducedPcgsWrtFamilyPcgs(G), mat);\n fi;\n \n IRREDSOL_DATA.PRIM_GUARDIANS[n][q] := \n PcGroupExtensionByMatrixAction(InducedPcgsWrtFamilyPcgs(G), hom);\n\n fi;\n ext := IRREDSOL_DATA.PRIM_GUARDIANS[n][q];\n if n = 1 then\n Assert(1, Length(MinimalGeneratingSet(ext.C)) = 1);\n o := IRREDSOL_DATA.GROUPS_DIM1[q][k][1];\n pcgsC := InducedPcgsByGenerators(FamilyPcgs(ext.E),\n [MinimalGeneratingSet(ext.C)[1]^((q-1)/o)]);\n else\n pcgsC := CanonicalPcgsByNumber(ext.pcgsC, desc[2]);\n fi;\n pcgs := InducedPcgsByPcSequenceNC(FamilyPcgs(ext.E), Concatenation(pcgsC, ext.pcgsV));\n H := GroupOfPcgs(pcgs);\n SetIdPrimitiveSolubleGroup(H, [nd,p,d,k]);\n SetSocle(H, ext.V);\n SetFittingSubgroup(H, ext.V);\n SetSocleComplement(H, GroupOfPcgs(pcgsC));\n\n # the following sets attributes/properties which are defined \n # in the CRISP packages\n \n if IsBoundGlobal(\"SetIsPrimitiveSoluble\") then\n ValueGlobal(\"SetIsPrimitiveSoluble\")(H, true);\n fi;\n return H;\n fi;\n end);\n \n \n############################################################################\n##\n#F IrreducibleMatrixGroupPrimitiveSolubleGroup(<G>)\n##\n## see IRREDSOL documentation\n## \nInstallGlobalFunction(IrreducibleMatrixGroupPrimitiveSolubleGroup,\n function(G)\n\n local F, p, matgrp, compl;\n\n if not IsFinite(G) or not IsSolvableGroup(G) then\n Error(\"G must be finite and soluble\");\n \n # test if primitive - use the CRISP method if it is available \n elif IsBoundGlobal(\"IsPrimitiveSoluble\") \n and ValueGlobal(\"IsPrimitiveSoluble\")(G) then\n return IrreducibleMatrixGroupPrimitiveSolubleGroupNC(G);\n \n else # test for primitivity\n F := FittingSubgroup(G);\n \n if not IsPGroup(F) or not IsAbelian(F) then\n Error(\"G must be primitive\");\n else\n p := PrimePGroup(F);\n\n if ForAny(GeneratorsOfGroup(F), x -> x^p <> One(G)) then\n Error(\"G must be primitive\");\n else\n matgrp := IrreducibleMatrixGroupPrimitiveSolubleGroupNC(G);\n if not IsIrreducibleMatrixGroup(matgrp, GF(p)) then\n Error(\"G must be primitive\");\n else\n compl := ComplementClassesRepresentatives(G, F);\n if Length(compl) <> 1 then\n Error(\"G must be primitive\");\n fi;\n SetSocle(G, F);\n return matgrp;\n fi;\n fi;\n fi;\n fi;\n end);\n \n \n############################################################################\n##\n#F IrreducibleMatrixGroupPrimitiveSolubleGroupNC(<G>)\n##\n## see IRREDSOL documentation\n## \nInstallGlobalFunction(IrreducibleMatrixGroupPrimitiveSolubleGroupNC,\n function(G)\n \n local N, p, F, pcgsN, pcgsGmodN, GmodN, one, mat, mats, g, h, i, H, hom;\n \n N := FittingSubgroup(G);\n \n pcgsN := Pcgs(N);\n p := RelativeOrders(pcgsN)[1];\n F := GF(p);\n one := One(F);\n \n mats := [];\n \n pcgsGmodN := ModuloPcgs(G, N);\n for g in pcgsGmodN do\n mat := [];\n for i in [1..Length(pcgsN)] do\n mat[i] := ExponentsOfPcElement(pcgsN, pcgsN[i]^g)one;\n od;\n Add(mats, ImmutableMatrix(F, mat));\n od;\n H := Group(mats);\n SetSize(H, Size(G)/Size(N));\n GmodN := PcGroupWithPcgs(pcgsGmodN);\n hom := GroupGeneralMappingByImagesNC(GmodN, H, FamilyPcgs(GmodN), mats);\n SetIsGroupHomomorphism(hom, true);\n SetIsBijective(hom, true);\n SetRepresentationIsomorphism(H, hom);\n return H;\n end);\n \n\n############################################################################\n##\n#F DoIteratorPrimitiveSolubleGroups(<convert_func>, <arg_list>)\n##\n## generic constructor function for an iterator of all primitive soluble groups\n## which can construct permutation groups or pc groups (or other types of groups),\n## depending on convert_func\n## \nInstallGlobalFunction(DoIteratorPrimitiveSolubleGroups, \n function(convert_func, arg_list)\n\n local r, iter;\n \n r := CheckAndExtractArguments([\n [[Degree, NrMovedPoints, LargestMovedPoint], IsPosInt],\n [[Order, Size], IsPosInt]],\n arg_list, \n \"IteratorPrimitivePcGroups\");\n if ForAny(r.specialvalues, v -> IsEmpty(v)) then\n return Iterator([]);\n fi;\n\n iter := rec(convert_func := convert_func);\n\n if not IsBound(r.specialvalues[1]) then \n Error(\"IteratorPrimitivePcGroupsIterator: You must specify the degree(s) of the desired primitive groups\");\n else\n iter.degs := Filtered(r.specialvalues[1], IsPPowerInt);\n fi; \n \n iter.degind := 0;\n \n if IsBound(r.specialvalues[2]) then\n iter.orders := r.specialvalues[2];\n else\n iter.orders := fail;\n fi;\n \n iter.iteratormatgrp := Iterator([]);\n\n iter.IsDoneIterator := function(iterator)\n\n local d, p, n, orders, o;\n \n if iterator!.degind > Length(iterator!.degs) then\n Error(\"isDoneIterator called after it returned true\");\n fi;\n \n while IsDoneIterator(iterator!.iteratormatgrp) do\n iterator!.degind := iterator!.degind + 1;\n if iterator!.degind > Length(iterator!.degs) then\n return true;\n fi;\n d := iterator!.degs[iterator!.degind];\n p := SmallestRootInt(d);\n n := LogInt(d, p);\n if IsAvailableIrreducibleSolubleGroupData(n, p) then \n if iterator!.orders <> fail then\n orders := [];\n for o in iterator!.orders do\n if o mod d = 0 then\n Add(orders, o/d);\n fi;\n od;\n iterator!.iteratormatgrp := IteratorIrreducibleSolubleMatrixGroups(\n Degree, n, Field, GF(p), Order, orders);\n else\n iterator!.iteratormatgrp := IteratorIrreducibleSolubleMatrixGroups(\n Degree, n, Field, GF(p));\n\n fi;\n else\n Error(\"groups of degree \", d, \" are beyond the scope of the IRREDSOL library\");\n iterator!.iteratormatgrp := Iterator([]);\n fi;\n od;\n return false;\n end;\n\n iter.NextIterator := function(iterator)\n \n local G;\n \n G := NextIterator(iterator!.iteratormatgrp);\n return iterator!.convert_func(G);\n end;\n \n iter.ShallowCopy := function(iterator)\n return rec(\n orders := iterator!.orders,\n degs := iterator!.degs,\n degind := iterator!.degind,\n convert_func := iterator!.convert_func,\n iteratormatgrp := ShallowCopy(iterator!.iteratormatgrp),\n IsDoneIterator := iterator!.IsDoneIterator,\n NextIterator := iterator!.NextIterator,\n ShallowCopy := iterator!.ShallowCopy);\n end;\n return IteratorByFunctions(iter);\n end);\n \n \n############################################################################\n##\n#F IteratorPrimitivePcGroups(<func_1>, <val_1>, ...)\n##\n## see the IRREDSOL manual\n## \nInstallGlobalFunction(IteratorPrimitivePcGroups,\n function(arg)\n return DoIteratorPrimitiveSolubleGroups(\n PrimitivePcGroupIrreducibleMatrixGroupNC,\n arg);\n end);\n \n\n###########################################################################\n##\n#F AllPrimitivePcGroups(<arg>)\n##\n## see IRREDSOL documentation\n## \nInstallGlobalFunction(AllPrimitivePcGroups,\n function(arg)\n \n local iter, l, G;\n \n iter := CallFuncList(IteratorPrimitivePcGroups, arg);\n \n l := [];\n for G in iter do\n Add(l, G);\n od;\n return l;\n end);\n\n\n###########################################################################\n##\n#F OnePrimitivePcGroup(<arg>)\n##\n## see IRREDSOL documentation\n## \nInstallGlobalFunction(OnePrimitivePcGroup,\n function(arg)\n \n local iter;\n \n iter := CallFuncList(IteratorPrimitivePcGroups, arg);\n if IsDoneIterator(iter) then\n return fail;\n else \n return NextIterator(iter);\n fi;\n end);\n\n\n############################################################################\n##\n#F PrimitivePermGroupIrreducibleMatrixGroup(<G>)\n##\n## see IRREDSOL documentation\n## \nInstallGlobalFunction(PrimitivePermGroupIrreducibleMatrixGroup,\n function(G)\n \n if not IsMatrixGroup(G) or not IsFinite(FieldOfMatrixGroup(G))\n or not IsPrimeInt(Size(FieldOfMatrixGroup(G)))\n or not IsIrreducibleMatrixGroup(G) then\n Error(\"G must be an irreducible matrix group over a prime field\");\n fi;\n\n return PrimitivePermGroupIrreducibleMatrixGroupNC(G);\n end);\n \n \n############################################################################\n##\n#F PrimitivePermGroupIrreducibleMatrixGroupNC(<G>)\n##\n## see IRREDSOL documentation\n## \nInstallGlobalFunction(PrimitivePermGroupIrreducibleMatrixGroupNC, \n function( M )\n local gensc, genss, V, bas, enum, G;\n V := FieldOfMatrixGroup( M ) ^ DimensionOfMatrixGroup( M );\n bas := CanonicalBasis(V);\n enum := EnumeratorByBasis(bas);\n gensc := List(GeneratorsOfGroup(M), x -> Permutation(x, enum));\n genss := List( bas, x -> Permutation( x, enum, \\+));\n G := GroupByGenerators(Concatenation(genss, gensc));\n SetSize( G, Size( M ) * Size( V ) );\n SetSocle(G, Subgroup(G, genss));\n SetSocleComplement(G, Subgroup(G, gensc));\n \n # the following sets attributes/properties which are defined \n # in the CRISP packages\n\n if IsBoundGlobal(\"SetIsPrimitiveSoluble\") then\n ValueGlobal(\"SetIsPrimitiveSoluble\")(G, true);\n fi;\n return G;\n end);\n\n\n############################################################################\n##\n#F PrimitiveSolublePermGroup(<n>,<p>,<d>,<k>)\n##\n## see IRREDSOL documentation\n## \nInstallGlobalFunction(PrimitiveSolublePermGroup,\n function(n, p, d, k)\n\n local G;\n if not IsPosInt(n) or not IsPosInt(d) or not IsPosInt(p) or not IsPrimeInt(p) then\n Error(\"n, p, and d must be positive integers, \",\n \"p must be a prime, and d must divide n\");\n elif not k in IndicesIrreducibleSolubleMatrixGroups(n, p, d) then\n Error(\"k must be in IndicesIrreducibleSolubleMatrixGroups(n, p, d)\");\n else\n G := PrimitivePermGroupIrreducibleMatrixGroupNC(\n IrreducibleSolubleMatrixGroup(n, p, d, k));\n SetIdPrimitiveSolubleGroup(G, [n,p,d,k]);\n fi;\n return G;\n end);\n \n \n############################################################################\n##\n#F IteratorPrimitiveSolublePermGroups(<func_1>, <val_1>, ...)\n##\n## see the IRREDSOL manual\n## \nInstallGlobalFunction(IteratorPrimitiveSolublePermGroups,\n function(arg)\n return DoIteratorPrimitiveSolubleGroups(\n PrimitivePermGroupIrreducibleMatrixGroupNC,\n arg);\n end);\n \n\n###########################################################################\n##\n#F AllPrimitiveSolublePermGroups(<arg>)\n##\n## see IRREDSOL documentation\n## \nInstallGlobalFunction(AllPrimitiveSolublePermGroups,\n function(arg)\n \n local iter, l, G;\n \n iter := CallFuncList(IteratorPrimitiveSolublePermGroups, arg);\n \n l := [];\n for G in iter do\n Add(l, G);\n od;\n return l;\n end);\n\n\n###########################################################################\n##\n#F OnePrimitiveSolublePermGroup(<arg>)\n##\n## see IRREDSOL documentation\n## \nInstallGlobalFunction(OnePrimitiveSolublePermGroup,\n function(arg)\n \n local iter;\n \n iter := CallFuncList(IteratorPrimitiveSolublePermGroups, arg);\n if IsDoneIterator(iter) then\n return fail;\n else \n return NextIterator(iter);\n fi;\n end);\n\n\n############################################################################\n##\n#E\n##\n \n \n \n\n \n", "meta": {"hexsha": "a6312c0eaacdf858709da9e0c35e07d6ca2c21f2", "size": 21072, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "lib/primitive.gi", "max_stars_repo_name": "fingolfin/irredsol", "max_stars_repo_head_hexsha": "c7ab06f5123650049142a5ae3a1c1e05a38d2151", "max_stars_repo_licenses": ["BSD-2-Clause"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2017-09-01T16:53:11.000Z", "max_stars_repo_stars_event_max_datetime": "2017-09-01T16:53:11.000Z", "max_issues_repo_path": "lib/primitive.gi", "max_issues_repo_name": "fingolfin/irredsol", "max_issues_repo_head_hexsha": "c7ab06f5123650049142a5ae3a1c1e05a38d2151", "max_issues_repo_licenses": ["BSD-2-Clause"], "max_issues_count": 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	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n#F Circulant(<n>, <filt-func>, <valuation>) -- n x n circulant matrix non-terminal\n#F\n#F The circulant matrix with coefficients of the first row given by\n#F the filter function <filt-func>.\n#F\n#F <valuation> is the offset, default = 0, meaning no offset.\n#F\n#F Examples:\n#F\n#F spiral> PrintMat(MatSPL( Circulant(5, FList(TInt, [1..3]), 0)));\n#F [ [ 1, 2, 3, , ], \n#F [ , 1, 2, 3, ], \n#F [ , , 1, 2, 3 ], \n#F [ 3, , , 1, 2 ], \n#F [ 2, 3, , , 1 ] ]\n#F spiral> PrintMat(MatSPL( Circulant(5, FList(TInt, [1..3]), -1)));\n#F [ [ 2, 3, , , 1 ], \n#F [ 1, 2, 3, , ], \n#F [ , 1, 2, 3, ], \n#F [ , , 1, 2, 3 ], \n#F [ 3, , , 1, 2 ] ]\n\nClass(Circulant, NonTerminal, rec(\n _short_print := true,\n\n abbrevs := [ \n (L) -> [ toSize(L), toFunc(L), toValuation(L) ],\n (n,L) -> [ Checked(IsPosInt(n), n), toFunc(L), toValuation(L) ],\n (n,L,v) -> [ Checked(IsPosInt(n), n), toFunc(L), Checked(IsInt(v), v) ], \n ], \n\n dims := self >> Replicate(2, self.params[1]), \n\n setData := meth(self, newdata) self.params[2] := newdata; return self; end,\n\n column := self >> let(\n\tcoeffs := List(self.params[2].tolist(), x->x.ev()),\n\tvaluation := self.params[3],\n\tCircularWrap([coeffs, valuation], self.params[1])),\n\n terminate := meth(self)\n local i, j, n, L, Ls, mat;\n L := self.column();\n n := Length(L);\n mat := [ ];\n for i in [0..n-1] do\n Ls := Replicate(n, 0);\n\t for j in [0..n-1] do Ls[(i-j) mod n + 1] := L[j+1]; od;\n\t Add(mat,Ls);\n od;\n return Mat(mat); \n end,\n\n filtlen := self >> self.params[2].domain(),\n\n transpose := self >> Circulant(\n\tself.params[1],\n\tfCompose(self.params[2], J(self.filtlen())),\n\t-self.params[3]-self.filtlen()+1),\n \n isReal := self >> not IsComplexT(self.params[2].range()),\n\n hashAs := self >> let(\n\tt := ObjId(self)(\n\t self.params[1], fUnk(self.params[2].range(), self.params[2].domain()), self.params[3]),\n\tWhen(self.transposed, t.transpose(), t)),\n\n SmallRandom := () -> let(n := Random([2..16]),\n\tList([1..n], i -> Float(Random([-2^10..2^10]), Random([-20..10])))),\n\n LargeRandom := () -> let(n := Random([16, 32, 64]),\n\tList([1..n], i -> Float(Random([-2^10..2^10]), Random([-20..10]))))\n));\n\n## \n## Rules\n##\nRulesFor(Circulant, rec(\n ###################################################################\n ## Time domain methods\n ###################################################################\n\n #F Circulant_Base: (base case)\n #F\n Circulant_Base := rec (\n\tinfo := \"Circulant -> Mat\",\n\tforTransposition := false,\n\tisApplicable := P -> P[1] <= 32, \n\tallChildren := P -> [[ ]],\n\trule := (P, C) -> ApplyFunc(Circulant, P).terminate()\n ),\n\n# Circulant_toFilt := rec (\n# \tinfo := \"Circulant -> VStack(.., Filt, ...)\",\n# \tforTransposition := false,\n# \tisApplicable := P -> P[1] > 2 and (P[1]-P[2].domain()) > 2 and P[2].domain() <= 32 and P[3] <= 0, \n# \tallChildren := P -> let(\n# \t n := P[1], l := -P[3], r := P[3] + P[2].domain() - 1,\n# \t [[ Filt(n-l-r, Poly(List(P[2].tolist(),EvalScalar), P[3])) ]]),\n\n# \trule := (P, C) -> let(\n# \t coeffs := P[2], nc := coeffs.domain(), n := P[1], l := -P[3], \n# \t r := -l + nc - 1, \n# \t j := Ind(l), k := Ind(r), v := Ind(nc),\n# \t VStack(\n# \t\tBB(ISum(j, j.range, \n# \t\t Scat(fBase(j)) * \n# \t\t RowVec(fCompose(coeffs, Lambda(v, cond(leq(v,r+j), v-j+l, v-j+l-nc))))) \n# \t\t Gath(n, nc,\tLambda(v, cond(leq(v,r+j), v, v+(n-l-r)-1 )))),\n# \t\tC[1],\n# \t\tBB(ISum(k, k.range, \n# \t\t Scat(fBase(k)) \n# \t\t RowVec(fCompose(coeffs, Lambda(v, cond(leq(v,k), v-k+(nc-1), v-k-1)))) \n# \t\t Gath(n, nc, Lambda(v, cond(leq(v,k), v, v+(n-l-r)-1 )))))))\n# ),\n\n #F Circulant_Blocking\n #F \n #F Circulant -> Blocks (Toeplitzes)\n #F\n #F Circulant is partitioned into square blocks of sizes \n #F given by all proper divisors of the input size.\n #F \n #F NOTE: this rule is invalid, Circulant_BlockingDense seems valid\n #F whats the difference between the two ???\n Circulant_Blocking := rec(\n\tinfo := \"Circulant -> Toeplitz\",\n\tforTransposition := false,\n\tisApplicable := P -> let(n := P[1],\n\t n > 2 and not IsPrime(n)), # and n <= 2Length(P[2])),\n\n\tallChildren := P -> let(\n\t divs := DivisorPairs(P[1]),\n\t ratio := P[2].domain() / P[1], \n\t List(divs, d -> [ Toeplitz(FUnk(2d[1]-1), 0, CeilingRat(ratio (2d[1]-1))) ])\n\t),\n\n prepData := (self, L, b, nc) >> let(\n\t n := Length(L),\n\t Concatenation(\n\t\tList([1..nc], k -> \n\t\t List([1..2b-1], j -> L[((n-kb+j) mod n) + 1])))),\n\n\trule := (self,P,C,Nonterms) >> let(\n\t n := P[1],\n\t b := Rows(C[1]), \n\t nc := n/b,\n\t new_data := FData(self.prepData(ApplyFunc(Circulant, P).column(), b, nc)),\n\t i := Ind(nc),\n\t k := Ind(nc),\n\t ofs := DataInd(TInt, nc (2b-1)).setAttr(\"live_out\"),\n\t bnum := DataInd(TInt, nc).setAttr(\"live_out\"),\n\t gfunc := fCompose(new_data, fAdd(nc(2b-1), 2b-1, ofs)),\n\n\t len := P[2].domain(),\n\t val := P[3] mod n,\n\t btoep_len := 2b-1,\n\n\t left := val,\n\t right := When(len+b >= n, val-1, (val + (len-1) + (b-1)) mod n), \n\t exact_right := (val + (len-1)) mod n,\n\n\t # we \"quantize\" the condition to tell us which block #s (ofs) are 0\n\t lblock := btoep_len Int(left/b),\n\t rblock := btoep_len * Int(right/b),\n\n\t rproj := bbnum + (b - 1 - left),\n\t lproj := bbnum + (b - 1 - exact_right), \n\t nt := Nonterms[1].setData(gfunc)\n\t .setNonZero(lproj, rproj),\n\n\t open := leq(rblock+1, lblock), \n\t A := leq(lblock, ofs), \n\t B := leq(ofs, rblock),\n\t isNonZero := logic_or(logic_and(A, B), logic_and(open, logic_or(A, B))),\n\n\t ISum(i, i.range, \n\t\tScat(fTensor(fBase(i), fId(b))) * \n\t\tISumAcc(k, k.range, \n\t\t Data(bnum, imod(nc+k-i, nc), \n\t\t\tData(ofs, (2b-1)bnum, \n\t\t\t COND(isNonZero, C[1], O(b)))) * \n\t\t Gath(fTensor(fBase(k), fId(b)))))\n )\n # RowDirectSum( ncb, List([1..nc], i-> \n # ColDirectSum( b, List([1..nc], k-> C[((k-i) mod nc) + 1]))))\n ),\n\n #F Circulant_BlockingDense\n #F \n #F Circulant -> Blocks (Toeplitzes)\n #F\n #F Circulant is partitioned into square blocks of sizes \n #F given by all proper divisors of the input size.\n #F \n Circulant_BlockingDense := rec(\n\tinfo := \"Circulant -> Toeplitz\",\n\tforTransposition := false,\n\tisApplicable := P -> let(n := P[1],\n\t n > 2 and not IsPrime(n) and n <= 2P[2].domain()),\n\n\tallChildren := P -> let(\n\t divs := DivisorPairs(P[1]),\n\t ratio := P[2].domain() / P[1], \n\t List(divs, d -> [ Toeplitz(FUnk(2d[1]-1), 0, CeilingRat(ratio (2d[1]-1))) ])\n\t),\n\n prepData := (self, L, b, nc) >> let(\n\t n := Length(L),\n\t Concatenation(\n\t\tList([1..nc], k -> \n\t\t List([1..2b-1], j -> L[((n-kb+j) mod n) + 1])))),\n\n\trule := (self,P,C,Nonterms) >> let(\n\t n := P[1],\n\t b := Rows(C[1]), \n\t nc := n/b,\n\t new_data := FData(self.prepData(ApplyFunc(Circulant, P).column(), b, nc)),\n\t i := Ind(nc),\n\t k := Ind(nc),\n\t ofs := DataInd(TInt, nc (2b-1)).setAttr(\"live_out\"),\n\t bnum := DataInd(TInt, nc).setAttr(\"live_out\"),\n\n\t gfunc := fCompose(new_data, fAdd(nc(2b-1), 2b-1, ofs)),\n\n\t len := P[2].domain(),\n\t val := P[3] mod n,\n\t left := val,\n\t exact_right := (val + (len-1)) mod n,\n\n\t rproj := bbnum + (b - 1 - left),\n\t lproj := bbnum + (b - 1 - exact_right), \n\t nt := Nonterms[1].setData(gfunc)\n\t .setNonZero(lproj, rproj),\n\n\t ISum(i, i.range, \n\t\tScat(fTensor(fBase(i), fId(b))) * \n\t\tISumAcc(k, k.range, \n\t\t Data(bnum, imod(nc+k-i, nc), \n\t\t\tData(ofs, (2b-1)bnum, \n\t\t\t C[1])) \n\t\t Gath(fTensor(fBase(k), fId(b)))))\n )\n # RowDirectSum( ncb, List([1..nc], i-> \n # ColDirectSum( b, List([1..nc], k-> C[((k-i) mod nc) + 1]))))\n ),\n\n #F Circulant_DiagonalizeStep\n #F\n #F Circulant_n -> (F2 tensor I2) \n #F (Circulant_n/2 dirsum Toeplitz_n/2) \n #F (F2 tensor I2)\n #F \n #F Computes circulant matrix through DFT.\n #F h is the first column of the circulant \n #F (params of Circulant nonterminal).\n #F\n Circulant_DiagonalizeStep := rec(\n\tinfo := \"Circulant_n -> Circulant_n/2 dirsum Toeplitz_n/2\",\n\tforTransposition := false,\n\tisApplicable := P -> let(n := P[1],\n\t n > 2 and n mod 2 = 0 and n<=16),\n\n\tallChildren := P -> let(n := P[1], \n\t [[ Circulant(FUnk(n/2)), Toeplitz(FUnk(n-1)) ]]),\n\n\tprepData := function(L)\n\t local l, L1, L2, circ, toep; \n\t l := Length(L);\n\t L1 := L{[1 .. l/2]}; # first half\n\t L2 := L{[l/2+1 .. l ]}; # second half\n\n\t circ := 1/2 * (L1 + L2);\n\t toep := 1/2 * Concat(Drop(L2,1) - Drop(L1,1), \n\t\t L1 - L2);\n\t return [circ, toep];\n\tend,\n\n\trule := (self, P, C, Nonterms) >> let(\n\t n := P[1], \n\t data := self.prepData(ApplyFunc(Circulant,P).column()),\n\t circ := Nonterms[1].setData(FData(data[1])),\n\t toep := Nonterms[2].setData(FData(data[2])),\n\n\t Tensor(F(2), I(n/2)) \n\t DirectSum(C[1], C[2]) \n\t Tensor(F(2), I(n/2))\n\t)\n ),\n\n ###################################################################\n ## Frequency domain methods\n ###################################################################\n\n #F Circulant_DFT\n #F\n #F Circulant -> invDFT * diag(DFT(h)) * DFT\n #F \n #F Computes circulant matrix through DFT.\n #F h is the first column of the circulant \n #F (params of Circulant nonterminal).\n #F\n Circulant_DFT := rec(\n\tinfo := \"Circulant -> invDFT * diag(DFT(h)) * DFT\",\n\tforTransposition := false,\n\tswitch := false,\n\tisApplicable := P -> P[1] > 1,\n\tallChildren := P -> [[ transforms.DFT(P[1], -1), transforms.DFT(P[1], 1) ]],\n\n\trule := function(P, C)\n local l, coef, L;\n\t L := ApplyFunc(Circulant, P).column();\n\t l := Length(L);\n\t coef := List([1..l], i -> ComplexAny(L[i]));\n\t coef := 1/l * ComplexFFT(coef);\n\t return C[1] * Diag(FData(coef)) * C[2];\n\tend\n ),\n\n #F Circulant_RDFT\n #F\n #F Circulant -> invRDFT * block(RDFT(h)) * RDFT\n #F \n #F Computes circulant matrix through the Real DFT.\n #F h is the first column of the circulant \n #F (params of nonterminal Circulant).\n #F\n Circulant_RDFT := rec(\n\tinfo := \"Circulant -> invRDFT * block(RDFT(h)) * RDFT\",\n\tforTransposition := false,\n\tswitch := false,\n\n\tisApplicable := P -> let(n := P[1],\n\t n > 2 and n <= 64 and (n mod 2 = 0) and\n\t ForAll(Factors(n), f -> f in [2, 3])),\n\n\tallChildren := P -> let(n := P[1],\n\t [[ RDFT(n).transpose(), RDFT(n) ]]),\n\n\trule := function( P, C )\n \t local i, L, M, X, l, coef, ccoef;\n\n\t L := ApplyFunc(Circulant, P).column();\n\t l := Length(L);\n\t ccoef := List([1..l], i -> ComplexAny(L[i]));\n\t ccoef := ComplexFFT(ccoef); \n\t coef := List([1..Int(l/2)+1], i -> 2/l * ReComplex(ccoef[i]));\n\t Append(coef, List([Int(l/2)+2..l], i -> 2/l * (-ImComplex(ccoef[i])) ));\n\n\t X := Diag([ 1/2 * coef[1]]);\n\t for i in [2..Int(l/2)] do\n\t M := Mat([[coef[i], coef[l-i+2]], \n\t\t\t [-coef[l-i+2], coef[i]]]);\n\t\tX := DirectSum(X, M);\n\t od;\n\t if (l mod 2 = 0) then \n\t\tX := DirectSum(X, Diag( [1/2 * coef[l/2+1]] ));\n\t fi;\n\t X := X^perm4(l);\n\t return C[1] * X * C[2];\n\tend\n ),\n\n #F Circulant_PRDFT\n #F\n #F Circulant -> IPRDFT * diag(PRDFT(h)) * PRDFT\n #F \n #F Computes circulant matrix through the Packed Real DFT.\n #F h is the first column of the circulant \n #F (params of nonterminal Circulant).\n #F\n Circulant_PRDFT := rec(\n\tinfo := \" Circulant -> IPRDFT * diag(PRDFT(h)) * PRDFT\",\n\tforTransposition := false,\n\tswitch := false,\n\n\tisApplicable := P -> true,\n\n\tallChildren := P -> let(n := P[1],\n\t [[ IPRDFT(n), PRDFT(n) ]]),\n\n\trule := function( P, C )\n \t local i, n, L, l, coef, D;\n\t n := Cols(C[1]);\n\t L := ApplyFunc(Circulant, P).column();\n\t l := Length(L);\n\t coef := List(L, EvalScalar);\n\t coef := 1/l * ComplexFFT(coef);\n\t D:=Diag(FData(coef{[1..n/2]}));\n\t return C[1] * RC(D) * C[2]; \n\tend\n ), \n\n #F Circulant_DHT\n #F\n #F Circulant -> DHT * block(DHT(h)) * DHT\n #F \n #F Computes circulant matrix through the Discrete Hartley transform.\n #F h is the first column of the circulant \n #F (params of nonterminal Circulant).\n #F\n Circulant_DHT := rec(\n\tinfo := \"Circulant -> DHT * block(DHT(h)) * DHT\",\n\tforTransposition := false,\n\tswitch := false, \n\tisApplicable := P -> let(n := P[1], n > 1 and Is2Power(n)),\n\n\tallChildren := P -> let(n := P[1], [[ DHT(n) ]]),\n\n\trule := function(P, C)\n\t local i,M,X,l,L,coef,ccoef, rcoef, icoef;\n\t L := ApplyFunc(Circulant, P).column();\n\t l := Length(L);\n\t ccoef := List([1..l], i -> ComplexAny(L[i]));\n\t ccoef := ComplexFFT(ccoef); \n\t rcoef := List([1..l/2+1], i -> 1/l * ReComplex(ccoef[i]));\n\t icoef := List([2..l/2], i -> 1/l * ImComplex(ccoef[i]));\n\t X := Diag([rcoef[1]]);\n\t for i in [2..Int(l/2)] do\n\t M := Mat([[rcoef[i], -icoef[i-1]], \n\t\t\t [icoef[i-1], rcoef[i]]]);\n\t\tX := DirectSum(X,M);\n\t od;\n\t X := DirectSum(X, Diag( [rcoef[l/2+1]] ));\n\t X := X^perm4(l);\n\t return C[1] * X * C[1];\n\tend\n )\n));\n", "meta": {"hexsha": "cdd313d33420205c34f764a7d527cb1e5ac58861", "size": 13479, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/filtering/circulant.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/transforms/filtering/circulant.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": 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	{"text": "# In reality we only need a list indexed by triples, so we\n# will quite probably end up with a tree where the leaves have\n# weights as labels.\nInstallGlobalFunction(CyclicSubList,\nfunction(l, pos, len)\n local r, i, j, llen;\n\n llen := Length(l);\n r := [];\n i := pos; j := 1;\n while j <= len do\n r[j] := l[i];\n i := i + 1; j := j + 1;\n if i > llen then\n i := 1;\n fi;\n od;\n\n return r;\nend);\n\nInstallGlobalFunction( EnterAllSubwords,\nfunction(idx, word, value)\n local i, v, pos, ww;\n pos := [1..Length(word)];\n ww := List(word, x -> __ID(x));\n for i in pos do\n v := idx[ ww{ CyclicSubList(pos, i, 3) } ];\n if value < v then\n idx[ ww{ CyclicSubList(pos, i, 3) } ] := value;\n fi;\n od;\nend);\n\n\n#\nInstallGlobalFunction( DigraphDijkstraST,\nfunction(graph, s, t)\n local vertices, dist, prev, queue, u, v, alt;\n\n dist := [];\n prev := [];\n queue := BinaryHeap({x,y} -> x[1] < y[1]);\n\n for v in DigraphVertices(graph) do\n dist[v] := infinity;\n prev[v] := -1;\n od;\n\n dist[s] := 0;\n Push(queue, [0, s]);\n\n while not IsEmpty(queue) do\n u := Pop(queue);\n u := u[2];\n if u = t then\n return [ dist, prev ];\n fi;\n for v in OutNeighbours(graph)[u] do\n alt := dist[u] + DigraphEdgeLabel(graph, u, v);\n if alt < dist[v] then\n dist[v] := alt;\n prev[v] := u;\n Push(queue, [dist[v], v]);\n fi;\n od;\n od;\n return infinity;\nend);\n\nInstallGlobalFunction( DigraphDijkstraS,\nfunction(graph, s)\n local vertices, dist, prev, queue, u, v, alt;\n\n dist := [];\n prev := [];\n queue := BinaryHeap({x,y} -> x[1] < y[1]);\n\n for v in DigraphVertices(graph) do\n dist[v] := infinity;\n prev[v] := -1;\n od;\n\n dist[s] := 0;\n Push(queue, [0, s]);\n\n while not IsEmpty(queue) do\n u := Pop(queue);\n u := u[2];\n for v in OutNeighbours(graph)[u] do\n alt := dist[u] + DigraphEdgeLabel(graph, u, v);\n if alt < dist[v] then\n dist[v] := alt;\n prev[v] := u;\n Push(queue, [dist[v], v]);\n fi;\n od;\n od;\n\n return [ dist, prev ];\nend);\n\n\n", "meta": {"hexsha": "0a1a2802abc5255775926f99b06e7e2ef91943be", "size": 2313, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "gap/anadata.gi", "max_stars_repo_name": "RussWoodroofe/walrus", "max_stars_repo_head_hexsha": "f7a4e3597f288c6d9518aaa39091826dadc864b8", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-10-02T14:55:52.000Z", "max_stars_repo_stars_event_max_datetime": "2021-10-02T14:55:52.000Z", "max_issues_repo_path": "gap/anadata.gi", "max_issues_repo_name": "RussWoodroofe/walrus", "max_issues_repo_head_hexsha": "f7a4e3597f288c6d9518aaa39091826dadc864b8", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 26, "max_issues_repo_issues_event_min_datetime": "2018-11-22T11:15:07.000Z", "max_issues_repo_issues_event_max_datetime": "2022-02-21T13:31:01.000Z", "max_forks_repo_path": "gap/anadata.gi", "max_forks_repo_name": "RussWoodroofe/walrus", "max_forks_repo_head_hexsha": "f7a4e3597f288c6d9518aaa39091826dadc864b8", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 4, "max_forks_repo_forks_event_min_datetime": "2019-02-11T14:47:47.000Z", "max_forks_repo_forks_event_max_datetime": "2021-05-20T10:22:09.000Z", "avg_line_length": 22.2403846154, "max_line_length": 62, "alphanum_fraction": 0.4807609166, "num_tokens": 675, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7185943805178138, "lm_q2_score": 0.7025300573952054, "lm_q1q2_score": 0.5048341513890517}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\nClass(InterpolateSegmentDFT, TaggedNonTerminal, rec(\n abbrevs := [ (numseg, outsize, insize, overlap, dsfunc,usfunc) -> [numseg, outsize, insize, overlap, dsfunc, usfunc] ],\n\n dims := self >> [self.params[2], self.params[3]],\n\n terminate := self >> let(\n numseg := self.params[1], \n rowlength := self.params[2],\n insize := self.params[3], \n j := Ind(numseg),\n overlap := self.params[4], \n downsample := self.params[5].at(j), \n upsample := self.params[6],\n n := upsample.domain(), \n N := downsample.range(), \n substrec := i -> rec((j.id):=V(i)),\n \n kernel := Mat(MatAMat(RowDirectSum(\n overlap,\n List([1..numseg], i -> \n Downsample(SubstVars(Copy(downsample), substrec(i-1))).terminate() \n DFT(N, 1).terminate() \n Upsample(upsample).terminate() \n Scale(1/n, DFT(n, -1).terminate())\n )).toAMat() \n Scat(fAdd(nnumseg-(numseg-1)overlap, insize, 0)).toAMat()\n )),\n When(Rows(kernel) = rowlength, kernel, VStack(kernel, O(rowlength-Rows(kernel), Cols(kernel)))) \n ),\n isReal := False,\n normalizedArithCost := self >> let(numseg := self.params[1], n:=self.params[6].domain(), N := self.params[6].range(), \n numseg * (n + IntDouble(5 * n * d_log(n) / d_log(2)) + IntDouble(5 * N * d_log(N) / d_log(2)))),\n TType := T_Complex(T_Real(64)),\n\n HashId := self >> let(h := [ self.params[1], self.params[2], self.params[3], self.params[4], self.params[5].domain(), self.params[5].range()],\n When(IsBound(self.tags), Concatenation(h, self.tags), h)),\n doNotMeasure := true\n));\n\n\n_sumSegDims := function(numsegs, seglen)\n local l, lfact, lsum, divsum, ssum;\n\n l := List([0..numsegs-1], i->seglen.at(i).domain());\n \n # check to pull out the mul\n if ForAll(l, i->ObjId(i) = mul and IsValue(i.args[1]) and i.args[1].v = l[1].args[1].v) then\n lfact := l[1].args[1];\n lsum := List(l, i -> i.args[2]);\n # we may need to create a table, but not sure yet...\n divsum := ApplyFunc(add, lsum);\n ssum := mul(lfact, divsum);\n else\n ssum := ApplyFunc(add, l);\n fi;\n \n return ssum;\nend;\n\nNewRulesFor(InterpolateSegmentDFT, rec(\n InterpolateSegmentDFT_base := rec(\n switch := false,\n applicable := (self, nt) >> not nt.hasTags() and ObjId(nt.params[6]) = fZeroPadMiddle,\n children := nt -> let(numseg := nt.params[1], j := Ind(numseg), downsample := nt.params[5].at(j), upsample := nt.params[6],\n insize := nt.params[3], overlap := nt.params[4], n:=upsample.domain(), N := downsample.range(), \n us := N/n, blk := n/2, \n inp := n + (numseg-1)(n-overlap), over := inp - insize, l := n - over,\n [[ \n Downsample(downsample),\n DFT(N, 1), \n Upsample(upsample),\n DFT(n, -1),\n Upsample(fAdd(n, l, 0)),\n InfoNt(j)\n ]]),\n apply := (nt, C, cnt) -> let(numseg := nt.params[1], _j := cnt[6].params[1], j := Ind(_j.range-1), downsample := nt.params[5].at(j), upsample := nt.params[6], \n outsize := nt.params[2], insize := nt.params[2], overlap := nt.params[4], n:=upsample.domain(), N := downsample.range(), \n ids_rows := _sumSegDims(numseg-1, nt.params[5]),\n RowDirectSum(overlap,[\n IRowDirSum(j, numseg-1, overlap, \n SubstVars(Copy(C[1]), rec((_j.id) := j)) C[2] * C[3] * Scale(1/n, C[4])).overrideDims([ids_rows, insize - C[4].dims()[2] + overlap]),\n SubstVars(Copy(C[1]), rec((_j.id) := V(numseg-1))) * C[2] * C[3] * Scale(1/n, C[4] * C[5]) \n ]).overrideDims([nt.params[2], nt.params[3]])\n )\n ),\n InterpolateSegmentDFT_PrunedDFT := rec(\n applicable := (self, nt) >> not nt.hasTags() and ObjId(nt.params[6]) = fZeroPadMiddle,\n children := nt -> let(numseg := nt.params[1], j := Ind(numseg), downsample := nt.params[5].at(j), upsample := nt.params[6], \n insize := nt.params[3], overlap := nt.params[4], n:=upsample.domain(), N := downsample.range(), \n us := N/n, blk := n/2, \n inp := n + (numseg-1)(n-overlap), over := inp - insize, l := n - over, g := Gcd(n, l), \n [[ \n Downsample(downsample),\n PrunedDFT(N, 1, blk, [0, 2us-1]), \n DFT(n, -1),\n PrunedDFT(n, -1, g, [0..l/g-1]),\n InfoNt(j) \n ]]),\n apply := (nt, C, cnt) -> let(numseg := nt.params[1], _j := cnt[5].params[1], j := Ind(_j.range-1), downsample := nt.params[5].at(j), upsample := nt.params[6],\n outsize := nt.params[2], insize := nt.params[3], overlap := nt.params[4], n := upsample.domain(), N := downsample.range(), \n ids_rows := _sumSegDims(numseg-1, nt.params[5]),\n RowDirectSum(overlap,[\n IRowDirSum(j, numseg-1, overlap, \n SubstVars(Copy(C[1]), rec((_j.id) := j)) * C[2] * Diag(fConst(n, 1/n)) * C[3]).overrideDims([ids_rows, insize - C[4].dims()[2] + overlap]),\n SubstVars(Copy(C[1]), rec((_j.id) := V(numseg-1))) * C[2] * Diag(fConst(n, 1/n)) * C[4]\n ]).overrideDims([nt.params[2], nt.params[3]])\n )\n )\n));\n", "meta": {"hexsha": "425f2c8248522229f048d63c135564a15e69587b", "size": 5711, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/interpolate/segmentdft.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/transforms/interpolate/segmentdft.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/transforms/interpolate/segmentdft.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 50.0964912281, "max_line_length": 167, "alphanum_fraction": 0.4995622483, "num_tokens": 1687, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.831143031127974, "lm_q2_score": 0.6039318337259584, "lm_q1q2_score": 0.5019537348776687}}
	{"text": "# The incidence graph of a Desarguesian projective plane.\nBindGlobal(\"DesarguesianPlaneIncidenceGraph\", function(q)\n local G, V, dp;\n V := GF(q)^3;\n dp := DirectProduct(GL(3, q), SymmetricGroup(2));\n G := Graph(dp, Union(List([1,2], d -> Subspaces(V, d))),\n OnProjectivePlane(V, dp), function(x, y)\n return x <> y and Intersection(x, y) in [x, y];\n end, true);\n G.halfDuality := Sum;\n G.halfPrimality := Intersection;\n return G;\nend);\n\n# The incidence graph of a Hall plane.\nBindGlobal(\"HallPlaneIncidenceGraph\", function(q)\n local c, p, G, H, L, P, dp, mul;\n H := GF(q)^2;\n p := DefiningPolynomial(GF(GF(q), 2));\n c := CoefficientsOfUnivariatePolynomial(p);\n mul := HallMultiplication(p);\n P := Union([[]], List(H, x -> [x]), Cartesian(H, H));\n L := Union([Union([[]], List(H, z -> [z]))],\n List(H, x -> Union([[]], List(H, z -> [x, z]))),\n List(Cartesian(H, H), w -> Union([[w[1]]],\n List(H, z -> [z, mul(z, w[1]) + w[2]]))));\n dp := DirectProduct(Concatenation(ListWithIdenticalEntries(5,\n FieldAdditionPermutationGroup(q)),\n [FieldMultiplicationPermutationGroup(q),\n Group([[c[2], Z(q)^0], [-c[1], 0Z(q)]])]));\n G := Graph(dp, Union(P, L), OnHallPlane(q, dp),\n PointLineIncidence, true);\n G.halfDuality := DefaultDualityFunction;\n G.halfPrimality := DefaultPrimalityFunction;\n return G;\nend);\n\n# The incidence graph of a Hughes plane. If the second parameter n is zero or\n# unspecified, a Dickson semifield of order q^2 is used and the first parameter\n# q must be an odd prime power. Otherwise, an exceptional near-field of order\n# q^2 is used, so q must be 5, 7, 11, 23, 29, or 59. As there are two\n# exceptional near-fields of order 11^2, setting n to 1 or 2 chooses one of\n# these semifields when q = 11.\nBindGlobal(\"HughesPlaneIncidenceGraph\", function(arg)\n local c, n, q, A, B, F, G, H, P, df, dp, th, mul, rdiv, gens, orth;\n if Length(arg) < 1 then\n Error(\"at least one argument expected\");\n return fail;\n fi;\n q := arg[1];\n if Length(arg) > 1 then\n n := arg[2];\n else\n n := 0;\n fi;\n th := Z(q^2)^((q+1)/2);\n B := Basis(GF(q^2), [Z(q)^0, th]);\n if n = 0 then\n mul := DicksonMultiplication(q);\n rdiv := DicksonRightDivision(q);\n else\n gens := [[[0, -1], [1, 0]]];\n if q = 5 then\n gens[2] := [[1, -2], [-1, -2]];\n elif q = 7 then\n gens[2] := [[1, 3], [-1, -2]];\n elif q = 11 and n = 1 then\n gens[2] := [[1, 5], [-5, -2]];\n gens[3] := [[4, 0], [0, 4]];\n elif q = 11 and n = 2 then\n gens[2] := [[2, 4], [1, -3]];\n elif q = 23 then\n gens[2] := [[1, -6], [12, -2]];\n gens[3] := [[2, 0], [0, 2]];\n elif q = 29 then\n gens[2] := [[1, -7], [-12, -2]];\n gens[3] := [[16, 0], [0, 16]];\n elif q = 59 then\n gens[2] := [[9, 15], [-10, -10]];\n gens[3] := [[4, 0], [0, 4]];\n else\n Error(\"the specified exceptional near-field does not exist\");\n return fail;\n fi;\n G := Group(gens Z(q)^0);\n F := Union([NullMat(2, 2, GF(q))], Elements(G));\n SortBy(F, x -> IntVecFFE(x[1]));\n mul := ExceptionalMultiplication(q, F, B);\n rdiv := ExceptionalRightDivision(q, F, B);\n fi;\n c := CoefficientsOfUnivariatePolynomial(DefiningPolynomial(GF(GF(q), 3)));\n A := [[-c[3], Z(q)^0, 0Z(q)],\n [-c[2], 0Z(q), Z(q)^0],\n [-c[1], 0Z(q), 0Z(q)]];\n P := Filtered(GF(q^2)^3,\n x -> not IsZero(x) and IsOne(First(x, y -> not IsZero(y))));\n dp := DirectProduct(Group(A), SymmetricGroup(2));\n orth := function(x, y)\n local z;\n z := TransposedMat(List(y, w -> Coefficients(B, w)));\n return IsZero(xz[1] + mul(th, xz[2]));\n end;\n H := Graph(dp, Cartesian([1, 2], P), OnHughesPlane(q, rdiv, dp),\n function(x, y)\n return x[1] <> y[1] and orth(x[2], y[2]);\n end, true);\n df := x -> [x[1][1]^(1, 2),\n Intersection(List(x,\n y -> Filtered(P, z -> orth(y[2], z))))[1]];\n H.halfDuality := df;\n H.halfPrimality := df;\n return H;\nend);\n\n# The collinearity graph of the generalized quadrangle Q(d, q)\n# of order (q, q^{d-3}).\nBindGlobal(\"GeneralizedQuadrangleQ\", function(d, q)\n return PolarGraphO(4-d, d+1, q);\nend);\n\n# The collinearity graph of the generalized quadrangle H(d, r^2)\n# of order (r^2, r^{d-5/2}).\nBindGlobal(\"GeneralizedQuadrangleH\", function(d, r)\n return PolarGraphU(d+1, r);\nend);\n\n# The collinearity graph of the generalized quadrangle W(q) of order (q, q).\nBindGlobal(\"GeneralizedQuadrangleW\", q -> PolarGraphSp(4, q));\n\n# The collinearity graph of the generalized quadrangle T_d(O) of order\n# (q, q^{d-1}) derived from the projective space PG(d+1, q) containing the\n# oval or ovoid O in a hyperplane.\nBindGlobal(\"GeneralizedQuadrangleT\", function(arg)\n local d, o, q, G, H, O, V, gr;\n if Length(arg) < 1 then\n Error(\"at least one argument expected\");\n return fail;\n elif Length(arg) < 3 then\n d := arg[1].d;\n q := arg[1].q;\n o := arg[1].points;\n G := arg[1].group;\n else\n d := arg[1];\n q := arg[2];\n o := arg[3];\n if Length(arg) > 3 then\n G := arg[4];\n else\n G := Group(IdentityMat(d+1, GF(q)));\n fi;\n fi;\n V := GF(q)^(d+2);\n H := Subspace(V, BasisVectors(CanonicalBasis(V)){[2..d+2]}, \"basis\");\n O := List(o, x -> Subspace(V,\n [Concatenation([0Z(q)], BasisVectors(Basis(x))[1])], \"basis\"));\n gr := Graph(Group(List(GeneratorsOfGroup(G),\n g -> Concatenation([Concatenation([Z(q)^0],\n ListWithIdenticalEntries(d+1, 0Z(q)))],\n List(g, l -> Concatenation([0Z(q)], l))))),\n Union(Filtered(Subspaces(V, 1), x -> not IsSubset(H, x)),\n Filtered(Subspaces(V, d+1),\n x -> Length(Filtered(O, y -> IsSubset(x, y))) = 1), [V]),\n OnSubspaces(V), function(x, y)\n local dx, dy, xy, yx;\n dx := Dimension(x);\n dy := Dimension(y);\n xy := x+y;\n yx := Intersection(x, y);\n return (dx = d+2 and dy = d+1) or (dx = d+1 and dy = d+2) or\n (dx = 1 and dy = 1 and ForAny(O, z -> IsSubset(xy, z))) or\n (dx = 1 and dy = d+1 and ForAny(O, z -> IsSubset(y, x+z))) or\n (dx = d+1 and dy = 1 and ForAny(O, z -> IsSubset(x, y+z))) or\n (dx = d+1 and dy = d+1 and x <> y and\n ForAny(O, z -> IsSubset(yx, z)));\n end, true);\n gr.duality := function(x)\n if V in x then\n return First(O, y -> IsSubset(Intersection(x), y));\n else\n return Sum(Filtered(x, y -> Dimension(y) = 1));\n fi;\n end;\n gr.primality := function(x)\n if ForAll(x, y -> Dimension(y) = 1) then\n return V;\n elif ForAll(x, y -> Dimension(y) = 2) then\n return Intersection(x);\n else\n return Sum(x);\n fi;\n end;\n return gr;\nend);\n\n# The collinearity graph of the generalized quadrangle T(O) of order\n# (2^h-1, 2^h+1) derived from the projective space PG(3, 2^h) containing the\n# hyperoval O in a hyperplane.\nBindGlobal(\"GeneralizedQuadrangleTstar\", function(arg)\n local o, q, G, H, O, V, gr;\n if Length(arg) < 1 then\n Error(\"at least one argument expected\");\n return fail;\n elif Length(arg) < 3 then\n q := arg[1].q;\n o := arg[1].points;\n G := arg[1].group;\n else\n q := 2^arg[1];\n o := arg[2];\n if Length(arg) > 2 then\n G := arg[3];\n else\n G := Group(IdentityMat(3, GF(q)));\n fi;\n fi;\n V := GF(q)^4;\n H := Subspace(V, BasisVectors(CanonicalBasis(V)){[2..4]}, \"basis\");\n O := List(o, x -> Subspace(V,\n [Concatenation([0Z(q)], BasisVectors(Basis(x))[1])], \"basis\"));\n gr := Graph(Group(List(GeneratorsOfGroup(G),\n g -> Concatenation([Concatenation([Z(q)^0],\n ListWithIdenticalEntries(3, 0Z(q)))],\n List(g, l -> Concatenation([0Z(q)], l))))),\n Filtered(Subspaces(V, 1), x -> not IsSubset(H, x)),\n OnSubspaces(V), function(x, y)\n local xy;\n xy := x+y;\n return not IsSubset(H, xy)\n and ForAny(O, z -> IsSubset(xy, z));\n end, true);\n gr.duality := Sum;\n gr.primality := Intersection;\n return gr;\nend);\n\n# The collinearity graph of the generalized quadrangle P(G, z) of\n# order (s-1, s+1) derived by removing the neighbourhood of a regular point z\n# of a generalized quadrangle G of order (s, s).\nBindGlobal(\"GeneralizedQuadrangleP\", function(Q, z)\n local H, P;\n H := Graph(Stabilizer(Q.group, z), DistanceSet(Q, 2, z), OnPoints,\n function(x, y)\n local c;\n c := Intersection(Adjacency(Q, x), Adjacency(Q, y));\n return not z in c and (y in Adjacency(Q, x)\n or ForAll(c, w -> z in Adjacency(Q, w)));\n end, true);\n AssignVertexNames(H, Q.names{H.names});\n CheckDualityFunctions(Q);\n H.duality := function(x)\n local p;\n p := List(x, u -> Position(Q.names, u));\n if ForAny(Cartesian(p, p), w -> Distance(Q, w[1], w[2]) = 2) then\n return [2, Set(x)];\n else\n return [1, Q.duality(Union(x,\n Q.names{Intersection(List(p, v -> Adjacency(Q, v)))}))];\n fi;\n end;\n H.primality := x -> Q.primality(List(Filtered(x, y -> y[1] = 1),\n w -> w[2]));\n return H;\nend);\n\n# The collinearity graph of the generalized quadrangle AS(q)\n# of order (q-1, q+1).\nBindGlobal(\"GeneralizedQuadrangleAS\",\n q -> GeneralizedQuadrangleP(GeneralizedQuadrangleW(q), 1));\n\n# The incidence graph of a projective plane read from a file as on\n# http://www.uwyo.edu/moorhouse/pub/planes/ or\n# http://www.uwyo.edu/moorhouse/pub/genpoly/\n# The optional second parameter is a file containing generators of the\n# automorphism group.\nBindGlobal(\"IncidenceGraphFromFile\", function(arg)\n local l, m, n, G, L, fst, lst, lns;\n if Length(arg) < 1 then\n Error(\"at least one argument expected\");\n return fail;\n fi;\n lns := ReadLines(arg[1]);\n n := Length(lns);\n L := List(lns, l -> List(SplitString(l, \" \"), x -> Int(x)+n+1));\n if Length(arg) > 1 then\n lns := ReadLines(arg[2]);\n m := Length(lns);\n fst := Filtered([1..m], i -> IntChar(lns[i][1]) <> 32);\n l := Length(fst);\n lst := List(fst{[2..l]}, i -> i-1);\n Add(lst, m);\n G := Group(List([1..l], i -> PermList(List(SplitString(\n JoinStringsWithSeparator(lns{[fst[i]..lst[i]]}, \"\"),\n \" \"), x -> Int(x)+1))));\n else\n G := Group(());\n fi;\n return Graph(G, [1..2n], OnPoints, function(x, y)\n return (x <= n and y in L[x]) or (y <= n and x in L[y]);\n end, true);\nend);\n\n# The collinearity graph of a projective plane read from a file as on\n# http://www.uwyo.edu/moorhouse/pub/genpoly/\n# The optional second parameter is a file containing generators of the\n# automorphism group.\nBindGlobal(\"CollinearityGraphFromFile\", function(arg)\n local l, m, n, G, L, fst, lst, lns;\n if Length(arg) < 1 then\n Error(\"at least one argument expected\");\n return fail;\n fi;\n lns := ReadLines(arg[1]);\n n := Length(lns);\n L := List(lns, l -> List(SplitString(l, \" \"), x -> Int(x)));\n if Length(arg) > 1 then\n lns := ReadLines(arg[2]);\n m := Length(lns);\n fst := Filtered([1..m], i -> IntChar(lns[i][1]) <> 32);\n l := Length(fst);\n lst := List(fst{[2..l]}, i -> i-1);\n Add(lst, m);\n G := Group(List([1..l], i -> PermList(Filtered(List(SplitString(\n JoinStringsWithSeparator(lns{[fst[i]..lst[i]]}, \"\"),\n \" \"), x -> Int(x)+1), y -> y <= n))));\n else\n G := Group(());\n fi;\n return Graph(G, [1..n], OnPoints, function(x, y)\n return Length(Intersection(L[x], L[y])) = 1;\n end, true);\nend);\n", "meta": {"hexsha": "6911997d7f639d632a09bbbf72ad187ad0f874a4", "size": 12730, "ext": "gap", "lang": "GAP", "max_stars_repo_path": "lib/GeometryGraphs.gap", "max_stars_repo_name": "jaanos/gap-graphs", "max_stars_repo_head_hexsha": "18dd56c9b90a12a717a0cc893fdd72c6343ee79b", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2015-10-27T15:54:29.000Z", "max_stars_repo_stars_event_max_datetime": "2016-11-07T14:09:44.000Z", "max_issues_repo_path": "lib/GeometryGraphs.gap", "max_issues_repo_name": "jaanos/gap-graphs", "max_issues_repo_head_hexsha": "18dd56c9b90a12a717a0cc893fdd72c6343ee79b", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": 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YES\n2. YES", "lm_q1_score": 0.84594244507642, "lm_q2_score": 0.5926665999540698, "lm_q1q2_score": 0.5013618326802742}}