AutoMathText / data /code /gap /0.40-0.45.jsonl

add batch 3/5 (200 files)

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	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n_DHT_CONST := 2.5;\n\n#F TDHT(<n>, <k>) - RDFT Nonterminal\nClass(TDHT, TaggedNonTerminal, rec(\n abbrevs := [ (n) -> Checked(IsPosInt(n), [n]) ],\n dims := self >> [self.params[1], self.params[1]],\n isReal := True,\n terminate := self >> PkDHT1(self.params[1]).terminate(),\n SmallRandom := () -> Random([2,4,6,8,10,12,16,18,24,30,32]),\n normalizedArithCost := (self) >> let(n := self.params[1], IntDouble(_DHT_CONST * n * d_log(n) / d_log(2)))\n));\n\n\n_DHTtoRDFT := N -> DirectSum(I(2), Tensor(I(N/2-1), F(2)));\n\n#F TXMatDHT(<n>) - X-matrix to translate a RC(DFT(N)) -> DHT(2N)\nClass(TXMatDHT, TaggedNonTerminal, rec(\n abbrevs := [ (n) -> Checked(IsPosIntSym(n), [n]) ],\n dims := self >> [self.params[1], self.params[1]],\n isReal := True,\n terminate := self >> _DHTtoRDFT(self.params[1]) TConjEven(self.params[1]).terminate(),\n SmallRandom := () -> Random([2,4,6,8,10,12,16,18,24,30,32]),\n doNotMeasure := true\n));\n\n\n#F Translate DHT into RDFT\nNewRulesFor(TDHT, rec(\n DHT_DFT_tSPL := rec(\n switch := true,\n applicable := (self, t) >> IsEvenInt(t.params[1]), # and t.hasTags(),\n children := (self, t) >> let(N := t.params[1], tags := t.getTags(),\n [[\n TXMatDHT(N).withTags(tags),\n TRC(DFT(N/2)).withTags(tags)\n ]]),\n apply := (self, t, C, Nonterms) >> C[1] * C[2]\n )\n));\n\n\nNewRulesFor(TXMatDHT, rec(\n TXMatDHT_TConjEven := rec(\n switch := true,\n applicable := (self, t) >> IsEvenInt(t.params[1]),\n children := (self, t) >> let(N := t.params[1], tags := t.getTags(),\n [[\n TConjEven(N).withTags(tags),\n ]]),\n apply := (self, t, C, Nonterms) >> _DHTtoRDFT(t.params[1]) * C[1]\n )\n));\n", "meta": {"hexsha": "b626b4696baa437164bd9deee9c8d31510211121", "size": 1854, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/common/dht.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/common/dht.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/common/dht.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": 31.9655172414, "max_line_length": 110, "alphanum_fraction": 0.5469255663, "num_tokens": 619, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7341195152660687, "lm_q2_score": 0.6076631698328916, "lm_q1q2_score": 0.44609739168276513}}
	{"text": "\nInstallMethod(NilpotentChv,\n \"NilpotentChv element in simple Lie type\",\n [IsChevalleyAdj,IsList],\n function(sys,coeffs)\n local object,\n B,admat,l;\n \n if Filtered(coeffs,i->not i[2] in Integers)=[] then\n coeffs:=List(coeffs,i->[i[1],One(ring(sys))i[2]]);\n elif Filtered(coeffs,i->not i[2] in ring(sys))<>[] then\n Error(\"NilpotentChv: The coefficients ar not in indicated ring.\");\n fi;\n\n object:=Objectify(NewType(NewFamily(\"NilpotentChvFamily\"),\n IsAttributeStoringRep and\n IsNilpotentChv and\n IsAdditiveElementWithInverse and\n IsAdditiveElementWithZero),\n rec());\n\n SetchevalleyAdj(object,sys);\n\n # Simplified form of the element (negative root vectors are also allowd \"2Len..\")\n coeffs:=Filtered(List([1..2Length(positiveRoots(sys))],\n i->[i,One(ring(sys))Sum(List(Filtered(coeffs,\n j->j[1]=i),\n k->k[2]))]),\n l->l[2]<>Zero(ring(sys)));\n\n Setcoefficients(object,coeffs);\n\n B:=Basis(lieAlgebra(sys));\n if coeffs<>[] then SetLieAlgebraElement(object,Sum(coeffs,i->i[2]B[i[1]]));\n else SetLieAlgebraElement(object,Zero(lieAlgebra(sys))); fi;\n SetLieAlgebraCoeffs(object,Coefficients(B,LieAlgebraElement(object)));\n\n# l:=Length(PRoots(R));\n# admat:=AdjointMatrix(B,LieAlgebraElement(e));\n# SetPositiveAde(object,List([1..l],i->admat[i]{[1..l]}));\n \n SetName(object,Concatenation(\"<nilpotent element for \",\n type(sys),String(rank(sys)),\n \" in characteristic \",String(Characteristic(sys)),\">\"));\n return object;\nend);\n\nInstallMethod(Ascend,\n \"If possible embed the parameters in a polynomial ring with coefficients ring the base ring\",\n [IsNilpotentChv,IsPolynomialRing],\n function(e,inel)\n local sys,\n check;\n\n sys:=chevalleyAdj(e);\n\n if not IsPolynomialRing(inel) then\n Error(\"Ascend NilpotentChv: The new ring is not a polynomial ring to embed in!\\n\");\n elif CoefficientsRing(inel)<>ring(sys) then\n Error(\"Ascend NilpotentChv: CoefficientsRing and ring(sys) do not coincide!\\n\");\n fi;\n \n return NilpotentChv(ChevalleyAdj(sys,inel),List(coefficients(e),i->[i[1],One(inel)i[2]]));\nend);\n\nInstallMethod(Ascend,\n \"If possible embed the parameters in a polynomial ring with coefficients ring the base ring\",\n [IsNilpotentChv,IsChevalleyAdj],\n function(e,sys)\n local syse,\n check;\n\n syse:=chevalleyAdj(e);\n\n if not IsPolynomialRing(ring(sys)) then\n Error(\"The new ring is not a polynomial ring to embed in.\");\n elif CoefficientsRing(ring(sys))<>ring(syse) then\n Error(\"CoefficientsRing and ring(syse) do not coincide.\");\n fi;\n \n return NilpotentChv(sys,List(coefficients(e),i->[i[1],One(ring(sys))i[2]]));\nend);\n\nInstallMethod(\\,\n \"multiplication by scalar for nilpotent elements se\",\n [IsRingElement,IsNilpotentChv],\n function(s,e)\n local sys;\n\n sys:=chevalleyAdj(e);\n if not s in ring(sys) then\n Error(\"ScalarNilpotentChv: Scalar not in ring of nilpotent!\\n\");\n fi;\n \n return NilpotentChv(sys,List(coefficients(e),i->[i[1],s*i[2]]));\nend);\n\nInstallMethod(\\+,\n \"addition for nilpotent elements e1+e2\",\n [IsNilpotentChv,IsNilpotentChv],\n function(e1,e2)\n local sys1,sys2;\n\n sys1:=chevalleyAdj(e1);\n sys2:=chevalleyAdj(e2);\n if type(sys1)<>type(sys2) or\n rank(sys1)<>rank(sys2) or\n ring(sys1)<>ring(sys2) then\n Error(\"NilpotentChv+NilpotentChv: Not in the same family!\\n\");\n fi;\n \n return NilpotentChv(sys1,Concatenation(coefficients(e1),coefficients(e2)));\nend);\n\nInstallMethod(AdditiveInverseMutable,\n \"additive inverse for nilpotent elements -e1\",\n [IsNilpotentChv],\n function(e)\n local sys;\n\n sys:=chevalleyAdj(e);\n \n return NilpotentChv(sys,List(coefficients(e),i->[i[1],-i[2]]));\nend);\n\nInstallMethod(ZeroMutable,\n \"Zero vector of the Lie algebra\",\n [IsNilpotentChv],\n function(e)\n local sys;\n \n return NilpotentChv(chevalleyAdj(e),[]);\nend);\n", "meta": {"hexsha": "6d404a60c279bdce9dfef43290f6db8c8ea38821", "size": 5268, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "lib/nilchv.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/nilchv.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/nilchv.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": 39.3134328358, "max_line_length": 107, "alphanum_fraction": 0.5034168565, "num_tokens": 1199, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.7279754489059774, "lm_q2_score": 0.6113819732941511, "lm_q1q2_score": 0.445071066461832}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n# ==========================================================================\n# ColDirectSum\n# ==========================================================================\nClass(ColDirectSum, BaseOverlap, rec(\n #-----------------------------------------------------------------------\n abbrevs := [ \n function(arg) \n arg:=Flat(arg); \n return [arg[1], arg{[2..Length(arg)]}];\n end ],\n #-----------------------------------------------------------------------\n new := meth(self, overlap, spls)\n return self._new(0, overlap, spls);\n end,\n #-----------------------------------------------------------------------\n dims := meth(self)\n local ovdim;\n\tovdim := self.ovDim(self.overlap,\n\t List(self._children, t -> t.dimensions[1]));\n\treturn [ ovdim[3] - ovdim[2] + 1, # max - min + 1\n\t Sum(self._children, t -> t.dimensions[2]) ];\n end,\n #-----------------------------------------------------------------------\n toAMat := meth(self) \n return \n\t AMatSPL(\n\t Sparse(\n\t\t self._coloverlap(\n\t\t List(self._children, t -> t.dimensions[1]),\n\t\t self.overlap\n\t\t )\n\t )\n\t ) *\n\t DirectSumAMat(List(self._children, AMatSPL));\n end,\n));\n\nColDirectSum._transpose_class := RowDirectSum;\nRowDirectSum._transpose_class := ColDirectSum;\n", "meta": {"hexsha": "9fc6e37d40ad33c6edf2e565ffdd544f9a729ec0", "size": 1432, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/spl/ColDirectSum.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/ColDirectSum.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/ColDirectSum.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": 31.8222222222, "max_line_length": 76, "alphanum_fraction": 0.3868715084, "num_tokens": 295, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7279754371026368, "lm_q2_score": 0.6113819732941511, "lm_q1q2_score": 0.4450710592454823}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n#P Permutations\n#P ------------\n#P\n#P Under different circumstances different objects are called permutations,\n#P even in the context of linear algrebra.\n#P\n#P Following list describes these objects and their representation in SPIRAL:\n#P\n#P 1. Regular permutations\n#P (a) in cycle notation : (1,2)(3,4)\n#P (b) as lists : [2,1,4,3]\n#P (c) as index space mapping function: i -> i+1 mod N\n#P\n#P 2. Parametrized permutation classes\n#P [For example stride permutations L(size,str) \| size mod str = 0]\n#P Represented as a construction function, which returns an index mapping\n#P function - (c) above.\n#P\n#P Conversions: ListPerm (b) <- (a) [gap.perm]\n#P PermList (a) <- (b) [gap.perm]\n#P PermFunc (a) <- (c) [spiral.spl.perm]\n#P ListPermFunc (b) <- (c) [spiral.spl.perm]\n#P\n#P -------------------\n\n#F PermFunc(<func>, <size>) . . . . . convert perm. function into explicit GAP perm.\n#F\n#F PermFunc converts a 0-based permutation function used in SPLs, into an explicit\n#F GAP permutation. Recall that GAP permutations are 1-based, and are in cycle\n#F representation.\n#F\nPermFunc := (func, size) ->\n PermList( List([0..size-1], func) + 1 );\n\n#F PermFunc(<func>, <size>) . . . . . convert perm. function into explicit list perm.\n#F\n#F PermFunc converts a 0-based permutation function used in SPLs, into an explicit\n#F 1-based list permutation. List permutations can be converted to GAP permutations\n#F using PermList. Alternatively PermFunc can be used, wihch returns GAP permutation.\n#F\nListPermFunc := (func, size) ->\n List([0..size-1], func) + 1;\n\n# ==========================================================================\n# FuncClass\n#\n# Base class for symbolic functions\n# ==========================================================================\nClass(FuncClass, BaseMat, Function, rec(\n #-----------------------------------------------------------------------\n # Must be implemented in subclasses\n #-----------------------------------------------------------------------\n lambda := self >> Error(\"not implemented\"), \n domain := self >> Error(\"not implemented\"), \n range := self >> Error(\"not implemented\"), \n\n #-----------------------------------------------------------------------\n _perm := true,\n isReal := True,\n isPermutation := self >> false,\n perm := self >> Checked(self.isPermutation(), PermFunc(x->self.lambda().at(x), self.range())),\n\n #-----------------------------------------------------------------------\n print := (self,i,is) >> Print(\n\tself.name, \"(\", PrintCS(self.params), \")\", When(self.transposed, \".transpose()\")),\n #-----------------------------------------------------------------------\n equals := (self, other) >> ObjId(other) = ObjId(self) and self.params=other.params,\n dims := self >> [self.range(), self.domain()],\n\n advdims := self >> [ [[ self.range() ]], [[ self.domain() ]] ],\n\n # size along each dimension, for a multidimensional range\n # for compatibility with ClassSPL, we wrap this into another list \n # (list of outputs, since ClassSPL can have >1 output)\n advrange := self >> [[ self.range() ]],\n\n # size along each dimension, for a multidimensional domain\n # for compatibility with ClassSPL, we wrap this into another list \n # (list of outputs, since ClassSPL can have >1 output)\n advdomain := self >> [[ self.domain() ]],\n\n # dimensionality of range (1-d, 2-d, etc)\n advrangeDim := self >> Length(self.advrange()[1]),\n # dimensionality of domain (1-d, 2-d, etc)\n advdomainDim := self >> Length(self.advdomain()[1]),\n #-----------------------------------------------------------------------\n toAMat := self >> Gath(self).toAMat(),\n #-----------------------------------------------------------------------\n arithmeticCost := (self, costMul, costAddMul) >> costMul(0) - costMul(0),\n #-----------------------------------------------------------------------\n transpose := self >> CopyFields(self, rec(transposed := not self.transposed )),\n #-----------------------------------------------------------------------\n conjTranspose := self >> self.transpose(),\n #-----------------------------------------------------------------------\n normalizedArithCost := self >> 0,\n #-----------------------------------------------------------------------\n free := self >> Union(List(self.params, FreeVars)),\n #-----------------------------------------------------------------------\n # Rewrite rules support \n #\n from_rChildren := (self, rch) >> CopyFields(ApplyFunc(ObjId(self), rch), \n\trec(transposed:=self.transposed)),\n\n # NOTE: self.transposed not exposed\n rChildren := self >> self.params, \n\n rSetChild := meth(self, n, newChild)\n self.params[n] := newChild;\n # self.canonizeParams(); ??\n\tself.dimensions := self.dims();\n end,\n # ----------------------------------------------------------------------\n checkParams := meth(self, params)\n local nargs, nump;\n\tnargs := NumArgs(self.def);\n\tnump := Length(params);\n\tif nargs <> -1 and nargs <> nump then\n Error(self.name, \" needs \", NumArgs(self.def), \" parameters: \",\n\t\tParamsFunc(self.def), \"\\n\");\n\tfi;\n end,\n #-----------------------------------------------------------------------\n canonizeParams := meth(self, params)\n local A, nump;\n\tnump := Length(params);\n\tif IsBound(self.abbrevs) then\n for A in self.abbrevs do\n if NumArgs(A) = -1 or NumArgs(A) = nump then\n\t\t return ApplyFunc(A, params);\n\t\tfi;\n\t od;\n return params;\n\telse\n return params;\n\tfi;\n end,\n #-----------------------------------------------------------------------\n __call__ := meth(arg)\n local result, self, params, lkup, h;\n self := arg[1];\n params := arg{[2..Length(arg)]};\n params := self.canonizeParams(params);\n self.checkParams(params);\n\n h := self.hash;\n if h<>false then\n lkup := h.objLookup(self, params);\n if lkup[1] <> false then return lkup[1]; fi;\n fi;\n \n result := SPL(WithBases(self, rec(params := params, transposed := false)));\n result := Inherit(result, ApplyFunc(result.def, params));\n\tresult.dimensions := result.dims();\n \n if h<>false then return h.objAdd(result, lkup[2]);\n else return result;\n fi;\n end,\n\n# obsolete\n# checkInverse := self >> Checked(self.isPermutation(),\n# PermFunc(self.direct, self.range()) * PermFunc(self.inverse, self.domain())),\n));\n\nClass(PermClass, FuncClass, rec(\n isPermutation := self >> true,\n toAMat := self >> Gath(self).toAMat(),\n equals := (self, other) >> ObjId(other) = ObjId(self) and self.params=other.params\n));\n", "meta": {"hexsha": "5eeb94fc7b4ab3f15f8391facbe6595d572a87ba", "size": 6927, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/spl/PermClass.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/PermClass.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/PermClass.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": 39.5828571429, "max_line_length": 98, "alphanum_fraction": 0.5006496319, "num_tokens": 1589, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7025300698514777, "lm_q2_score": 0.6334102567576901, "lm_q1q2_score": 0.4449897519246225}}
	{"text": "# Copyright (c) 2018-2020, Carnegie Mellon University\n# See LICENSE for details\n\n# Radix n kernel for FFTE, targeting ARM SVE\n\nbuildSVEKernel_a := function(n, kk, conf, opts)\n local vlen, name, suffix, filesuffix, t, j, k, l, m, tmp1, tmp2, tmp3,\n gi, g, gc, si, ss, s, sc, dft, rts, rt, opcnts, dfts, dftc, i, twt, twf, twl, tws, twc,\n cl, cc, c, clp, useFMA, _FMA, lp;\n\n name := DFTnameStr(n, kk);\n suffix := \"a\";\n filesuffix := \"sve_\";\n# suffix := \"_j\";\n Print(\"\\n\\n// == Generating \\\"\", name, \"\\\" ==================================================\\n\\n\"); \n\n vlen := TInt;\n useFMA := When(IsBound(conf.useFMA), conf.useFMA, true);\n _FMA := When(useFMA, FMA, p -> p);\n\n # variables\n t := var.fresh_t(\"t\", TInt);\n j := var.fresh_t(\"j\", TInt);\n k := V(0);\n l := var.fresh_t(\"l\", TInt);\n m := V(1);\n lp := var.fresh_t(\"lp\", TPtr(TInt));\n# mp := var.fresh_t(\"mp\", TPtr(TInt));\n\n\n # temp arrays\n tmp1 := var.fresh_t(\"R\", TArray(TVectSVE, 2n));\n tmp2 := var.fresh_t(\"S\", TArray(TVectSVE, 2n));\n tmp3 := var.fresh_t(\"T\", TArray(TVectSVE, 2n));\n\n # gather\n gi := _i -> VGath_L(1, vlen, 2(k + jm + _ilm));\n g := RulesSums(SumsSPL(VStack(List([0..n-1], gi)), opts));\n gc := Compile(opts.codegen(g, tmp1, X, opts), opts);\n \n # scatter\n si := _i -> ScatH(1, 1, 2nj+_i, 2n);\n ss := SumsSPL(HStack(List([0..2n-1], si)), opts);\n s := RulesSums(SubstTopDown(ss, @(1, ScatAcc), e->Scat(@(1).val.func)));\n sc := Compile(opts.codegen(s, 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 i := var.fresh_t(\"i\", 2n);\n twt := var.fresh_t(\"TW\", TPtr(TReal)); \n twf := Lambda(i, cond(\n eq(i, 0), 1, \n eq(i, 1), 0, \n sve_gath(nth(twt, 2((n-1)j) + 2 * idiv(i, 2) + (imod(i, 2) - 2)).toPtr(TReal), TInt, opts.pg, 2*(n-1))\n ));\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 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, opts.pg], \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, l, opts.pg], \n decl(cc.vars, _FMA(cc.cmd.cmds[1].cmd)));\n \n # print Radix N FFTE kernel as function\n #PrintCode(name, c, opts);\n #PrintTo(name::\".c\", PrintCode(name, c, opts));\n \n ########################################################\n # version with j loop vectorized as m == 1, k == 0\n clp := func(TVoid, \"transform\", [Y, X, twt, lp], \n decl(c.cmd.vars::c.free()::[opts.pg, l], \n chain(\n assign(l, deref(lp)),\n sve_loopn(j, l, \n c.cmd.cmd\n )\n )\n )\n );\n\n # print Radix N FFTE kernel as function\n PrintCode(opts.FortranIze(name::suffix), clp, opts);\n PrintTo(name::filesuffix::suffix::\".c\", PrintCode(opts.FortranIze(name::suffix), clp, opts));\nend;\n\n\n\n\n", "meta": {"hexsha": "012d60ac9fe916cf3f0783131e46200063b8a9e6", "size": 3576, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "kernelgen/sve_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/sve_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/sve_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": 34.3846153846, "max_line_length": 112, "alphanum_fraction": 0.5212527964, "num_tokens": 1246, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7549149868676283, "lm_q2_score": 0.588889130767832, "lm_q1q2_score": 0.44456123042008694}}
	{"text": "#############################################################################\n##\n#W listops.gi automgrp package Yevgen Muntyan\n#W Dmytro Savchuk\n##\n#Y Copyright (C) 2003 - 2018 Yevgen Muntyan, Dmytro Savchuk\n##\n\n\n###############################################################################\n##\n## AG_IsCorrectAutomatonList( <list>, <invertible> )\n##\nInstallGlobalFunction(AG_IsCorrectAutomatonList,\nfunction(list, invertible)\n local len, deg, i, j, sym, semi;\n\n if not IsDenseList(list) then\n return false;\n fi;\n\n len := Length(list);\n if len = 0 then\n return false;\n fi;\n\n for i in [1..len] do\n if not IsDenseList(list[i]) then\n return false;\n fi;\n if Length(list[i]) <> Length(list[1]) then\n return false;\n fi;\n od;\n\n deg := Length(list[1]) - 1;\n if deg < 1 then\n return false;\n fi;\n\n sym := SymmetricGroup(deg);\n semi := FullTransformationSemigroup(deg);\n\n for i in [1..len] do\n for j in [1..deg] do\n if not IsInt(list[i][j]) then\n return false;\n fi;\n if list[i][j] > len or list[i][j] < 1 then\n return false;\n fi;\n od;\n\n if not list[i][deg + 1] in sym then\n if not list[i][deg + 1] in semi then\n return false;\n fi;\n if invertible and list[i][deg + 1]^-1=fail then\n return false;\n fi;\n fi;\n od;\n\n return true;\nend);\n\n\n###############################################################################\n##\n## AG_IsCorrectRecurList( <list>, <invertible> )\n##\nInstallGlobalFunction(AG_IsCorrectRecurList,\nfunction(list, invertible)\n local len, deg, i, j, k, sym, semi, inv_states;\n\n if not IsDenseList(list) then\n return false;\n fi;\n\n len := Length(list);\n if len = 0 then\n return false;\n fi;\n\n for i in [1..len] do\n if not IsDenseList(list[i]) then\n return false;\n fi;\n if Length(list[i]) <> Length(list[1]) then\n return false;\n fi;\n od;\n\n deg := Length(list[1]) - 1;\n if deg < 2 then\n return false;\n fi;\n\n sym := SymmetricGroup(deg);\n semi := FullTransformationSemigroup(deg);\n\n for i in [1..len] do\n for j in [1..deg] do\n if IsInt(list[i][j]) then\n if list[i][j] > len or list[i][j] < -len or list[i][j] = 0 then\n return false;\n fi;\n elif IsList(list[i][j]) then\n if not IsDenseList(list[i][j]) then\n return false;\n fi;\n for k in list[i][j] do\n if (not IsInt(k)) or k > len or k < -len or k = 0 then\n return false;\n fi;\n od;\n else\n return false;\n fi;\n od;\n\n\n # Check that everything is correct here\n if (not IsPerm(list[i][deg + 1])) and (not IsTransformation(list[i][deg + 1])) then\n return false;\n elif LargestMovedPoint(list[i][deg + 1]) > deg then\n return false;\n elif IsTransformation(list[i][deg + 1]) and invertible and list[i][deg + 1]^-1=fail then\n return false;\n fi;\n od;\n\n\n# check if there is x^-1 in the list, while x is not invertible\n inv_states:=[];\n for i in [1..len] do\n if AG_IsInvertibleStateInList(i,list) then Add(inv_states,i); fi;\n od;\n\n for i in [1..len] do\n for j in [1..deg] do\n if IsInt(list[i][j]) then\n if list[i][j]<0 and not -list[i][j] in inv_states then\n return false;\n fi;\n else\n for k in list[i][j] do\n if k<0 and not -k in inv_states then\n return false;\n fi;\n od;\n fi;\n od;\n od;\n\n return true;\nend);\n\n\n###############################################################################\n##\n## AG_ConnectedStatesInList(state, list)\n##\n## Returns list of states which are reachable from given state,\n## it does not check correctness of arguments\n##\nInstallGlobalFunction(AG_ConnectedStatesInList,\nfunction(state, list)\n local i, j, s, d, to_check, checked;\n\n d := Length(list[1]) - 1;\n\n to_check := [state];\n checked := [];\n\n while Length(to_check) <> 0 do\n for s in to_check do\n for i in [1..d] do\n if IsList(list[s][i]) then\n for j in AsSet(List(list[s][i],AbsInt)) do\n if (not j in checked) and (not j in to_check) then\n to_check := Union(to_check, [j]);\n fi;\n od;\n else\n if (not AbsInt(list[s][i]) in checked) and (not AbsInt(list[s][i]) in to_check) then\n to_check := Union(to_check, [AbsInt(list[s][i])]);\n fi;\n fi;\n od;\n checked := Union(checked, [s]);\n to_check := Difference(to_check, [s]);\n od;\n od;\n\n return checked;\nend);\n\n\n###############################################################################\n##\n## AG_IsTrivialStateInList( <state>, <list>)\n##\n## Checks whether given state is trivial.\n## Does not check correctness of arguments.\n##\nInstallGlobalFunction(AG_IsTrivialStateInList,\nfunction(state, list)\n local deg;\n deg := Length(list[1]) - 1;\n # IsOne works for Transformation's\n return ForAll(AG_ConnectedStatesInList(state, list),\n s -> IsOne(list[s][deg+1]));\nend);\n\n\n###############################################################################\n##\n## AG_IsObviouslyTrivialStateInList( <state>, <list>)\n##\n## Checks whether given state is obviously trivial.\n## Works for lists generating self-similar groups.\n## Returns `true' if <state>=(,...,)(), where\n## * could be either +-<state> or [+-<state>], or [].\n##\nInstallGlobalFunction(AG_IsObviouslyTrivialStateInList,\nfunction(state, list)\n local deg, check;\n\n check := function(s)\n if IsInt(s) then return state=AbsInt(s);\n else return s=[] or (Length(s)=1 and state=AbsInt(s[1]));\n fi;\n end;\n\n\n deg := Length(list[1]) - 1;\n if not IsOne(list[state][deg+1]) then return false; fi;\n # IsOne works for Transformation's\n return ForAll(list[state]{[1..deg]}, check);\nend);\n\n\n\n###############################################################################\n##\n## AG_IsInvertibleStateInList( <state>, <list> )\n##\n## Checks whether given state is invertible.\n## Does not check correctness of arguments.\n##\nInstallGlobalFunction(AG_IsInvertibleStateInList,\nfunction(state, list)\n local deg;\n deg := Length(list[1]) - 1;\n return ForAll(AG_ConnectedStatesInList(state, list),\n s -> (list[s][deg+1]^-1<>fail));\nend);\n\n\n###############################################################################\n##\n## AG_AreEquivalentStatesInList( <state1>, <state2>, <list> )\n##\n## Checks whether two given states are equivalent.\n## Does not check correctness of arguments.\n##\nInstallGlobalFunction(AG_AreEquivalentStatesInList,\nfunction(state1, state2, list)\n local d, checked_pairs, pos, s1, s2, np, i;\n\n d := Length(list[1]) - 1;\n checked_pairs := [[state1, state2]];\n pos := 0;\n\n while Length(checked_pairs) <> pos do\n pos := pos + 1;\n s1 := checked_pairs[pos][1];\n s2 := checked_pairs[pos][2];\n\n if list[s1][d+1] <> list[s2][d+1] then\n return false;\n fi;\n\n for i in [1..d] do\n np := [list[s1][i], list[s2][i]];\n if not np in checked_pairs then\n checked_pairs := Concatenation(checked_pairs, [np]);\n fi;\n od;\n od;\n\n return true;\nend);\n\n\n###############################################################################\n##\n## AG_AreEquivalentStatesInLists( <state1>, <state2>, <list1>, <list2>)\n##\n## Checks whether two given states in different lists are equivalent.\n## Does not check correctness of arguments.\n##\nInstallGlobalFunction(AG_AreEquivalentStatesInLists,\nfunction(state1, state2, list1, list2)\n local d, checked_pairs, pos, s1, s2, np, i;\n\n d := Length(list1[1]) - 1;\n checked_pairs := [[state1, state2]];\n pos := 0;\n\n while Length(checked_pairs) <> pos do\n pos := pos + 1;\n s1 := checked_pairs[pos][1];\n s2 := checked_pairs[pos][2];\n\n if list1[s1][d+1] <> list2[s2][d+1] then\n return false;\n fi;\n\n for i in [1..d] do\n np := [list1[s1][i], list2[s2][i]];\n if not np in checked_pairs then\n checked_pairs := Concatenation(checked_pairs, [np]);\n fi;\n od;\n od;\n\n return true;\nend);\n\n\n###############################################################################\n##\n## AG_ReducedAutomatonInList( <list> )\n##\n## Returns [new_list, list_of_states, old_states] where new_list is a new list\n## which represents reduced form of given automaton, i-th elmt of list_of_states\n## is the number of i-th state of new automaton in the old one.\n## old_states[i] is the number of state which corresponds to the i-th state\n## of the original automaton.\n##\n## First state of returned list is always first state of given one.\n## It does not remove trivial state, so it's not really \"reduced automaton\",\n## it just removes equivalent states.\n## TODO: write such function which removes trivial state\n##\n## Does not check correctness of list.\n##\n## WARNING: do NOT change it.\n##\nInstallGlobalFunction(AG_ReducedAutomatonInList,\nfunction(list)\n local i, n, triv_states, equiv_classes, checked_states, s, s1, s2,\n eq_cl, eq_cl_1, eq_cl_2, are_equiv, eq_cl_reprs,\n new_states, new_list, deg,\n reduced_automaton, state, states_reprs;\n\n n := Length(list);\n triv_states := [];\n equiv_classes := [];\n checked_states := [];\n deg := Length(list[1]) - 1;\n\n for s in [1..n] do\n if AG_IsTrivialStateInList(s, list) then\n triv_states := Union(triv_states, [s]);\n fi;\n od;\n\n equiv_classes:=[triv_states];\n for s1 in Difference([1..n], triv_states) do\n for s2 in Difference([s1+1..n], triv_states) do\n are_equiv := AG_AreEquivalentStatesInList(s1, s2, list);\n\n if s1 in checked_states then\n for eq_cl in equiv_classes do\n if s1 in eq_cl then\n eq_cl_1 := StructuralCopy(eq_cl);\n break; fi; od;\n else\n equiv_classes := Union(equiv_classes, [[s1]]);\n eq_cl_1 := [s1];\n checked_states := Union(checked_states, [s1]);\n fi;\n if s2 in checked_states then\n for eq_cl in equiv_classes do\n if s2 in eq_cl then\n eq_cl_2 := StructuralCopy(eq_cl);\n break; fi; od;\n else\n equiv_classes := Union(equiv_classes, [[s2]]);\n eq_cl_2 := [s2];\n checked_states := Union(checked_states, [s2]);\n fi;\n\n if are_equiv then\n equiv_classes := Difference(equiv_classes, [eq_cl_1, eq_cl_2]);\n equiv_classes := Union(equiv_classes, [Union(eq_cl_1, eq_cl_2)]);\n fi;\n od;\n od;\n states_reprs := [1..n];\n for eq_cl in equiv_classes do\n for s in eq_cl do\n states_reprs[s] := Minimum(eq_cl);\n od;\n od;\n\n\n new_states := Set(states_reprs);\n new_list := [];\n\n for s in new_states do\n state := [];\n state[deg+1] := list[s][deg+1];\n for i in [1..deg] do\n state[i] := Position(new_states, states_reprs[list[s][i]]);\n od;\n new_list := Concatenation(new_list, [state]);\n od;\n\n return [new_list, new_states, List([1..n], i -> Position(new_states, states_reprs[i]))];\nend);\n\n\n###############################################################################\n##\n## AG_MinimalSubAutomatonInlist(<states>, <list>)\n##\n## Returns list representation of automaton given by <list> which is minimal\n## subatomaton of automaton containing states <states>.\n##\n## Does not check correctness of list.\n##\nInstallGlobalFunction(AG_MinimalSubAutomatonInlist,\nfunction(states, list)\n local s, new_states, state, new_list, i, deg;\n\n new_states := [];\n for s in states do\n new_states := Union(new_states, AG_ConnectedStatesInList(s, list));\n od;\n\n new_list := [];\n deg := Length(list[1]) - 1;\n\n for s in new_states do\n state := [];\n for i in [1..deg] do\n state[i] := Position(new_states, list[s][i]);\n od;\n state[deg+1] := list[s][deg+1];\n new_list := Concatenation(new_list, [state]);\n od;\n\n return [new_list, new_states];\nend);\n\n\n###############################################################################\n##\n## AG_PermuteStatesInList(<list>, <perm>)\n##\n## Does not check correctness of arguments.\n##\nInstallGlobalFunction(AG_PermuteStatesInList,\nfunction(list, perm)\n local new_list, i, j, deg;\n\n deg := Length(list[1]) - 1;\n new_list := [];\n for i in [1..Length(list)] do\n new_list[i^perm] := [];\n for j in [1..deg] do\n new_list[i^perm][j] := list[i][j]^perm;\n od;\n new_list[i^perm][deg+1] := list[i][deg+1];\n od;\n\n return new_list;\nend);\n\n\n###############################################################################\n##\n## AG_WordStateInList(<w>, <s>, <list>, <reduce>, <trivstate>)\n##\n## It's ProjectWord from selfs.g\n## Does not check correctness of arguments.\n##\nInstallGlobalFunction(AG_WordStateInList,\nfunction(w, s, list, reduce, trivstate)\n local i, perm, d, proj, red, reduce_word;\n\n reduce_word := function(v)\n local len, red, x;\n len := 0;\n red := [];\n for x in v do\n if x <> trivstate then\n if len <> 0 and x = -red[len] then\n Remove(red, len);\n len := len - 1;\n else\n Add(red, x);\n len := len + 1;\n fi;\n fi;\n od;\n return red;\n end;\n\n d := Length(list[1])-1;\n proj := [];\n perm := ();\n for i in [1..Length(w)] do\n Add(proj, list[w[i]][s^perm]);\n perm := perm * list[w[i]][d+1];\n od;\n if reduce then\n return reduce_word(proj);\n else\n return proj;\n fi;\nend);\n\n\n###############################################################################\n##\n## AG_WordStateAndPermInList(<w>, <s>, <list>)\n##\n## Does not check correctness of arguments.\n##\nInstallGlobalFunction(AG_WordStateAndPermInList,\nfunction(w, s, list)\n local i, perm, perm_res, new_state, d, proj;\n d := Length(list[1])-1;\n proj := [];\n perm := ();\n perm_res := ();\n for i in [1..Length(w)] do\n new_state := list[w[i]][s^perm];\n Add(proj, new_state);\n perm := perm * list[w[i]][d+1];\n perm_res := perm_res * list[new_state][d+1];\n od;\n return [proj, perm_res];\nend);\n\n\n###############################################################################\n##\n## AG_ImageOfVertexInList(<list>, <init>, <vertex>)\n##\n## Does not check correctness of arguments.\n##\nInstallGlobalFunction(AG_ImageOfVertexInList,\nfunction(list, s, seq)\n local deg, img, x;\n\n deg := Length(list[1]) - 1;\n img := [];\n for x in seq do\n Add(img, x^list[s][deg+1]);\n s := list[s][x];\n od;\n\n return img;\nend);\n\n\n###############################################################################\n##\n## AG_DiagonalPowerInList(<list>, <n>)\n##\nInstallGlobalFunction(AG_DiagonalPowerInList,\nfunction(list, n, names)\n local d, nlist, nd, nalph, nstates, nperm,\n i, j, k, letter, n_letter, n_state, state,\n nnames;\n\n d := Length(list[1]) - 1;\n nd := d ^ n;\n nalph := Tuples([1..d], n);\n nstates := Tuples([1..Length(list)], n);\n nlist := List([1..Length(nstates)], i -> []);\n nnames := List(nstates, s->List(s, i->names[i]));\n\n for i in [1..Length(nlist)] do\n nperm := [];\n state := nstates[i];\n for j in [1..nd] do\n letter := nalph[j];\n n_letter := [];\n n_state := [];\n for k in [1..n] do\n n_letter[k] := letter[k]^list[state[k]][d+1];\n n_state[k] := list[state[k]][letter[k]];\n od;\n nperm[j] := n_letter;\n nlist[i][j] := Position(nstates, n_state);\n od;\n nlist[i][nd+1] := PermListList(nalph, nperm);\n od;\n\n nnames := List(nnames, l->Concatenation(l));\n return [nlist, nnames];\nend);\n\n\n###############################################################################\n##\n## AG_MultAlphabetInList(<list>, <n>)\n##\nInstallGlobalFunction(AG_MultAlphabetInList,\nfunction(list, n)\n local d, nlist, nd, nalph, nperm,\n i, j, k, letter, n_letter, st;\n\n d := Length(list[1]) - 1;\n nd := d ^ n;\n nalph := Tuples([1..d], n);\n nlist := List(list, i -> []);\n\n for i in [1..Length(nlist)] do\n nperm := [];\n for j in [1..Length(nalph)] do\n letter := nalph[j];\n n_letter := [];\n st := i;\n for k in [1..n] do\n Add(n_letter, letter[k]^list[st][d+1]);\n st := list[st][letter[k]];\n od;\n nlist[i][j] := st;\n nperm[j] := n_letter;\n od;\n nlist[i][nd+1] := PermListList(nalph, nperm);\n od;\n\n return nlist;\nend);\n\n\n###############################################################################\n##\n## AG_HasDualInList(<list>)\n##\nInstallGlobalFunction(AG_HasDualInList,\nfunction(list)\n local i, j, p, d, n;\n d := Length(list[1]) - 1;\n n := Length(list);\n for i in [1..d] do\n p := [];\n for j in [1..n] do\n p[j] := list[j][i];\n od;\n if PermListList([1..n], p) = fail then\n return false;\n fi;\n od;\n return true;\nend);\n\n\n###############################################################################\n##\n## AG_DualAutomatonList(<list>)\n##\nInstallGlobalFunction(AG_DualAutomatonList,\nfunction(list)\n local dual, d, n;\n d := Length(list[1]) - 1;\n n := Length(list);\n return List([1..d], i -> Concatenation(List([1..n], j -> i^list[j][d+1]),\n [PermList(List([1..n], j -> list[j][i]))]));\nend);\n\n\n###############################################################################\n##\n## AG_HasDualOfInverseInList(<list>)\n##\nInstallGlobalFunction(AG_HasDualOfInverseInList,\nfunction(list)\n return AG_HasDualInList(AG_InverseAutomatonList(list));\nend);\n\n\n###############################################################################\n##\n## AG_InverseAutomatonList(<list>)\n##\nInstallGlobalFunction(AG_InverseAutomatonList,\nfunction(list)\n local inv, d, i;\n d := Length(list[1]) - 1;\n inv := List(list, l -> Permuted(l, l[d+1]));\n for i in [1..Length(list)] do inv[i][d+1] := inv[i][d+1]^-1; od;\n return inv;\nend);\n\n\n#E\n", "meta": {"hexsha": "46feabccc68565e100d50b9c2a580f8cb234374a", "size": 17625, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "gap/listops.gi", "max_stars_repo_name": "gap-packages/automgrp", "max_stars_repo_head_hexsha": "1beb0cbc96c9748cf912433c27c661e1f87ef5dc", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-10-02T15:00:11.000Z", "max_stars_repo_stars_event_max_datetime": "2021-10-02T15:00:11.000Z", "max_issues_repo_path": "gap/listops.gi", "max_issues_repo_name": "gap-packages/automgrp", "max_issues_repo_head_hexsha": "1beb0cbc96c9748cf912433c27c661e1f87ef5dc", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 9, "max_issues_repo_issues_event_min_datetime": "2019-09-21T22:10:40.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-26T23:51:41.000Z", "max_forks_repo_path": "gap/listops.gi", "max_forks_repo_name": "gap-packages/automgrp", "max_forks_repo_head_hexsha": "1beb0cbc96c9748cf912433c27c661e1f87ef5dc", "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": 24.9292786421, "max_line_length": 94, "alphanum_fraction": 0.5400283688, "num_tokens": 4920, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6688802735722128, "lm_q2_score": 0.6619228758499942, "lm_q1q2_score": 0.44274715428225}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nDeclare(TDCT2, TDCT3, TDCT4);\n\n_DCT_CONST := 2.5;\n\n#######################################################################################\n# tSPL DCT rules\n\n\n# PDCT4_CT_SPL := rec(\n# isApplicable := P -> P > 2 and ForAny(DivisorPairs(2P), d->IsEvenInt(d[1]) and IsEvenInt(d[2])),\n# forTransposition := false,\n#\n# allChildren := P -> let(N := P,\n# Map2(Filtered(DivisorPairs(2N), d -> IsEvenInt(d[1]) and IsEvenInt(d[2])),\n# (m,n) -> [ PRDFT3(m,-1).transpose(), PRDFT3(n) ])),\n#\n# rule := (P,C) -> let(N := P, m := Rows(C[1]), n := Cols(C[2]),\n# j := Ind(n/2),\n# T := Diag(Twid(2N, m/2, 1, 1/2, 1/2, j)),\n#\n# Prm(Refl(N, 2N-1, N, L(mn, m))) \n# IterDirectSum(j, j.range, Diag(BHN(m)) * C[1] * RC(T)) \n# RC(L(mn/4, n/2)) \n# Tensor(I(m/2), C[2] Diag(BHN(n))) \n# Prm(Refl(N, 2N-1, N, L(mn, m)))\n# )\n# )\n#\n\n\n#F TDCT4(<size>, tags) - Discrete Cosine Transform, Type IV, non-terminal\n#F Definition: (n x n)-matrix [ cos((k+1/2)(l+1/2)pi/n) \| k,l = 0...n-1 ]\n#F Note: DCT4 is symmetric\n#F Example: DCT4(8)\nClass(TDCT4, TaggedNonTerminal, rec(\n abbrevs := [ N -> Checked(IsInt(N), N >= 1, [N]) ] ,\n dims := self >> [self.params[1], self.params[1]],\n isReal := True,\n terminate := self >> Mat(DCT_IVunscaled(self.params[1])),\n transpose := self >> Copy(self),\n SmallRandom := () -> Random([2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32]),\n normalizedArithCost := (self) >> let(n := self.params[1], IntDouble(_DCT_CONST n * d_log(n) / d_log(2)))\n));\n\n\nNewRulesFor(TDCT4, rec(\n# DCT4_CT_tSPL := rec(\n# switch := false,\n#\n# applicable := (self, t) >> let(P:=t.params, P[1] > 2 and ForAny(DivisorPairs(2P[1]), d->IsEvenInt(d[1]) and IsEvenInt(d[2])) and HasTags(t)),\n#\n# children := (self, t) >> let(tags := GetTags(t), N := t.params[1],\n# Map2(Filtered(DivisorPairs(2N), d -> IsEvenInt(d[1]) and IsEvenInt(d[2])),\n# (m,n) -> [\n# SetTag(TCompose([\n# TScat(Refl(N, 2N-1, N, L(mn, m))),\n# TTensorI(Diag(BHN(m)) * PRDFT3(m,-1).transpose(), n/2, APar, APar),\n# TRC(TDiag(fPrecompute(\n# fCompose(dOmega(8 * N, 1), diagTensor(dLin(N/m, 2, 1, TInt), dLin(m/2, 2, 1, TInt)))\n# ))),\n# TRC(TL(mn/4, n/2, 1, 1)),\n# TTensorI(PRDFT3(n) Diag(BHN(n)), m/2, APar, APar),\n# TGath(Refl(N, 2N-1, N, L(mn, m))) ]),\n# tags)\n# ])),\n#\n# apply := (self, t, C, Nonterms) >> C[1]\n# ),\n#\n# # Variant better suited for vectorization\n# PDCT4_CT_SPL_Vec := rec(\n# isApplicable := P -> P > 2 and (P mod 2) = 0,\n# forTransposition := false,\n#\n# allChildren := P -> let(N := P,\n# Map2(Filtered(DivisorPairs(2N), d -> IsEvenInt(d[1]) and IsEvenInt(d[2])),\n# (m,n) -> [ PRDFT3(m,-1).transpose(), PRDFT3(n) ])),\n#\n# rule := (P,C) -> let(N := P, m := Rows(C[1]), n := Cols(C[2]),\n# TT := Diag(fPrecompute(fCompose(dOmega(8 N, 1),\n# diagTensor(dLin(N/m, 2, 1, TInt), dLin(m/2, 2, 1, TInt))))),\n#\n# IJ(N, n/2) \n# L(N, m) \n# Tensor(I(n/2),\n# M(m,m/2) * Diag(BHN(m)) * C[1]) \n# RC(TT) \n# L(N, n/2) \n# Tensor(I(m/2),\n# L(n, 2) C[2] * Diag(BHN(n)) * K(n, 2)) \n# L(N, m/2) \n# IJ(N, m/2)\n# )\n# )\n\n\n DCT4_CT_tSPL := rec(\n switch := false,\n\n applicable := (self, t) >> let(\n P:=t.params,\n P[1] > 2\n and ForAny(DivisorPairs(2P[1]), d ->\n IsEvenInt(d[1]) and IsEvenInt(d[2])\n )\n and t.hasTags()\n ),\n\n children := (self, t) >> let(\n tags := t.getTags(),\n N := t.params[1],\n Map2(\n Filtered(DivisorPairs(2N), d -> IsEvenInt(d[1]) and IsEvenInt(d[2])),\n (m,n) -> List([\n TPrm(IJ(N, n/2)),\n TTensorI(condM(m,m/2) * Diag(BHN(m)) * PRDFT3(m,-1).transpose(), n/2, AVec, AVec),\n TTensorI(L(n, 2) * PRDFT3(n) * Diag(BHN(n)) * condK(n, 2), m/2, APar, AVec),\n TPrm(IJ(N, m/2))\n ], i -> i.setTags(tags))\n )\n ),\n\n apply := (self, t, C, Nonterms) >> let(\n N:=t.params[1],\n n:=2Rows(Nonterms[1].params[1].params[2]),\n m:=2Rows(Nonterms[4].params[1].params[2]),\n Grp(\n C[1] * C[2]\n * ConjDiag(RC(Diag(fPrecompute(\n fCompose(dOmega(8 * N, 1), diagTensor(dLin(N/m, 2, 1, TInt), dLin(m/2, 2, 1, TInt)))\n ))), L(N, m), L(N, n/2))\n )\n * C[3] * C[4]\n )\n )\n));\n\n\n#F TDCT2(<n>) - Discrete Cosine Transform, Type II, non-terminal\n#F Definition: (n x n)-matrix [ cos(k(l+1/2)pi/n) \| k,l = 0...n-1 ]\n#F Note: DCT2 is the transpose of DCT3\n#F Example: DCT2(8)\nClass(TDCT2, TaggedNonTerminal, rec(\n abbrevs := [ N -> Checked(IsInt(N), N >= 1, [N]) ] ,\n dims := self >> [self.params[1], self.params[1]],\n isReal := True,\n terminate := self >> Mat(DCT_IIunscaled(self.params[1])),\n transpose := self >> TDCT3(self.params[1]),\n SmallRandom := () -> Random([2,3,4,5,6,8,9,10,12,15,16,18,24,27,30,32]),\n normalizedArithCost := (self) >> let(n := self.params[1], IntDouble(_DCT_CONST * n * d_log(n) / d_log(2)))\n));\n\n\nNewRulesFor(TDCT2, rec(\n DCT2_DCT4_tSPL := rec(\n switch := false,\n applicable := (self, t) >> true,\n children := (self, t) >> [[ TS(t.params[1]).withTags(t.getTags()), TDCT4(t.params[1]).withTags(t.getTags()) ]],\n apply := (self, t, C, Nonterms) >> let(P := t.params[1],\n Diag(Concat([V(2.0)], List([1..P-1], i->V(1.0)))) \n C[1].transpose() C[2] \n Diag(List([0..P - 1], i -> 1/(2 CosPi((2i + 1)/(4P))))))\n ))\n);\n\n\n\n#F TDCT3(<n>) - Discrete Cosine Transform, Type III, non-terminal (unscaled)\n#F Definition: (n x n)-matrix [ cos((k+1/2)lpi/n) \| k,l = 0...n-1 ]\n#F [scaled] (n x n)-matrix [ a_lcos((k+1/2)lpi/n) \| k,l = 0...n-1 ]\n#F a_j = 1/sqrt(2) for j = 0 and = 1 else\n#F Note: DCT3 is the transpose of DCT2, scaled NOT supported yet\n#F Example: DCT3(8)\nClass(TDCT3, TaggedNonTerminal, rec(\n abbrevs := [ N -> Checked(IsInt(N), N >= 1, [N]) ] ,\n dims := self >> [self.params[1], self.params[1]],\n isReal := True,\n terminate := self >> Mat(DCT_IIIunscaled(self.params[1])),\n transpose := self >> TDCT2(self.params[1]),\n SmallRandom := () -> Random([2,3,4,5,6,8,9,10,12,15,16,18,24,27,30,32]),\n normalizedArithCost := (self) >> let(n := self.params[1], IntDouble(_DCT_CONST n * d_log(n) / d_log(2)))\n));\n\n\nNewRulesFor(TDCT3, rec(\n DCT3_DCT2_tSPL := rec(\n switch := false,\n applicable := (self, t) >> true,\n children := (self, t) >> [[ TDCT2(t.params[1]).withTags(t.getTags()) ]],\n apply := (self, t, C, Nonterms) >> C[1].transpose()\n ),\n DCT3_DCT4_tSPL := rec(\n switch := false,\n applicable := (self, t) >> true,\n children := (self, t) >> [[ TDCT4(t.params[1]).withTags(t.getTags()), TS(t.params[1]).withTags(t.getTags()) ]],\n apply := (self, t, C, Nonterms) >> let(P := t.params[1],\n Diag(List([0..P - 1], i -> 1/(2 * CosPi((2i + 1)/(4P))))) \n C[1] C[2] *\n Diag(Concat([V(2.0)], List([1..P-1], i->V(1.0)))))\n )\n));\n", "meta": {"hexsha": "49dad3b65443d73e410b28749144292e1e9502fd", "size": 8093, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/common/dct.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/common/dct.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/common/dct.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": 39.0966183575, "max_line_length": 151, "alphanum_fraction": 0.4470530088, "num_tokens": 2768, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. 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	{"text": "\n#\n# ---------- Constructors ----------\n#\n\nInstallMethod(UnipotentMod,\n \"Unipotent element in simple adjoint type\",\n [IsChevalleyAdj,IsList,IsList,IsInt,IsPosInt],\n function(sys,coeffs,ordering,order,root)\n local object;\n \n if Filtered(coeffs,i->not i[2] in Integers)=[] then coeffs:=List(coeffs,i->[i[1],One(ring(sys))i[2]]);\n elif Filtered(coeffs,i->not i[2] in ring(sys))<>[] then Error(\"The coefficients ar not in indicated ring.\"); fi;\n\n object:=Objectify(NewType(NewFamily(\"UnipotentFamily\"),\n IsAttributeStoringRep and\n IsUnipotent and\n IsMultiplicativeElementWithInverse),\n rec());\n\n SetchevalleyAdj(object,sys);\n SetOrdering(object,ordering);\n\n Setcoefficients(object,CanonicMod(sys,coeffs,ordering,root));\n# SetInverse(object,InverseOp(object)); This is set at the first call Inverse(obj);\n\n if order = -1 and Characteristic(sys)>0 then\n SetOrder(object,OrderOp(object));\n elif order > -1 then\n SetOrder(object,order);\n fi;\n \n SetName(object,Concatenation(\"<unipotent element for \",\n type(sys),String(rank(sys)),\n \" in characteristic \",String(Characteristic(sys)),\">\"));\n return object;\nend);\n\nInstallMethod(UnipotentMod,\n \"Unipotent element in simple adjoint type\",\n [IsChevalleyAdj,IsList,IsList,IsPosInt],\n function(sys,coeffs,ordering,root)\n\n return UnipotentMod(sys,coeffs,ordering,-2,root);\nend);\n\n\n#\n# ---------- Canonic form of element modulo some roots ----------\n#\n\nInstallMethod(CanonicMod,\n \"Canonic form of coefficients of unipotent element in given ordering modulo some roots\",\n [IsChevalleyAdj,IsList,IsList,IsPosInt],\n function(sys,coeffs,Ordering,root)\n local lista,\n pr,Cijrs,\n flag,i,temp,suma,param,cc,k,pos;\n \n lista:=[];\n for i in coeffs do\n if Ordering[i[1]]<=Ordering[root] then\n Add(lista,ShallowCopy(i));\n fi;\n od;\n \n pr:=positiveRoots(sys);\n\n Cijrs:=C(sys);\n flag:=true;\n while flag do\n flag:=false;\n i:=Length(lista);\n while 0 < i do\n if lista[i][2] = Zero(ring(sys)) then \n Remove(lista,i);\n flag:=true;\n elif 1 < i and lista[i][1] = lista[i-1][1] then\n lista[i-1][2]:=lista[i-1][2]+lista[i][2];\n Remove(lista,i);\n flag:=true;\n elif 1 < i and Ordering[lista[i][1]] < Ordering[lista[i-1][1]] then\n temp:=lista[i]; lista[i]:=lista[i-1]; lista[i-1]:=temp;\n \n #aici r si s sunt pe pozitia i-1 si repsectiv i\n k:=1;\n for cc in Cijrs[lista[i-1][1]][lista[i][1]] do\n suma:=cc[1]pr[lista[i-1][1]]+cc[2]pr[lista[i][1]];\n pos:=Position(pr,suma);\n if Ordering[pos]<=Ordering[root] then\n param:=cc[3]((-1)^cc[1])(lista[i-1][2]^cc[1])(lista[i][2]^cc[2]);\n Add(lista,[pos,param],i+k);\n k:=k+1;\n fi;\n od;\n flag:=true;\n fi;\n i:=i-1;\n od;\n od;\n\n return Immutable(lista);\nend);\n\n\n#\n# ---------- Arithmetic Operations modulo some roots ----------\n#\n\nInstallMethod(MMod,\n \"Multiplication for unipotent elements a*b modulo some roots and with the ordering of b\",\n [IsUnipotent,IsUnipotent,IsPosInt],\n function(u1,u2,root)\n local sys1,sys2,\n generic,result,coeffs1,coeffs2,\n APR,avars,pr_len,\n i;\n\n sys1:=chevalleyAdj(u1);\n sys2:=chevalleyAdj(u2);\n if type(sys1)<>type(sys2) or\n rank(sys1)<>rank(sys2) or\n ring(sys1)<>ring(sys2) then Error(\"Not in the same family.\"); fi;\n \n return UnipotentMod(sys2,Concatenation(coefficients(u1),coefficients(u2)),Ordering(u2));\nend);\n\nInstallMethod(CommMod,\n \"Commutator for unipotent elements a^-1b^-1ab with the ordering of b\",\n [IsUnipotent,IsUnipotent,IsPosInt],\n function(u1,u2,root)\n local sys1,sys2;\n\n sys1:=chevalleyAdj(u1);\n sys2:=chevalleyAdj(u2);\n if type(sys1)<>type(sys2) or\n rank(sys1)<>rank(sys2) or\n ring(sys1)<>ring(sys2) then Error(\"Not in the same family.\"); fi;\n return UnipotentMod(sys2,\n Concatenation(coefficients(u1^-1),coefficients(u2^-1),\n coefficients(u1),coefficients(u2)),\n Ordering(u2),\n root);\nend);\n\nInstallMethod(ConjMod,\n \"Conjugation for unipotent elements b^-1ab with the ordering of b\",\n [IsUnipotent,IsUnipotent,IsPosInt],\n function(u1,u2,root)\n local sys1,sys2;\n\n sys1:=chevalleyAdj(u1);\n sys2:=chevalleyAdj(u2);\n if type(sys1)<>type(sys2) or\n rank(sys1)<>rank(sys2) or\n ring(sys1)<>ring(sys2) then Error(\"Not in the same family.\"); fi;\n return Unipotent(sys2,\n Concatenation(coefficients(u2^-1),coefficients(u1),coefficients(u2)),\n Ordering(u2),\n root);\nend);\n\n", "meta": {"hexsha": "9af598ddff039e009eef1547af0c2410e4e2c03e", "size": 6478, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "lib/unimod.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/unimod.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/unimod.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": 39.7423312883, "max_line_length": 126, "alphanum_fraction": 0.4487496141, "num_tokens": 1400, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7606506526772884, "lm_q2_score": 0.5774953651858118, "lm_q1q2_score": 0.4392722264466967}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nsetLeft := function(tags)\n local i, retval;\n retval := Copy(tags);\n for i in retval do\n i.isLeftChild := true;\n i.isRightChild := false;\n od;\n return(retval);\nend; \n\nsetRight := function(tags)\n local i, retval;\n retval := Copy(tags);\n for i in retval do\n i.isLeftChild := false;\n i.isRightChild := true;\n od;\n return(retval);\nend; \n\n\nNewRulesFor(WHT, rec(\n WHT_GT := rec(\n switch := false,\n maxSize := false,\n minSize := false,\n codeletSize := false,\n inplace := false,\n\n applicable := (self, t) >> let(n := Rows(t),\n n > 2 and\n (self.maxSize=false or n <= self.maxSize) and\n (self.minSize=false or n >= self.minSize) and\n not IsPrime(n)),\n\n children := (self, t) >> Map2(Filtered(DivisorPairs(Rows(t)), d->When(IsInt(self.codeletSize), d[1]<=self.codeletSize, true)),\n (m,n) -> [\n GT(WHT(LogInt(m, 2)), XChain([0, 1]), XChain([0, 1]), [n]).withTags(t.getTags()),\n GT(WHT(LogInt(n, 2)), XChain([1, 0]), XChain([1, 0]), [m]).withTags(t.getTags()),\n #GT(WHT(LogInt(m, 2)), XChain([0, 1]), XChain([0, 1]), [n]).withTags( let(ts := t.getTags(), setLeft(ts)) ),\n #GT(WHT(LogInt(n, 2)), XChain([1, 0]), XChain([1, 0]), [m]).withTags( let(ts := t.getTags(), setRight(ts)) ),\n ]),\n\n apply := (self, t, C, Nonterms) >> C[1] * C[2]\n )\n));\n\nNewRulesFor(DFT, rec(\n DFT_GT_CT := rec(\n switch := false,\n maxSize := false,\n minSize := 2,\n codeletSize := false,\n inplace := false,\n\n a := rec(\n precompute := true\n ),\n\n applicable := (self, t) >> let(n := Rows(t),\n n > 2 and\n (self.maxSize=false or n <= self.maxSize) and\n (self.minSize=false or n >= self.minSize) and\n not IsPrime(n)),\n\n #GT(DFT(m, t.params[2] mod m), XChain([0, 1]), XChain([0, 1]), [n]).withTags( let(a := t.getTags(), ),\n #GT(DFT(n, t.params[2] mod n), XChain([0, 1]), XChain([1, 0]), [m]).withTags( t.getTags())\n\n #GT(DFT(m, t.params[2] mod m), XChain([0, 1]), XChain([0, 1]), [n]).withTags(t.getTags()),\n #GT(DFT(n, t.params[2] mod n), XChain([0, 1]), XChain([1, 0]), [m]).withTags(t.getTags())\n\n children := (self, t) >> Map2(Filtered(DivisorPairs(Rows(t)), d->When(IsInt(self.codeletSize), d[1]<=self.codeletSize, true)),\n (m,n) -> [\n GT(DFT(m, t.params[2] mod m), XChain([0, 1]), XChain([0, 1]), [n]).withTags(t.getTags()),\n GT(DFT(n, t.params[2] mod n), XChain([0, 1]), XChain([1, 0]), [m]).withTags(t.getTags()),\n #GT(DFT(m, t.params[2] mod m), XChain([0, 1]), XChain([0, 1]), [n]).withTags( let(ts := t.getTags(), setLeft(ts)) ),\n #GT(DFT(n, t.params[2] mod n), XChain([0, 1]), XChain([1, 0]), [m]).withTags( let(ts := t.getTags(), setRight(ts)) ),\n ]),\n\n apply := (self, t, C, Nonterms) >> let(\n inplace := When(self.inplace, Inplace, Grp),\n n := Rows(Nonterms[2].params[1]),\n rot := t.params[2],\n compute := When(self.a.precompute, fPrecompute, fComputeOnline),\n\n inplace(Buf(C[1] * Diag(compute(Tw1(Rows(t), n, rot))))) * C[2])\n )\n));\n\n# GT(DFT(), ...) rules\n#\nNewRulesFor(GT, rec(\n GT_DFT_Base2 := rec(\n applicable := (self, t) >> let(rank := Length(t.params[4]),\n rank = 0 and PatternMatch(t, [GT, DFT, @, @, @, @, @], empty_cx()) and Rows(t.params[1])=2),\n apply := (t, C, Nonterms) -> F(2)\n ),\n\n GT_DFT_CT := rec(\n maxSize := false,\n minSize := false,\n minRank := 0,\n maxRank := 1,\n codeletSize := 32,\n inplace := true,\n\n a := rec(\n precompute := true\n ),\n\n applicable := (self, t) >> let(\n rank := Length(t.params[4]), \n dft := t.params[1],\n\n rank >= self.minRank \n and rank <= self.maxRank \n and When(rank>0, t.getTags()=[], true) \n and (self.maxSize=false or Rows(dft) <= self.maxSize) \n and (self.minSize=false or Rows(dft) >= self.minSize) \n and PatternMatch(t, [GT, DFT, XChain, XChain, @, @, @], empty_cx()) \n and DFT_GT_CT.applicable(dft)\n ),\n \n children := (self, t) >> let(\n dft := t.params[1], \n g := t.params[2], s := t.params[3], \n rot := dft.params[2],\n loop_dims := t.params[4],\n nloops := Length(loop_dims),\n tags := t.getTags(),\n \n Map2( Filtered(DivisorPairs(Rows(dft)), d->d[1]<=self.codeletSize),\n (m,n) -> [\n GT(DFT(m, rot mod m),\n s.composeWith(XChain([0, 1])), s.composeWith(XChain([0, 1])),\n Concatenation([n], loop_dims)\n ).withTags(tags),\n \n GT(DFT(n, rot mod n),\n g.composeWith(XChain([0, 1])), s.composeWith(XChain([1, 0])),\n Concatenation([m], loop_dims)\n ).withTags(tags)\n ]\n )\n ),\n \n apply := (self, t, C, Nonterms) >> let(\n loop_dims := t.params[4], \n s := t.params[3],\n N := Rows(t.params[1]), \n k := t.params[1].params[2], \n n := Rows(Nonterms[2].params[1]),\n\n inplace := When(self.inplace, Inplace, Grp),\n compute := When(self.a.precompute, fPrecompute, fComputeOnline),\n \n inplace(Buf(C[1] * Diag(compute(s.toDiag(loop_dims, Tw1(N,n,k)))))) * C[2]\n )\n )\n));\n", "meta": {"hexsha": "8143b5639a5d6d718360508d22938100c2b64e19", "size": 5653, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/common/gtdft.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/common/gtdft.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/common/gtdft.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": 34.0542168675, "max_line_length": 134, "alphanum_fraction": 0.4900053069, "num_tokens": 1740, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7248702642896702, "lm_q2_score": 0.6039318337259584, "lm_q1q2_score": 0.4377722279258806}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nIsIntSym := x -> (IsSymbolic(x) and IsOrdT(x.t)) or (IsValue(x) and IsOrdT(x.t)) or IsInt(x);\nIsPosIntSym := x -> (IsSymbolic(x) and IsOrdT(x.t)) or (IsValue(x) and IsOrdT(x.t) and x.v > 0) or (IsInt(x) and x > 0);\nIsPosInt0Sym := x -> (IsSymbolic(x) and IsOrdT(x.t)) or (IsValue(x) and IsOrdT(x.t) and x.v >= 0) or (IsInt(x) and x >= 0);\nIsRatSym := x -> (IsSymbolic(x) and (IsOrdT(x.t) or IsRealT(x.t) or x.t=TUnknown)) or IsRat(x) or (IsValue(x) and (IsOrdT(x.t) or IsRealT(x.t)));\nIsBoolSym := x -> x.t=TBool and (IsSymbolic(x) or IsValue(x));\n\nAnySyms := arg -> ForAny(arg, IsSymbolic);\n\n_ev := x->When(IsRec(x) and IsBound(x.ev), x.ev(), x);\n\n# in functions below\n# vec elements could be non-values (i.e. symbolic == expressions)\n\nisValueZero := e ->\n (e.v=0 or IsDouble(e.v) and AbsFloat(e.v)<TReal.cutoff) or\n (IsVecT(e.t) and ForAll(e.v, x->not IsSymbolic(x) and AbsFloat(_ev(x)) < TDouble.cutoff));\n\nisValueOne := e ->\n (e.v=1 or IsDouble(e.v) and AbsFloat(e.v-1)<TReal.cutoff) or\n (IsVecT(e.t) and ForAll(e.v, x->not IsSymbolic(x) and AbsFloat(_ev(x)-1) < TDouble.cutoff));\n\nisValueNegOne := e ->\n (e.v=-1 or IsDouble(e.v) and AbsFloat(e.v+1)<TReal.cutoff) or\n (IsVecT(e.t) and ForAll(e.v, x->not IsSymbolic(x) and AbsFloat(_ev(x)+1) < TReal.cutoff));\n\n_is0none := e -> Cond(IsValue(e), isValueZero(e), ObjId(e)=noneExp or e=0); \n_is1 := e -> Cond(IsValue(e), isValueOne(e), e=1);\n\n# in the patterns below 'e' could be a plan GAP integer or other non-class GAP object\n_0 := @(0).cond(e -> Cond(IsValue(e), isValueZero(e), e=0)); \n_0none:= @(0).cond(_is0none); \n_1 := @(0).cond(_is1);\n_2 := @(0).cond(x -> x=2);\n_neg1 := @(0).cond(e -> Cond(IsValue(e), isValueNegOne(e), e=-1)); \n\n_v0 := @(0, Value, isValueZero); \n_v0none:= @(0, [Value, noneExp], e -> Cond(ObjId(e)=noneExp, true, isValueZero(e))); \n_v1 := @(0, Value, isValueOne); \n_vneg1 := @(0, Value, isValueNegOne); \n\n_vtrivial := @(0, Value, e->isValueZero(e) or isValueOne(e) or isValueNegOne(e));\n\n\n_vtrue := @(0, Value, e -> e.v=true); \n_vfalse := @(0, Value, e -> e.v=false); \n\n\nDeclare(_divides_rec);\n\n_divides_rec := (d,n) -> Cond(\n ObjId(n) = add and ForAll( n.args, e -> _divides_rec(d, e) ), true,\n ObjId(n) = mul and ForAny( n.args, e -> _divides_rec(d, e) ), true,\n IsSymbolic(d) or IsSymbolic(n), d=n or n=0,\n (EvalScalar(n) mod EvalScalar(d)) = 0);\n\n_divides := (d,n) -> CondPat( d, \n [mul, param, param, ...], # product of distinct params\n ForAll( d.args, p -> IsParam(p) and _divides_rec(p,n) ) and Length(Set(d.args))=Length(d.args),\n [mul, Value, param],\n _divides_rec(d.args[1], n) and _divides_rec(d.args[2], n),\n # else\n _divides_rec(d,n));\n\n_isEven := x -> _divides(2, x);\n\n# We can't know for sure that d\|n, because _dividesUnsafe returns true if either d or n is a variable\n_dividesUnsafe := (d,n) -> Cond(IsSymbolic(d) or IsSymbolic(n), true,\n (EvalScalar(n) mod EvalScalar(d)) = 0);\n\n\n_unwrap := n -> Cond(IsValue(n), n.v, n);\nDeclare(_stripval);\n_stripval := n -> Cond( IsValue(n), _stripval(n.v),\n IsList(n), List(n, _stripval),\n n );\n\n_unwrapV := (n) -> let(_n := EvalScalar(n), Cond(IsValue(_n), n.v, _n));\n", "meta": {"hexsha": "ff4735bdb74df7c5cf486bd25f7289a3742eadb5", "size": 3327, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/code/constraints.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/code/constraints.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/code/constraints.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": 40.0843373494, "max_line_length": 149, "alphanum_fraction": 0.6086564472, "num_tokens": 1181, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7577943712746406, "lm_q2_score": 0.5774953651858117, "lm_q1q2_score": 0.4376227371750011}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nClass(PDTT_Base, TaggedNonTerminal, rec(\n abbrevs := [ n -> Checked(IsPosIntSym(n), [n]) ],\n dims := self >> [self.params[1], self.params[1]],\n isReal := True,\n print := (self,i,is) >> Print(self.__name__, \"(\", PrintCS(self.params), \")\", \n\tWhen(self.transposed, Print(\".transpose()\")),\n When(self.tags<>[], Print(\".withTags(\", self.tags, \")\"))),\n\n normalizedArithCost := self >> let(n := self.params[1],\n\tfloor(2.5 * n * log(n) / log(2.0)) )\n));\n\n#\n# Discrete Trigonometric Transforms (DTTs) via PRF\n# \nDeclare(PDST3, PDCT3);\n\nClass(PDST4, PDTT_Base, rec(\n transpose := self >> Copy(self),\n terminate := self >> Mat(DST_IVunscaled(EvalScalar(self.params[1]))),\n));\n\nClass(PDCT4, PDTT_Base, rec(\n transpose := self >> Copy(self),\n terminate := self >> Mat(DCT_IVunscaled(EvalScalar(self.params[1]))),\n));\n\nClass(PDCT2, PDTT_Base, rec(\n terminate := self >> Mat(DCT_IIunscaled(EvalScalar(self.params[1]))), \n transpose := self >> PDCT3(self.params[1])\n));\n\nClass(PDST2, PDTT_Base, rec(\n terminate := self >> Mat(DST_IIunscaled(EvalScalar(self.params[1]))), \n transpose := self >> PDST3(self.params[1])\n));\n\nClass(PDCT3, PDTT_Base, rec(\n terminate := self >> Mat(DCT_IIIunscaled(EvalScalar(self.params[1]))), \n transpose := self >> PDCT2(self.params[1])\n));\n\nClass(PDST3, PDTT_Base, rec(\n terminate := self >> Mat(DST_IIIunscaled(EvalScalar(self.params[1]))), \n transpose := self >> PDST2(self.params[1])\n));\n\nRulesFor(PDST4, rec(\n PDST4_Base2 := DST4_Base, #BaseRule(PDST4, 2),\n PDST4_CT := rec(\n\tisApplicable := P -> P[1] > 2, #not IsPrime(P),\n\tforTransposition := false,\n\tallChildren := P -> let(N := P[1], Map2(DivisorPairs(2N), (m,n) -> Cond(\n\t\tIsEvenInt(m) and IsEvenInt(n), [ PRDFT3(m,-1).transpose(), PRDFT3(n) ],\n\t\t#IsEvenInt(m) and IsEvenInt(n), [ PDHT3(m).transpose(), PDHT3(n) ],\n\t\tIsEvenInt(m) and IsOddInt(n), [ PRDFT3(m,-1).transpose(), PRDFT3(n), PDST4(m/2) ],\n\t\tIsOddInt(m) and IsEvenInt(n), [ PRDFT3(m,-1).transpose(), PRDFT3(n), PDST4(n/2) ],\n\t\tIsOddInt(m) and IsOddInt(n), Error(\"This can't happen\")))),\n\n\trule := (P,C) -> let(N := P[1], m := Rows(C[1]), n := Cols(C[2]),\n\t nf:=Int(n/2), nc:=Int((n+1)/2), mf:=Int(m/2), mc:=Int((m+1)/2), j:=Ind(nf), i:=Ind(mf), \n\t # mult twid by -E(4) for RDFT, by 1/2 for DHT\n\t t := ScaledTwid(2N, mf, 1, 1/2, 1/2, j, -E(4)),\n\t T := When(IsOddInt(m), Diag(diagDirsum(t,fConst(1,1))), Diag(t)), \n\t Et := Tensor(I(mf),Mat([[0,-1],[-1,0]])),\n\t Ett := Tensor(I(mf),Mat([[0,-1],[1,0]])),\n\t SUM(\n\t\tISum(j, \n\t\t Scat(BH(N, 2N-1, m, j, n)) C[1] * #Ett \n\t\t RC(T) \n\t\t #Et * # DHT only\n\t\t RC(Gath(H(mcnc, mc, j, nc)))\n\t\t),\n\t\tWhen(IsEvenInt(n), [], Scat(H(N,m/2,nf,n))C[3]Gath(H(2mcnc, m/2, 2nf, 2nc)))\n\t ) \n\t SUM(\n\t\tISum(i, RC(Scat(H(mcnc, nc, inc, 1))) * C[2] * Gath(BH(N, 2N-1, n, i, m))),\n # output is imaginary, but we output into real slot, because subseq transform\n\t\t# is jIR2, which we implement as IR2 (-j)\n\t\tWhen(IsEvenInt(m), [], Scat(H(2mcnc, nc, 2mfnc, 2))C[3]Gath(H(N,n/2,mf,m)))\n\t ))),\n\n PDST4_CT_SPL := rec(\n\tisApplicable := P -> P[1] > 2 and ForAny(DivisorPairs(2P[1]), d->IsEvenInt(d[1]) and IsEvenInt(d[2])), \n\tforTransposition := false,\n\n\tallChildren := P -> let(N := P[1], \n\t Map2(Filtered(DivisorPairs(2N), d -> IsEvenInt(d[1]) and IsEvenInt(d[2])),\n\t\t(m,n) -> [ PRDFT3(m,-1).transpose(), PRDFT3(n) ])),\n\n\trule := (P,C) -> let(N := P[1], m := Rows(C[1]), n := Cols(C[2]),\n TT := Diag(fPrecompute(diagMul(fConst(N/2, -E(4)), \n fCompose(dOmega(8 * N, 1), \n diagTensor(dLin(N/m, 2, 1, TInt), dLin(m/2, 2, 1, TInt)))))),\n\n\t Prm(Refl(N, 2N-1, N, L(mn, m))) \n\t Tensor(I(n/2), C[1]) \n RC(TT) * \n RC(L(mn/4, n/2)) \n\t Tensor(I(m/2), C[2]) \n\t Prm(Refl(N, 2N-1, N, L(mn, m)))\n\t)\n )\n));\n\nRulesFor(PDCT4, rec(\n PDCT4_Base2 := rec(isApplicable:=P->P[1]=2, rule:=(P,C)->DCT4(2).terminate()),\n PDCT4_Base4 := rec(isApplicable:=P->P[1]=4, \n\t allChildren := P -> [[ DCT4(4) ]], \n\t\t rule:=(P,C)->C[1]),\n\n PDCT4_CT := rec(\n\tisApplicable := P -> P[1] > 2, #not IsPrime(P),\n\tforTransposition := false,\n\tallChildren := P -> let(N := P[1], Map2(DivisorPairs(2N), (m,n) -> Cond(\n\t\tIsEvenInt(m) and IsEvenInt(n), [ PRDFT3(m,-1).transpose(), PRDFT3(n) ],\n\t\t#IsEvenInt(m) and IsEvenInt(n), [ PDHT3(m).transpose(), PDHT3(n) ],\n\t\tIsEvenInt(m) and IsOddInt(n), [ PRDFT3(m,-1).transpose(), PRDFT3(n), PDCT4(m/2) ],\n\t\tIsOddInt(m) and IsEvenInt(n), [ PRDFT3(m,-1).transpose(), PRDFT3(n), PDCT4(n/2) ],\n\t\tIsOddInt(m) and IsOddInt(n), Error(\"This can't happen\")))),\n\n\trule := (P,C) -> let(N := P[1], m := Rows(C[1]), n := Cols(C[2]),\n\t nf:=Int(n/2), nc:=Int((n+1)/2), mf:=Int(m/2), mc:=Int((m+1)/2), j:=Ind(nf), i:=Ind(mf), \n\t t := fPrecompute(Twid(2N, mf, 1, 1/2, 1/2, j)),\n\t T := When(IsOddInt(m), Diag(diagDirsum(t,fConst(1,1))), Diag(t)), \n\t Et := Tensor(I(mf),Mat([[0,1],[1,0]])),\n\t SUM(\n\t\tISum(j, \n\t\t Scat(BH(N, 2N-1, m, j, n)) * Diag(BHN(m)) * C[1] \n\t\t # mult twid by 1/2 for DHT\n\t\t RC(T) \n\t\t #Et * # DHT only\n\t\t RC(Gath(H(mcnc, mc, j, nc)))\n\t\t),\n\t\tWhen(IsEvenInt(n), [], Scat(H(N,m/2,nf,n))C[3]Gath(H(2mcnc, m/2, 2nf, 2nc)))\n\t ) \n\t SUM(\n\t\tISum(i, RC(Scat(H(mcnc, nc, inc, 1))) * C[2] * Diag(BHN(n)) * Gath(BH(N, 2N-1, n, i, m))),\n\t\tWhen(IsEvenInt(m), [], Scat(H(2mcnc, nc, 2mfnc, 2))C[3]Gath(H(N,n/2,mf,m)))\n\t ))),\n));\n\nNewRulesFor(PDCT4, rec(\n PDCT4_CT_SPL := rec(\n libApplicable := t -> eq(imod(t.params[1], 2), 0),\n\tapplicable := t -> IsSymbolic(t.params[1]) or (t.params[1] > 2 and (t.params[1] mod 4) = 0), \n extraLeftTags := [],\n\tforTransposition := false,\n\n freedoms := t -> [ divisorsIntNonTriv(t.params[1]/2) ], \n\n\tchild := (self, t, fr) >> let(N := t.params[1], f := fr[1], \n\t [ spiral.sym.ASP(-1).RDFT3(2f).withTags(self.extraLeftTags).transpose(), \n\t spiral.sym.ASP.RDFT3(div(N,f)) ]),\n\n\tapply := (t,C,Nonterms) -> let(N := t.params[1], m := Rows(C[1]), n := Cols(C[2]),\n mh := Rows(C[1])/2, nh := Cols(C[2])/2,\n D := RC(Diag(fPrecompute(fCompose(dOmega(8 * N, 1), \n diagTensor(dLin(N/m, 2, 1, TInt), dLin(m/2, 2, 1, TInt)))))),\n\n Grp(Scat(Refl1(nh, m)) * \n Tensor(I(nh), Diag(BHN(m)) * C[1]) * \n D \n Tensor(I(nh), Tr(2, mh))) \n #RC(Tr(mh, nh)) \n Grp(Tr(mh, n) \n Tensor(I(mh), C[2] * Diag(BHN(n))) \n Gath(Refl1(mh, n)))\n\t)\n )\n));\n\nRulesFor(PDCT4, rec(\n # Variant better suited for vectorization\n PDCT4_CT_SPL_Vec := rec(\n\tisApplicable := P -> P[1] > 2 and (P[1] mod 2) = 0, \n\tforTransposition := false,\n\n\tallChildren := P -> let(N := P[1], \n\t Map2(Filtered(DivisorPairs(2N), d -> IsEvenInt(d[1]) and IsEvenInt(d[2])),\n\t\t(m,n) -> [ PRDFT3(m,-1).transpose(), PRDFT3(n) ])),\n\n\trule := (P,C) -> let(N := P[1], m := Rows(C[1]), n := Cols(C[2]),\n TT := Diag(fPrecompute(fCompose(dOmega(8 * N, 1), \n diagTensor(dLin(N/m, 2, 1, TInt), dLin(m/2, 2, 1, TInt))))),\n\n Prm(condIJ(N, n/2)) * \n Prm(L(N, m)) * \n\t Tensor(I(n/2), \n condM(m,m/2) * Diag(BHN(m)) * C[1]) * \n RC(TT) * \n Prm(L(N, n/2)) \n\t Tensor(I(m/2), \n L(n, 2) C[2] * Diag(BHN(n)) * condK(n, 2)) \n Prm(L(N, m/2)) \n Prm(condIJ(N, m/2))\n\t)\n )\n\n));\n\ntestPDCT4 := function(n)\n local opts, r, s;\n opts := CopyFields(SpiralDefaults, rec(\n breakdownRules := rec(\n PDCT4 := [PDCT4_Base2, PDCT4_CT_SPL_Vec],\n PRDFT1 := [PRDFT1_Base1, PRDFT1_Base2, PRDFT1_CT],\n PRDFT3 := [PRDFT3_Base1, PRDFT3_Base2, PRDFT3_CT],\n DFT := [DFT_Base, DFT_CT]\n )));\n r := RandomRuleTree(PDCT4(n), opts);\n s := SumsRuleTree(r, opts);\n return [opts,r,s];\nend;\n\n \nNewRulesFor(PDCT2, rec(\n PDCT2_Base2 := rec(\n\tforTransposition := true,\n applicable := t -> t.params[1] = 2, \n apply := (t, C, Nonterms) -> DCT2(2).terminate()\n ),\n\n PDCT2_Base4 := rec(\n\tforTransposition := true,\n applicable := t -> t.params[1] = 4, \n apply := (t, C, Nonterms) -> \n LIJ(4) * \n DirectSum(\n Diag(FList(TReal, [ 1, 0.70710678118654757 ])) * F(2),\n Rot(cospi(13/8), sinpi(13/8)) * J(2)) * \n (Tensor(I(2), F(2))) ^ LIJ(4)\n ),\n\n PDCT2_CT_SPL := rec(\n\tforTransposition := true,\n libApplicable := t -> eq(imod(t.params[1], 2), 0),\n extraLeftTags := [],\n\n\tapplicable := t -> let(N:=t.params[1], \n IsSymbolic(N) or \n (N > 2 and IsEvenInt(N) and (N mod 4) = 0)),\n\n\tfreedoms := t -> [ divisorsIntNonTriv(t.params[1]/2) ], \n\n # N/2 = km\n child := (self, t, fr) >> let(N:=t.params[1], k:=fr[1], m:=N/2/k, \n [ PDCT2(2k).withTags(self.extraLeftTags), \n spiral.sym.ASP(-1).RDFT3(2k).transpose().withTags(self.extraLeftTags), \n spiral.sym.ASP(+1).URDFT(2m) ]), \n\n\tapply := (t,C,Nonterms) -> let(N:=t.params[1], k:=Rows(C[1])/2, m:=Cols(C[3])/2,\n D := RC(Diag(fPrecompute(fCompose(dOmega(4 * N, 1), \n diagTensor(dLin(m-1, 1, 1, TInt), dLin(k, 2, 1, TInt)))))),\n Grp(\n Scat(Refl0_u(m, 2k)) \n DirectSum(\n C[1] * KK(k, 2), \n Tensor(I(m-1), Diag(BHN(2k)) C[2]) * D\n )) \n Grp(\n RC(Tr(k, m)) \n Tensor(I(k), C[3]) \n Gath(Refl1(k, 2m))\n )\n\t)\n )\n));\n\nNewRulesFor(PDST2, rec(\n PDST2_Base2 := rec(\n applicable := t -> t.params[1] = 2, \n apply := (t, C, Nonterms) -> DST2(2).terminate()\n ),\n\n PDST2_CT_SPL := rec(\n\tforTransposition := true,\n\tapplicable := t -> let(N:=t.params[1], N > 2 and IsEvenInt(N) and (N mod 4) = 0),\n\tfreedoms := t -> [ DivisorsIntNonTriv(t.params[1]/2) ], \n\n # N/2 = km\n child := (t, fr) -> let(N:=t.params, k:=fr[1], m:=N/2/k, \n [ DST2(2k), PRDFT3(2k,-1).transpose(), URDFT(2m) ]), \n\n\tapply := (t,C,Nonterms) -> let(N:=t.params[1], k:=Rows(C[1])/2, m:=Cols(C[3])/2,\n TT := Diag(fPrecompute(fCompose(dOmega(4 * N, 1), \n # ie multiply all twiddles by -E(4)\n diagAdd(diagDirsum(fConst(k, 0), fConst(k(m-1), 3N)), \n diagTensor(dLin(m, 1, 0, TInt), dLin(k, 2, 1, TInt)))))),\n\n J(N) * \n Kp(N, 2k) \n\t DirectSum(\n J(2k) C[1] * Diag(BHN(2k)) K(2k, 2), \n Tensor(I(m-1), J(2k) * M(2k, k) C[2])\n ) * \n RC(TT) * \n RC(L(N/2, m)) \n\t Tensor(I(k), C[3] Diag(BHN(2m))) \n\t Prm(Refl(N, 2N-1, N, L(2N, 2k)))\n\t)\n )\n\n));\n\nRulesFor(DCT5, rec(\n DCT5_Rader := rec(\n\tforTransposition := false,\n\tisApplicable := P -> P > 2 and IsPrime(2P-1),\n\tallChildren := P -> [[ IPRDFT(P-1,-1), PRDFT(P-1,-1) ]],\n\n\tdiag := N -> Sublist(\n\t DFT_Rader.raderDiag(2N-1,1,PrimitiveRootMod(2N-1)), \n\t [1..Int((N-1)/2)]2),\n\n\t# 3rd col with 0's is for PRDFT, not necessary for (non-packed) RDFT\n\traderMid := (self, N) >> let(Fsize := 2N-1, \n\t DirectSum(Mat([[1, 1, 0], [1, -1/(Fsize-1), 0], [0,0,0]]),\n\t\t\t RC(Diag(FData(self.diag(N)))))),\n\n\t# NOTE, special case for even P-1\n\trule := (self,P,C) >> let(N := P, \n\t #RealRR(N).transpose() * \n\t\t\n\t Gath(H(2P-1, P, 0, 1)) \n\t RR(2P-1).transpose() \n\t DirectSum(I(1), VStack(I(P-1), I(P-1))) \n\n\t DirectSum(I(1), C[1]) \n#\t\tC[1]Diag(1,1, Replicate(2Int((P-2)/2), 2), \n#\t\t When(IsEvenInt(P-1), [1,1],[]))) * \n\t self.raderMid(N) \n\t DirectSum(I(1), C[2]) \n\n # replace by RealRR\n\t Gath(H(2P-1, P, 0, 1)) \n\t RR(2P-1) DirectSum(I(1), VStack(I(P-1), J(P-1)))\n ))\n));\n\n#q:=ExpandSPL(DCT5(6))[1];\n#s:=SPLRuleTree(q);\n#me := MatSPL(s);\n#them := remat(MatSPL(q.node));\n\n#RDFT-11, DCT5(6) 15(6/9 rots) + 19(12/7 irdft) + 17(12/5 rdft) = 30/21 = 51\n# DST5(5)\n# 10(blk) \n# fftw 60/50\n\n# RDFT-13\n# DCT5(7) 18(8/10=4/8+0/1+2/1 rots) + 18(14/4 irdft) + 18(14/4 rdft) = 36/18=54\n# DST5(6) \n# 12(blk)\n# fftw 76/34=110\n\n# DFT-13\n# fftw 176+68=244\n# us = 542 (dct5) + 24(blk)2 + dst5 \n", "meta": {"hexsha": "7dc3b1b35016bdd470a04dd8f5ad0ea1b9698020", "size": 12631, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/realdft/pdtt4.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/pdtt4.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/pdtt4.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": 34.6054794521, "max_line_length": 109, "alphanum_fraction": 0.4979811575, "num_tokens": 4901, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7634837635542924, "lm_q2_score": 0.5698526514141571, "lm_q1q2_score": 0.4350732469730729}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n# input: imaginary, output: co1 (?)\n_j := N -> Tensor(I(approx.CeilingRat(N/2)),J(2)Diag(-1,1));\n\nRealRR_Out := (N, root) -> let(\n rrind := RR(N, 1, root).tolist(),\n outind := List(rrind{[1..(N+1)/2]}, x->When(x.v >= (N+1)/2, N-x.v, x.v)),\n #same as Refl((N+1)/2, N, (N+1)/2, RR(N,1,root)).tolist(),\n\n # Reflective RR\n Scat(fTensor(FList((N+1)/2, outind), fId(2))) \n # Conjugate complex elements that will be reflected\n Diag(ConcatList([0..(N-1)/2], x->When(rrind[x+1].v >= (N+1)/2, [1,-1], [1,1])))\n);\n\nRulesFor(PRDFT, rec(\n\n # PRDFT_PD : Projection of complex DFT partial diagonalization rule to real DFT \n # See also : PRDFT_Rader\n #\n PRDFT_PD := rec(\n\tforTransposition := true,\n\tmaxSize := 13,\n\tisApplicable := (self, P) >> P[1] > 2 and P[1] <= self.maxSize and IsPrime(P[1]),\n\t\n\trule := (self,P,C) >> let(N:=P[1], n:=N-1, k:=P[2], root:=PrimitiveRootMod(N),\n\t BB(RealRR_Out(N, root) \n\t DirectSum(Mat([[1],[0]]), L(n, n/2)) \n\t Mat(MatSPL(DFT_PD.core(N, k, root, true) * DFT_PD.A(N))) \n\t DirectSum(I(1), Tensor(F(2), I(n/2))) \n\t DirectSum(I(1), OS(n, -1)) \n\t Gath(RR(N, 1, root)))\n\t)\n ),\n\n # PRDFT_Rader : Projection of complex DFT Rader rule to real DFT \n #\n # Note: PRDFT of types 2--4 of odd size (which includes all primes > 2)\n # can be converted without arithmetic cost to PRDFT1,\n # which means that this rule enables implementation of a prime \n # size PRDFT of any type.\n PRDFT_Rader := rec(\n\tisApplicable := (self, P) >> P[1] > 3 and IsPrime(P[1]),\n\t\n\tdiag := (N, k, root) -> let(fulldiag := DFT_Rader.raderDiag(N,k,root),\n\t last := Int((N-1)/2),\n\t Concatenation(2fulldiag{[1..last-1]}, [fulldiag[last]])),\n\n\t# 3rd col with 0's is for padding used by PRDFT\n\traderMid := (self, N, k, root) >> let(n:=N-1,\n\t DirectSum(Mat([[1, 1, 0], [1, -1/n, 0], [0,0,0]]),\n\t\t RCDiag(RCData(FData(self.diag(N, k, root)))))),\n\n\tallChildren := P -> let(n:=P[1]-1,\n\t [[ PRDFT(n/2).transpose(), PRDFT3(n/2).transpose(), PRDFT(n, -1) ]]),\n\n\trule := (self,P,C) >> let(N:=P[1], n:=N-1, k:=P[2], root:=PrimitiveRootMod(N),\n\t RealRR_Out(N, root) \n\t DirectSum(Mat([[1],[0]]), ##\n\t\t L(n, n/2) \n\t\t DirectSum(C[1], C[2] * _j(n/2)) \n\t\t RC(L_or_OS(n/2+1, 2))) \n\t self.raderMid(N, k, root) \n\t DirectSum(I(1), C[3]) \n\t Gath(RR(N, 1, root))\n\t)\n )\n));\n\nRulesFor(IPRDFT, rec(\n\n # IPRDFT_PD : Projection of complex DFT partial diagonalization rule to inverse real DFT \n # See also : IPRDFT_Rader\n #\n IPRDFT_PD := rec(\n\tforTransposition := true,\n\tmaxSize := 13,\n\tisApplicable := (self, P) >> P[1] > 2 and P[1] <= self.maxSize and IsPrime(P[1]),\n\trule := (self,P,C) >> let(N:=P[1], n:=N-1, k:=P[2], root:=PrimitiveRootMod(N),\n\t BB(Scat(RR(N, 1, root)) \n\t DirectSum(I(1), OS(n, -1)) \n\t DirectSum(I(1), Tensor(F(2), I(n/2))) * \n\t Mat(MatSPL(TransposedSPL(DFT_PD.core(N, -k, root, true) * DFT_PD.A(N)) * DirectSum(I(1), 2I(n)))) \n\t DirectSum(Mat([[1,0]]), L(n, 2)) * \n\t RealRR_Out(N, root).transpose())\n\t)\n ),\n\n # IPRDFT_Rader : Projection of complex DFT Rader rule to inverse real DFT \n #\n # Note: IPRDFT of types 2--4 of odd size (which includes all primes > 2)\n # can be converted without arithmetic cost to IPRDFT1,\n # which means that this rule enables implementation of a prime \n # size IPRDFT of any type.\n IPRDFT_Rader := CopyFields(PRDFT_Rader, rec(\n\t# 3rd col with 0's is for padding, we also scale everything but 1st elt by 2,\n\t# as IPRDFT requires. \n\traderMid := (self, N, k, root) >> let(n:=N-1,\n\t DirectSum(Mat([[1, 2, 0], [1, -2/n, 0], [0,0,0]]),\n\t\t RCDiag(RCData(FConj(FData(2self.diag(N, -k, root))))))),\n\n\tallChildren := P -> let(n:=P[1]-1,\n\t [[ PRDFT(n/2), PRDFT3(n/2), PRDFT(n,-1).transpose() ]]),\n\n\trule := (self,P,C) >> let(N:=P[1], n:=N-1, k:=P[2], root:=PrimitiveRootMod(N),\n\t Scat(RR(N, 1, root)) \n\t DirectSum(I(1), C[3]) \n\t self.raderMid(N, k, root) \n\t DirectSum(Mat([[1,0]]), ##\n\t\t RC(L_or_OS(n/2+1, 2).transpose()) \n\t\t DirectSum(C[1], _j(n/2).transpose() C[2]) \n\t\t L(n, 2)) \n\t RealRR_Out(N, root).transpose()\n\t)\n ))\n));", "meta": {"hexsha": "d6ff32d471f83a5c606986e74dd4b8d89f2a0905", "size": 4303, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/realdft/rpd.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/rpd.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/rpd.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": 35.8583333333, "max_line_length": 105, "alphanum_fraction": 0.5596095747, "num_tokens": 1623, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7520125737597972, "lm_q2_score": 0.5774953651858117, "lm_q1q2_score": 0.43428377590773626}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n# NOTE: MISSING (YV)\nClass(VScat_red);\n\nClass(BaseVScat, BaseMat, SumsBase, rec(\n isVScat := true,\n sums := self >> self,\n dims := self >> self.dimensions,\n isReal := self >> true,\n needInterleavedLeft := False,\n needInterleavedRight := False,\n area := self >> self.transpose().area(),\n toAMat := self >> TransposedAMat(self.transpose().toAMat()),\n conjTranspose := self >> self.transpose(), \n));\n\nClass(BaseSVScat, BaseMat, SumsBase, rec(\n isVScat := true,\n isSVScat := true,\n #-----------------------------------------------------------------------\n abbrevs := BaseSVGath.abbrevs, \n new := BaseSVGath.new, \n print := BaseSVGath.print,\n getConstantRem := BaseSVGath.getConstantRem,\n #-----------------------------------------------------------------------\n dims := self >> Error(ObjId(self), \".dims() is undefined\"),\n #-----------------------------------------------------------------------\n sums := self >> self,\n isReal := self >> true,\n needInterleavedLeft := True,\n needInterleavedRight := False,\n #-----------------------------------------------------------------------\n conjTranspose := self >> self.transpose(), \n area := self >> self.transpose().area(),\n toAMat := self >> TransposedAMat(self.transpose().toAMat())\n));\n\nIsVScat := x -> IsRec(x) and IsBound(x.isVScat) and x.isVScat;\nIsSVScat := x -> IsRec(x) and IsBound(x.isSVScat) and x.isSVScat;\n\n# ==========================================================================\n# VScat(<func>, <v>) - vector scatter (write) matrix, assumes aligned output\n# ==========================================================================\nClass(VScat, BaseVScat, rec(\n #-----------------------------------------------------------------------\n rChildren := self >> [self.func],\n rSetChild := rSetChildFields(\"func\"),\n from_rChildren := (self, rch) >> ObjId(self)(rch[1], self.v),\n #-----------------------------------------------------------------------\n new := (self, func, v) >> SPL(WithBases(self, \n rec(func := func, v := v))).setDims(),\n #-----------------------------------------------------------------------\n dims := self >> [self.v * self.func.range(), self.v * self.func.domain()],\n #-----------------------------------------------------------------------\n transpose := self >> VGath(self.func, self.v),\n #-----------------------------------------------------------------------\n print := (self,i,is) >> Print(self.__name__, \"(\", self.func, \", \", self.v, \")\", self.printA()),\n ));\n\n# ==========================================================================\n# VScat_u(<func>, <v>) -- same as VScat but assumes that output is unaligned\n# ==========================================================================\nClass(VScat_u, VScat, rec(\n dims := self >> [ self.func.range(), self.v * self.func.domain()],\n transpose := self >> VGath_u(self.func, self.v)\n));\n\n# ==========================================================================\n# VScat_zero(N, n, <v>) - vector scatter (write) matrix\n# ==========================================================================\nClass(VScat_zero, BaseVScat, rec(\n #-----------------------------------------------------------------------\n rChildren := self >> [],\n rSetChild := rSetChildFields(),\n from_rChildren := (self, rch) >> ObjId(self)(self.N, self.n, self.v),\n #-----------------------------------------------------------------------\n new := (self, N, n, v) >> SPL(WithBases(self,\n rec(n := n, N := N, v := v))).setDims(),\n #-----------------------------------------------------------------------\n dims := self >> [self.v * self.N, self.v * self.n],\n #-----------------------------------------------------------------------\n transpose := self >> VGath_zero(self.N, self.n, self.v),\n #-----------------------------------------------------------------------\n print := (self,i,is) >> Print(self.__name__, \"(\", self.N, \", \",\n self.n, \", \", self.v,\")\", self.printA()),\n ));\n\n# ==========================================================================\n# VScat_sv(<func>, <v>, <sv>) - vector scatter (write) matrix on subvectors\n# ==========================================================================\nClass(VScat_sv, BaseSVScat, rec(\n #-----------------------------------------------------------------------\n rChildren := self >> [self.func], # self >> [self.func, self.v, self.sv],\n rSetChild := rSetChildFields(\"func\"), # rSetChildFields(\"func\", \"v\", \"sv\"),\n from_rChildren := (self, rch) >> ObjId(self)(rch[1], self.v, self.sv, self.rem),\n #-----------------------------------------------------------------------\n dims := self >> [self.sv * self.func.range(),\n _roundup(self.sv * self.func.domain(), self.v)],\n #-----------------------------------------------------------------------\n transpose := self >> VGath_sv(self.func, self.v, self.sv, self.rem),\n));\n\n# ==========================================================================\n# RCVScat_sv(<func>, <v>, <sv>) - vector scatter (write) matrix on subvectors\n# ==========================================================================\nClass(RCVScat_sv, BaseSVScat, rec(\n #-----------------------------------------------------------------------\n rChildren := self >> [self.func], # self >> [self.func, self.v, self.sv],\n rSetChild := rSetChildFields(\"func\"), # rSetChildFields(\"func\", \"v\", \"sv\"),\n from_rChildren := (self, rch) >> ObjId(self)(rch[1], self.v, self.sv, self.rem),\n #-----------------------------------------------------------------------\n dims := self >> let(\n\tn := self.func.domain() * self.sv, nv := _roundup(n, self.v), \n\tN := self.func.range() * self.sv, \n\t[2N, 2nv]),\n #-----------------------------------------------------------------------\n transpose := self >> RCVGath_sv(self.func, self.v, self.sv, self.rem),\n));\n\n# ==========================================================================\n# VStretchScat(<func>, part, <v>) - vector scatter (write) matrix on subvectors\n# ==========================================================================\nClass(VStretchScat, BaseSVScat, rec(\n #-----------------------------------------------------------------------\n rChildren := self >> [self.func],\n rSetChild := rSetChildFields(\"func\"),\n from_rChildren := (self, rch) >> ObjId(self)(rch[1], self.part, self.v),\n #-----------------------------------------------------------------------\n dims := self >> let(\n\tn := self.func.domain(), N := self.func.range(), \n\tnv := self.part * _roundup(n / self.part, self.v),\n [N, nv]),\n #-----------------------------------------------------------------------\n abbrevs := [],\n new := (self, func, part, v) >> SPL(WithBases(self, \n\trec(func := func, part := part, v := v))).setDims(),\n #-----------------------------------------------------------------------\n transpose := self >> VStretchGath(self.func, self.part, self.v),\n #-----------------------------------------------------------------------\n print := (self,i,is) >> Print(self.__name__, \"(\", self.func, \", \",\n self.part, \", \", self.v, \")\", self.printA()),\n));\n\n\n# ==========================================================================\n# vRCStretchScat(<func>, part, <v>) - vector scatter (write) matrix on subvectors\n# ==========================================================================\nClass(vRCStretchScat, BaseSVScat, rec(\n #-----------------------------------------------------------------------\n rChildren := self >> [self.func],\n rSetChild := rSetChildFields(\"func\"),\n from_rChildren := (self, rch) >> ObjId(self)(rch[1], self.part, self.v),\n #-----------------------------------------------------------------------\n dims := self >> let(\n\tn := self.func.domain(), N := self.func.range(), \n\tnv := self.part * _roundup(n / self.part, self.v/2),\n 2[N, nv]),\n #-----------------------------------------------------------------------\n abbrevs := [],\n new := (self, func, part, v) >> SPL(WithBases(self, \n rec(func := func, part := part, v := v))).setDims(),\n #-----------------------------------------------------------------------\n transpose := self >> vRCStretchGath(self.func, self.part, self.v),\n #-----------------------------------------------------------------------\n print := (self,i,is) >> Print(self.__name__, \"(\", self.func, \", \",\n self.part, \", \", self.v, \")\", self.printA()),\n));\n\n# ==========================================================================\n# RCVStretchScat(<func>, part, <v>) - vector scatter (write) matrix on subvectors\n# ==========================================================================\nClass(RCVStretchScat, BaseSVScat, rec(\n #-----------------------------------------------------------------------\n rChildren := self >> [self.func],\n rSetChild := rSetChildFields(\"func\"),\n from_rChildren := (self, rch) >> ObjId(self)(rch[1], self.part, self.v),\n #-----------------------------------------------------------------------\n dims := self >> let(\n\tn := self.func.domain(), N := self.func.range(), \n\tnv := self.part _roundup(n / self.part, self.v),\n 2[N, nv]),\n #-----------------------------------------------------------------------\n abbrevs := [],\n new := (self, func, part, v) >> SPL(WithBases(self, rec(\n func := func, part := part, v := v))).setDims(),\n #-----------------------------------------------------------------------\n transpose := self >> RCVStretchGath(self.func, self.part, self.v),\n #-----------------------------------------------------------------------\n print := (self,i,is) >> Print(self.__name__, \"(\", self.func, \", \",\n self.part, \", \", self.v, \")\", self.printA()),\n ));\n\n# ==========================================================================\n# VScat_pc(N, n, ofs, v) - vector scatter (write) matrix writing unaligned\n# partial contiguous vectors\n# ==========================================================================\nClass(VScat_pc, BaseSVScat, rec(\n #-----------------------------------------------------------------------\n rChildren := self >> [self.N, self.n, self.ofs, self.v],\n rSetChild := rSetChildFields(\"N\", \"n\", \"ofs\", \"v\"),\n #-----------------------------------------------------------------------\n dims := self >> let(nv := _roundup(self.n, self.v), [self.N, nv]),\n #-----------------------------------------------------------------------\n abbrevs := [],\n new := (self, N, n, ofs, v) >> SPL(WithBases(self, rec(\n N := N, n:= n, ofs := ofs, v := v))).setDims(),\n #-----------------------------------------------------------------------\n transpose := self >> VGath_pc(self.N, self.n, self.ofs, self.v),\n #-----------------------------------------------------------------------\n print := (self,i,is) >> Print(self.__name__, \"(\", self.N, \", \", self.n, \", \",\n self.ofs, \", \", self.v,\")\", self.printA()),\n));\n\n# ==========================================================================\n# IxVScat_pc(k, N, n, ofs, v) - vector gather (read)\n# matrix reading unaligned\n# partial REAL contiguous vectors\n# ==========================================================================\nClass(IxVScat_pc, BaseSVScat, rec(\n #-----------------------------------------------------------------------\n rChildren := self >> [self.k, self.N, self.n, self.ofs, self.v],\n rSetChild := rSetChildFields(\"k\", \"N\", \"n\", \"ofs\", \"v\"),\n\n from_rChildren := (self, rch) >> ObjId(self)(self.k, self.N, self.n, self.ofs, self.v),\n #-----------------------------------------------------------------------\n dims := self >> let(nv := _roundup(self.n, self.v), [self.kself.N, self.knv]),\n #-----------------------------------------------------------------------\n abbrevs := [],\n new := (self, k, N, n, ofs, v) >> SPL(WithBases(self, rec(\n k := k, N := N, n:= n, ofs := ofs, v := v))).setDims(),\n #-----------------------------------------------------------------------\n transpose := self >> IxVGath_pc(self.k, self.N, self.n, self.ofs, self.v),\n #-----------------------------------------------------------------------\n toloop := (self, bksize) >> self.transpose().toloop(bksize).transpose(),\n #-----------------------------------------------------------------------\n print := (self,i,is) >> Print(self.__name__, \"(\", self.k, \", \", self.N, \", \",\n self.n, \", \", self.ofs, \", \", self.v,\")\", self.printA()),\n));\n\n# ==========================================================================\n# IxRCVScat_pc(k, N, n, ofs, v) - vector gather (read)\n# matrix reading unaligned\n# partial REAL contiguous vectors\n# ==========================================================================\nClass(IxRCVScat_pc, BaseSVScat, rec(\n #-----------------------------------------------------------------------\n rChildren := self >> [], # self >> [self.ofs], # SEEMS NOT TO WORK?!\n rSetChild := rSetChildFields(), # rSetChildFields(\"ofs\"),\n from_rChildren := (self, rch) >> ObjId(self)(self.k, self.N, self.n, self.ofs, self.v),\n #-----------------------------------------------------------------------\n dims := self >> let(nv := _roundup(self.n, self.v), 2 [self.kself.N, self.knv]),\n #-----------------------------------------------------------------------\n abbrevs := [],\n new := (self, k, N, n, ofs, v) >> SPL(WithBases(self, rec(\n k := k, N := N, n := n, ofs := ofs, v := v))).setDims(),\n #-----------------------------------------------------------------------\n transpose := self >> IxRCVGath_pc(self.k, self.N, self.n, self.ofs, self.v),\n #-----------------------------------------------------------------------\n print := (self,i,is) >> Print(self.__name__, \"(\", self.k, \", \", self.N, \", \",\n self.n, \", \", self.ofs, \", \", self.v,\")\", self.printA()),\n));\n\n\n# ==========================================================================\n# Accumulative scatter versions\n# NOTE: to be replaced by a Sigma-SPL lowering step, CodeSumsAcc, and \n# a specialized CodegenAcc\n#\n# NOTE(!!!): .transpose().transpose() on below classes will lead to non-accumulative\n# versions, and thus invalid code!\nClass(VScatAcc, VScat, rec());\nClass(VScatAcc_u, VScat_u, rec());\nClass(VScat_svAcc, VScat_sv, rec());\nClass(VScat_pcAcc, VScat_pc, rec());\n\n\n# ==========================================================================\n# Methods for vectorization of ScatGath constructs\n# NOTE: This is a hack\n\n# BB needed, as basic block size is not known due to varying function domain\nScatGath.toloopRCVec := (self, _bksize, v) >> let(\n bksize := When(_bksize = 1, v, _bksize),\n dom := RulesMergedStrengthReduce(_divideFunc(self.gfunc.domain(), bksize)), \n i := Ind(dom), #ok := Error(\"caught\"),\n sfunc := RulesFuncSimp(self.sfunc),\n ISum(i, dom,\n BB(\n Compose(When(ObjId(sfunc)=fId, [], [RCVScat_sv(sfunc, v, 1)]) ::\n\t\t [VScat(fTensor(fBase(i), fId(2bksize/v)), v)]) \n RCVGath_sv(fCompose(self.gfunc, fTensor(fBase(i), fId(bksize))).setDomain(bksize), v, 1)\n )\n )\n);\n\nScatGath.toloopVec := (self, _bksize, v) >> let(\n bksize := When(_bksize = 1, v, _bksize),\n dom := RulesMergedStrengthReduce(_divideFunc(self.gfunc.domain(), bksize)), \n i := Ind(dom),\n sfunc := RulesFuncSimp(self.sfunc),\n ISum(i, dom,\n BB(\n Compose(When(ObjId(sfunc)=fId, [], [VScat_sv(sfunc, v, 1)]) :: \n\t\t [ VScat(fTensor(fBase(i), fId(bksize/v)), v)]) *\n VGath_sv(fCompose(self.gfunc, fTensor(fBase(i), fId(bksize))).setDomain(bksize), v, 1)\n )\n )\n);\n", "meta": {"hexsha": "729579d50f2a29c5d0dbf5e6a614725bcd7b7199", "size": 15944, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/vector/sigmaspl/scatter.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/scatter.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/scatter.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": 50.9392971246, "max_line_length": 100, "alphanum_fraction": 0.3724912193, "num_tokens": 3484, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7310585669110202, "lm_q2_score": 0.5926665999540698, "lm_q1q2_score": 0.43327399521844917}}
	{"text": "\nlocal reps,tori,labels,I,II,ords,mizuno,blocks;\n\nmizuno:=[[ 1, 2, 3, 4, 5, 6, fail,\n 7, 8, 9, 10,\n 11, 6, 12, 13,\n 15, 14, 16, 11,\n 17, 18, 19, 21,\n 20, 16, 22, 23,\n 24, 25, 21, 20,\n 26, 27, 23, 28,\n 25, 29, 30, 27,\n 31, 28, 32, 33,\n 30, 31, 34, 32,\n 33, fail, 35, 34,\n fail, 36, 35, fail,\n 36, fail, fail, fail,\n fail, fail, fail, fail ],\n []];\n\nreps:=[[[1,1],[2,1],[3,1],[4,1],[5,1],[6,1]], # E_6\n [[2,1],[4,1],[5,1],[6,1],[8,1],[16,1]], # E_6(a_1)\n [[1,1],[2,1],[10,1],[11,1],[12,1]], # D_5\n [[8,1],[9,1],[12,1],[10,1],[11,1],[16,1]], # A_5+A_1\n [[8,1],[9,1],[16,1],[12,1],[18,1]], # D_5(a_1)\n [[1,1],[15,1],[16,1],[17,1],[6,1]], # A_5\n [[14,1],[15,1],[16,1],[17,1],[12,1]], # A_4+A_1\n [[2,1],[14,1],[16,1],[18,1]], # D_4\n [[14,1],[15,1],[17,1],[12,1]], # A_4\n [[14,1],[16,1],[22,1],[24,1]], # D_4(a_1)\n [[14,1],[22,1],[23,1],[24,1]], # A_3+A_1\n [[20,1],[21,1],[28,1],[23,1],[24,1]], # 2A_2+A_1\n [[14,1],[22,1],[24,1]], # A_3\n [[26,1],[27,1],[28,1],[29,1]], # A_2+2A_1\n [[20,1],[21,1],[23,1],[24,1]], # 2A_2\n [[26,1],[27,1],[35,1]], # A_2+A_1\n [[26,1],[35,1]], # A_2\n [[37,1],[38,1],[40,1]], # 3A_1\n [[42,1],[43,1]], # 2A_1\n [[53,1]] # A_1\n ];\n\nlabels:=[\"E_6\",\n \"E_6(a_1)\",\n \"D_5\",\n \"A_5+A_1\",\n \"D_5(a_1)\",\n \"A_5\",\n \"A_4+A_1\",\n \"D_4\",\n \"A_4\",\n \"D_4(a_1)\",\n \"A_3+A_1\",\n \"2A_2+A_1\",\n \"A_3\",\n \"A_2+2A_1\",\n \"2A_2\",\n \"A_2+A_1\",\n \"A_2\",\n \"3A_1\",\n \"2A_1\",\n \"A_1\",\n ];\n\nI:=[ [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ] ];\n\nII:=[ [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ] ];\n\ntori:=[ [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ] ];\n\n#blocks:=[];\nblocks:=[[[16, 4], [8, 1], [6, 1]], [[16, 2], [11, 2], [8, 2], [4, 2]], [[8, 9], [6, 1]], [[8, 8], [4, 2], [3, 2]], [[8, 5], [6, 1], [4, 8]], [[8, 8], [2, 6], [1, 2]], [[8, 4], [6, 2], [5, 2], [4, 4], [2, 4]], [[8, 1], [6, 9], [2, 8]], [[8, 2], [7, 4], [5, 2], [4, 2], [3, 4], [1, 4]], [[4, 18], [3, 2]], [[4, 16], [2, 6], [1, 2]], [[4, 16], [2, 6], [1, 2]], [[4, 16], [2, 4], [1, 6]], [[4, 10], [3, 2], [2, 16]], [[4, 16], [1, 14]], [[4, 8], [3, 6], [2, 10], [1, 8]], [[4, 2], [3, 18], [1, 16]], [[2, 38], [1, 2]], [[2, 32], [1, 14]], [[2, 22], [1, 34]]];\n\n#ords:=[];\nords:=[ 16, 16, 8, 8, 8, 8, 8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2 ];\n\nreturn [reps,tori,labels,I,II,ords,blocks,mizuno];\n", "meta": {"hexsha": "0f3ef03ce49c351abd66d723ec48d4b317f2b95e", "size": 3243, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "lib/data/dataE6char2Mizuno.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/data/dataE6char2Mizuno.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/data/dataE6char2Mizuno.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": 41.5769230769, "max_line_length": 556, "alphanum_fraction": 0.2553191489, "num_tokens": 1555, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7341195152660688, "lm_q2_score": 0.588889130767832, "lm_q1q2_score": 0.4323150032247374}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n#F PolyDTT( <dtt-nonterminal> )\n#F Parameters: <nonterminal for a (optionally skew) DCT or DST of type 1--8>\n#F Definition: Let <t> be an (otionally skew) DCT or DST of type 1--8. Then\n#F Transform( \"PolyDTT\", <t> ) represents the (n x n)-matrix\n#F obtained from dividing every row in <t> by its first\n#F entry.\n#F This transform is called the polynomial version of\n#F the DCT or DST.\n#F Note: The transpose of PolyDTT(<t>) is\n#F TPolyDTT(<t>^T).\n#F Example: PolyDTT(DCT2(8)).\n#F\nClass(PolyDTT, NonTerminal, rec(\n _short_print := true,\n abbrevs := [ nt -> Checked(IsNonTerminal(nt), \n\t ObjId(nt) in \n\t [ DCT1, DCT3, DCT5, DCT7, # PolyDTT(T)=T for these\n\t DCT2, DCT4, DCT6, DCT8, \n\t DST1, DST2, DST3, DST4,\n\t DST5, DST6, DST7, DST8,\n\t SkewDTT],\n\t [ Copy(nt) ]\n\t)],\n dims := self >> self.params[1].dimensions,\n terminate := self >> Mat(PolynomialDTT(MatSPL(TerminateSPL(self.params[1])))),\n isReal := True\n));\n\nClass(fr, Exp, rec(\n ev := self >> let(\n\tm := self.args[1].ev(),\n\ti := self.args[2].ev(),\n\tr := self.args[3].ev(),\n\tCond(i mod 2 = 0, (r + 2 * Int(i/2)) / m,\n\t i mod 2 = 1, (2 - r + 2 * Int(i/2)) / m))));\n\n#F Rules\n#F -----\nRulesFor(PolyDTT, rec(\n PolyDTT_ToNormal := rec(\n\tisApplicable := P -> ObjId(P[1]) in [DCT1, DCT3, DCT5, DCT7],\n\tallChildren := P -> [P[1]],\n\trule := P -> P[1]\n ),\n\n #F PolyDTT_Base2: (base case for non-skew DTTs of size 2)\n #F\n #F pDCT2_2 = F_2\n #F pDCT4_2 = F_2 * [[1, -1], [0, sqrt(2)]]\n #F pDCT6_2 = [ [ 1, 1 ], [ 1, -2 ] ]\n #F pDCT8_2 = [ [ 1, cos(2pi/5) ], [ 1, cos(4pi/5) ] ]\n #F pDST4_2 = F_2 * [[1, 1], [0, sqrt(2)]]\n #F\n #F Pueschel/Moura: Discrete Cosine and Sine Transforms, in preparation\n #F\n PolyDTT_Base2 := rec (\n\tinfo := \"pDTT_2 -> F_2\",\n\tisApplicable := P -> Rows(P[1]) = 2 and ObjId(P[1]) <> SkewDTT,\n\tallChildren := P -> [[ ]],\n\trule := (P, C) -> let(nt := ObjId(P[1]), Cond(\n\t\tnt = DCT2, F(2),\n\t\tnt = DCT4, F(2) * Mat([[1, -1], [0,sqrt(2)]]),\n\t\tnt = DCT6, Mat([[1,1], [1,-2]]),\n\t\tnt = DCT8, Mat([[1,2CosPi(2/5)], [1,2CosPi(4/5)]]),\n\t\tnt = DST2, F(2),\n\t\tnt = DST3, F(2) * Diag([1, sqrt(2)]),\n\t\tnt = DST4, F(2) * Mat([[1, 1], [0, sqrt(2)]]),\n\t\tnt = DST5, Mat([[1,2CosPi(2/5)], [1,2CosPi(4/5)]]),\n\t\tnt = DST6, Mat([[1,2CosPi(1/5)], [1,2CosPi(3/5)]]),\n\t\tnt = DST7, Mat([[1,2CosPi(1/5)], [1,2CosPi(3/5)]]),\n\t\tnt = DST8, Mat([[1,2], [1,-1]]), \n\t\tError(\"unrecognized <L.symbol>\"))\n\t)\n ),\n\n PolyDTT_SkewBase2 := rec (\n\tinfo := \"pDTT_2 -> F_2\",\n\tisApplicable := P -> Rows(P[1]) = 2 and ObjId(P[1]) = SkewDTT and\n\t ObjId(P[1].params[1]) = DST3, \n\tallChildren := P -> [[ ]],\n\trule := (P, C) -> let(skewnt := ObjId(P[1].params[1]), r := P[1].params[2], \n\t Cond(\n\t\tskewnt = DST3, F(2) * Diag(1, 2CosPi(r/2)),\n\t\tError(\"unrecognized <L.symbol>\"))\n\t)\n ),\n\n PolyDTT_SkewDST3_CT := rec(\n isApplicable := P -> ObjId(P[1]) = SkewDTT and\n ObjId(P[1].params[1]) = DST3 and\n Rows(P[1]) > 2 and not IsPrime(Rows(P[1])),\n\n allChildren := P -> let(\n\t N := Rows(P[1].params[1]), r := P[1].params[2],\n\t List(DivisorPairs(N), d->\n\t let(i := Ind(d[2]),\n\t\t ri := fr(d[2], i, r),\n\t\t [ PolyDTT(SkewDTT(DST3(d[1]), ri)), \n\t\t PolyDTT(SkewDTT(DST3(d[2]), r)) ]))), \n\t\t\n rule := (P,C) -> let(\n\t MN := Rows(P[1]), N := Rows(C[1]), M := Rows(C[2]), \n\t r := P[1].params[2],\n\t i := C[1].root.params.params[2].args[2],\n\n\t K(MN, N) \n\t IterDirectSum(i, i.range, C[1]) \n\t Tensor(C[2], I(N)) \n\t B_DST3_U(MN, M)\n )\n )\n));\n", "meta": {"hexsha": "abe956f4b77ad55bde64beefd42b519dd57e23f6", "size": 3853, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/dtt/polydtt.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/dtt/polydtt.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/dtt/polydtt.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": 32.6525423729, "max_line_length": 82, "alphanum_fraction": 0.4949390086, "num_tokens": 1552, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7634837743174788, "lm_q2_score": 0.5660185351961015, "lm_q1q2_score": 0.43214596758517027}}
	{"text": "#############################################################################\n##\n#W matgrp4.gi Karel Dekimpe\n#W Bettina Eick\n##\n## This file contains the 4-dimensional almost crystallographic groups\n## as integral matrix groups. There are 95 types of groups.\n##\nACDim4Nr001 := function ( k1, k2, k3)\nlocal a, b, c, d;\na :=[[1, 0, -k1/2, -k2/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, -k3/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nc :=[[1, k2/2, k3/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d] , IdentityMat(5) );\nend;\n \nACDim4Nr002 := function ( k1, k2, k3, k4, k5, k6, k7)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, -k2/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, -k3/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nc :=[[1, k2/2, k3/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k4, k5, k6, k7/2], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr003 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, 0, k3, k4/2], [0, -1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr004 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, 0, - k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, 0, k3, k4/2], [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr004b := function ( k1, k2, k3)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, -k2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, k2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, -k1/2, 2k3, k2/2, 0], [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr005 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k2, k3, k4/2], [0, 0, -1, 0, 0], [0, -1, 0, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr006 := function ( k1, k2, k3)\nlocal a, b, c, d, alfa;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, 0, k2, 0, k3/2], [0, 1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr007 := function ( k1, k2, k3)\nlocal a, b, c, d, alfa;\na :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k1/2, k2, 0, k3/2], [0, 1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr007b := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, -k2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, k2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, -k3, -k2/2, 2k4, 0], [0, 1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr008 := function ( k1, k2, k3)\nlocal a, b, c, d, alfa;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k2, 0, k3/2], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr009 := function ( k1, k2, k3)\nlocal a, b, c, d, alfa;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -k1/4 + k2, (3k1)/4 - k2, 0, k3/2], [0, 0, 1, 0, 0], \n [0, 1, 0, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr009b := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, -k2/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, k2/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nc :=[[1, k2/2, -k2/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, k2/4 - k3, (3k2)/4 - k3, 2k4, 0], [0, 0, 1, 0, 0], \n [0, 1, 0, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr010 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, 0, k3, k4/2], [0, -1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[1, k2, k5, k3, k6/2], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr011 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, 0, k3, k4/2], [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[1, k2, -2k6, k3, k5/2], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr012 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k2, k3, k4/2], [0, 0, -1, 0, 0], [0, -1, 0, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[1, k5, 2k2 - k5, k3, k6/2], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr013 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k1/2 + k2, 0, -2k6, k3/2 + k6/2], [0, -1, 0, 0, 0], \n [0, 0, 1, 0, 0], [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, k1 + k2, k4, -2k6, k5/2], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr014 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na:=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb:=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc:=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd:=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:=[[1, k1/2+ k2, 0, k3, -k3/4 + k4/2], [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\nbeta:=[[1, k1 + k2, -k3 - 2k6, k3, k5/2], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr014b := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, -k2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, k2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, -k1/2, -k2/2 + 2k3, k2/2, 0], [0, -1, 0, 0, 0], \n [0, 0, 1, 0, 1/2], [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, k4, k2 - 2k3, k2 + 2k3 - 2k5 + 2k6, k5/2], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr015 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k1/4 + k2, k1/4 + k2, -2k6, k3/2 + k6/2], [0, 0, -1, 0, 0], \n [0, -1, 0, 0, 0], [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, k4, k1 + 2k2 - k4, -2k6, k5/2], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr018 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -k1 + 2k2 - 2k3 + 2k4, k1/2 - 2k3, 0, \n k2/2 - (-k1 + 2k2 - 2k3 + 2k4)/4], [0, -1, 0, 0, 1/2], \n [0, 0, -1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1/2, 2k3, 0, 0], [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr019 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, -k1/2, 0, k1/2 + 2k2, 0], [0, -1, 0, 0, 1/2], \n [0, 0, -1, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, 3k1 + 2k2 - 2k3 + 2k4, 0, -k1 - 2k2, k3/2], \n [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr019b := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -k1 + 2k2 - 2k3 + 2k4, k1/2 - 2k3, 0, \n k2/2 - (-k1 + 2k2 - 2k3 + 2k4)/4], [0, -1, 0, 0, 1/2], \n [0, 0, -1, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1/2, 2k3, 0, 0], [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr019c := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, k1, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, 0, -k1/2, 2k2, -(- (3k1)/2 - k4)/2], [0, -1, 0, 0, 1/2], \n [0, 0, -1, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[-1, 0, 2k3, k1/2, 0], [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr026 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, -k1/2, 0, 2k2, 0], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, 0, k3, 0, k4/2], [0, 1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr027 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k3, 0, k4/2], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k2, 0, 2k5, 0], [0, 1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr029 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, -k1/2, 0, 2k2, 0], [0, -1, 0, 0, 0], [0, 0, -1, 0, 1/2], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, k1/2, 2k2 - 2k3 + 2k4, 0, k3/2], [0, 1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr029b := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k1/2 + k2, 2k3 - 2k4 + 2k5, 0, k3/2 - (2k3 - 2k4 + 2k5)/4], \n [0, -1, 0, 0, 0], [0, 0, -1, 0, 1/2], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1 - k2, 0, 2k4, 0], [0, 1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr029c := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, -2k1, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 2k1, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, 0, -k1, -k1 + 2(k1 + k2), -k1], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 1/2], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k3, -k1, 2(k1 + k2), -k4/2], [0, 1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr030 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k1/2 + k2, 2k3 + 2k5, 0, k3/2 - (2k3 + 2k5)/4], \n [0, -1, 0, 0, 0], [0, 0, -1, 0, 1/2], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1 - k2, 0, 2k4, 0], [0, 1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr031 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, -k1/2, 0, 2k2, 0], [0, -1, 0, 0, 0], [0, 0, -1, 0, 1/2], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, 0, -2k3 + 2k4, 0, k3/2], [0, 1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr032 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -k1/2 - 2k4, -3k1 + 2k2 - 2k4 + 2k5, 0, \n k2/2 - (-3k1 + 2k2 - 2k4 + 2k5)/4], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 1/2], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, 2k4, k1/2, -k3, 0], [0, 1, 0, 0, 1/2], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr033 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, -k1/2, 0, 2k2, 0], [0, -1, 0, 0, 0], [0, 0, -1, 0, 1/2], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, 0, -k1 - 2k3 + 2k4, -k1/2, k3/2], [0, 1, 0, 0, 1/2], \n [0, 0, -1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr033b := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -k1/2 - 2k4, -3k1 + 2k2 + k3 - 2k4 + 2k5, 0, \n k2/2 - (-3k1 + 2k2 + k3 - 2k4 + 2k5)/4], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 1/2], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[-1, 2k4, k1/2, -k3, 0], [0, 1, 0, 0, 1/2], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr033c := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, k1, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, 0, -k1/2, k1/2 + 2k2, k2/2], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 1/2], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[-1, 2k3, 0, k1 + 2k2, -k4/2], [0, 1, 0, 0, 1/2], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr034 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k1/2 + k2, -2k1 + k2 + 2k3 + 2k5, 0, \n k3/2 - (-2k1 + k2 + 2k3 + 2k5)/4], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 1/2], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1 - k2, k1/2, k1 + k2 + 2k4, 0], [0, 1, 0, 0, 1/2], \n [0, 0, -1, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr036 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1, k1, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, -k1/2, -k1/2, 2k2, 0], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, k3, -k3, 0, k4/2], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr037 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k2 + 2k4, 0, k3/2], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k4, -k4, 2k5, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr041 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1, k1, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k2, k1 - 2k5, -k2/2 + k3/2], [0, 0, -1, 0, 1/2], \n [0, -1, 0, 0, 1/2], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, k1/2 - k4, (-3k1)/2 + k4, 2k5, 0], [0, 0, -1, 0, 0], \n [0, -1, 0, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr043 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1/2, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, -k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -k1/4 + k2 + 2k3 + 2k5, k1/4 + k2, 2k2 + 2k3 + 2k5, \n k3/2 - (2k2 + 2k3 + 2k5)/4], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], \n [0, -1, -1, -1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1/4 + k2 + 2k4, 2k4, -k1/4 - k2, 0], [0, 0, 0, -1, 0], \n [0, 1, 1, 1, 1/2], [0, -1, 0, 0, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr045 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na:=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb:=[[1, 0, 0, k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc:=[[1, k1/2, -k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd:=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:=[[1,k2, -k2, k2 - 2k4 - 2k5, k3/2], [0, 0, 1, -1, 0], [0, 1, 0, -1, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nbeta:=[[-1, -k4, k4 + 2k5, k4, 0], [0, 0, 1, -1, 1/2], [0, 0, 1, 0, 1/2], \n [0, -1, 1, 0, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr055 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta, gamma;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -k1 - 2k2 + 2k3 - 2k4, -k1 - 2k3, 0, k2/2], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1/2, k1/2 + 2k3, 0, 0], [0, -1, 0, 0, 1/2], \n [0, 0, 1, 0, 1/2], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\ngamma :=[[1, -k1 - 2k2 + 2k3 - 2k4, -k1 - 2k3, k5, \n (2k1 + k2 + k4 + k6)/2], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta, gamma] , IdentityMat(5) );\nend;\n \nACDim4Nr056 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta, gamma;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -k1/2 + 2k2 - 2k3 + 2(k1 - k2 + 2k3 - k4), k1/2 - 2k3, 0, \n k2/2 - (k1 - 2k3)/4 - (-k1 + 2k2 - 2k3 + 2(k1 - k2 + 2k3 - k4))/4], \n [0, -1, 0, 0, 1/2], [0, 0, -1, 0, 1/2], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1/2, 2k3, 0, 0], [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\ngamma :=[[1, 2k2 - 2k3 + 2(k1 - k2 + 2k3 - k4), -2k3, \n 2k3 + 2k5 - 2k6, k6/2], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta, gamma] , IdentityMat(5) );\nend;\n \nACDim4Nr058 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta, gamma;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -k1 - 2k2 + 2k3 - 2k4, -k1 - 2k3, 0, k2/2], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1/2, k1/2 + 2k3, 0, 0], [0, -1, 0, 0, 1/2], \n [0, 0, 1, 0, 1/2], [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\ngamma :=[[1, -k1 - 2k2 + 2k3 - 2k4, -k1 - 2k3, \n 4k1 + 2k2 + 2k4 + 2k5 - 2k6, k6/2], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta, gamma] , IdentityMat(5) );\nend;\n \nACDim4Nr060 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta, gamma;\na :=[[1, 0, -2k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 2k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -2(k1 - k2 + k3 - k4), k1 - 2k3, 0, \n k2/2 + (k1 - k2 + k3 - k4)/2], [0, -1, 0, 0, 1/2], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1, 2k3, 0, 0], [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\ngamma :=[[1, -2(k1 - k2 + k3 - k4), -2k3, 2k3 + 2k5 - 2k6, k6/2], \n [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta, gamma] , IdentityMat(5) );\nend;\n \nACDim4Nr061 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta, gamma;\na :=[[1, 0, 0, -2k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 2k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, -k1, 0, k1 + 2k2, 0], [0, -1, 0, 0, 1/2], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, 7k1 + 2k2 - 2k3 + 2k4, 0, -2k1 - 2k2, \n -(-2k1 - 2k2)/4 + k3/2], [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\ngamma :=[[1, 8k1 + 2k2 - 2k3 + 2k4, 2k1 + 2k2 - 2k6, -2k1 - 2k2, \n (-k1 + k3 - k4 + k5)/2], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta, gamma] , IdentityMat(5) );\nend;\n \nACDim4Nr061b := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta, gamma;\na :=[[1, 0, -2k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 2k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -2k3 - 2k5 - 2k6 + 2(-k1 + k2 + k4 + k5 + k6), k1 - 2k3, 0, \n k2/2 - (-2k3 - 2k5 - 2k6 + 2(-k1 + k2 + k4 + k5 + k6))/4], \n [0, -1, 0, 0, 1/2], [0, 0, -1, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1, 2k3, 0, 0], [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\ngamma :=[[1, -2k3 - 2k5 - 2k6 + 2(-k1 + k2 + k4 + k5 + k6), -2k3, \n 2k3 + 2k6 - 2(-k1 + k2 + k4 + k5 + k6), (-k1 + k2 + k4 + k5 + k6)/2], \n [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta, gamma] , IdentityMat(5) );\nend;\n \nACDim4Nr061c := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta, gamma;\na :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, -2k1, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 2k1, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, 0, -k1, 2k2, 2k1 - k2/2], [0, -1, 0, 0, 1/2], \n [0, 0, -1, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[-1, 0, -3k1 - 2k2 - 2k6 + 2(k1 + k2 + k3 + k6), k1, -k4/2], \n [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\ngamma :=[[1, 2k2 + 2k5 - 2(k1 + k2 + k3 + k6), \n 4k1 + 2k2 + 2k6 - 2(k1 + k2 + k3 + k6), -2k2, (k1 + k2 + k3 + k6)/2], \n [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta, gamma] , IdentityMat(5) );\nend;\n \nACDim4Nr062 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta, gamma;\na :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, -k1/2, 0, k1/2 + 2k2, 0], [0, -1, 0, 0, 1/2], \n [0, 0, -1, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, 3k1 + 2k2 - 2k3 + 2k4, 0, -k1 - 2k2, k3/2], \n [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\ngamma :=[[1, 3k1 + 2k2 - 2k3 + 2k4, -2k6, -k1 - 2k2, (k3 - k4 + k5)/2], \n [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta, gamma] , IdentityMat(5) );\nend;\n \nACDim4Nr075 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k3, 0, k4/4], [0, 0, -1, 0, 0], [0, 1, 0, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr076 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k3, 0, k4/4], [0, 0, -1, 0, 0], [0, 1, 0, 0, 0], \n [0, 0, 0, 1, 1/4], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr077 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k3, 0, k4/4], [0, 0, -1, 0, 0], [0, 1, 0, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr079 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, -k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k2, k3, k4/4], [0, 0, 1, 0, 0], [0, 0, 1, -1, 0], \n [0, -1, 1, 0, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr080 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, -k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -k1/4 + k2, k1/4 - k2, k3, k1/16 - k2/4 + k3/4 + k4/4], \n [0, 0, 1, 0, 1/2], [0, 0, 1, -1, 0], [0, -1, 1, 0, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr081 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k3, k4, k5/4], [0, 0, 1, 0, 0], [0, -1, 0, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr082 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, -k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k3, k4, k5/4], [0, 0, -1, 0, 0], [0, 0, -1, 1, 0], \n [0, 1, -1, 0, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr083 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k3, 0, k4/4], [0, 0, -1, 0, 0], [0, 1, 0, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[1, k2 + k3, -k2 + k3, k5, k6/2], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr084 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k3, 0, k4/4], [0, 0, -1, 0, 0], [0, 1, 0, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, k2 + k3, -k2 + k3, -2k6, k5/2], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr085 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k1/2 + k2 - 2k6, 0, \n -k1/8 + k2/4 + k3/4 - (-k1 + k2 - 2k6)/4], [0, 0, -1, 0, 0], \n [0, 1, 0, 0, 1/2], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[1, 2k2 - 2k6, -2k6, k4, k5/2], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr086 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k1/2 + k3, 0, -k1/8 + k2/4 - k3/4 + k4/4], [0, 0, -1, 0, 0], \n [0, 1, 0, 0, 1/2], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, k1 + k2 + k3, k1 - k2 + k3, -k1 + k2 - k3 - 2k6, k5/2], \n [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr087 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, -k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k2, k3, k4/4], [0, 0, 1, 0, 0], [0, 0, 1, -1, 0], \n [0, -1, 1, 0, 0], [0, 0, 0, 0, 1]];\nbeta :=[[1, k5, -2k2 + 2k3 + k5, 2k2 - k5, k6/2], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr088 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, -k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k2, -k1/4 + k3, -(-k1/4 + k2 + k3 - k4)/4], [0, 0, 1, 0, 0], \n [0, 0, 1, -1, 0], [0, -1, 1, 0, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, 2k2 + 2k6, -k1 + 2k3 + 2k6, -2k6, k5/2], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr103 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k3, 0, k4/4], [0, 0, -1, 0, 0], [0, 1, 0, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k2 - k3, 0, 2k5, 0], [0, 1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr104 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k1/2 + k2, -k1 + k2 + 2k3 + 2k5, 0, \n -k1/8 - k2/4 + k3/4 - (-k1 + k2 + 2k3 + 2k5)/4], [0, 0, -1, 0, 1/2], \n [0, 1, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -2k2 - 2k3 - 2k5, k1/2, 2k2 + 2k3 + 2k4 + 2k5, 0], \n [0, 1, 0, 0, 1/2], [0, 0, -1, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr106 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k1/2 + k2, -k1 - k2 - 2k5, 0, \n -k1/8 - k2/4 + k3/4 - (-k1 - k2 - 2k5)/4], [0, 0, -1, 0, 1/2], \n [0, 1, 0, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[-1, 2k5, k1/2, -2k4, 0], [0, 1, 0, 0, 1/2], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr110 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, k1, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1, -k1, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, 4k1 - 4k2 + 2k3 - 3k4 + 2k5, \n -4k1 + 4k2 - 2k3 + 3k4 - 2k5, -k1/2 + k2, \n -(-k1/2 + k2 - k3 - (3(-4k1 + 4k2 - 2k3 + 3k4 - 2k5))/2 - \n (4k1 - 4k2 + 2k3 - 3k4 + 2k5)/2)/4], [0, 0, 1, 0, 0], \n [0, 0, 1, -1, 0], [0, -1, 1, 0, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k4, 2(k1 - k2 - k4) + k4, k4, 0], [0, 0, 1, -1, 1/2], \n [0, 0, 1, 0, 1/2], [0, -1, 1, 0, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr114 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -k1/2 + k2, k1 - k2 - 2k4, 2k1 - 2k2 + 2k3 - 2k4 + 2k5, \n -(k1/2 + k3 + 2k5)/4], [0, 0, 1, 0, 1/2], [0, -1, 0, 0, 0], \n [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1/2, 2k4, 0, 0], [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr143 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na:= [[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb:= [[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc:= [[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[1, k2, -k1/2 + k3, 0, k4/3], [0, 0, -1, 0, 0], [0, 1, -1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr144 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k1/2 + k3, 0, k4/3], [0, 0, -1, 0, 0], [0, 1, -1, 0, 0], \n [0, 0, 0, 1, 1/3], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr146 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, -k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nc :=[[1, -k1/2, k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k3, -k2 - k3, k4/3], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0], \n [0, 0, 1, 0, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr147 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k1/2 + k3, k4, k5/6], [0, 0, 1, 0, 0], [0, -1, 1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr148 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, -k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nc :=[[1, -k1/2, k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k3, k4, k5/6], [0, 0, 0, -1, 0], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr158 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k1/2 + k3, 0, k4/3], [0, 0, -1, 0, 0], [0, 1, -1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k2, k2, 2k5, 0], [0, 0, -1, 0, 0], [0, -1, 0, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr159 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k1 - 2k2 + 3k4, -k1/2 + k2, 0, k3/3], [0, 0, -1, 0, 0], \n [0, 1, -1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k4, -k4, 2k5, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr161 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1/2, k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, -k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nc :=[[1, -k1/2, k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k1/4 + k2, k3, -k1/4 - k2 - k3, \n -((5k1)/8 + k2 + (-k2 - k3)/2 + (3k3)/2 - k4)/3], [0, 0, 0, 1, 1/2], \n [0, 1, 0, 0, 1/2], [0, 0, 1, 0, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1/4 - k2 - 2k3 + 2k5, (-3k1)/4 - k2 - 2k3 + 2k5, 2k5, \n 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr168 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k1/2 + k3, 0, k4/6], [0, 0, 1, 0, 0], [0, -1, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr169 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k1/2 + k3, 0, k4/6], [0, 0, 1, 0, 0], [0, -1, 1, 0, 0], \n [0, 0, 0, 1, 5/6], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr172 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k1/2 + k3, 0, k4/6], [0, 0, 1, 0, 0], [0, -1, 1, 0, 0], \n [0, 0, 0, 1, 1/3], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr173 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k1/2 + k3, 0, k4/6], [0, 0, 1, 0, 0], [0, -1, 1, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr174 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k1/2 + k3, k4, k5/6], [0, 0, -1, 0, 0], [0, 1, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr175 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k1/2 + k3, 0, k4/6], [0, 0, 1, 0, 0], [0, -1, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[1, k1 - 2k3, -k1 + 2k2 + 2k3, k5, k6/2], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr176 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k1/2 + k3, 0, k4/6], [0, 0, 1, 0, 0], [0, -1, 1, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, k1 - 2k3, -k1 + 2k2 + 2k3, 2k6, k5/2], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr184 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k1/2 + k3, 0, k4/6], [0, 0, 1, 0, 0], [0, -1, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1 + k2 + 2k3, k1 - k2 - 2k3, 2k5, 0], [0, 0, -1, 0, 0], \n [0, -1, 0, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4NrB1 := function ( k, k1, k2, k3)\nlocal a, b, c, d;\na:= [[1, (-2k2)/3, 0, -k1/2 - (2kk3)/3 + (2k(k2 + k3))/3, 0], \n [0, 1, 0, -k/2, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb:= [[1, (-2k3)/3, k1/2 - (2kk3)/3, 0, 0], [0, 1, k/2, 0, 0], \n [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, k2/3, k3/3, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d] , IdentityMat(5) );\nend;\n \nACDim4NrB2 := function ( k, k1, k2, k3)\nlocal a, b, c, d, alfa;\na:= [[1, (-4k1)/3, 0, (2kk1)/3 + (2kk2)/3 - 2kk3 + \n (-4kk1 - (16kk2)/3 - 2kk3 + 2(2kk1 + 2kk2 + 2kk3))/2, 0], \n [0, 1, 0, -k, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb:= [[1, (-4k2)/3, (-4kk1 - (16kk2)/3 - 2kk3 + \n 2(2kk1 + 2kk2 + 2kk3))/2, 0, 0], [0, 1, k, 0, 0], \n [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, (2k1)/3, (2k2)/3, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[-1, 2k3, -k1/3, -k2/3, 0], [0, 1, 0, 0, 1/2], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4NrB3c := function (l, k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na:= [[1, 0, 0, (k1l)/3 + k3l + ((-8k1l)/3 + k3l + 2(k1l - k3l))/2, \n 0], [0, 1, 0, -l, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb:= [[1, (-2k1)/3, ((-8k1l)/3 + k3l + 2(k1l - k3l))/2, -k2, 0], \n [0, 1, l, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, 0, k1/3, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[1, k3, 0, 0, k4/2], [0, -1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4NrB3b := function (l, k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na:= [[1, 0, 0, k1 + (2k1l)/3 - 2k2l + ((2k1)/3 - (16k1l)/3 - 2k2l + \n 2(-k1 + 2k1l + 2k2l))/2, 0], [0, 1, 0, -l, 0], [0, 0, 1, 0, 1], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb:= [[1, (-4k1)/3, ((2k1)/3 - (16k1l)/3 - 2k2l + \n 2(-k1 + 2k1l + 2k2l))/2, -k3, 0], [0, 1, l, 0, 0], \n [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, 0, (2k1)/3, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[1, -2k2, -k2, 0, k4/2], [0, -1, -1, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4NrB3 := function (l, k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na:= [[1, 0, 0, (2k1)/3 + (k1l)/3 + (-k1 - (2k1l)/3)/2, 0], \n [0, 1, 0, (-1 - 2l)/2, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb:= [[1, (-2k1)/3, (-k1 - (2k1l)/3)/2, -k3, 0], [0, 1, (1 + 2l)/2, 0, 0], \n [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, 0, k1/3, -k2], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[1, 0, 0, 0, k4/2], [0, -1, -1, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4NrB4 := function (k, k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na:= [[1, 0, 0, (kk1)/3 + kk3 + ((-2kk1)/3 - kk3)/2, -k4], \n [0, 1, 0, -k, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb:= [[1, (-2k1)/3, ((-2kk1)/3 - kk3)/2, -(kk1)/2 - k2 + (3kk3)/4, 0], \n [0, 1, k, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, 0, k1/3, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[1, k3, 0, 0, 0], [0, -1, 0, k/2, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4NrB4b := function (k, k1, k2, k3)\nlocal a, b, c, d, alfa;\na:= [[1, (4k1)/3, 0, (-5kk1)/3 + 2k2 - 2((-2kk1)/3 + k2), -k3], \n [0, 1, 0, -k, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb:= [[1, 0, -2((-2kk1)/3 + k2), 0, 0], [0, 1, k, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, (-2k1)/3, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[-1, (-2k1)/3, 0, 0, 0], [0, -1, 0, k/2, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4NrB5 := function (l, k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na:= [[1, (-2k1)/3, 0, k3l, k2], [0, 1, 0, -l, 0], [0, 0, 1, 0, 1], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb:= [[1, (2k1)/3, 0, 0, 0], [0, 1, l, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, k1/3, -k1/3, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[1, k3, 0, 0, k4/2], [0, -1, 0, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 1, 0, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4NrB5b := function (l, k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na:= [[1, (-2k1)/3, 0, k3(1 + 2l), k2], [0, 1, 0, (-1 - 2l)/2, 0], \n [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb:= [[1, (2k1)/3, 0, 0, 0], [0, 1, (1 + 2l)/2, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, k1/3, -k1/3, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[1, 2k3, 0, 0, k4/2], [0, -1, 0, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 1, 0, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4NrB7 := function (l, k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na:= [[1, 0, 0, (4k1l)/3 - 4k2l + ((-8k1l)/3 + 4k2l)/2, 0], \n [0, 1, 0, -2l, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb:= [[1, (-4k1)/3, ((-8k1l)/3 + 4k2l)/2, 0, (5k1)/6 - 2k2 + \n ((-2k1)/3 + 2k2)/2 - k4], [0, 1, 2l, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, 0, (2k1)/3, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[-1, 2k2, 0, -k1/3, 0], [0, 1, 0, 0, 1/2], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nbeta:= [[1, (2k1)/3 - 2k2, -(((2k1)/3 - 2k2)l)/2, 2k3, 0], \n [0, -1, l, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4NrB7b := function (l, k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na:= [[1, 0, 0, (4k1(1 + 2l))/3 - 2k2(1 + 2l) + \n ((-8k1(1 + 2l))/3 + 2k2(1 + 2l))/2, 0], [0, 1, 0, -1 - 2l, 0], \n [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb:= [[1, (-8k1)/3, ((-8k1(1 + 2l))/3 + 2k2(1 + 2l))/2, 0, \n (5k1)/3 - 2k2 + ((-4k1)/3 + 2k2)/2 - k4], [0, 1, 1 + 2l, 0, 0], \n [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, 0, (4k1)/3, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[-1, 2k2, 0, (-2k1)/3, 0], [0, 1, 0, 0, 1/2], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nbeta:= [[1, (4k1)/3 - 2k2, -(((4k1)/3 - 2k2)(1 + 2l))/4, 2k3, 0], \n [0, -1, (1 + 2l)/2, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, -1, 1/2], \n [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4NrB8 := function (k, k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na:= [[1, 0, 0, -2k(k1 - 2k2) - 8kk2 + (8k(2(k1 - 2k2) + 4k2))/3 + \n (-4kk2 - (14k(2(k1 - 2k2) + 4k2))/3 + \n 2(2k(k1 - 2k2) + 8kk2))/2, \n (k(k1 + (-2(k1 - 2k2) - 4k2)/6 - 2k2))/4 - k3 + \n (k1 + (17k(k1 - 2k2))/3 - 3k2 + (34kk2)/3 + (-k1 + 2k2)/2 + \n (-2k(k1 - 2k2) - 8kk2)/2 + (k1 - 2k(k1 - 2k2) - 6kk2)/2 + \n 2k3 - 2k4)/2], [0, 1, 0, -2k, 0], [0, 0, 1, 0, 1], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb:= [[1, (-2(2(k1 - 2k2) + 4k2))/3, \n (-4kk2 - (14k(2(k1 - 2k2) + 4k2))/3 + \n 2(2k(k1 - 2k2) + 8kk2))/2, k1 + (-2(k1 - 2k2) - 4k2)/3 - \n 2k(k1 - 2k2) - 2kk2 + (4k(2(k1 - 2k2) + 4k2))/3 + \n ((-2(k1 - 2k2) - 4k2)/3 - 4kk2)/2, 0], [0, 1, 2k, 0, 0], \n [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, 0, (2(k1 - 2k2) + 4k2)/3, 0], [0, 1, 0, 0, 1], \n [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[-1, 2k2, 2kk2, ((-2(k1 - 2k2) - 4k2)/3 - 4kk2)/2, 0], \n [0, 1, 2k, -2k, 1/2], [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], \n [0, 0, 0, 0, 1]];\nbeta:= [[1, k1 + (-2(k1 - 2k2) - 4k2)/6 - 2k2, \n (k(k1 + (-2(k1 - 2k2) - 4k2)/6 - 2k2))/2, \n k1 + (17k(k1 - 2k2))/3 - 3k2 + (34kk2)/3 + (-k1 + 2k2)/2 + \n (-2k(k1 - 2k2) - 8kk2)/2 + (k1 - 2k(k1 - 2k2) - 6kk2)/2 + \n 2k3 - 2k4, 0], [0, -1, -k, k, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4NrB8b := function (k, k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na:= [[1, (4k1)/3, (-2k1)/3 + (4kk1)/3 + \n ((-16kk1)/3 + 8kk2 - 2(-2kk1 + 4kk2))/2 + \n 2(k1/3 - (2kk1)/3 + ((16kk1)/3 - 8kk2 + \n 2(-2kk1 + 4kk2))/ 2), (-10kk1)/3 + ((16kk1)/3 - 8kk2 + \n 2(-2kk1 + 4kk2))/2, \n ((8kk1)/3 - 2kk2 + (-2kk1 + 4kk2)/2 + \n ((-16kk1)/3 + 8kk2 - 2(-2kk1 + 4kk2))/2)/2 - k3], \n [0, 1, 0, -2k, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb:= [[1, 0, ((16kk1)/3 - 8kk2 + 2(-2kk1 + 4kk2))/2, 0, \n (-2k1)/3 - (2kk1)/3 + k2 + 4kk2 + (2kk1 - 4kk2)/2 + \n ((-16kk1)/3 + 8kk2 - 2(-2kk1 + 4kk2))/4 + \n (k1/3 - (2kk1)/3 + ((16kk1)/3 - 8kk2 + 2(-2kk1 + 4kk2))/2)/ 2 \n + ((-8kk1)/3 + 2kk2 + (2kk1 - 4kk2)/2 + \n ((16kk1)/3 - 8kk2 + 2(-2kk1 + 4kk2))/2)/2 + k3 + k4], \n [0, 1, 2k, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, (-2k1)/3, 0, -k2], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[-1, 0, k1/3 - (2kk1)/3 + ((16kk1)/3 - 8kk2 + \n 2(-2kk1 + 4kk2))/2, 0, 0], [0, 1, 2k, -2k, 1/2], \n [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nbeta:= [[-1, (-2k1)/3, 0, (8kk1)/3 - 2kk2 + (-2kk1 + 4kk2)/2 + \n ((-16kk1)/3 + 8kk2 - 2(-2kk1 + 4kk2))/2, 0], \n [0, -1, -k, k, 0], [0, 0, 1, 0, 1/2], [0, 0, 0, -1, 1/2], \n [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n\n#############################################################################\n##\n#V ACDim4Funcs\n#V ACDim4Param\n#V ACDim4Types\n##\n\n#############################################################################\n##\n## some small helpers\n##\nACDim4Funcs := [ ACDim4Nr001, ACDim4Nr002, ACDim4Nr003, ACDim4Nr004,\nACDim4Nr004b, ACDim4Nr005, ACDim4Nr006, ACDim4Nr007, ACDim4Nr007b,\nACDim4Nr008, ACDim4Nr009, ACDim4Nr009b, ACDim4Nr010, ACDim4Nr011,\nACDim4Nr012, ACDim4Nr013, ACDim4Nr014,\nACDim4Nr014b, ACDim4Nr015, ACDim4Nr018, ACDim4Nr019, ACDim4Nr019b,\nACDim4Nr019c, ACDim4Nr026, ACDim4Nr027, ACDim4Nr029, ACDim4Nr029b,\nACDim4Nr029c, ACDim4Nr030, ACDim4Nr031, ACDim4Nr032, ACDim4Nr033,\nACDim4Nr033b, ACDim4Nr033c, ACDim4Nr034, ACDim4Nr036, ACDim4Nr037,\nACDim4Nr041, ACDim4Nr043, ACDim4Nr045, ACDim4Nr055, ACDim4Nr056,\nACDim4Nr058, ACDim4Nr060, ACDim4Nr061, ACDim4Nr061b, ACDim4Nr061c,\nACDim4Nr062, ACDim4Nr075, ACDim4Nr076, ACDim4Nr077, ACDim4Nr079,\nACDim4Nr080, ACDim4Nr081, ACDim4Nr082, ACDim4Nr083, ACDim4Nr084, ACDim4Nr085,\nACDim4Nr086, ACDim4Nr087, ACDim4Nr088, ACDim4Nr103, ACDim4Nr104, ACDim4Nr106,\nACDim4Nr110, ACDim4Nr114, ACDim4Nr143, ACDim4Nr144, ACDim4Nr146, ACDim4Nr147,\nACDim4Nr148, ACDim4Nr158, ACDim4Nr159, ACDim4Nr161, ACDim4Nr168, ACDim4Nr169,\nACDim4Nr172, ACDim4Nr173, ACDim4Nr174, ACDim4Nr175, ACDim4Nr176, ACDim4Nr184,\nACDim4NrB1, ACDim4NrB2, ACDim4NrB3c, ACDim4NrB3b, ACDim4NrB3, ACDim4NrB4,\nACDim4NrB4b, ACDim4NrB5, ACDim4NrB5b, ACDim4NrB7, ACDim4NrB7b, ACDim4NrB8,\nACDim4NrB8b ];\nMakeReadOnlyGlobal( \"ACDim4Funcs\" );\n\n#############################################################################\nACDim4Types := [\n\"001\", \"002\", \"003\", \"004\", \"004b\", \"005\", \"006\", \"007\", \"007b\", \"008\",\n\"009\", \"009b\", \"010\", \"011\", \"012\", \"013\", \"014\", \"014b\", \"015\", \"018\",\n\"019\", \"019b\", \"019c\", \"026\", \"027\", \"029\", \"029b\", \"029c\", \"030\", \"031\",\n\"032\", \"033\", \"033b\", \"033c\", \"034\", \"036\", \"037\", \"041\", \"043\", \"045\",\n\"055\", \"056\", \"058\", \"060\", \"061\", \"061b\", \"061c\", \"062\", \"075\", \"076\",\n\"077\", \"079\", \"080\", \"081\", \"082\", \"083\", \"084\", \"085\", \"086\", \"087\", \"088\",\n\"103\", \"104\", \"106\", \"110\", \"114\", \"143\", \"144\", \"146\", \"147\", \"148\", \"158\",\n\"159\", \"161\", \"168\", \"169\", \"172\", \"173\", \"174\", \"175\", \"176\", \"184\", \"B1\",\n\"B2\", \"B3c\", \"B3b\", \"B3\", \"B4\", \"B4b\", \"B5\", \"B5b\", \"B7\", \"B7b\", \"B8\", \"B8b\"\n];\nMakeReadOnlyGlobal( \"ACDim4Types\" );\n\n#############################################################################\nACDim4Param :=\n[ 3, 7, 4, 4, 3, 4, 3, 3, 4, 3, 3, 4, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 5,\n 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4,\n 4, 4, 4, 5, 5, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 4, 4, 4, 5, 5, 5, 5, 5, 4,\n 4, 4, 4, 5, 6, 6, 5, 4, 4, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5 ];\nMakeReadOnlyGlobal( \"ACDim4Param\" );\n\n", "meta": {"hexsha": "eec6d2c6269174c6f6f8baa92d895223e01b0591", "size": 76488, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "gap/matgrp4.gi", "max_stars_repo_name": "alex-konovalov/aclib", 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	{"text": "# Copyright (c) 2018-2020, Carnegie Mellon University\n# See LICENSE for details\n#\n# Contains the rewrite rulesets for SPL-expression simplification\n# After the Breakdown Stage\n# Current Demo version focuses on CNOTs, and so we do not cancel single-qubit gates\n# Eventually we will convert all gates to generic rotations in Quantum_Format\n# Combine rotations in Quantum_Simplify, and convert back into non-generic rotations in Quantum_Terminate\n#\n# Additionally, Junction steps should be factored out in this stage versus in the unparser to enable a \n# few more optimizations. A SWE effort is underway.\n#\n\n##\n#F CheckIdentitySplit( <a>, <b> )\n##\n## return true if we can split an Identity transform into smaller matrices\nCheckIdentitySplit := function(a, b)\n if(ObjId(a) = I) then \n if a.params[1] > 2 then\n return true;\n fi;\n fi;\n if(ObjId(b) = I) then \n if b.params[1] > 2 then\n return true;\n fi;\n fi;\n return false;\nend;\n\n##\n#F CheckIdentity( <a>, <b> )\n##\n## are both objects identity\nCheckIdentity := function(a, b)\n if(ObjId(a) = I) then \n if(ObjId(b) = I) then \n return true;\n fi;\n fi;\n return false;\nend;\n\n##\n#F PullInTensor( <ch1>, <ch2> )\n##\n## compress two tensor expressions by pulling in symbols wherever sizes align\nPullInTensor := function(ch1, ch2)\n local pos1, pos2, e1, e2, up1, up2, siz1, siz2;\n pos1 := 1;\n pos2 := 1;\n siz1 := 0;\n siz2 := 0;\n while pos1 <= Length(ch1) and pos2 <= Length(ch2) do\n e1 := ch1[pos1];\n e2 := ch2[pos2];\n if ( (e1.dims()[1] = e2.dims()[1]) and (pos1 = pos2) ) then \n ch1[pos1] := ch1[pos1] * ch2[pos2];\n ch2[pos2] := I(e2.dims()[1]);\n fi;\n up1 := siz1 + log(e1.dims()[1], 2).v;\n up2 := siz2 + log(e2.dims()[1], 2).v;\n if (up1 <= up2) then \n pos1 := pos1 + 1;\n siz1 := siz1 + log(e1.dims()[1], 2).v;\n fi;\n if (up1 > up2) then \n pos2 := pos2 + 1;\n siz2 := siz2 + log(e2.dims()[1], 2).v;\n fi;\n od;\n return [ch1, ch2];\nend;\n\n##\n#F CanPullIn( <ch1>, <ch2> )\n##\n## Similar to PullInTensor, but just checks to see if there is any simplification possible\nCanPullIn := function(ch1, ch2)\n local pos1, pos2, e1, e2, up1, up2, siz1, siz2;\n pos1 := 1;\n pos2 := 1;\n siz1 := 0;\n siz2 := 0;\n while pos1 <= Length(ch1) and pos2 <= Length(ch2) do\n e1 := ch1[pos1];\n e2 := ch2[pos2];\n if ( (e1.dims()[1] = e2.dims()[1]) and (pos1 = pos2) and ObjId(e2) <> I) then \n return true;\n fi;\n up1 := siz1 + log(e1.dims()[1], 2).v;\n up2 := siz2 + log(e2.dims()[1], 2).v;\n if (up1 <= up2) then \n pos1 := pos1 + 1;\n siz1 := siz1 + log(e1.dims()[1], 2).v;\n fi;\n if (up1 > up2) then \n pos2 := pos2 + 1;\n siz2 := siz2 + log(e2.dims()[1], 2).v;\n fi;\n od;\n return false;\nend;\n\n##\n#F ValidTensSimplifyMatch( <e1>, <e2> )\n##\n## SWrapper function to deterrmine if the tensor rewrite rule can be applied\nValidTensSimplifyMatch := function(e1, e2)\n if ObjId(e1)=Tensor and ObjId(e2)=Tensor then \n if CanPullIn(e1._children, e2._children) then \n return true;\n fi;\n fi;\n return false;\nend;\n\n##\n#F CombineReord( <ord1>, <dir1>, <ord2>, <dir2>, <arch> )\n##\n## Combine Reorder steps\nCombineReord := function(ord1, dir1, ord2, dir2, arch)\n local idx, adj1, adj2, adj3, start, n, t1, t2, a, b, new_list, o1, o2;\n adj1 := [];\n adj2 := [];\n if dir1 = -1 then\n idx := 0;\n for o1 in ord1 do \n Add(adj1, [idx, o1]);\n idx := idx + 1;\n od;\n fi;\n if dir1 = 1 then\n idx := 0;\n for o1 in ord1 do \n Add(adj1, [o1, idx]);\n idx := idx + 1;\n od;\n fi;\n if dir2 = -1 then\n idx := 0;\n for o2 in ord2 do \n Add(adj2, [idx, o2]);\n idx := idx + 1;\n od;\n fi;\n if dir2 = 1 then\n idx := 0;\n for o2 in ord2 do \n Add(adj2, [o2, idx]);\n idx := idx + 1;\n od;\n fi;\n # now have adj1 and adj2\n adj3 := [];\n for a in adj1 do \n start := a[1];\n t1 := a[2];\n t2 := -1;\n for b in adj2 do\n if b[1] = t1 then \n t2 := b[2];\n fi;\n od;\n Add(adj3, [start, t2]);\n od;\n # full combine, and then check validity. If it isnt valid, then just dont simplify\n # TODO do a partial recombine if the entire reorder cannot be combined and be still implementable\n # not much harder, just a lot of code\n new_list := [0..Length(ord1)-1];\n idx := 1;\n for n in new_list do \n for a in adj3 do\n if n = a[1] then \n new_list[idx] := a[2];\n fi;\n od;\n idx := idx + 1;\n od;\n if VerifyPath(new_list, [0..Length(ord1)-1], arch) = true then \n return Reord(new_list, arch, 1);\n fi;\n return (Reord(ord1, arch, dir1) * Reord(ord2, arch, dir2));\nend;\n\n##\n#F Quantum_Format ruleset\n## \nClass(Quantum_Format, RuleSet);\nRewriteRules(Quantum_Format, rec(\n # Remove Grp structure \n remove_grp := ARule( Grp, [@(1)], x-> [(@(1).val)] ),\n\n # Flatten Tensors\n flatten_tensor_asoc := ARule(Tensor, [@(1), @(2).cond(e-> ObjId(@(1).val)=Tensor or ObjId(e)=Tensor)],\n\t e -> let(\n\t ch1 := Cond(ObjId(@(1).val)=Tensor, @(1).val._children, [@(1).val]),\n\t ch2 := Cond(ObjId(@(2).val)=Tensor, @(2).val._children, [@(2).val]),\n\t ch1::ch2\n\t )),\n\n #Split identities into I(2)\n split_identity := ARule(Tensor, [@(1), @(2).cond(e-> (CheckIdentitySplit(@(1).val, e)) )],\n\t e -> let(\n\t ch1 := Cond(ObjId(@(1).val)=I and @(1).val.params[1] > 2, Tensor(I(2), I(@(1).val.params[1]/2)), [@(1).val]),\n\t ch2 := Cond(ObjId(@(2).val)=I and @(2).val.params[1] > 2, Tensor(I(2), I(@(2).val.params[1]/2)), [@(2).val]),\n [ch1]::[ch2]\n\t )),\n));\n\n##\n#F Quantum_Simplify ruleset\n## \nClass(Quantum_Simplify, RuleSet);\nRewriteRules(Quantum_Simplify, rec(\n\n # Pull-In Tensors \n pull_in_tensor := ARule(Compose, [@(1), @(2).cond(e-> ValidTensSimplifyMatch(@(1).val, e))],\n\t e -> let(\n # both 1 ans 2 are tensors, can access a list of arguments via _children\n ch := PullInTensor(@(1).val._children, @(2).val._children),\n\t [Tensor(ch[1])]::[Tensor(ch[2])]\n\t )),\n\n # Remove Identity Multiplications\n remove_identity_right := ARule( Compose, [@(1), @(2).cond(e -> ObjId(e)=I)], x-> [(@(1).val)]),\n remove_identity_left := ARule( Compose, [@(1).cond(e -> ObjId(e)=I), @(2)], x-> [(@(2).val)]),\n\n # Cancel Composition of CNOTS\n cancel_cnot := ARule(Compose, [[CNOT, @(1), @(2)], [CNOT, @(3).cond(x -> (x = @(1).val)), @(4).cond(x -> (x = @(2).val))]], x->[I(2^(@(1).val + 1))] ),\n\n # Combine Reorder Compositions\n cancel_reorder := ARule(Compose, [[Reord, @(1), @(2), @(3)], [Reord, @(4), @(5), @(6)]], x-> [CombineReord(@(1).val, @(3).val, @(4).val, @(6).val, @(5).val)]),\n));\n\n\n##\n#F Quantum_Terminate ruleset\n## \nClass(Quantum_Terminate, RuleSet);\nRewriteRules(Quantum_Terminate, rec(\n # Recombine Identities - Good\n recomb_identity := ARule(Tensor, [@(1), @(2).cond(e-> (CheckIdentity(@(1).val, e) ))],\n\t e -> [I(@(1).val.params[1] * @(2).val.params[1])]),\n\n # Remove Identity Multiplications - Good\n remove_identity_right := ARule( Compose, [@(1), @(2).cond(e -> ObjId(e)=I)], x-> [(@(1).val)]),\n remove_identity_left := ARule( Compose, [@(1).cond(e -> ObjId(e)=I), @(2)], x-> [(@(2).val)]),\n\n));\n\n\n##\n#F QuantumRewriteInternal( <s>, <opts> )\n##\n## Rewrites a quantum SPL expression, for internal use\nQuantumRewriteInternal := function (s, opts)\n s := ApplyStrategy(s, [Quantum_Format], BUA, opts); \n s := ApplyStrategy(s, [Quantum_Simplify], BUA, opts);\n s := ApplyStrategy(s, [Quantum_Terminate], BUA, opts);\n return s;\nend;\n\n##\n#F BestCircuitInternal( <t>, <opts> )\n##\n## Finds the best circuit implementing transform t, for internal use\nBestCircuitInternal := function (t, opts)\n local dpopts, best, s;\n dpopts := rec(verbosity := 0, hashTable := HashTableDP()); \n dpopts.measureFunction := (rt, opts) ->\n let(c := SPLRuleTree(rt), # generate SPL Ruletree and then run a collect on CNOTs \n c2 := QuantumRewriteInternal(c, opts),\n Length(Collect(c2, @(1,CNOT)))\n ); \n best := DP(t, dpopts, opts);\n s := QuantumRewriteInternal(SPLRuleTree(best[1].ruletree), opts);\n return s;\nend;\n\n##\n#F TerminateReord( <l>, <arch>, <dir> )\n##\n## Convert a reorder object to CNOTs\nTerminateReord := function (l, arch, dir)\n local mats, mat, dir, spl;\n mats := ShiftMat(l, [0..Length(arch)-1], arch, Length(arch));\n if dir = -1 then \n mat := mats[2];\n fi;\n if dir = 1 then\n mat := mats[1];\n fi;\n # now mat in an unreduced Non-terminal expression\n # we need the SPL expression\n spl := BestCircuitInternal(mat, SpiralDefaults);\n return spl;\nend;\n\n##\n#F Quantum_Reorder ruleset\n## \nClass(Quantum_Reorder, RuleSet);\nRewriteRules(Quantum_Reorder, rec(\n\n # Combine Reorder Compositions\n reorder_convert := Rule([Reord, @(1), @(2), @(3)], x-> TerminateReord(@(1).val, @(2).val, @(3).val)),\n));\n\n\n# ------------------------- For External Use ----------------------------------------\n\n##\n#F QuantumRewrite( <s>, <opts> )\n##\n## Simplifies an SPL expression representing a quantum circuit (s)\nQuantumRewrite := function (s, opts)\n s := ApplyStrategy(s, [Quantum_Format], BUA, opts); \n s := ApplyStrategy(s, [Quantum_Simplify], BUA, opts);\n s := ApplyStrategy(s, [Quantum_Reorder], BUA, opts);\n s := RulesSums(s);\n s := ApplyStrategy(s, [Quantum_Format], BUA, opts); \n s := ApplyStrategy(s, [Quantum_Simplify], BUA, opts);\n s := ApplyStrategy(s, [Quantum_Terminate], BUA, opts);\n return s;\nend;\n\n##\n#F BestCircuit( <t>, <opts> )\n##\n## Finds the best circuit implementing transform t\n## Hardcoded to count number CNOT gates as the cost function\nBestCircuit := function (t, opts)\n local dpopts, best, s, cnot_list;\n dpopts := rec(verbosity := 1, hashTable := HashTableDP()); \n dpopts.measureFunction := (rt, opts) ->\n let(c := SPLRuleTree(rt), # generate SPL Ruletree and then run a collect on CNOTs \n c2 := QuantumRewrite(c, opts),\n Length(Collect(c2, @(1,CNOT)))\n ); \n best := DP(t, dpopts, opts);\n Print(\"\\n SPL \\n\");\n Print(SPLRuleTree(best[1].ruletree));\n Print(\"\\n\");\n s := QuantumRewrite(SPLRuleTree(best[1].ruletree), opts);\n Print(\"\\ncost :\");\n Print(Length(Collect(s, @(1,CNOT))));\n Print(\"\\n\");\n Print(\"---------------- BestCircuit: \\n\");\n return s;\nend;\n\n\n\n\n", "meta": {"hexsha": "a0a7e78606106d0c2dd9f5399597de1ad69942e3", "size": 10880, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "qrewrite.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": "qrewrite.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": "qrewrite.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": 30.4761904762, "max_line_length": 163, "alphanum_fraction": 0.5509191176, "num_tokens": 3439, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. 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	{"text": "\n\nNewRulesFor(PrunedMDPRDFT, rec(\n PrunedMDPRDFT_Base := rec(\n applicable := nt -> Length(nt.params[1]) = 1,\n\n children := nt -> [[ PrunedPRDFT(nt.params[1][1], nt.params[2]).withTags(nt.getTags()) ]],\n\n apply := (nt, C, Nonterms) -> C[1]\n ),\n\n PrunedMDPRDFT_RowCol1 := rec(\n applicable := nt -> Length(nt.params[1]) > 1 and not nt.hasTags(),\n\n children := nt -> [[ PrunedMDDFT(DropLast(nt.params[1], 1), nt.params[3], 1, DropLast(nt.params[2], 1)),\n PrunedPRDFT(Last(nt.params[1]), nt.params[3], 1, Last(nt.params[2])) ]],\n\n apply := (nt, C, cnt) -> RC(Tensor(C[1], I(C[2].dims()[1]/2))) * Tensor(I(Product(List(cnt[1].params[4], i->Length(i)))), C[2])\n )\n));\n\n\nNewRulesFor(PrunedIMDPRDFT, rec(\n PrunedIMDPRDFT_Base := rec(\n applicable := nt -> Length(nt.params[1]) = 1,\n\n children := nt -> [[ PrunedIPRDFT(nt.params[1][1], nt.params[2]).withTags(nt.getTags()) ]],\n\n apply := (nt, C, Nonterms) -> C[1]\n ),\n\n PrunedIMDPRDFT_RowCol1 := rec(\n applicable := nt -> Length(nt.params[1]) > 1 and not nt.hasTags(),\n\n children := nt -> [[ PrunedIPRDFT(Last(nt.params[1]), nt.params[3], 1, Last(nt.params[2])),\n PrunedIMDDFT(DropLast(nt.params[1], 1), nt.params[3], 1, DropLast(nt.params[2], 1)) ]],\n\n apply := (nt, C, cnt) -> Tensor(I(Product(List(cnt[2].params[4], i->Length(i)))), C[1]) * RC(Tensor(C[2], I(C[1].dims()[2]/2)))\n )\n));\n\n\n\n", "meta": {"hexsha": "28cb1fb3701aae461f9dd15e62e5f680d19b5373", "size": 1538, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "breakdown/prune.gi", "max_stars_repo_name": "mikefranusich/spiral-package-fftx", "max_stars_repo_head_hexsha": "a1a355f3764aade9665145aa63c2318201421543", "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": "breakdown/prune.gi", "max_issues_repo_name": "mikefranusich/spiral-package-fftx", "max_issues_repo_head_hexsha": "a1a355f3764aade9665145aa63c2318201421543", "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": "breakdown/prune.gi", "max_forks_repo_name": "mikefranusich/spiral-package-fftx", "max_forks_repo_head_hexsha": "a1a355f3764aade9665145aa63c2318201421543", "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": 34.9545454545, "max_line_length": 136, "alphanum_fraction": 0.5253576073, "num_tokens": 502, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6959583124210896, "lm_q2_score": 0.6150878555160665, "lm_q1q2_score": 0.4280755059156686}}
	{"text": "\n#\n# ---------- Constructors ----------\n#\n\nInstallMethod(Unipotent,\n \"Unipotent element in simple adjoint type\",\n [IsChevalleyAdj,IsList,IsList,IsInt],\n function(sys,coeffs,ordering,order)\n local object;\n \n if Filtered(coeffs,i->not i[2] in Integers)=[] then coeffs:=List(coeffs,i->[i[1],One(ring(sys))i[2]]);\n elif Filtered(coeffs,i->not i[2] in ring(sys))<>[] then Error(\"The coefficients ar not in indicated ring.\"); fi;\n\n object:=Objectify(NewType(NewFamily(\"UnipotentFamily\"),\n IsAttributeStoringRep and\n IsUnipotent and\n IsMultiplicativeElementWithInverse and\n IsMultiplicativeElementWithOne),\n rec());\n\n SetchevalleyAdj(object,sys);\n SetOrdering(object,ordering);\n \n Setcoefficients(object,Canonic(sys,coeffs,ordering));\n# SetInverse(object,InverseOp(object)); This is set at the first call Inverse(obj);\n\n if order = -1 and Characteristic(sys)>0 then\n SetOrder(object,OrderOp(object));\n elif order > -1 then\n SetOrder(object,order);\n fi;\n \n SetName(object,Concatenation(\"<unipotent element for \",type(sys),String(rank(sys)),\n \" in characteristic \",String(Characteristic(sys)),\">\"));\n return object;\nend);\n\nInstallMethod(Unipotent,\n \"Unipotent element in simple adjoint type\",\n [IsChevalleyAdj,IsList,IsList],\n function(sys,coeffs,ordering)\n\n return Unipotent(sys,coeffs,ordering,-2);\nend);\n\nInstallMethod(Unipotent,\n \"Unipotent element in simple adjoint type\",\n [IsChevalleyAdj,IsList,IsInt],\n function(sys,coeffs,order)\n local ordering,tmp,i,slot;\n \n tmp:=ShallowCopy(coeffs);\n Sort(tmp,function(a,b) return a[1]<b[1]; end);\n\n ordering:=[1..Length(positiveRoots(sys))];\n tmp:=List(tmp,i->ordering[i[1]]);\n\n for i in [1..Length(coeffs)] do\n ordering[coeffs[i][1]]:=tmp[i];\n od; \n\n return Unipotent(sys,Filtered(coeffs,i->i[2]<>Zero(ring(sys))),ordering,order);\nend);\n\nInstallMethod(Unipotent,\n \"Unipotent element in simple adjoint type\",\n [IsChevalleyAdj,IsList],\n function(sys,coeffs)\n\n return Unipotent(sys,coeffs,-2);#-1);\nend);\n\nInstallMethod(Unipotent,\n \"Unipotent element in simple adjoint type\",\n [IsNilpotentChv],\n function(e)\n\n return Unipotent(chevalleyAdj(e),coefficients(e));\nend);\n\n\n#\n# ---------- Canonic form of element ----------\n#\n\nInstallMethod(Canonic,\n \"Canonic form of coefficients of unipotent element in given ordering\",\n [IsChevalleyAdj,IsList,IsList],\n function(sys,coeffs,ordering)\n local lista,\n pr,Cijrs,\n flag,i,temp,suma,param,cc,k;\n \n lista:=List(coeffs,i->ShallowCopy(i));\n pr:=positiveRoots(sys);\n\n Cijrs:=C(sys);\n flag:=true;\n while flag do\n flag:=false;\n i:=Length(lista);\n while 0 < i do\n if lista[i][2] = Zero(ring(sys)) then \n Remove(lista,i);\n flag:=true;\n elif 1 < i and lista[i][1] = lista[i-1][1] then\n lista[i-1][2]:=lista[i-1][2]+lista[i][2];\n Remove(lista,i);\n flag:=true;\n elif 1 < i and ordering[lista[i][1]] < ordering[lista[i-1][1]] then\n temp:=lista[i]; lista[i]:=lista[i-1]; lista[i-1]:=temp;\n \n #aici r si s sunt pe pozitia i-1 si repsectiv i\n k:=1;\n for cc in Cijrs[lista[i-1][1]][lista[i][1]] do\n suma:=cc[1]pr[lista[i-1][1]]+cc[2]pr[lista[i][1]];\n param:=cc[3]((-1)^cc[1])(lista[i-1][2]^cc[1])(lista[i][2]^cc[2]);\n Add(lista,[Position(pr,suma),param],i+k);\n k:=k+1;\n od;\n flag:=true;\n fi;\n i:=i-1;\n od;\n od;\n\n return Immutable(lista);\nend);\n\n#\n# ---------- Arithmetic Operations ----------\n#\n\nInstallMethod(InverseMutable,\n \"Inverse of unipotent element\",\n [IsUnipotent],\n function(u)\n local i,lista,len,reverse_order;\n \n lista:=List(coefficients(u),i->StructuralCopy(i));\n len:=Length(lista);\n for i in [1..len] do\n Add(lista,[lista[len-i+1][1],-lista[len-i+1][2]]);\n Remove(lista,len-i+1);\n od;\n\n reverse_order:=function(o)\n local maxim;\n maxim:=Maximum(o);\n return List(o,i->maxim-i+1);\n end;\n \n return Unipotent(chevalleyAdj(u),lista,reverse_order(Ordering(u)),-2);#0);\nend);\n\nInstallMethod(OneMutable,\n \"Inverse of unipotent element\",\n [IsUnipotent],\n function(u)\n\n return One(chevalleyAdj(u),[],0);\nend);\n\nInstallMethod(\\,\n \"Multiplication for unipotent elements ab with the ordering of b\",\n [IsUnipotent,IsUnipotent],\n function(u1,u2)\n local sys1,sys2,\n generic,result,coeffs1,coeffs2,\n APR,avars,pr_len,\n i;\n\n sys1:=chevalleyAdj(u1);\n sys2:=chevalleyAdj(u2);\n if type(sys1)<>type(sys2) or\n rank(sys1)<>rank(sys2) or\n ring(sys1)<>ring(sys2) then Error(\"Not in the same family.\"); fi;\n \n return Unipotent(sys2,Concatenation(coefficients(u1),coefficients(u2)),Ordering(u2));\nend);\n\nInstallMethod(\\,\n \"Action of unipotent element u on nilpotent e: ue\",\n [IsUnipotent,IsNilpotentChv],\n function(u,e)\n local result,\n sys1,sys2,Mrsi,pr,\n uas,r,s,i,pos;\n \n sys1:=chevalleyAdj(u);\n sys2:=chevalleyAdj(e);\n if type(sys1)<>type(sys2) or\n rank(sys1)<>rank(sys2) or\n ring(sys1)<>ring(sys2) then Error(\"Not in the same family.\");\n fi;\n \n pr:=positiveRoots(sys1);\n Mrsi:=M(sys1);\n\n uas:=Reversed(coefficients(u));\n result:=List(coefficients(e),i->ShallowCopy(i));\n\n # for this see Carter pg.64\n for r in uas do\n for s in result do\n for i in [1..Length(Mrsi[r[1]][s[1]])] do\n pos:=Position(pr,ipr[r[1]]+pr[s[1]]);\n result:=Concatenation(result,[[pos,Mrsi[r[1]][s[1]][i]r[2]^is[2]]]);\n od;\n od;\n od;\n\n return NilpotentChv(sys2,result);\nend);\n\nInstallMethod(OrderOp,\n \"Order of unipotent element\",\n [IsUnipotent],\n function(u)\n local result,\n p,u_to_p,putere,i;\n\n if coefficients(u)=[] then return 1; fi;\n\n p:=Characteristic(chevalleyAdj(u));\n\n u_to_p:=u;\n for i in [1..p-1] do u_to_p:=u_to_pu; od;\n\n result:=1;\n putere:=u_to_p;\n while coefficients(putere)<>[] do\n putere:=putereu_to_p;\n result:=result+1;\n od;\n \n return presult;\nend);\n\nInstallMethod(Comm,\n \"Commutator for unipotent elements a^-1b^-1ab with the ordering of b\",\n [IsUnipotent,IsUnipotent],\n function(u1,u2)\n local sys1,sys2;\n\n sys1:=chevalleyAdj(u1);\n sys2:=chevalleyAdj(u2);\n if type(sys1)<>type(sys2) or\n rank(sys1)<>rank(sys2) or\n ring(sys1)<>ring(sys2) then Error(\"Not in the same family.\"); fi;\n return Unipotent(sys2,\n Concatenation(coefficients(u1^-1),coefficients(u2^-1),\n coefficients(u1),coefficients(u2)),\n Ordering(u2));\nend);\n\nInstallMethod(Conj,\n \"Conjugation for unipotent elements b^-1ab with the ordering of b\",\n [IsUnipotent,IsUnipotent],\n function(u1,u2)\n local sys1,sys2;\n\n sys1:=chevalleyAdj(u1);\n sys2:=chevalleyAdj(u2);\n if type(sys1)<>type(sys2) or\n rank(sys1)<>rank(sys2) or\n ring(sys1)<>ring(sys2) then Error(\"Not in the same family.\"); fi;\n return Unipotent(sys2,\n Concatenation(coefficients(u2^-1),coefficients(u1),coefficients(u2)),\n Ordering(u2));\nend);\n\nInstallMethod(Subword,\n \"Subword of a unipotent element by list of roots\",\n [IsUnipotent,IsList],\n function(u,l)\n local coeffs;\n coeffs:=Filtered(coefficients(u),i->i[1] in l);\n \n return Unipotent(chevalleyAdj(u),coeffs,Ordering(u));\nend);\n\nInstallMethod(InsertWord,\n \"Shuffles a word into a unipotent element u according to the ordering of u\",\n [IsUnipotent,IsList],\n function(u,word)\n local coeffs,\n sys,check,ord;\n\n sys:=chevalleyAdj(u);\n check:=ForAll(word,i-> i[2] in ring(sys));\n if not check then\n Error(\"The word cannot be shuffled into u: not over the same ring!\\n\");\n fi;\n\n coeffs:=coefficients(u);\n coeffs:=Concatenation(coeffs,word);\n ord:=Ordering(u);\n Sort(coeffs,function(a,b) return ord[a[1]]<ord[b[1]]; end);\n coeffs:=Canonic(sys,coeffs,ord);\n\n# Setcoefficients(u,coeffs); Doesn't work this way\n\n return Unipotent(sys,coeffs,Ordering(u));\nend);\n\n\n#\n# ---------- Lie Algebra Action ----------\n#\n\nInstallMethod(AduAlphat,\n \"Adu_{alpha}(t) on the whole Lie algebra\",\n [IsChevalleyAdj,IsPosInt,IsRingElement],\n function(sys,root,param)\n local result,\n pr,pr_len,roots,\n A_rs,M_rsi,\n L,CB,Rank,B,cochars,h,\n tmp,zero,unu,s,i,poz;\n\n pr:=positiveRoots(sys);\n pr_len:=Length(pr);\n roots:=Concatenation(pr,-pr);\n \n L:=lieAlgebra(sys);\n CB:=ChevalleyBasis(L);\n Rank:=rank(sys);\n B:=Basis(L);\n cochars:=Cocharacters(L);\n cochars:=List(cochars,i->Coefficients(B,i));\n \n zero:=Zero(ring(sys));\n unu:=One(ring(sys));\n\n A_rs:=A(sys);\n M_rsi:=M(sys);\n\n result:=[];\n # s in positive roots\n for s in [1..pr_len] do\n tmp:=List([1..Dimension(L)],i->zero);\n \n if s = root then\n tmp[s]:=unu;\n else\n tmp[s]:=unu;\n for i in [1..Length(M_rsi[root][s])] do\n poz:=Position(roots,iroots[root]+roots[s]);\n tmp[poz]:=M_rsi[root][s][i]param^i;\n od;\n fi;\n Add(result,tmp);\n od;\n\n # s in negative roots\n for s in [1..pr_len]+pr_len do\n tmp:=List([1..Dimension(L)],i->zero);\n \n if s = root+pr_len then\n # e_{-r}\n tmp[s]:=unu;\n # -t^2e_{r}\n tmp[root]:=-param^2;\n # th_{r}\n tmp:=tmp+paramcochars[root];\n else\n tmp[s]:=unu;\n for i in [1..Length(M_rsi[root][s])] do\n poz:=Position(roots,iroots[root]+roots[s]);\n tmp[poz]:=M_rsi[root][s][i]param^i;\n od;\n fi;\n Add(result,tmp);\n od;\n\n # h_s\n for s in [1..Rank] do\n tmp:=List([1..Dimension(L)],i->zero);\n # h_s\n tmp:=tmp+cochars[s];\n # -A_{sr}te_r\n tmp[root]:=-A_rs[s][root]param;\n Add(result,tmp);\n od;\n\n return result;#TransposedMat(result);\nend);\n\nInstallMethod(Adu,\n \"Adu on the whole Lie algebra\",\n [IsUnipotent],\n function(u)\n return Product(coefficients(u),i->AduAlphat(chevalleyAdj(u),i[1],i[2]));\nend);\n\nInstallMethod(AduJordanBlocksOp,\n \"Computes Jordan Blocks of Adu using SageMath\",\n [IsUnipotent],\n function(u)\n local sage_script,current_dir,tmp_file,result,\n ad,dim,i,j;\n\n sage_script:=Concatenation(\"~/sage/sage-4.7.2-linux-32bit-ubuntu_10.04_lts-i686-Linux/sage \",\n \"~/workspace/ChevalleyAdj/sage/tmp/jordan.sage\");\n current_dir:=Directory(\"~/workspace/ChevalleyAdj/sage/tmp/\");\n tmp_file:=Filename(current_dir,\"matrix.sage\");\n result:=Filename(current_dir,\"blocks.gap\");\n\n #while IsPolynomialRing(ring(chevalleyAdj(u))) do u:=Descend(u,CoefficientsRing(ring(chevalleyAdj(u)))); od;\n if IsAlgebraicU(chevalleyAdj(u)) then u:=Descend(u,chevalleyAdj(chevalleyAdj(u))); fi;\n ad:=Adu(u);\n ad:=List(ad,i->List(i,j->Int(j)));\n PrintTo(tmp_file,\"p=\",String(Characteristic(chevalleyAdj(u))),\"\\nmat=\");\n AppendTo(tmp_file,\"[\");\n dim:=Length(ad);\n for i in [1..dim] do\n AppendTo(tmp_file,\"[\");\n for j in [1..dim] do\n AppendTo(tmp_file,String(ad[i][j]));\n if j<>dim then AppendTo(tmp_file,\",\"); fi;\n od;\n AppendTo(tmp_file,\"]\");\n if i<>dim then AppendTo(tmp_file,\",\\n\"); fi;\n od;\n AppendTo(tmp_file,\"]\");\n\n Exec(sage_script);\n\n result:=ReadAsFunction(result);\n result:=result();\n\n return result;\nend);\n\nInstallMethod(PositiveAdu,\n \"Ad(u) restricted to Lie(U) where U is spanned by positive root groups\",\n [IsUnipotent],\n function(u)\n local result,\n sys,\n baza,b,pr,pr_len;\n\n sys:=chevalleyAdj(u);\n pr:=positiveRoots(sys);\n pr_len:=Length(pr);\n baza:=List([1..pr_len],i->NilpotentChv(sys,[[i,1]]));\n\n result:=[];\n for b in baza do\n result:=Concatenation(result,[ub]);\n od;\n\n return List(result,i->LieAlgebraCoeffs(i){[1..pr_len]});\nend);\n\nInstallMethod(RestrictedAdu,\n \"Ad(u) restricted to a subspace of Lie(U) spanned given (positive) roots\",\n [IsUnipotent,IsList],\n function(u,roots)\n local sys,adu,pr,\n croots,check;\n\n if not IsInt(roots[1]) then TryNextMethod(); fi;\n\n sys:=chevalleyAdj(u);\n adu:=PositiveAdu(u);\n pr:=positiveRoots(sys);\n croots:=Filtered([1..Length(pr)],i->not i in roots);\n\n check:=Filtered(Concatenation(List(croots,i->adu[i]{roots})),j->j<>Zero(ring(sys)));\n if check<>[] then Error(\"Ade cannot be restricted like this.\"); fi;\n check:=Filtered(Concatenation(List(roots,i->adu[i]{croots})),j->j<>Zero(ring(sys)));\n if check<>[] then Error(\"Ade cannot be restricted like this.\"); fi;\n \n return List(roots,i->adu[i]{roots});\nend);\n\nInstallMethod(RestrictedAdu,\n \"Ad(u) restricted to a subspace of Lie(U) spanned given (positive) roots\",\n [IsUnipotent,IsList],\n 1,\n function(u,vectors)\n local result,vectors_len,\n adu,img,\n CPR,cvar_names,cvars,cvectors,sysCPR,uu,\n tmp,generic,relations,relations_len,sol,i;\n\n vectors_len:=Length(vectors);\n\n cvar_names:=List([1..vectors_len],i->Concatenation(\"c_\",String(i)));\n CPR:=PolynomialRing(ring(chevalleyAdj(u)),cvar_names);\n cvars:=IndeterminatesOfPolynomialRing(CPR);\n sysCPR:=ChevalleyAdj(chevalleyAdj(u),CPR);\n\n cvectors:=List(vectors,i->Ascend(i,sysCPR));\n uu:=Ascend(u,sysCPR);\n img:=List(cvectors,i->uui);\n\n result:=[];\n for i in [1..vectors_len] do\n tmp:=ShallowCopy(cvars);\n generic:=Sum(List([1..vectors_len],i->tmp[i]cvectors[i]));\n relations:=List(coefficients(img[i]-generic),i->i[2]);\n relations:=Filtered(relations,i->i<>Zero(CPR));\n #Error(\"!\");\n tmp:=SolveRelations(relations,cvars,tmp,CPR);\n if tmp[2]<>[] then\n #Error(\"!\");\n Print(\"RestrictedAdu: did not solve all relations! \",relations,\"\\n\");\n fi;\n tmp:=List(tmp[1],i->Value(i,cvars,cvars));\n #tmp:=Sum(List([1..vectors_len],i->tmp[i]vectors[i])); # I want the matrix\n Add(result,tmp);\n od;\n\n return result; \nend);\n\nInstallMethod(PositiveFixedspace,\n \"Ker of PositiveAdu\",\n [IsUnipotent],\n function(u)\n local result,\n adu,sys,unu,pr,pr_len,ns;\n\n sys:=chevalleyAdj(u);\n pr:=positiveRoots(sys);\n pr_len:=Length(pr);\n\n adu:=PositiveAdu(u);\n unu:=DiagonalMat(List([1..pr_len],i->One(ring(sys))));\n ns:=NullspaceMat(adu-unu);\n\n result:=List(ns,v->List([1..pr_len],j->[j,v[j]]));\n result:=List(result,i->NilpotentChv(sys,i));\n \n return result;\nend);\n\nInstallMethod(RestrictedFixedspace,\n \"Ker of RestrictedAdu\",\n [IsUnipotent,IsList],\n function(u,roots)\n local result,\n radu,sys,unu,roots_len,ns;\n\n sys:=chevalleyAdj(u);\n roots_len:=Length(roots);\n\n radu:=RestrictedAdu(u,roots);\n unu:=DiagonalMat(List([1..roots_len],i->One(ring(sys))));\n ns:=NullspaceMat(radu-unu);\n\n result:=List(ns,v->List([1..roots_len],j->[roots[j],v[j]]));\n result:=List(result,i->NilpotentChv(sys,i));\n \n return result;\nend);\n\n\n", "meta": {"hexsha": "a1d3fc619e8b254502d90afd9af6b356c5182013", "size": 19936, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "lib/unichv.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/unichv.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/unichv.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": 35.4103019538, "max_line_length": 126, "alphanum_fraction": 0.4629313804, "num_tokens": 4607, "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(JoinDirectSums, RuleSet);\nRewriteRules(JoinDirectSums, rec(\n combine := ARule(Compose, [@(1, DelayedDirectSum), @(2, DelayedDirectSum,\n e -> let(c1:=@(1).val.children(), c2:=e.children(), Length(c1) = Length(c2) and ForAll([1..Length(c1)], i->c1[i].dims()[2] = c2[i].dims()[1]))) ],\n e -> let(c1:=@(1).val.children(), c2:=@(2).val.children(), [ DelayedDirectSum(List([1..Length(c1)], i -> c1[i] * c2[i])) ])\n )\n));\n\nClass(TerminateDirectSums, RuleSet);\nRewriteRules(TerminateDirectSums, rec(\n terminate := Rule(@(1, DelayedDirectSum), e-> DirectSum(@(1).val.children()).sums())\n));\n", "meta": {"hexsha": "964158d586ae0f472c596ce652b5faf1735eff5b", "size": 694, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/sigma/directsum.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/sigma/directsum.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/sigma/directsum.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": 38.5555555556, "max_line_length": 154, "alphanum_fraction": 0.6325648415, "num_tokens": 226, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7090191337850932, "lm_q2_score": 0.600188359260205, "lm_q1q2_score": 0.42554503059056686}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n# ==========================================================================\n# Sparse\n# ==========================================================================\nClass(Sparse, BaseMat, rec(\n new := meth(self, L)\n Constraint(IsList(L));\n\tif not ForAll(L, t -> IsList(t) and Length(t)=3 and \n\t\t IsInt(t[1]) and IsInt(t[2])) then\n\t Error(\"<L> must be a list of triples [i, j, a_(i,j)]\");\n\tfi;\t\n return SPL(WithBases( self, rec( element := L,\n\t\t\t\t dimensions := [ Maximum(List(L, t->t[1])),\n\t\t\t\t Maximum(List(L, t->t[2])) ]\n )));\n end,\n #-----------------------------------------------------------------------\n dims := self >> [ Maximum(List(self.element, t->t[1])), \n\t Maximum(List(self.element, t->t[2])) ],\n #-----------------------------------------------------------------------\n isPermutation := False, \n #-----------------------------------------------------------------------\n isReal := self >> ForAll(self.element, t -> IsRealNumber(t[3])),\n #-----------------------------------------------------------------------\n toAMat := self >> AMatMat(List(MatSparseSPL(self), r -> List(r, EvalScalar))),\n #-----------------------------------------------------------------------\n transpose := meth(self) # we use CopyFields to copy all fields of self\n local L, t;\n\tL := [ ];\n\tfor t in self.element do\n\t Add(L, [t[2], t[1], t[3]]);\n\tod;\n\treturn CopyFields(self, rec(element := L, \n\t\t dimensions := Reversed(self.dims())));\n end,\n conjTranspose := meth(self) # we use CopyFields to copy all fields of self\n local L, t;\n\tL := [ ];\n\tfor t in self.element do\n\t Add(L, [t[2], t[1], Global.Conjugate(t[3])]);\n\tod;\n\treturn CopyFields(self, rec(element := L, \n\t\t dimensions := Reversed(self.dims())));\n end,\n #-----------------------------------------------------------------------\n arithmeticCost := meth(self, costMul, costAddMul)\n local cost, row, elms;\n\tcost := costMul(0) - costMul(0); # will work even when costMul(0) <> 0\n\tfor row in [1..self.dimensions[1]] do\n\t elms := Filtered(self.element, e -> e[1]=row);\n\t if Length(elms) > 0 then\n\t\tcost := cost + costMul(elms[1][3]) \n\t\t + Sum(elms{[2..Length(elms)]}, e -> costAddMul(e[3]));\n\t fi;\n\tod;\n\treturn cost;\n end\n));\n\n", "meta": {"hexsha": "98600b50d9d7c68e417c1239c5f00dd26879f3ca", "size": 2474, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/spl/Sparse.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/Sparse.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/Sparse.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": 38.65625, "max_line_length": 82, "alphanum_fraction": 0.4114793856, "num_tokens": 583, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7090191214879992, "lm_q2_score": 0.600188359260205, "lm_q1q2_score": 0.42554502320999416}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n\n#F RuleTreeOps.\\=( <ruletree1>, <ruletree2> )\n#F returns true if <ruletree1> and <ruletree2> are equal, i.e., they\n#F represent the same breakdown strategy. Otherwise, false is returned.\n#F\n\nRuleTreeOps := CantCopy(OperationsRecord(\"RuleTreeOps\"));\n\n\nIsRuleTree := T -> IsRec(T) and IsBound(T.isRuleTree) and T.isRuleTree;\n\n\n#F Ruletrees\n#F =========\n#F\n#F A ruletree is a record with the following mandatory fields:\n#F\n#F isRuleTree = \"true\" # identifies ruletrees\n#F operations = RuleTreeOps # operations record\n#F node = <spl> # the spl expanded\n#F transposed = false/true # indicates whether <rule> or\n#F transpose - <rule> - transpose\n#F rule = <rule> # the rule chosen\n#F children = <list> # the children, a list of\n#F ruletrees/non-terminal spls\n#F\n#F Note that children can be a list of ruletrees as well as non-terminal spls.\n#F The field children is empty iff the ruletree is a leaf.\n#F In general, the .node is a non-terminal spl that is expanded by .rule.\n#F\n#F The following fields are optional:\n#F splOptions = [ <option1>, <option2>, .. ]\n#F valid <options> : \"unrolled\", \"pcl\"\n#F\n\nClass(RuleTreeClass, rec(\n spl := self >> SPLRuleTree(self),\n measure := self >> SPLRuleTree(self).measure(),\n shortPrint := false,\n dims := self >> self.node.dims(),\n dmn := self >> self.node.dmn(),\n rng := self >> self.node.rng(),\n\n print := meth(self, i, is)\n local ch;\n\n if Length(self.children) = 0 then\n # print leaves in one line\n Print(self.rule, \"( \");\n When (self.transposed, Print(\"\\\"T\\\",\"));\n self.node.print(i+is, is);\n When (IsBound(self.splOptions),\n Print(\", \", self.splOptions, \" )\"),\n Print(\" )\"));\n else\n # print children on separate lines\n Print(self.rule, \"( \",\n When(self.transposed, \"\\\"T\\\", \", \"\"),\n When(not self.shortPrint, self.node.print(i+is, is), \"\"), \",\\n\", Blanks(i+is)\n );\n self.children[1].print(i+is, is);\n for ch in Drop(self.children, 1) do\n Print(\",\\n\", Blanks(i+is));\n ch.print(i+is, is);\n od;\n\n When (IsBound(self.splOptions),\n Print(\"\\n\", Blanks(i), \", \", self.splOptions, \" )\"),\n Print(\" )\"));\n fi;\n end,\n\n # new with tSPL and opts.baseHash:\n # we cannot blindly transpose everything, as vector\n # permutations that are automatically generated\n # may not support transposition\n transpose := self >>\n When((not self.node.transposeSymmetric()) and self.node.isSymmetric(),\n self,\n RuleTree(\n self.rule,\n When(self.transposed, \"\", \"T\"),\n self.node.transpose(),\n List(self.children, x->x.transpose())\n )\n ),\n # RuleTreeRewriting enabled by default\n # one can disable it with \"EnableRuleTreeRewriting(false)\"\n rChildren := (self) >> [ self.node, self.children ],\n rSetChild := rSetChildFields(\"node\", \"children\"),\n from_rChildren := (self, rch) >>\n RuleTree(self.rule, When(self.transposed, \"T\", \"\"), rch[1], rch[2])\n));\n\nRuleTreeOps.\\= := function( T1, T2 )\n return\n IsRuleTree(T1) and IsRuleTree(T2) and\n T1.rule = T2.rule and\n T1.transposed = T2.transposed and\n IsIdenticalSPL(T1.node, T2.node) and\n T1.children = T2.children and\n ( ( IsBound(T1.splOptions) and \n\t\t IsBound(T2.splOptions) and\n T1.splOptions = T2.splOptions\n\t\t\t) or\n ( not IsBound(T1.splOptions) and \n\t\t\t not IsBound(T2.splOptions)\n\t\t\t)\n );\nend;\n\n#F RuleTreeNC( <rule>, <non-terminal spl>, <children> )\n#F returns the corresponding ruletree without any checking.\n\nRuleTreeNC := function ( R, S, C )\n return WithBases(RuleTreeClass,\n rec(\n isRuleTree := true,\n operations := RuleTreeOps,\n node := S,\n transposed := false,\n rule := R,\n children := C\n\t\t)\n );\nend;\n\n\n#F RuleTree(\n#F <rule>,\n#F [ \"T\" ,]\n#F <non-terminal spl>\n#F [, <children> ]\n#F [, <list-of-sploptions> ]\n#F )\n#F\n#F Creates a ruletree for <non-terminal spl>\n#F using <rule> with <children>. The <children> can be non-terminal spls\n#F or ruletrees. It is checked whether <children> can be derived\n#F from <non-terminal spl> using <rule>.\n#F If the string \"T\" is supplied, then instead of <rule>, the\n#F sequence transpose - <rule> - transpose is denoted. In this case\n#F <non-terminal spl> and <children> are also transposed. This construction\n#F avoids unnecessary recoding of rules that are just transposes of\n#F other rules. In this case, <rule> must have the field\n#F .forTransposition set to true.\n#F\n#F The argument <list-of-sploptions> provides options used for spl compilation.\n#F See top of this file for valid options; examples are \"unrolled\" and \"pcl\".\n#F <children> might be empty (default) in which case the ruletree\n#F returned is a leaf.\n#F\nRuleTree := function ( arg )\n local a, R, t, S, C, u, S1, C1, RT;\n S := false;\n t := false;\n u := [ ];\n C := [ ];\n R := false;\n\n for a in arg do\n if IsString(a) and a = \"T\" then \n\t t := true;\n elif IsList(a) and ForAll(a, IsString) then \n\t u := a;\n elif IsSPL(a) then\n\t\t\tif S=false then \n\t\t\t\tS := a;\n\t\t\telse \n\t\t\t\tAdd(C, a); \n\t\t\tfi;\n\t\telif IsRuleTree(a) then \n\t\t\tAdd(C, a);\n\t\telif IsList(a) then \n\t\t\tAppend(C, a);\n\t\telif IsRule(a) and R=false then \n\t\t\tR := a;\n\t\telse Error(\n\t\t\t\"usage: \\n\",\n\t\t\t\" RuleTree( \\n\",\n\t\t\t\" <rule>, [ \\\"T\\\" ,] <non-terminal spl> \\n\",\n\t\t\t\" [, <children> ] [, <list-of-sploptions> ] )\");\n\n\t\tfi;\n od;\n\n Constraint(IsRule(R));\n Constraint(IsSPL(S));\n\n if not IsList(u) and ForAll(u, IsString) then\n Error(\"<u> must be a list of spl options\");\n elif not (IsList(C) and ForAll(C, c -> IsSPL(c) or IsRuleTree(c))) then\n Error(\"<C> must be a list of ruletrees or non-terminal spls\");\n fi;\n\n RT := RuleTreeNC(R, S, C);\n if u <> [ ]\n\t then RT.splOptions := u;\n\tfi;\n return RT;\nend;\n\n\n#F ExtractChildrenSPL ( <spl> )\n#F returns the list of non-terminal spls contained in <spl>.\n#F The order is left first - depth first (non-terminals are\n#F always leaves.\n#F\nExtractChildrenSPL := S -> Collect(S, @.cond(IsNonTerminal));\n\n\n#F CopyRuleTree( <ruletree> )\n#F returns a copy of <ruletree>. All fields apart from .children\n#F are copied by reference.\n#F\nCopyRuleTree := function( orig )\n local new;\n new := ShallowCopy(orig);\n if IsRuleTree(new) then \n\t new.children := List(orig.children, CopyRuleTree);\n\tfi;\n return new;\nend;\n\n_matchChildren := (C1, C2) ->\n Length(C1)=Length(C2) and\n ForAll([1..Length(C1)],\n j -> IsHashIdenticalSPL(HashAsSPL(C1[j]), HashAsSPL(C2[j])) or\n (ObjId(C1[j])=InfoNt and ObjId(C2[j])=InfoNt));\n\n#F ApplyRuleTreeSPL( <ruletree>, <spl>, <opts> )\n#F creates a ruletree for <spl> using rules from the <ruletree>\n#F (if possible)\n#F Uses: opts.breakdownRules (for backwards compatibility of R.switch only)\nApplyRuleTreeSPL := function ( rtree, spl, opts )\n local i, R, C, C1, CC, children, L;\n Constraint(IsRuleTree(rtree));\n Constraint(IsSPL(spl));\n\n if rtree.transposed then\n return ApplyRuleTreeSPL(rtree.transpose(), spl.transpose(), opts).transpose();\n fi;\n\n R := rtree.rule;\n children:=[];\n\n # if <spl> was not compatible with <ruletree>.node to start with\n # then at some point there will be a split in <ruletree> that is not\n # applicable to the generated ruletree.\n if not IsApplicableRule( R, spl, opts.breakdownRules ) then\n Error(\"<rtree> can not be expanded from <spl>\");\n fi;\n\n # determine the right set of children from allChildren to be used\n # in expansion\n C1 := _allChildren(R, rtree.node, opts);\n C := List([1..Length(rtree.children)], c -> rtree.children[c].node);\n i := PositionProperty([1..Length(C1)], j -> _matchChildren(C1[j], C));\n\n # DEBUG HACK: AppendTo(\"applytree\", R, \"\\n\", C, \"\\n\", C1, \"\\n---------\\n\");\n if i = false then\n Error(\"<ruletree> can not be expanded from <spl>, could not find matching children\"); \n\tfi;\n\n # determine all children for <spl> and pick the right set\n L := _allChildren(R, spl, opts);\n if i > Length(L) then\n Error(\"<ruletree> can not be expanded from <spl>\");\n else\n C1 := L[i];\n fi;\n\n # recurse and return\n children := List([1..Length(rtree.children)], i -> ApplyRuleTreeSPL(rtree.children[i], C1[i], opts));\n\n return RuleTreeNC(R, spl, children);\nend;\n\n\n#F Printing RuleTrees\n#F ------------------\n#F\n\n#F RuleTreeOps.Print( <ruletree> [, <indent> , <indentStep> ] )\n#F prints <ruletree> with <indent>. Further indenting is done\n#F in steps of size <indentStep>. The default is\n#F indent = 0, indentStep = 2.\n#F\nRuleTreeOps.Print := function ( arg )\n local T, indent, indentStep; \n\tif Length(arg) = 1 then\n T := arg[1];\n indent := 0;\n indentStep := 2;\n elif Length(arg) = 3 then\n T := arg[1];\n indent := arg[2];\n indentStep := arg[3];\n else\n Error(\"usage: RuleTreeOps.Print( <ruletree> [, <indent> , <indentStep> ] )\");\n fi;\n Constraint(IsRuleTree(T));\n Constraint(IsPosInt0(indent));\n Constraint(IsPosInt0(indentStep));\n T.print(indent, indentStep);\nend;\n\nPrintRuleTreeCustom := function (T, i, is, spl_print, ruletree_print)\n local ch;\n Constraint(IsRuleTree(T) or IsSPL(T));\n Constraint(IsPosInt0(i));\n Constraint(IsPosInt0(is));\n\n if IsSPL(T) then \n spl_print(T);\n else # T is a ruletree\n Print(Blanks(i), ruletree_print(T), \"\\n\");\n for ch in T.children do\n PrintRuleTreeCustom(ch, i+is, is, spl_print, ruletree_print);\n od;\n fi;\nend;\n\n#F PrintNodesRuleTree(\n#F <ruletree/non-terminal spl> [, <indent> , <indentStep> ]\n#F )\n#F pretty prints <ruletree> by displaying only the nodes (non-terminals)\n#F and its parameters. The tree structure is expressed by indentation.\n#F Non-terminals are being marked by (nt).\n#F\n\nPrintNodesRuleTree := function ( arg )\n local T, i, is;\n if Length(arg) = 1 then\n T := arg[1]; \n\t\ti := 0; \n\t\tis := 2;\n elif Length(arg) = 3 then\n T := arg[1];\n\t\ti := arg[2];\n\t\tis := arg[3];\n else\n Error(\"usage: PrintNodesRuleTree( <ruletree> [, <indent> , <indentStep> ] )\");\n fi;\n PrintRuleTreeCustom(T, i, is,\n T -> Print(T, \" (nt)\"),\n T -> Print(T.node));\nend;\n\n\n#F PrintRulesRuleTree(\n#F <ruletree/non-terminal spl> [, <indent> , <indentStep> ]\n#F )\n#F pretty prints <ruletree> by displaying only the rules and\n#F the node sizes in parentheses. Transposed rules are marked\n#F by ^T. The tree structure is expressed by indentation.\n#F Non-terminals are denoted by nt.\n#F\nPrintRulesRuleTree := function(arg)\n local T, i, is;\n if Length(arg) = 1 then\n T := arg[1]; i := 0; is := 2;\n elif Length(arg) = 3 then\n T := arg[1]; i := arg[2]; is := arg[3];\n else\n Error(\"usage: PrintRulesRuleTree( <ruletree> [, <indent> , <indentStep> ] )\");\n fi;\n PrintRuleTreeCustom(T, i, is,\n T -> Print(\"nt (\", T.dimensions[1], \")\"),\n T -> Print(T.rule, When(T.transposed,\" ^ T\",\"\"), \"(\", T.node.dimensions[1], \")\"));\nend;\n\n\n\n#F PrettyPrintRuleTree(\n#F <ruletree/non-terminal spl> [, <whiteIndent> [, <linedIndent> ] ]\n#F )\n#F pretty prints <ruletree> by displaying only the nodes (non-terminals),\n#F their parameters, and the rules. The tree structure is expressed by\n#F indentation. Non-terminals are being marked by (nt).\n#F\n\nPrettyPrintRuleTree := function ( arg )\n local T, chIndent, whiteIndent, linedIndent, oldLinedIndent, newline, params, i;\n\n # new line plus indents\n newline := function ( )\n local i;\n\n Print(\"\\n\");\n for i in [1..whiteIndent] do\n Print(\" \");\n od;\n if not linedIndent = \"\" then\n Print( linedIndent, \"--\" );\n fi;\n end;\n\n # decode arg\n if Length(arg) = 1 then\n T := arg[1];\n whiteIndent := 0;\n linedIndent := \"\";\n elif Length(arg) = 2 then\n T := arg[1];\n whiteIndent := arg[2];\n linedIndent := \"\";\n elif Length(arg) = 3 then\n T := arg[1];\n whiteIndent := arg[2];\n linedIndent := arg[3];\n else\n Error(\"usage: PrintNodesRuleTree( <ruletree> [, <indent> , <indentStep> ] )\");\n fi;\n\n # check arguments\n if not ( IsRuleTree(T) or IsSPL(T) and T.type = \"nonTerminal\" ) then\n Error(\"<T> must be a ruletree or a non-terminal spl\");\n fi;\n if not IsInt(whiteIndent) and whiteIndent >= 0 then\n Error(\"<whiteIndent> must be pos-int\");\n fi;\n if not IsString(linedIndent) then\n Error(\"<linedIndent> must be a string\");\n fi;\n\n chIndent := whiteIndent+Length(linedIndent)+4;\n # spl case\n if IsSPL(T) then\n T.print(chIndent, 2); Print(\" (nt)\");\n return;\n fi;\n \n T.node.print(chIndent, 2);\n Print(\" {\" );\n Print(T.rule);\n if T.transposed then\n Print(\" ^ T\");\n fi;\n if IsBound(T.splOptions) then\n Print(\", \", T.splOptions);\n fi;\n Print( \"}\" );\n\n if Length(T.children) > 0 then\n if linedIndent = \"\" then\n oldLinedIndent := linedIndent;\n else\n oldLinedIndent := Concatenation( linedIndent, \" \" );\n fi;\n linedIndent := Concatenation( oldLinedIndent, \" \|\" );\n for i in [1..Length(T.children)-1] do\n newline();\n PrettyPrintRuleTree(T.children[i], whiteIndent, linedIndent);\n od;\n linedIndent := Concatenation( oldLinedIndent, \" \\`\" );\n newline();\n linedIndent := Concatenation( oldLinedIndent, \" \" );\n PrettyPrintRuleTree(T.children[Length(T.children)],\n whiteIndent, linedIndent);\n linedIndent := oldLinedIndent;\n fi;\n if whiteIndent = 0 and linedIndent = \"\" then\n newline();\n fi;\nend;\n\n\n#F Converting RuleTrees\n#F --------------------\n#F\n\n#F AMatRuleTree( <ruletree> ) - returns an amat corresponding to ruletree.\n#F\nAMatRuleTree := T -> AMatSPL(SPLRuleTree(T));\n\n#F MatRuleTree( <ruletree> ) - returns the matrix corresponding to ruletree.\n#F\nMatRuleTree := T -> MatSPL(SPLRuleTree(T));\n\n\n#F Creating Random RuleTrees\n#F -------------------------\n#F\n\nDeclare(SemiRandomRuleTree, _SemiRandomRuleTree);\n\n#F RandomRuleTree( <spl> , <opts>)\n#F returns a random rule tree for <spl>\n#F or 'false' if no breakdown rule combination leads to a\n#F fully expanded ruletree.\n#F\n#F Uses: opts.baseHashes\n#F opts.breakdownRules\n#F Optional: (see Doc(_allChildren) ) for usage\n#F opts.restrictSplit\n#F opts.restrictSplitSize\n#F\nRandomRuleTree := (spl, opts) -> _SemiRandomRuleTree(spl, false, s->false, opts);\n\nRandomRuleTreeCutoff := (spl, cutoff_func, opts) -> _SemiRandomRuleTree(spl, false, cutoff_func, opts);\n\nRandomRuleTreeDP := (t, opts) -> let(res := spiral.search.DP(t, rec(measureFunction := (R,O)->Random([1..10000]), verbosity := 0), opts), When(res = [], false, res[1].ruletree));\n\n#F SemiRandomRuleTree( <spl>, <top_rule>, opts )\n#F returns a random rule tree for <spl> with fixed top-level rule\n#F or 'false' if no breakdown rule combination leads to a\n#F fully expanded ruletree.\n#F\n#F Uses: opts.baseHashes\n#F opts.breakdownRules\n#F Optional: (see Doc(_allChildren) ) for usage\n#F opts.restrictSplit\n#F opts.restrictSplitSize\n#F\nSemiRandomRuleTree := (spl, top_rule, opts) -> _SemiRandomRuleTree(spl, top_rule, s->false, opts);\n\n\n_SemiRandomRuleTree := function(spl, top_rule, cutoff_func, opts)\n local ch, i, R, rules, rule, rand, candidates, ch, children, ch_candidates;\n\n if not (IsSPL(spl)) then\n Error(\"usage: SemiRandomRuleTree( <spl>, <top_rule>, <cutoff>, <opts> )\");\n elif cutoff_func(spl) then\n\t return spl;\n elif MultiHashLookup(opts.baseHashes, spl) <> false then\n return MultiHashLookup(opts.baseHashes, spl)[1].ruletree;\n else\n if top_rule <> false then\n rules := [top_rule];\n else\n rules := AllApplicableRulesDirect(spl, opts.breakdownRules);\n if rules = [ ] then\n return false;\n fi;\n fi;\n\n candidates := Set([1..(Length(rules))]);\n while candidates <> [] do\n rand := RandomList(candidates);\n RemoveSet(candidates, rand);\n\n if rand <= Length(rules) then\n rule := rules[rand];\n ch_candidates := _allChildren(rule, spl,opts);\n ch_candidates := Permuted(ch_candidates, Random(SymmetricGroup(Length(ch_candidates))));\n for children in ch_candidates do\n children := List( children, s -> _SemiRandomRuleTree(s, false, cutoff_func, opts) );\n if not ForAny(children, c -> IsBool(c) and c=false) then\n return RuleTreeNC( rule, spl, children );\n fi;\n od;\n fi;\n od;\n return false;\n fi;\nend;\n\n\n#F Creating all RuleTrees\n#F ----------------------\n#F\n#ExpandSPLRules := function( S, ruleset )\nExpandSPLRules := function( arg )\n local i, L, R, S, ruleset, opts;\n S := arg[1];\n ruleset := arg[2];\n Constraint(IsSPL(S));\n\n if IsBound(arg[3]) then\n\t opts := arg[3];\n else \n\t opts := rec();\n\tfi;\n\n L := [ ];\n for R in AllApplicableRulesDirect(S, ruleset) do\n Append(L, List(_allChildren(R,S,opts), c -> RuleTreeNC(R, S, c)));\n od;\n\n return L;\nend;\n\n#F ExpandSPL( <spl>, <opts> )\n#F performs one expansion of <spl> in all possible ways,\n#F and returns the list of the derived ruletrees.\n#F If there are no breakdown rules for <spl> (i.e., not a non-terminal)\n#F then the default base cases rule @_Base is used, which means that\n#F the recursion will continue on its children\n#F\n#F Uses: opts.baseHashes\n#F opts.breakdownRules\n#F\nExpandSPL := (S, opts) -> ExpandSPLRules(S, opts.breakdownRules, opts);\n\n\n_AllRuleTrees := function ( S, cutoff, memohash, opts )\n local L, L1, T, Lc, i, cs, T1, lkup;\n\n # check cutoff, baseHashes, and our memoization hash\n if cutoff(S) then\n\t\treturn [S];\n\tfi;\n lkup := MultiHashLookup(opts.baseHashes, S);\n if lkup <> false then\n\t\treturn [lkup[1].ruletree];\n\tfi;\n\n lkup := HashLookup(memohash, S);\n if lkup <> false\n\t\tthen return lkup;\n\tfi;\n\n L := ExpandSPL(S, opts);\n if ForAll(L, r -> r.children = [ ]) then\n\t\tHashAdd(memohash, S, L);\n\t\treturn L;\n fi;\n\n L1 := [ ];\n for T in L do\n Lc := [ ];\n\t\tfor i in [1..Length(T.children)] do\n Lc[i] := _AllRuleTrees(T.children[i], cutoff, memohash, opts);\n\t\tod;\n\t\tfor cs in Cartesian(Lc) do\n T1 := ShallowCopy(T);\n\t\t\tT1.children := cs;\n\t\t\tAdd(L1, T1);\n\t\tod;\n od;\n\n HashAdd(memohash, S, L1);\n return L1;\nend;\n\n#F AllRuleTrees( <spl>, <opts> )\n#F expands <spl> in all possible ways and returns the obtained list\n#F of fully expanded ruletrees (ruletrees containing no non-terminals).\n#F Note that subtrees are \"by reference\", i.e., modifying one subtree\n#F alters the same subtree in some other expansions.\n#F\n#F Uses: opts.baseHashes\n#F opts.breakdownRules\n#F Optional: (see Doc(_allChildren) ) for usage\n#F opts.restrictSplit\n#F opts.restrictSplitSize\n#F\nAllRuleTrees := (S, opts) -> _AllRuleTrees(S, x->false, HashTableSPL(), opts);\n\n#F AllRuleTreesCutoff( <spl>, <cutoff_func>, <opts> )\n#F expands <spl> in all possible ways and returns the obtained list\n#F of fully expanded ruletrees (ruletrees containing no non-terminals).\n#F Note that subtrees are \"by reference\", i.e., modifying one subtree\n#F alters the same subtree in some other expansions.\n#F <cutoff_func> is of the form e -> e = <cutoff>\n#F\n#F Uses: opts.baseHashes\n#F opts.breakdownRules\n#F\nAllRuleTreesCutoff := (S, cutoff_func, opts) -> _AllRuleTrees(S, cutoff_func, HashTableSPL(), opts);\n\n\n\n_NofRuleTrees := function ( S, cutoff, memohash, opts, level, trace )\n local p, Cs, n, lkup, indentstr, i;\n Constraint(IsSPL(S));\n Constraint(IsRec(opts));\n\n if trace then\n indentstr := \"\";\n for i in [2..level] do\n indentstr := Concat(indentstr, \". \");\n od;\n indentstr := Concat(indentstr, String(level), \" \");\n Print(indentstr, \">> _NofRuleTrees(\", S, \")\\n\");\n fi;\n\n # check cutoff, baseHashes, and our memoization hash\n if cutoff(S) then\n if trace then\n Print(indentstr, \"<< (cutoff) 1\\n\");\n fi;\n return 1; \n fi;\n if MultiHashLookup(opts.baseHashes, S) <> false then\n if trace then\n Print(indentstr, \"<< (MultiHashLookup) 1\\n\");\n fi;\n return 1; \n fi;\n lkup := HashLookup(memohash, S);\n if lkup <> false then\n if trace then\n Print(indentstr, \"<< hashed: \", lkup, \"\\n\");\n fi;\n return lkup; \n fi;\n\n # first apply rules as they are\n Cs := List(AllApplicableRulesDirect(S, opts.breakdownRules), r -> _allChildren(r,S, opts));\n\tif trace then\n Print(indentstr, \" Cs: \", Cs, \"\\n\");\n fi;\n\n if Cs = [ [ ] ] then\n n := 1;\n else\n n := Sum(Cs, c -> Sum(c, l -> Product(l, x -> _NofRuleTrees(x, cutoff, memohash, opts, level+1, trace))));\n fi;\n\n HashAdd(memohash, S, n);\n \n if trace then\n Print(indentstr, \"<< (\", S, \") \", n, \"\\n\");\n fi;\n \n return n;\nend;\n\n#F NofRuleTrees ( <spl>, <opts> )\n#F returns the number of ruletrees for <spl>.\n#F\n#F Uses: opts.baseHashes\n#F opts.breakdownRules\n#F Optional: (see Doc(_allChildren) ) for usage\n#F opts.restrictSplit\n#F opts.restrictSplitSize\n#F\n#F if opts.verbosity > 3 prints trace info\n\nNofRuleTrees := (spl, opts) -> _NofRuleTrees(spl, x->false, HashTableSPL(), opts, 1, IsBound(opts.verbosity) and (opts.verbosity > 3));\n\nNofRuleTreesCutoff := (spl, cutoff_func, opts) -> _NofRuleTrees(spl, cutoff_func, HashTableSPL(), opts, 1, IsBound(opts.verbosity) and (opts.verbosity > 3));\n\n\n#F RulesInRuleTree( <ruletree> )\n#F return the set of rules contained in <ruletree>.\n#F\nRulesInRuleTree := function ( T )\n local C;\n Constraint(IsRuleTree(T));\n\n # base case\n if T.children = [ ] then\n\t return Set([T.rule]);\n\tfi;\n\n # recurse with ruletree children\n C := Filtered(T.children, IsRuleTree);\n C := Set(Concatenation(List(C, RulesInRuleTree)));\n AddSet(C, T.rule);\n return C;\nend;\n\n\n#F RulesInRuleTreeAll( <ruletree> )\n#F return the histogram of all rules contained in <ruletree> as set\n#F of pairs [rule, number].\n#F\nRulesInRuleTreeAll := function ( T )\n local C, C1, c, i;\n Constraint(IsRuleTree(T));\n\n # base case\n if T.children = [ ] then\n\t return Set([ [T.rule, 1] ]);\n\tfi;\n\n # recurse with ruletree children\n C := Filtered(T.children, IsRuleTree);\n C := Concatenation(List(C, RulesInRuleTreeAll));\n\n # merge\n C1 := [ ];\n for c in C do\n i := PositionProperty(C1, p -> c[1] = p[1]);\n if i = false then\n AddSet(C1, c);\n else\n C1[i][2] := C1[i][2] + c[2];\n fi;\n od;\n\n i := PositionProperty(C1, p -> p[1] = T.rule);\n if i = false then\n AddSet(C1, [T.rule, 1]);\n else\n C1[i][2] := C1[i][2] + 1;\n fi;\n return C1;\nend;\n\n\nApplyRuleTreeStep := function ( rt, recurse )\n local nt, C, Nonterms, S, c;\n if IsNonTerminal(rt) or IsSPL(rt) then \n\t return rt;\n\tfi;\n\n Constraint(IsRuleTree(rt));\n\n C := List(rt.children, recurse);\n nt := rt.node;\n Nonterms := List(rt.children, c -> When(IsRuleTree(c), c.node, c));\n\n if rt.transposed then\n nt := TransposedSPL(nt);\n C := List(C, TransposedSPL);\n Nonterms := List(Nonterms, TransposedSPL);\n fi;\n\n S := _apply(rt.rule, nt, C, Nonterms);\n if rt.transposed then \n\t S := TransposedSPL(S); \n\tfi;\n\n trace_log.addTreeExpansion(rt.rule,nt,S,rt.children,CopyFields(rt.node, rec(params := C)), var);\n\n S.root := rt.node;\n return S;\nend;\n\nSPLRuleTreeStep := rt -> ApplyRuleTreeStep(rt, c -> RecursStep(\n When(IsRuleTree(c), RTWrap(c), c)));\n\n_SPLRuleTree := rt -> ApplyRuleTreeStep(rt, _SPLRuleTree);\n\nSPLRuleTree := function(rt)\n local spl, t, tag;\n trace_log.beginStage(\"tSPL\",\"SPL\", rt.node); \n spl := ApplyRuleTreeStep(rt, _SPLRuleTree);\n\n # tags may inject container objects\n t := rt.node;\n if IsBound(t.getTags) then\n for tag in Reversed(t.getTags()) do\n if IsBound(tag.container)\n\t\t\t then spl := tag.container(spl);\n\t\t\tfi;\n od;\n fi;\n trace_log.endStage(\"tSPL\",\"SPL\", spl); \n return spl;\nend;\n\n# forward declaration for function that does all the work.\nDeclare(_ruleTreeN);\n\n#F RandomRuleTrees( <spl>, <num>, <opts>)\n#F returns <num> random rule trees for <spl>\n#F uniformly distributed amongst the potential trees\n#F or 'false' if no breakdown rule combination leads to a\n#F fully expanded ruletree.\n#F\n#F Uses: opts.baseHashes\n#F opts.breakdownRules\n#F Optional: (see Doc(_allChildren) ) for usage\n#F\nRandomRuleTrees := function(spl, num, opts)\n local n, rand, memohash;\n\n memohash := HashTableSPL();\n\n n := _NofRuleTrees(spl, s -> false, memohash, opts, 1, false);\n\n if num >= n then\n rand := [1..n];\n else\n rand := [];\n while Length(rand) <> num do\n rand := Set(Concat(rand, [RandomList([1..n])]));\n od;\n fi;\n\n return List(rand, e -> _ruleTreeN(spl, e-1, memohash, opts));\nend;\n\n# helper functions/arrays for _ruleTreeN and _ruleTree1\n\n_getNumTrees := (s, memohash, opts) -> let(\n n := HashLookup(memohash, s), \n When(n = false,\n _NofRuleTrees(s, e -> false, memohash, opts, 1, false),\n n\n )\n);\n#F RuleTreeN(<spl>, <num>, <opts>)\n#F returns ruletree of index <num>\n#F\n#F Uses: opts.basHashes, opts.breakdownRules.\n#F\nRuleTreeN := function(spl, num, opts)\n local memohash, n, r;\n\n memohash := HashTableSPL();\n n := _NofRuleTrees(spl, s -> false, memohash, opts, 1, false);\n\n if num in [1..n] then\n r := _ruleTreeN(spl, num-1, memohash, opts);\n\n else\n r := false;\n fi;\n\n return r;\nend;\n\n\n# fold list inside out, favoring the right hand side\n\n_foldedMidFirst := function(origlist)\n\tlocal len, midpt, front, back, newlist;\n\t\n\tlen := Length(origlist);\n\tif len < 2 then\n\t\treturn origlist;\n\tfi;\n\tmidpt := Int(len/2);\n\tfront := Reversed(Sublist(origlist, [1..midpt]));\n\tback := Sublist(origlist, [midpt+1..len]);\n\t\n\tnewlist := [];\n\t\n\tif IsOddInt(len) then\n\t\tAppend(newlist, [back[1]]);\n\t\tback := Drop(back,1);\n\tfi;\n\t\n\twhile (front <> []) or (back <> []) do\n\t\tif back <> [] then\n\t\t\tAppend(newlist, [back[1]]);\n\t\t\tback := Drop(back,1);\n\t\tfi;\n\t\tif front <> [] then\n\t\t\tAppend(newlist, [front[1]]);\n\t\t\tfront := Drop(front, 1);\n\t\tfi;\t\n\tod;\n\t\n\treturn newlist;\nend;\n\n\nDeclare(_ruleTreeMid);\n\n#F RuleTreeMid(spl, opts)\n#F\n#F Similar to RuleTree1, but tries to grab the middle of each range of choices\n#F \n\nRuleTreeMid := (spl, opts) -> _ruleTreeMid(spl, HashTableSPL(), opts);\n\n_ruleTreeMid := function(spl, memohash, opts)\n local h, R, r, C, c, ch, npc, idx, idxlist, ridx, ridxlist;\n\n h := MultiHashLookup(opts.baseHashes, spl);\n\n if h <> false then\n return h[1].ruletree;\n fi;\n\n R := AllApplicableRulesDirect(spl, opts.breakdownRules);\n\tridxlist := [1..Length(R)];\n\tif Length(ridxlist) > 1 then\n\t\tif Length(_allChildren(R[1], spl, opts)) < 2 then\n\t\t\tridxlist := _foldedMidFirst(ridxlist);\n\t\tfi;\n\tfi;\n for ridx in ridxlist do\n\t\tr := R[ridx];\n\t\tC := _allChildren(r, spl, opts);\n\t\tidxlist := _foldedMidFirst([1..Length(C)]);\n\t\tfor idx in idxlist do \n\t\t\tc := C[idx];\n\t\t\tnpc := Product(c, e -> _getNumTrees(e, memohash, opts));\n\t\t\tif npc > 0 then\n\t\t\t\tch := List(c, e -> _ruleTreeMid(e, memohash, opts));\n\t\t\t\tif not ForAny(ch, e -> IsBool(e) and e=false) then\n\t\t\t\t\treturn RuleTreeNC(r, spl, ch);\n\t\t\t\tfi;\n\t\t\tfi;\n\n od;\n od;\n\t# no tree, return original spl\n return spl;\nend;\n\n\nDeclare(_ruleTree1);\n\n#F RuleTree1(spl, opts)\n#F\n#F returns the first ruletree. this is often useful for\n#F testing whether a particular rule is firing, and you\n#F want to avoid the randomness of RandomRuleTree\n#F\n#F NOTE: this function does not check if a tree can\n#F actually just be created, it just tries to return\n#F the first one. RuleTreeN(spl, 1, opts) does the\n#F same thing but first checks.\n#F \n\nRuleTree1 := (spl, opts) -> _ruleTree1(spl, HashTableSPL(), opts);\n\n_ruleTree1 := function(spl, memohash, opts)\n local h, R, r, i, c, ch, npc;\n\n h := MultiHashLookup(opts.baseHashes, spl);\n\n if h <> false then\n return h[1].ruletree;\n fi;\n\n R := AllApplicableRulesDirect(spl, opts.breakdownRules);\n for r in R do\n\t\tfor c in _allChildren(r, spl, opts) do \n\t\t\tnpc := Product(c, e -> _getNumTrees(e, memohash, opts));\n\t\t\tif npc > 0 then\n\t\t\t\tch := List(c, e -> _ruleTree1(e, memohash, opts));\n\t\t\t\tif not ForAny(ch, e -> IsBool(e) and e=false) then\n\t\t\t\t\treturn RuleTreeNC(r, spl, ch);\n\t\t\t\tfi;\n\t\t\tfi;\n od;\n od;\n\t# no tree, return original spl\n return spl;\nend;\n \n\n#F _ruleTreeN(<spl>, <num>, <memohash>, <opts>)\n#F internal function which returns a ruletree for \n#F <spl> with index given by <num>. This is a recursive\n#F routine. Note that <num> is 0-based, unlike everything\n#F else in SPIRAL, which is 1-based.\n#F \n_ruleTreeN := function(spl, num, memohash, opts)\n local R, rtNC, h, r, c, npc, off, ch, i, n, p, offset;\n\n # lookup stuff like SSE base cases.\n h := MultiHashLookup(opts.baseHashes, spl);\n\n if h <> false then\n return h[1].ruletree;\n fi;\n\n # get list of normal rules\n R := AllApplicableRulesDirect(spl, opts.breakdownRules);\n offset := 0;\n\n for r in R do\n for c in _allChildren(r, spl, opts) do \n # figure out which group of children we should be looking at.\n npc := Product(c, e -> _getNumTrees(e, memohash, opts));\n\n # is this the correct group?\n if num < offset + npc then\n off := npc;\n ch := [];\n\n # step through the kids, and push down the ruletree number\n for i in [1..Length(c)] do\n n := _getNumTrees(c[i], memohash, opts);\n\n off := When(n > 0, off / n, off);\n\n p := When(n <= 0 or num <= offset, \n 0, \n RemInt(QuoInt(num - offset, off), n)\n );\n\n # all the kids get evaluated\n Add(ch, _ruleTreeN(c[i], p, memohash, opts));\n od;\n\n # no kids should be false, but just in case.\n if not ForAny(ch, e -> IsBool(e) and e=false) then\n return RuleTreeNC(r, spl, ch);\n fi;\n fi;\n\n # fixup offset\n offset := offset + npc;\n od;\n od;\n\n\t# no tree, return original spl\n return spl;\nend;\n\nDeclare(_ruleTreeGetN);\n\n#F RuleTreeGetN(<ruletree>, <opts>)\n#F given a ruletree, determine the index\n#F\n#F uses:\n#F opts.breakdownRules\n#F opts.baseHashes\n#F\n\nRuleTreeGetN := function(ruletree, opts)\n local memohash, r;\n \n memohash := HashTableSPL();\n\n # prime the memohash.\n _NofRuleTrees(ruletree.node, s -> false, memohash, opts, 1, false);\n\n r := _ruleTreeGetN(ruletree, memohash, opts, 0);\n\n # ruleTreeGetN may return false if we couldn't match the tree in the passed\n # in breakdownRules/baseHashes.\n return When(IsInt(r), r + 1, false);\nend;\n\n_ruleTreeGetN := function(rt, memohash, opts, offset)\n local h, R, r, c, ch, off, n;\n\n # is the ruletree something from the baseHashes?\n h := MultiHashLookup(opts.baseHashes, rt.node);\n if IsList(h) and rt = h[1].ruletree then\n return offset;\n fi;\n\n R := AllApplicableRulesDirect(rt.node, opts.breakdownRules);\n\n for r in R do\n # does rule match?\n if r = rt.rule then\n for c in _allChildren(r, rt.node, opts) do\n # does child match?\n if c = List(rt.children, e -> e.node) then\n off := Product(rt.children, e -> _getNumTrees(e.node, memohash, opts));\n for ch in rt.children do\n n := _getNumTrees(ch.node, memohash, opts);\n off := When(n > 0, off / n, off);\n offset := offset + (off * _ruleTreeGetN(ch, memohash, opts, 0));\n od;\n return offset;\n # child doesn't match, increase offset\n else\n offset := offset + Product(c, e -> _getNumTrees(e, memohash, opts));\n fi; \n od;\n # rule doesn't match, so increase offset by all possible expansions we didn't use\n else\n offset := offset \n + Sum(_allChildren(r, rt.node, opts), C -> \n Product(C, c -> _getNumTrees(c, memohash, opts))\n );\n fi;\n od;\n\n return offset;\nend;\n", "meta": {"hexsha": "1d0009a09272fd41a4782af754b83ad098ad272d", "size": 33659, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/formgen/ruletree.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/formgen/ruletree.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/formgen/ruletree.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": 28.9415305245, "max_line_length": 178, "alphanum_fraction": 0.5857868624, "num_tokens": 9761, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6513548646660543, "lm_q2_score": 0.6513548646660542, "lm_q1q2_score": 0.42426315972413386}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n# ================================================================\n# Simplification of Intervals\n# ================================================================\n\nfull_II := (int, size) -> \n [int.target(II), size, 0, @.cond(e->e=size.val)];\n\nempty_II := (int, size) -> \n [int.target(II).cond(e->e.params[2]=e.params[3]), size, @, @];\n\nleft_II := (int, size, endd) -> \n [int.target(II), size, 0, endd];\n\nright_II := (int, size,start) -> \n [int.target(II), size, start, @.cond(e->e=size.val)];\n\nClass(RulesII, RuleSet);\n\nRewriteRules(RulesII, rec(\n # full II o index mapping func @(3) = II with domain of @(3)\n # II(n, 0, n) o f = II(domain(f), 0, domain(f))\n FullII_f := ARule(fCompose, [ full_II(@, @(1)), @(2) ], e -> [ II(@(2).val.domain()) ]),\n EmptyII_f := ARule(fCompose, [ empty_II(@, @(1)), @(2) ], e -> [ II(@(2).val.domain(),0,0) ]),\n\n # partial II o dirsum of perms\n # II(n, 0, k) o fDirsum(perm_k, perm_?) -> II(n,0,k)\n LeftII_fDirsum := ARule(fCompose, \n [ left_II(@(0), @(1), @(2)), [fDirsum, @(3).cond(e -> is_perm(e) and e.range()=@(2).val), ...]],\n e -> [ @(0).val ]),\n\n # partial II o dirsum of perms\n # II(n, n-k, n) o fDirsum(perm_?, perm_k) -> II(n,n-k,n)\n RightII_fDirsum := ARule( fCompose, \n [ right_II(@(0), @(1), @(2)), [fDirsum, ..., @(4).cond(e -> is_perm(e) and e.range() = @(1).val-@(2).val)]],\n e -> [ @(0).val ]),\n\n # fTensor(IIn, IIk) -> II(nk)\n fullII_tensor_fullII := ARule(diagTensor, [full_II(@(0), @(1)), full_II(@(0), @(2))], \n e -> [ II(@(1).val @(2).val) ]),\n\n # fDirsum(IIn, IIk) -> II(n+k)\n fullII_dirsum_fullII := ARule(diagDirsum, [full_II(@(0), @(1)), full_II(@(0), @(2))], \n e -> [ II(@(1).val + @(2).val) ]),\n\n diagTensor_emptyII := Rule([diagTensor, ..., empty_II(@(1), @(2)), ...], e -> II(e.domain(),0,0)),\n diagTensor_fullII_Id1 := ARule(diagTensor, [@(0), full_II(@(1), @(2).cond(e->e=1))], e -> [ @(0).val ]),\n diagTensor_fullII_Id2 := ARule(diagTensor, [full_II(@(1), @(2).cond(e->e=1)), @(0)], e -> [ @(0).val ]),\n\n\n II_dirsum_emptyII := ARule(diagDirsum, [[II, @(1), @(2), @(3)], empty_II(@(4), @(5))], \n e -> [ II(@(1).val + @(5).val), @(2).val, @(3).val ]),\n\n emptyII_dirsum_II := ARule(diagDirsum, [empty_II(@(4), @(5)), [II, @(1), @(2), @(3)]], \n e -> [ II(@(1).val + @(5).val), @(5).val + @(2).val, @(5).val + @(3).val ]),\n\n # II Shifting, we support shift left (shift <= start), and right (shift >= end)\n # II o Z = shifted II# \n II_Z := ARule(fCompose, [[II, @(1), @(2), @(3)], [Z, @(4), @(5).cond(e -> (e<=@(2).val) or (e >= @(3).val))]],\n e -> [II(@(1).val, (@(2).val-@(5).val) mod @(1).val, \n # this makes 0->size, because size mod size = 0\n let(last:=(@(3).val-@(5).val) mod @(1).val, \n When(last=0, @(1).val, last))) ]),\n\n DiagFullII_toId := Rule([Diag, full_II(@(1), @(2))], e -> I(@(2).val)),\n Diag_fConst_toId := Rule([Diag, [fConst, @(2), @(1), 1]], e -> I(@(1).val)),\n Diag_fConstV_toId := Rule([Diag, [fConst, @(2), @(1), _1]], e -> I(@(1).val)),\n\n COND_fullII := Rule([COND, full_II(@(1), @(2)), @(3), @(4)], e -> @(3).val),\n COND_emptyII := Rule([COND, full_II(@(1), @(2)), @(3), @(4)], e -> @(4).val)\n));\n", "meta": {"hexsha": "1ffde4fb9b8a73ad175686815d1f2bb4d2458ed4", "size": 3376, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/sigma/ii_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/sigma/ii_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/sigma/ii_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": 45.0133333333, "max_line_length": 116, "alphanum_fraction": 0.4721563981, "num_tokens": 1235, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6992544210587585, "lm_q2_score": 0.600188359260205, "lm_q1q2_score": 0.4196843636807008}}
	{"text": "#############################################################################\n##\n## ExternalPolymakePolytope.gi JConvex package\n## Martin Bies\n##\n## Copyright 2021 University of Pennsylvania\n##\n## A Gap package to do convex geometry by Polymake, Cdd and Normaliz\n##\n## Chapter Polytopes in Polymake\n##\n#############################################################################\n\n\n##############################################################################################\n##\n## Section GAP category of PolymakePolytopes\n##\n##############################################################################################\n\nDeclareRepresentation( \"IsPolymakePolytopeRep\", IsPolymakePolytope and IsAttributeStoringRep, [ ] );\n\nBindGlobal( \"TheFamilyOfPolymakePolytopes\", NewFamily( \"TheFamilyOfPolymakePolytopes\" ) );\n\nBindGlobal( \"TheTypeOfPolymakePolytope\", NewType( TheFamilyOfPolymakePolytopes, IsPolymakePolytopeRep ) );\n\nBindGlobal( \"MakePolymakePolytopeVRep\", function( vertices, lineality )\n local poly, kwargs, new_vertices, new_lin, v;\n poly := Objectify( TheTypeOfPolymakePolytope,\n rec( vertices := Immutable( vertices ),\n lineality := Immutable( lineality ),\n number_type := \"rational\",\n rep_type := \"V-rep\" ) );\n\n # add 1s at the beginning, since Polymake always considers polytopes as intersections with the hyperplane x0 = 1\n new_vertices := [];\n for v in vertices do\n v := ShallowCopy( v );\n Add( v, 1, 1 );\n Add( new_vertices, v );\n od;\n new_lin := [];\n for v in lineality do\n v := ShallowCopy( v );\n Add( v, 1, 1 );\n Add( new_lin, v );\n od;\n\n kwargs := rec();\n\n # TODO: verify that kwargs is set correctly, also if one or both lists are empty\n\n # check for degenerate case\n if Length( new_vertices ) > 0 then\n kwargs.POINTS := JuliaMatrixInt( new_vertices );\n\n # if we also have lineality, add them\n if Length( new_lin ) > 0 then\n kwargs.INPUT_LINEALITY := JuliaMatrixInt( new_lin );\n fi;\n elif Length( new_lin ) > 0 then\n kwargs.POINTS := JuliaMatrixInt( new_lin );\n kwargs.INPUT_LINEALITY := kwargs.POINTS;\n fi;\n\n poly!.pmobj := CallJuliaFunctionWithKeywordArguments( _Polymake_jl.polytope.Polytope, [], kwargs );\n return poly;\nend);\n\nBindGlobal( \"MakePolymakePolytopeHRep\", function( inequalities, equalities )\n local poly, kwargs;\n poly := Objectify( TheTypeOfPolymakePolytope,\n rec( inequalities := Immutable( inequalities ),\n equalities := Immutable( equalities ),\n number_type := \"rational\",\n rep_type := \"H-rep\" ) );\n\n kwargs := rec();\n\n # TODO: verify that kwargs is set correctly, also if one or both lists are empty\n\n # check for degenerate case\n if Length( inequalities ) > 0 then\n kwargs.INEQUALITIES := JuliaMatrixInt( inequalities );\n\n # check if we also need equalities\n if Length( equalities ) > 0 then\n kwargs.EQUATIONS := JuliaMatrixInt( equalities );\n fi;\n elif Length( equalities ) > 0 then\n kwargs.INEQUALITIES := JuliaMatrixInt( equalities );\n kwargs.EQUATIONS := kwargs.INEQUALITIES;\n fi;\n\n poly!.pmobj := CallJuliaFunctionWithKeywordArguments( _Polymake_jl.polytope.Polytope, [], kwargs );\n return poly;\nend);\n\n\n##############################################################################################\n##\n## Constructors for PolymakePolytopes\n##\n##############################################################################################\n\n\nInstallGlobalFunction( Polymake_PolytopeByGenerators,\n function( arg )\n local poly, i, matrix, temp, dim;\n \n if Length( arg )= 0 or ForAll( arg, IsEmpty ) then\n \n Error( \"Wrong input: Please provide some input!\" );\n \n elif Length( arg ) = 1 and IsList( arg[1] ) then\n \n return Polymake_PolytopeByGenerators( arg[ 1 ], [ ] );\n \n elif Length( arg ) = 2 and IsList( arg[ 1 ] ) and IsList( arg[ 2 ] ) then\n \n if ( not IsEmpty( arg[ 1 ] ) ) and not ( IsMatrix( arg[ 1 ] ) ) then\n Error( \"Wrong input: The first argument should be a Gap matrix!\" );\n fi;\n \n if ( not IsEmpty( arg[ 2 ] ) ) and not ( IsMatrix( arg[ 2 ] ) ) then\n Error( \"Wrong input: The second argument should be a Gap matrix!\" );\n fi;\n \n poly := MakePolymakePolytopeVRep( arg[ 1 ], arg[ 2 ] );\n return Polymake_CanonicalPolytopeByGenerators( poly );\n \n fi;\n \nend );\n\n\nInstallGlobalFunction( Polymake_PolytopeFromInequalities,\n function( arg )\n local poly, i, temp, matrix, dim;\n \n if Length( arg ) = 0 or ForAll( arg, IsEmpty ) then\n \n Error( \"Wrong input: Please provide some input!\" );\n \n elif Length( arg ) = 1 and IsList( arg[ 1 ] ) then\n \n return Polymake_PolytopeFromInequalities( arg[ 1 ], [ ] );\n \n elif Length( arg ) = 2 and IsList( arg[ 1 ] ) and IsList( arg[ 2 ] ) then\n \n if ( not IsEmpty( arg[ 1 ] ) ) and not ( IsMatrix( arg[ 1 ] ) ) then\n Error( \"Wrong input: The first argument should be a Gap matrix!\" );\n fi;\n \n if ( not IsEmpty( arg[ 2 ] ) ) and not ( IsMatrix( arg[ 2 ] ) ) then\n Error( \"Wrong input: The second argument should be a Gap matrix!\" );\n fi;\n \n poly := MakePolymakePolytopeHRep( arg[ 1 ], arg[ 2 ] );\n return Polymake_CanonicalPolytopeFromInequalities( poly );\n \n fi;\n \nend );\n\n\n##############################################################################################\n##\n## Canonicalize polytopes\n##\n##############################################################################################\n\nInstallMethod( Polymake_CanonicalPolytopeByGenerators,\n [ IsPolymakePolytope ],\n function( poly )\n local vertices, v_copy, scaled_vertices, i, scale, lineality, scaled_lineality;\n \n if poly!.rep_type = \"H-rep\" then\n \n return fail;\n \n else\n \n # compute vertices\n vertices := PolymakeMatrixToGAP( poly!.pmobj.VERTICES );\n \n # sometimes, Polymake returns rational vertices - we turn them into integral vectors\n # also, Polymake requires x0 = 1 in affine coordinates - we remove this 1\n scaled_vertices := [];\n for i in [ 1 .. Length( vertices ) ] do\n v_copy := ShallowCopy( vertices[ i ] );\n Remove( v_copy, 1 );\n Add( scaled_vertices, v_copy );\n od;\n \n # extract lineality\n lineality := PolymakeMatrixToGAP( poly!.pmobj.LINEALITY_SPACE );\n \n # sometimes, Polymake returns rational lineality - we turn them into integral vectors\n scaled_lineality := [];\n for i in [ 1 .. Length( lineality ) ] do\n v_copy := ShallowCopy( lineality[ i ] );\n Remove( v_copy, 1 );\n Add( scaled_lineality, v_copy );\n od;\n \n # construct the new poly\n return MakePolymakePolytopeVRep( scaled_vertices, scaled_lineality );\n \n fi;\n \nend );\n\nInstallMethod( Polymake_CanonicalPolytopeFromInequalities,\n [ IsPolymakePolytope ],\n function( poly )\n local ineqs, eqs;\n \n if poly!.rep_type = \"V-rep\" then\n \n return fail;\n \n else\n \n # compute facets\n ineqs := PolymakeMatrixToGAP( poly!.pmobj.FACETS );\n \n # compute affine hull\n eqs := PolymakeMatrixToGAP( poly!.pmobj.AFFINE_HULL );\n \n # construct the new poly\n return MakePolymakePolytopeHRep( ineqs, eqs );\n \n fi;\n \nend );\n\n\n##############################################################################################\n##\n## Conversion of polytopes\n##\n##############################################################################################\n\nInstallMethod( Polymake_V_Rep,\n [ IsPolymakePolytope ],\n function( poly )\n local vertices, v_copy, scaled_vertices, i, lineality, scaled_lineality;\n \n if poly!.rep_type = \"V-rep\" then\n \n return poly;\n \n else\n \n # compute vertices\n vertices := PolymakeMatrixToGAP( poly!.pmobj.VERTICES );\n \n # sometimes, Polymake returns rational vertices - we turn them into integral vectors\n scaled_vertices := [];\n for i in [ 1 .. Length( vertices ) ] do\n v_copy := ShallowCopy( vertices[ i ] );\n Remove( v_copy, 1 );\n Add( scaled_vertices, v_copy );\n od;\n \n # compute lineality\n lineality := PolymakeMatrixToGAP( poly!.pmobj.LINEALITY_SPACE );\n \n # sometimes, Polymake returns rational lineality - we turn them into integral vectors\n scaled_lineality := [];\n for i in [ 1 .. Length( lineality ) ] do\n v_copy := ShallowCopy( lineality[ i ] );\n Remove( v_copy, 1 );\n Add( scaled_lineality, v_copy );\n od;\n \n # construct the new poly\n return MakePolymakePolytopeVRep( scaled_vertices, scaled_lineality );\n \n fi;\n \nend );\n\n\nInstallMethod( Polymake_H_Rep,\n [ IsPolymakePolytope ],\n function( poly )\n local ineqs, eqs;\n \n if poly!.rep_type = \"H-rep\" then\n \n return poly;\n \n else\n \n if poly!.rep_type = \"V-rep\" and poly!.vertices = [] then\n return Polymake_PolytopeFromInequalities( [ [ 0, 1 ], [ -1, -1 ] ] );\n fi;\n \n # compute inequalities\n ineqs := PolymakeMatrixToGAP( poly!.pmobj.FACETS );\n \n # compute equalities\n eqs := PolymakeMatrixToGAP( poly!.pmobj.AFFINE_HULL );\n \n # construct the new poly\n return MakePolymakePolytopeHRep( ineqs, eqs );\n \n fi;\n \nend );\n\n\n##############################################################################################\n##\n## Attributes of PolymakeCones\n##\n##############################################################################################\n\nInstallMethod( Polymake_AmbientSpaceDimension,\n \"finding the dimension of the ambient space of the poly\",\n [ IsPolymakePolytope ],\n function( poly )\n \n return Length( Polymake_V_Rep( poly )!.vertices[0] );\n \nend );\n\n\nInstallMethod( Polymake_Dimension,\n \" returns the dimension of the poly\",\n [ IsPolymakePolytope ],\n function( poly )\n \n if Polymake_IsEmpty( poly ) then\n return -1;\n fi;\n \n return poly!.pmobj.CONE_DIM - 1;\n \nend );\n\n\nInstallMethod( Polymake_Vertices,\n \" return the list of generating vertices\",\n [ IsPolymakePolytope ],\n function( poly )\n \n return Set( Polymake_V_Rep( poly )!.vertices );\n \nend );\n\n\nInstallMethod( Polymake_Linealities,\n \" return the list of linealities\",\n [ IsPolymakePolytope ],\n function( poly )\n \n return Set( Polymake_V_Rep( poly )!.linealities );\n \nend );\n\n\nInstallMethod( Polymake_Equalities,\n \" return the list of equalities of a poly\",\n [ IsPolymakePolytope ],\n function( poly )\n \n return Set( ( Polymake_H_Rep( poly ) )!.equalities );\n \nend );\n\n\nInstallMethod( Polymake_Inequalities,\n \" return the list of inequalities of a poly\",\n [ IsPolymakePolytope ],\n function( poly )\n \n return Set( ( Polymake_H_Rep( poly ) )!.inequalities );\n \nend );\n\n\nInstallMethod( Polymake_LatticePoints,\n \" return the list of the lattice points of poly\",\n [ IsPolymakePolytope ],\n function( poly )\n local point_list, lattice_points, i, copy;\n \n point_list := JuliaToGAP( IsList, JuliaMatrixInt( poly!.pmobj.LATTICE_POINTS_GENERATORS[1] ), true );\n\n # the point list is in affine coordinate, that is we have a 1 at position one, which should be removed\n lattice_points := [];\n for i in [ 1 .. Length( point_list ) ] do\n copy := ShallowCopy( point_list[ i ] );\n Remove( copy, 1 );\n Add( lattice_points, copy );\n od;\n \n # return result\n return lattice_points;\n \nend );\n\n\nInstallMethod( Polymake_Intersection,\n [ IsPolymakePolytope, IsPolymakePolytope ],\n function( poly1, poly2 )\n local poly1_h, poly2_h, new_ineqs, new_equ;\n \n # compute H-reps\n poly1_h := Polymake_H_Rep( poly1 );\n poly2_h := Polymake_H_Rep( poly2 );\n \n # add the inequalities and equalities\n new_ineqs := Concatenation( poly1_h!.inequalities, poly2_h!.inequalities );\n new_equ := Concatenation( poly1_h!.equalities, poly2_h!.equalities );\n \n # return result\n return Polymake_PolytopeFromInequalities( new_ineqs, new_equ );\n \nend );\n\n\n##############################################################################################\n##\n## Properties of PolymakeCones\n##\n##############################################################################################\n\nInstallMethod( Polymake_IsEmpty,\n \"finding if the poly empty is or not\",\n [ IsPolymakePolytope ],\n function( poly )\n \n return Length( Polymake_V_Rep( poly )!.vertices ) = 0;\n \nend );\n\n\nInstallMethod( Polymake_IsPointed,\n \"finding if the poly is pointed or not\",\n [ IsPolymakePolytope ],\n function( poly )\n return poly!.pmobj.POINTED;\n \nend );\n\n\nInstallMethod( Polymake_IsBounded,\n \" returns if the polytope is bounded or not\",\n [ IsPolymakePolytope ],\n function( poly )\n return poly!.pmobj.BOUNDED;\n \nend );\n", "meta": {"hexsha": "c969f54a2ca86be189c7a4ab0d0f99f4f58edd28", "size": 13778, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "pkg/JConvex/gap/ExternalPolymakePolytope.gi", "max_stars_repo_name": "HereAround/JToric.jl", "max_stars_repo_head_hexsha": "e8907f1ccd10a637254808916f859e354e479296", "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": "pkg/JConvex/gap/ExternalPolymakePolytope.gi", "max_issues_repo_name": "HereAround/JToric.jl", "max_issues_repo_head_hexsha": "e8907f1ccd10a637254808916f859e354e479296", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 44, "max_issues_repo_issues_event_min_datetime": "2021-09-17T01:15:32.000Z", "max_issues_repo_issues_event_max_datetime": "2021-11-25T00:15:13.000Z", "max_forks_repo_path": "pkg/JConvex/gap/ExternalPolymakePolytope.gi", "max_forks_repo_name": "HereAround/JToric.jl", "max_forks_repo_head_hexsha": "e8907f1ccd10a637254808916f859e354e479296", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2021-08-20T12:56:11.000Z", "max_forks_repo_forks_event_max_datetime": "2021-08-20T12:56:11.000Z", "avg_line_length": 30.0829694323, "max_line_length": 116, "alphanum_fraction": 0.5379590652, "num_tokens": 3364, "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\nClass(WarpXOpts, FFTXConvOpts, rec(\n tags := [],\n operations := rec(Print := s -> Print(\"<FFTX WarpX options record>\")) \n));\n\nwarpxOpts := function(arg) # specific to WarpX size 100...\n local opts, rfs;\n \n rfs := Copy(RulesFuncSimp);\n Unbind(rfs.rules.TensorIdId);\n \n opts := Copy(WarpXOpts);\n opts.breakdownRules.Circulant := [Circulant_PRDFT_FDataNT];\n opts.breakdownRules.PRDFT := List([PRDFT1_Base1, PRDFT1_Base2, CopyFields(PRDFT1_CT, \n rec(allChildren := P ->Filtered(PRDFT1_CT.allChildren(P), i->When(P[1] = 100, Cols(i[1]) = 4, true)))), \n PRDFT_PD], _noT);\n opts.breakdownRules.IPRDFT := List([ IPRDFT1_Base1, IPRDFT1_Base2, IPRDFT1_CT, IPRDFT_PD ], _noT);\n opts.breakdownRules.PRDFT3 := List([ PRDFT3_Base1, PRDFT3_Base2, PRDFT3_CT ], _noT);\n opts.breakdownRules.IPRDFT2 := List([ IPRDFT2_Base1, IPRDFT2_Base2, IPRDFT2_CT ], _noT);\n opts.breakdownRules.DFT := [ DFT_Base, \n CopyFields(DFT_CT, rec(children := nt ->Filtered(DFT_CT.children(nt), i->When(nt.params[1] = 100, Cols(i[1]) = 4, true)))), \n DFT_PD ];\n opts.breakdownRules.TTensorInd := [dsA_base, L_dsA_L_base, dsA_L_base, L_dsA_base]; \n opts.breakdownRules.MDDFT := [ MDDFT_Base, MDDFT_RowCol ];\n opts.breakdownRules.TL := [L_base];\n opts.breakdownRules.TSparseMat := [ TSparseMat_base ];\n \n opts.globalUnrolling := 23;\n opts.codegen := CopyFields( MultiPtrCodegenMixin, spiral.libgen.VecRecCodegen);\n opts.sumsgen.IterHStack := MultiPtrSumsgenMixin.IterHStack;\n opts.preProcess := t -> ApplyStrategy(t, \n [ RulesFFTXPromoteWarpX1, \n MergedRuleSet(rfs, RulesSums, RulesFFTXPromoteWarpX2), \n RulesFFTXPromoteNT, \n MergedRuleSet(rfs, RulesSums, RulesFFTXPromoteWarpX3) ],\n BUA, opts);\n opts.useDeref := false;\n # for debugging...\n opts.generateInitFunc := false;\n# opts.codegen := DefaultCodegen;\n opts.arrayBufModifier := \"\";\n opts.arrayDataModifier := \"static\";\n \n return opts;\nend;\n\n\nwarpxConf := rec(\n defaultName := \"defaultWarpXConf\",\n defaultOpts := (arg) >> rec(useWarpX := true),\n confHandler := warpxOpts \n);\n\nfftx.FFTXGlobals.registerConf(warpxConf);\n\n\n\n", "meta": {"hexsha": "0568b507b3b64208089c740a99feb5c2e144ddda", "size": 2348, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "knowledgebase/warpx.gi", "max_stars_repo_name": "franzfranchetti/spiral-package-fftx", "max_stars_repo_head_hexsha": "3149606d3d60a9b50c225ec1e8450628d543698b", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-06-15T12:40:19.000Z", "max_stars_repo_stars_event_max_datetime": "2021-06-15T12:40:19.000Z", "max_issues_repo_path": "knowledgebase/warpx.gi", "max_issues_repo_name": "franzfranchetti/spiral-package-fftx", "max_issues_repo_head_hexsha": "3149606d3d60a9b50c225ec1e8450628d543698b", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2021-01-05T20:58:29.000Z", "max_issues_repo_issues_event_max_datetime": "2021-08-18T20:10:45.000Z", "max_forks_repo_path": "knowledgebase/warpx.gi", "max_forks_repo_name": "franzfranchetti/spiral-package-fftx", "max_forks_repo_head_hexsha": "3149606d3d60a9b50c225ec1e8450628d543698b", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 5, "max_forks_repo_forks_event_min_datetime": "2020-12-14T18:24:29.000Z", "max_forks_repo_forks_event_max_datetime": "2021-06-15T12:40:20.000Z", "avg_line_length": 37.8709677419, "max_line_length": 132, "alphanum_fraction": 0.6528960818, "num_tokens": 732, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7956580903722561, "lm_q2_score": 0.523420348936324, "lm_q1q2_score": 0.41646363529665553}}
	{"text": "#############################################################################\n##\n#W autom.gi automgrp package Yevgen Muntyan\n#W Dmytro Savchuk\n##\n#Y Copyright (C) 2003 - 2018 Yevgen Muntyan, Dmytro Savchuk\n##\n\n\n###############################################################################\n##\n#R IsAutomRep\n##\n## This is how IsAutom object is stored in GAP:\n## IsAutom object is a thing of kind \"w = (w_1, w_2, ..., w_d)\\pi\", where\n## deg = d - arity of tree;\n## perm = \\pi - permutation on first level;\n## w, w_1, ..., w_d - elements of free group representing elements of\n## automata group;\n## word = w;\n## states = [w_1, ..., w_d].\n##\nDeclareRepresentation(\"IsAutomRep\",\n IsComponentObjectRep and IsAttributeStoringRep,\n [\"word\", \"states\", \"perm\", \"deg\"]);\n\n\nInstallGlobalFunction(__AG_CreateAutom,\nfunction(family, word, states, perm, invertible)\n local a, cat;\n\n if invertible then\n cat := IsInvertibleAutom and IsAutomRep;\n\n if perm^-1=fail then\n Error(perm, \" is not invertible\");\n else\n perm := AG_PermFromTransformation(perm);\n fi;\n else\n cat := IsAutom and IsAutomRep;\n fi;\n\n a := Objectify(NewType(family, cat),\n rec(word := word,\n states := states,\n perm := perm,\n deg := family!.deg));\n\n SetIsActingOnBinaryTree(a, a!.deg = 2);\n\n return a;\nend);\n\n###############################################################################\n##\n#M Autom(<word>, <fam>)\n##\nInstallMethod(Autom, \"for [IsAssocWord, IsAutomFamily]\",\n [IsAssocWord, IsAutomFamily],\nfunction(w, fam)\n local exp, wstates, curstate, newstate, curletter, newletter,\n nperm, i, j, perm, a, wtmp, reduced, invertible;\n\n if fam!.use_rws then\n w := AG_ReducedForm(fam!.rws, w);\n fi;\n\n if Length(w) = 0 then\n return One(fam);\n elif Length(w) = 1 then\n if ExponentSyllable(w, 1) = 1 then\n return fam!.automgens[GeneratorSyllable(w, 1)];\n else\n return fam!.automgens[GeneratorSyllable(w, 1) + fam!.numstates];\n fi;\n fi;\n\n # TODO\n exp := LetterRepAssocWord(w);\n for i in [1..Length(exp)] do\n if exp[i] < 0 then exp[i] := -exp[i] + fam!.numstates; fi;\n od;\n wstates := [];\n nperm := ();\n for i in [1..Length(exp)] do\n nperm := nperm * fam!.automatonlist[exp[i]][fam!.deg+1];\n od;\n\n for i in [1..fam!.deg] do\n wstates[i] := [];\n perm := ();\n\n for j in [1..Length(exp)] do\n newstate := fam!.automatonlist[exp[j]][i^perm];\n if newstate <> fam!.trivstate then\n if newstate > fam!.numstates then\n newstate := -(newstate - fam!.numstates);\n fi;\n if Length(wstates[i]) > 0 and wstates[i][Length(wstates[i])] = -newstate then\n Remove(wstates[i], Length(wstates[i]));\n else\n Add(wstates[i], newstate);\n fi;\n fi;\n perm := perm * fam!.automatonlist[exp[j]][fam!.deg+1];\n od;\n if Length(wstates[i]) > 0 then\n wstates[i] := AssocWordByLetterRep(FamilyObj(w), wstates[i]);\n else\n wstates[i] := One(fam!.freegroup);\n fi;\n if fam!.use_rws and not IsOne(wstates[i]) then\n wstates[i] := AG_ReducedForm(fam!.rws, wstates[i]);\n fi;\n od;\n\n invertible := true;\n if not fam!.isgroup then\n for i in exp do\n if i <= fam!.numstates and not IsInvertibleAutom(fam!.automgens[i]) then\n invertible := false;\n break;\n fi;\n od;\n fi;\n\n return __AG_CreateAutom(fam, w, wstates, nperm, invertible);\nend);\n\n\n###############################################################################\n##\n#M Autom(<word>, <a>)\n##\nInstallMethod(Autom, \"for [IsAssocWord, IsAutom]\", [IsAssocWord, IsAutom],\nfunction(w, a)\n return Autom(w, FamilyObj(a));\nend);\n\n\nInstallMethod(MappedWord, [IsAssocWord,\n IsList and IsAssocWordCollection,\n IsList and IsAutomCollection],\nfunction(w, fgens, agens)\n local img;\n img := MappedWord(w, fgens, List(agens, a -> a!.word));\n return Autom(img, FamilyObj(agens[1]));\nend);\n\n\n###############################################################################\n##\n#M Autom(<word>, <list>)\n##\nInstallMethod(Autom, \"for [IsAssocWord, IsList]\",\n [IsAssocWord, IsList],\nfunction(w, list)\n local fam;\n fam := AutomFamily(list);\n if fam = fail then\n return fail;\n fi;\n return Autom(w, fam);\nend);\n\n\n###############################################################################\n##\n#M PrintObj(<a>)\n##\nInstallMethod(PrintObj, \"for [IsAutom]\",\n [IsAutom],\nfunction (a)\n local deg, printword, i;\n\n printword := function(w)\n if IsOne(w) then Print(AG_Globals.identity_symbol);\n else Print(w); fi;\n end;\n\n if true then\n View(a);\n return;\n fi;\n\n deg := a!.deg;\n printword(a!.word);\n Print(\" = (\");\n for i in [1..deg] do\n printword(a!.states[i]);\n if i <> deg then Print(\", \"); fi;\n od;\n Print(\")\");\n if not IsOne(a!.perm) then AG_PrintTransformation(a!.perm); fi;\nend);\n\n\n###############################################################################\n##\n#M ViewObj(<a>)\n##\nInstallMethod(ViewObj, \"for [IsAutom]\",\n [IsAutom],\nfunction (a)\n if IsOne(a!.word) then Print(AG_Globals.identity_symbol);\n else Print(a!.word); fi;\nend);\n\n\n###############################################################################\n##\n#M String(<a>)\n##\nInstallMethod(String, \"for [IsAutom]\",\n [IsAutom],\nfunction (a)\n if IsOne(a!.word) then return AG_Globals.identity_symbol;\n else return String(a!.word); fi;\nend);\n\n\n###############################################################################\n##\n#M Perm(<a>)\n##\nInstallMethod(Perm, \"for [IsAutom]\", [IsAutom],\nfunction(a)\n return a!.perm;\nend);\n\n\n###############################################################################\n##\n#M Word(<a>)\n##\nInstallMethod(Word, \"for [IsAutom]\", [IsAutom],\nfunction(a)\n return a!.word;\nend);\n\n\n###############################################################################\n##\n#M <a1> * <a2>\n##\nInstallMethod(\\, \"for [IsAutom, IsAutom]\", [IsAutom, IsAutom],\nfunction(a1, a2)\n local a, i, fam, word, states;\n\n fam := FamilyObj(a1);\n word := a1!.word a2!.word;\n\n if fam!.use_rws then\n word := AG_ReducedForm(fam!.rws, word);\n fi;\n\n if IsOne(word) then\n return One(a1);\n fi;\n\n states := List([1..a1!.deg], i -> a1!.states[i] * a2!.states[i^(a1!.perm)]);\n\n if fam!.use_rws then\n for i in [1..a1!.deg] do\n states[i] := AG_ReducedForm(fam!.rws, states[i]);\n od;\n fi;\n\n return __AG_CreateAutom(FamilyObj(a1), word, states, a1!.perm * a2!.perm,\n IsInvertibleAutom(a1) and IsInvertibleAutom(a2));\nend);\n\n\nAG_IsOne_Autom := function(a)\n local deg, w, aw, checked, to_check;\n\n if IsOne(a!.word) then\n return true;\n fi;\n\n if not IsOne(a!.perm) then\n return false;\n fi;\n\n deg := a!.deg;\n checked := [];\n to_check := Filtered(a!.states, w -> not IsOne(w) and w <> a!.word);\n\n while not IsEmpty(to_check) do\n w := Remove(to_check, Length(to_check));\n # TODO Use AddSet() here?\n Add(checked, w);\n aw := Autom(w, a);\n if not IsOne(aw!.perm) then\n return false;\n fi;\n for w in aw!.states do\n if not IsOne(w) and not w in checked and not w in to_check then\n # TODO Use AddSet() here?\n Add(to_check, w);\n fi;\n od;\n od;\n\n return true;\nend;\n\n###############################################################################\n##\n#M IsOne(a)\n##\nInstallMethod(IsOne, \"for [IsAutom]\", [IsAutom],\nfunction(a)\n local i, w, nw, d, to_check, checked, deb_i, perm, autlist, pos, istrivstate, exp, G, trivstate;\n\n if IsOne(a!.word) then return true; fi;\n\n G := GroupOfAutomFamily(FamilyObj(a));\n if G <>fail and HasIsContracting(G) and IsContracting(G) and FamilyObj(a)!.use_contraction = true then\n return IsOneContr(a);\n fi;\n\n # this seems working well enough\n return AG_IsOne_Autom(a);\n\n d := a!.deg;\n autlist := FamilyObj(a)!.automatonlist;\n trivstate := FamilyObj(a)!.trivstate;\n checked := [];\n\n istrivstate := function(v)\n local i, j, perm;\n\n if IsEmpty(v) then\n return true;\n fi;\n\n if v in checked then\n return true;\n else\n perm := ();\n for i in [1..Length(v)] do perm := perm * autlist[v[i]][d+1]; od;\n if perm <> () then return false; fi;\n Add(checked, v);\n for j in [1..d] do\n if not istrivstate(AG_WordStateInList(v, j, autlist, true, trivstate)) then\n return false;\n fi;\n od;\n return true;\n fi;\n end;\n\n exp := LetterRepAssocWord(a!.word);\n for i in [1..Length(exp)] do\n if exp[i] < 0 then\n exp[i] := -exp[i] + FamilyObj(a)!.numstates;\n fi;\n od;\n\n return istrivstate(exp);\nend);\n\n\n###############################################################################\n##\n#M a1 = a2\n##\nInstallMethod(\\=, \"for [IsAutom, IsAutom]\", IsIdenticalObj, [IsAutom, IsAutom],\nfunction(a1, a2)\n local areequalstates, exp, i, d, checked, autlist, G, trivstate;\n\n G := GroupOfAutomFamily(FamilyObj(a1));\n if G <> fail and HasIsContracting(G) and IsContracting(G) and UseContraction(G) then\n return IsOneContr(a1a2^-1);\n fi;\n\n # TODO can there be a problem if we do this?\n if G <> fail then\n return AG_IsOne_Autom(a1a2^-1);\n fi;\n\n d := a1!.deg;\n checked := [];\n autlist := FamilyObj(a1)!.automatonlist;\n trivstate := FamilyObj(a1)!.trivstate;\n\n areequalstates := function(p)\n local i, j, perm1, perm2;\n\n if p[1] = p[2] then\n return true;\n fi;\n\n if p in checked then\n return true;\n else\n perm1 := ();\n perm2 := ();\n\n for i in [1..Length(p[1])] do\n perm1 := perm1 * autlist[p[1][i]][d+1];\n od;\n for i in [1..Length(p[2])] do\n perm2 := perm2 * autlist[p[2][i]][d+1];\n od;\n\n if perm1 <> perm2 then\n return false;\n fi;\n\n AddSet(checked, p);\n for j in [1..d] do\n if not areequalstates([AG_WordStateInList(p[1], j, autlist, true, trivstate),\n AG_WordStateInList(p[2], j, autlist, true, trivstate)])\n then\n return false;\n fi;\n od;\n return true;\n fi;\n end;\n\n exp := [LetterRepAssocWord(a1!.word), LetterRepAssocWord(a2!.word)];\n for i in [1..Length(exp[1])] do\n if exp[1][i] < 0 then exp[1][i] := -exp[1][i] + FamilyObj(a1)!.numstates; fi;\n od;\n for i in [1..Length(exp[2])] do\n if exp[2][i] < 0 then exp[2][i] := -exp[2][i] + FamilyObj(a2)!.numstates; fi;\n od;\n return areequalstates(exp);\nend);\n\n\n###############################################################################\n##\n#M a1 < a2\n##\nInstallMethod(\\<, \"for [IsAutom, IsAutom]\", IsIdenticalObj, [IsAutom, IsAutom],\nfunction(a1, a2)\n local d, checked, pos, aw1, aw2, p, np, i, exp, perm1, perm2, autlist, cmp;\n\n d := a1!.deg;\n autlist := FamilyObj(a1)!.automatonlist;\n exp := [LetterRepAssocWord(a1!.word), LetterRepAssocWord(a2!.word)];\n for i in [1..Length(exp[1])] do\n if exp[1][i] < 0 then exp[1][i] := -exp[1][i] + FamilyObj(a1)!.numstates; fi;\n od;\n for i in [1..Length(exp[2])] do\n if exp[2][i] < 0 then exp[2][i] := -exp[2][i] + FamilyObj(a2)!.numstates; fi;\n od;\n checked := [exp];\n pos := 0;\n\n while Length(checked) <> pos do\n pos := pos + 1;\n p := checked[pos];\n perm1 := ();\n perm2 := ();\n for i in [1..Length(p[1])] do perm1 := perm1 * autlist[p[1][i]][d+1]; od;\n for i in [1..Length(p[2])] do perm2 := perm2 * autlist[p[2][i]][d+1]; od;\n cmp := AG_TrCmp(perm1, perm2, d);\n if cmp < 0 then\n return true;\n elif cmp > 0 then\n return false;\n fi;\n for i in [1..d] do\n np := [AG_WordStateInList(p[1], i, autlist, false, 0),\n AG_WordStateInList(p[2], i, autlist, false, 0)];\n if not np in checked then\n Add(checked, np);\n fi;\n od;\n od;\n\n return false;\nend);\n\n\n###############################################################################\n##\n#M InverseOp(<a>)\n##\nInstallMethod(InverseOp, \"for [IsInvertibleAutom]\", [IsInvertibleAutom],\nfunction(a)\n local i, inv, fam, word, states;\n\n fam := FamilyObj(a);\n word := a!.word ^ -1;\n if fam!.use_rws then\n word := AG_ReducedForm(fam!.rws, word);\n if IsOne(word) then\n return One(a);\n fi;\n fi;\n\n states := List([1..a!.deg], i -> a!.states[i^(a!.perm^-1)]^-1);\n\n if fam!.use_rws then\n for i in [1..a!.deg] do\n states[i] := AG_ReducedForm(fam!.rws, states[i]);\n od;\n fi;\n\n return __AG_CreateAutom(FamilyObj(a), word, states, a!.perm^-1, true);\nend);\n\n\n###############################################################################\n##\n#M OneOp(<a>)\n##\nInstallMethod(OneOp, \"for [IsAutom]\", [IsAutom],\nfunction(a)\n return One(FamilyObj(a));\nend);\n\n\n###############################################################################\n##\n#M StatesWords(<a>)\n##\nInstallMethod(StatesWords, \"for [IsAutom]\", [IsAutom],\nfunction(a)\n return a!.states;\nend);\n\n\n###############################################################################\n##\n#M Sections(a)\n##\nInstallMethod(Sections, \"for [IsAutom]\", [IsAutom],\nfunction(a)\n return List(a!.states, s -> Autom(s, a));\nend);\n\n\n###############################################################################\n##\n#M Section(a, k)\n##\nInstallMethod(Section, \"for [IsAutom, IsPosInt]\", [IsAutom, IsPosInt],\nfunction(a, k)\n if k > a!.deg then\n Error(\"in Section(IsAutom, IsPosInt): invalid vertex \", k);\n fi;\n return Autom(a!.states[k], a);\nend);\n\n\n###############################################################################\n##\n#M Section(a, seq)\n##\n## TODO\nInstallMethod(Section, \"for [IsAutom, IsList]\", [IsAutom, IsList],\nfunction(a, v)\n if Length(v) = 0 then\n return a;\n fi;\n\n if Length(v) = 1 then\n return Section(a, v[1]);\n fi;\n\n return Section(Section(a, v[1]), v{[2..Length(v)]});\nend);\n\n\n###############################################################################\n##\n#M k ^ a\n##\nInstallMethod(\\^, \"for [IsPosInt, IsAutom]\", [IsPosInt, IsAutom],\nfunction(k, a)\n return k ^ Perm(a);\nend);\n\n\n###############################################################################\n##\n#M seq ^ a\n##\nInstallMethod(\\^, \"for [IsList, IsAutom]\", [IsList, IsAutom],\nfunction(seq, a)\n local i, deg, img, cur;\n\n deg := DegreeOfTree(a);\n for i in seq do\n if not IsInt(i) or i < 1 or i > deg then\n Error(\"\\^(IsList, IsAutom): \",\n i, \" is out of range 1..\", deg, \" and is not a letter of the alphabet\\n\");\n# Print(\"\\^(IsList, IsAutom): \",\n# i, \" is out of range 1..\", deg, \" and is not a letter of the alphabet\\n\");\n# return seq;\n fi;\n od;\n\n if Length(seq) = 0 then return []; fi;\n if Length(seq) = 1 then return [seq[1]^Perm(a)]; fi;\n\n cur := LetterRepAssocWord(Word(a));\n for i in [1..Length(cur)] do\n if cur[i] < 0 then cur[i] := -cur[i]+FamilyObj(a)!.numstates; fi;\n od;\n cur := [cur, Perm(a)];\n\n img := [];\n for i in [1..Length(seq)] do\n img[i] := seq[i]^cur[2];\n cur := AG_WordStateAndPermInList(cur[1], seq[i],\n FamilyObj(a)!.automatonlist);\n od;\n\n return img;\nend);\n\n\n###############################################################################\n##\n#M PermOnLevelOp(a, k)\n##\n## TODO\nInstallMethod(PermOnLevelOp, \"for [IsIsInvertibleAutom, IsPosInt]\",\n [IsInvertibleAutom, IsPosInt],\nfunction(a, k)\n local dom, perm;\n\n if k = 1 then\n return a!.perm;\n fi;\n\n dom := AsList(Tuples([1.. a!.deg], k));\n perm := List(dom, s -> s ^ a);\n perm := PermListList(dom, perm);\n\n return perm;\nend);\n\nInstallMethod(TransformationOnFirstLevel, [IsAutom],\nfunction(a)\n return AsTransformation(a!.perm);\nend);\n\n\n###############################################################################\n##\n#M IsActingOnBinaryTree(<a>)\n##\nInstallMethod(IsActingOnBinaryTree, \"for [IsAutom]\",\n [IsAutom],\nfunction(a)\n return a!.deg = 2;\nend);\n\n\nInstallMethod(SphericalIndex, \"for [IsAutom]\", [IsAutom],\nfunction(a)\n # XXX check uses of SphericalIndex everywhere\n return rec(start := [], period := [a!.deg]);\nend);\n\n# XXX check uses of this everywhere\nInstallMethod(DegreeOfTree, \"for [IsAutom]\", [IsAutom],\nfunction(a)\n return a!.deg;\nend);\n\n# XXX check uses of this everywhere\nInstallMethod(TopDegreeOfTree, \"for [IsAutom]\", [IsAutom],\nfunction(a)\n return a!.deg;\nend);\n\n\n###############################################################################\n##\n#M CanEasilyTestSphericalTransitivity(<a>)\n##\nInstallTrueMethod(CanEasilyTestSphericalTransitivity,\n IsActingOnBinaryTree and IsAutom);\n\n\n###############################################################################\n##\n#M IsSphericallyTransitive(<a>)\n##\nInstallMethod(IsSphericallyTransitive, \"for [IsAutom]\",\n [IsInvertibleAutom],\nfunction(a)\n local w, i, ab, abs;\n\n if IsOne(Word(a)) then\n Info(InfoAutomGrp, 3, \"IsSphericallyTransitive(a): false\");\n Info(InfoAutomGrp, 3, \" IsOne(Word(a)): a = \", a);\n return false;\n fi;\n\n TryNextMethod();\nend);\n\n\n#########################################################################\n##\n#M Order(<a>)\n##\nInstallMethod(Order, \"for [IsInvertibleAutom]\", true,\n [IsInvertibleAutom],\nfunction(a)\n local ord_loc;\n if IsGeneratedByBoundedAutomaton(GroupOfAutomFamily(FamilyObj(a))) then\n return OrderUsingSections(a, infinity);\n fi;\n if IsActingOnBinaryTree(a) and IsSphericallyTransitive(a) then\n return infinity;\n fi;\n ord_loc := OrderUsingSections(a, 10);\n if ord_loc <> fail then\n return ord_loc;\n fi;\n return OrderUsingSections(a, infinity);\nend);\n\n\n#########################################################################\n##\n#M IsTransitiveOnLevel( <a>, <lev> )\n##\nInstallMethod(IsTransitiveOnLevel, \"for [IsInvertibleAutom, IsPosInt]\",\n [IsInvertibleAutom, IsPosInt],\nfunction(a, lev)\n return Length(OrbitPerms([PermOnLevel(a, lev)], 1)) = a!.deg^lev;\nend);\n\n\n\n#########################################################################\n##\n#M AllSections( <a> )\n##\nInstallMethod(AllSections, \"for [IsAutom]\",\n [IsAutom],\nfunction(a)\n local states, find_all_sections;\n\n find_all_sections := function(s)\n local i;\n if not s in states then\n Add(states, s);\n for i in [1..s!.deg] do find_all_sections(Section(s, i)); od;\n fi;\n end;\n\n states := [];\n find_all_sections(a);\n return states;\nend);\n\n\n#E\n", "meta": {"hexsha": "1a258a4efd57dc34d94a2cc904edf914da996765", "size": 18607, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "gap/autom.gi", "max_stars_repo_name": "gap-packages/automgrp", "max_stars_repo_head_hexsha": "1beb0cbc96c9748cf912433c27c661e1f87ef5dc", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-10-02T15:00:11.000Z", "max_stars_repo_stars_event_max_datetime": "2021-10-02T15:00:11.000Z", "max_issues_repo_path": "gap/autom.gi", "max_issues_repo_name": "gap-packages/automgrp", "max_issues_repo_head_hexsha": "1beb0cbc96c9748cf912433c27c661e1f87ef5dc", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 9, "max_issues_repo_issues_event_min_datetime": "2019-09-21T22:10:40.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-26T23:51:41.000Z", "max_forks_repo_path": "gap/autom.gi", "max_forks_repo_name": "gap-packages/automgrp", "max_forks_repo_head_hexsha": "1beb0cbc96c9748cf912433c27c661e1f87ef5dc", "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": 24.3547120419, "max_line_length": 105, "alphanum_fraction": 0.5134626753, "num_tokens": 5207, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6959583376458152, "lm_q2_score": 0.5964331462646254, "lm_q1q2_score": 0.41509262099119204}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n# ==========================================================================\n# IDirSum(<var>, <range>, <spl>) - Iterative direct sum.\n# Dimensions of <spl> are assumed to not depend on <var>.\n# ==========================================================================\nClass(IDirSum, BaseIterative, rec(\n directOper := DirectSum,\n #-----------------------------------------------------------------------\n dims := self >> let(d:=self._children[1].dimensions,\n [d[1]* self.domain, d[2]self.domain]),\n# dims := self >> _evInt(self.unroll().dims()),\n #-----------------------------------------------------------------------\n unroll := self >> DirectSum(self.unrolledChildren()),\n #-----------------------------------------------------------------------\n transpose := self >> CopyFields(self, rec(\n _children := [self._children[1].transpose()],\n dimensions := Reversed(self.dimensions))),\n #-----------------------------------------------------------------------\n conjTranspose := self >> CopyFields(self, rec(\n _children := [self._children[1].conjTranspose()],\n dimensions := Reversed(self.dimensions))),\n #-----------------------------------------------------------------------\n inverse := self >> CopyFields(self, rec(\n _children := [self._children[1].inverse()],\n dimensions := Reversed(self.dimensions)))\n));\n\nDeclare(IColDirSum, IRowDirSum);\n\n# ==========================================================================\n# IRowDirSum(<var>, <range>, <overlap>, <spl>) - Iterative direct sum.\n# Dimensions of <spl> are assumed to not depend on <var>.\n# ==========================================================================\nClass(IRowDirSum, BaseIterative, rec(\n directOper := RowDirectSum,\n transposeOper := self >> IColDirSum,\n abbrevs := [ (v, expr) -> [v, v.range, 0, expr] ],\n\n rChildren := self >> Concat([self.var, self.overlap, self._children], When(IsBound(self._setDims), [self._setDims],[])),\n rSetChild := rSetChildFields(\"var\", \"overlap\", \"_children\", \"_setDims\"),\n\n new := meth(self, var, domain, overlap, expr)\n local res;\n Constraint(IsSPL(expr));\n Constraint(not IsInt(domain) or domain > 0);\n var.isLoopIndex := true;\n res := SPL(WithBases(self, rec(_children := [expr], var := var, domain := domain, overlap := overlap)));\n res.dimensions := res.dims();\n return res;\n end,\n #-----------------------------------------------------------------------\n print := meth(self, indent, indentStep)\n Print(self.name, \"(\", self.var, \", \", self.domain, \", \", self.overlap, \",\");\n self._newline(indent + indentStep);\n SPLOps.Print(self._children[1], indent+indentStep, indentStep); #, \", \", self.nt_maps);\n self._newline(indent);\n Print(\")\");\n if IsBound(self._setDims) then\n Print(\".overrideDims(\", self._setDims, \")\");\n fi;\n end,\n #-----------------------------------------------------------------------\n _dims := self >> self.unroll().dims(),\n dims := self >> When(IsBound(self._setDims), self._setDims, let(d := Try(self._dims()), When(d[1], d[2], [errExp(), errExp()]))),\n #-----------------------------------------------------------------------\n unroll := self >> ApplyFunc(self.directOper, [self.overlap, self.unrolledChildren()]),\n #-----------------------------------------------------------------------\n transpose := self >> ApplyFunc(self.transposeOper(), [self.var, self.domain, self.overlap, self.child(1).transpose()]),\n #-----------------------------------------------------------------------\n conjTranspose := self >> ApplyFunc(self.transposeOper(), [self.var, self.domain, self.overlap, self.child(1).conjTranspose()])\n));\n\n\n# ==========================================================================\n# IColDirSum(<var>, <range>, <overlap>, <spl>) - Iterative direct sum.\n# Dimensions of <spl> are assumed to not depend on <var>.\n# ==========================================================================\nClass(IColDirSum, IRowDirSum, rec(\n directOper := ColDirectSum,\n transposeOper := self >> IRowDirSum\n));\n\n\n# ==========================================================================\n# IterCompose(<var>, <domain>, <spl>) - iterative compose\n# <spl> must be square\n# ==========================================================================\nClass(IterCompose, BaseIterative, rec(\n directOper := Compose,\n #-----------------------------------------------------------------------\n dims := self >> self._children[1].dimensions,\n #-----------------------------------------------------------------------\n unroll := self >> Compose(self.unrolledChildren()),\n #-----------------------------------------------------------------------\n # NOTE: this is incorrect, one has to reverse the order\n transpose := self >> CopyFields(self, rec(\n _children := [self._children[1].transpose()],\n domain := self.domain,\n dimensions := self.dimensions))\n # NOTE: conjTranspose() is missing\n));\n\nDeclare(IterVStack);\n\n# ==========================================================================\n# IterHStack(<var>, <domain>, <spl>)\n# Dimensions of <spl> are assumed to not depend on <var>.\n# ==========================================================================\nClass(IterHStack, BaseIterative, rec(\n directOper := HStack,\n #-----------------------------------------------------------------------\n unroll := self >> HStack(self.unrolledChildren()),\n #-----------------------------------------------------------------------\n dims := self >> [ self.child(1).dimensions[1],\n self.child(1).dimensions[2] self.domain ],\n #-----------------------------------------------------------------------\n transpose := self >> IterVStack(self.var, self.domain, self.child(1).transpose()),\n conjTranspose := self >> IterVStack(self.var, self.domain, self.child(1).conjTranspose())\n));\n\n# this is a HStack that is guaranteed not to perform any ops, and doesnt need ScatAcc in SumsGen\nClass(IterHStack1, IterHStack);\n# ==========================================================================\n# IterVStack(<var>, <domain>, <spl>)\n# Dimensions of <spl> are assumed to not depend on <var>.\n# ==========================================================================\nClass(IterVStack, BaseIterative, rec(\n directOper := VStack,\n #-----------------------------------------------------------------------\n unroll := self >> VStack(self.unrolledChildren()),\n #-----------------------------------------------------------------------\n dims := self >> [ self.child(1).dimensions[1] * self.domain,\n self.child(1).dimensions[2] ],\n #-----------------------------------------------------------------------\n transpose := self >> IterHStack(self.var, self.domain, self.child(1).transpose()),\n conjTranspose := self >> IterHStack(self.var, self.domain, self.child(1).conjTranspose())\n));\n\n#IterDirectSum := IDirSum;\n# ==========================================================================\n# IterDirectSum(<var>, <domain>, <spl>)\n# Dimensions of <spl> are assumed to not depend on <var>.\n# ==========================================================================\nClass(IterDirectSum, BaseIterative, rec(\n directOper := DirectSum, \n #-----------------------------------------------------------------------\n unroll := self >> DirectSum(self.unrolledChildren()),\n #-----------------------------------------------------------------------\n dims := self >> [self.child(1).dimensions[1] * self.domain, self.child(1).dimensions[2]*self.domain],\n #-----------------------------------------------------------------------\n transpose := self >> IterHStack(self.var, self.domain, self.child(1).transpose()),\n conjTranspose := self >> IterHStack(self.var, self.domain, self.child(1).conjTranspose())\n));\n", "meta": {"hexsha": "1603ccc9edf04657c1e08a4645385925d5a4bd46", "size": 8097, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/spl/Iter.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/Iter.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/Iter.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": 51.246835443, "max_line_length": 133, "alphanum_fraction": 0.4213906385, "num_tokens": 1527, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6297746213017459, "lm_q2_score": 0.6584175072643413, "lm_q1q2_score": 0.4146546362958401}}
	{"text": "################################################################################\n##\n#W TY_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 near_group_data functions of the GroupTheoretical Package\n##\n#Y Copyright (C) 2016, Battelle Memorial Institute\n##\n################################################################################\n\n\n################################################################################\n##\n#F near_group_data(<group>,<int>). . . . . . compute the data\n## . . . . . . . . . . . . . . . . . . . . . for a neargroup category k=0 is TY.\n##\nInstallGlobalFunction(near_group_data, function(G,k)\n local Simples,m,N,rank,x,FPdimC,FPdim,S,T,g_idx,h_idx,g,h;\n\n if k < 0 or not(IsInt(k)) then\n Error(\"k must be a non-negative integer\\n\");\n fi;\n\n if k > 0 then\n\n Error(\"k > 0 is not currently supported. We need to unravel Siehler's paper 'Near-group categories\\n\");\n\n if Order(G) > k+1 then\n Error(\"near group categories only admit monoidal structure for \|G\| <= k+1\");\n fi;\n\n if Order(G) = k+1 and not(IsCyclic(G) and Size(Set(FactorsInt(Order(G)+1))) = 1) then\n Error(\"for \|G\| = k+1, the near group category only admits monoidal structure if G is the multiplicative group of a finite field.\");\n fi;\n\n if Order(G) = 1 and ( (k mod 4) = 2 or (k mod 4) = 3) then\n Error(\"For \|G\| = 1, the near group category does not admit monoidal structure if k = 2 or 3 mod 4.\");\n fi;\n fi;\n\n Simples := ShallowCopy(AsSet(G));\n m:=\"m\";\n Add(Simples,m);\n rank:=Size(Simples);\n N:=List([1..rank],x->NullMat(rank,rank));\n # compute the fusion rules\n for g_idx in [1..rank] do\n g:=Simples[g_idx];\n for h_idx in [1..rank] do\n h:=Simples[h_idx];\n if g_idx = rank then\n if h_idx = rank then\n # m\\otimes m = Sum_{k\\in G}k+km\n N[g_idx][h_idx]:=List([1..rank],x->1);\n N[g_idx][h_idx][rank] := k;\n else\n N[g_idx][h_idx][rank] := 1; # m\\otimes h = m\n fi;\n else\n if h_idx = rank then\n N[g_idx][h_idx][rank] := 1; # g\\otimes m = m\n else \n # g\\otimes h = gh\n N[g_idx][h_idx][Position(Simples,gh)] := 1;\n fi;\n fi;\n od;\n od;\n\n FPdimC := 2Order(G);\n FPdim := List([1..rank],x->1);\n FPdim[rank] := Sqrt(Order(G));\n return [Simples, N, FPdim, FPdimC];\nend);\n\n################################################################################\n##\n#F TY_data(<group>,<bicharacter>,<num>,<list>,<sign>). . . . compute the data for TY(G,chi,tau,delta,Tsign)\n##\nInstallGlobalFunction(TY_data, function(G,chi,tau,delta,Tsign)\n local Simples,m,N,rank,x,FPdimC,FPdim,S,T,sigma1,sigma3_1,sigma3,sigma3_squared,sigma3_squared_trace,g_idx,h_idx,g,h;\n\n if not(IsInt(Tsign)) or Tsign^2 <> 1 then\n Error(\"Tsign must be +/-1\");\n fi;\n\n if Size(delta)<>Order(G)+1 or false in List(delta,x->(IsInt(x) and x^2=1)) then\n Error(\"delta must be a list of length \|G\|+1 and consist entirely of +/- 1\");\n fi;\n\n if (1/tau)^2 <> Order(G) then\n Error(\"tau must be a choice of squareroot of 1/\|G\|\");\n fi;\n\n Simples := ShallowCopy(AsSet(G));\n m:=\"m\";\n Add(Simples,m);\n rank:=Size(Simples);\n N:=List([1..rank],x->NullMat(rank,rank));\n # compute the fusion rules\n for g_idx in [1..rank] do\n g:=Simples[g_idx];\n for h_idx in [1..rank] do\n h:=Simples[h_idx];\n if g_idx = rank then\n if h_idx = rank then\n # m\\otimes m = Sum_{k\\in G}k+km\n N[g_idx][h_idx]:=List([1..rank],x->1);\n N[g_idx][h_idx][rank] := 0;\n else\n N[g_idx][h_idx][rank] := 1; # m\\otimes h = m\n fi;\n else\n if h_idx = rank then\n N[g_idx][h_idx][rank] := 1; # g\\otimes m = m\n else \n # g\\otimes h = gh\n N[g_idx][h_idx][Position(Simples,gh)] := 1;\n fi;\n fi;\n od;\n od;\n\n FPdimC := 2Order(G);\n FPdim := List([1..rank],x->1);\n FPdim[rank] := Sqrt(Order(G));\n\n if not(IsAbelian(G) and Exponent(G)=2) then\n # not braided. Return the fusion rules and simples (arxiv:math/0011037v1)\n Display(\"G is not an elementary abelian 2-group and so the associated category does not admit a braiding.\");\n return [Simples, N, FPdim, FPdimC];\n else\n # the category admits a braiding.\n # \n # need to compute the S-matrix and T-matrix\n #\n # First we compute T\n sigma1:=List([1..rank-1],x->delta[x]Sqrt(chi[x][x]));\n sigma3_1:=delta[1]Sqrt(tauSum(sigma1));\n T:=List([1..rank],x->0);\n for x in [1..rank-1] do\n T[x] := chi[x][x];\n od;\n T[rank]:=Tsign/sigma3_1;\n S:=NullMat(rank,rank);\n # sigma1 = sigma2 (Seihler section 2.3)\n # since delta[x] = pm1 we have sigma1[g]sigma2[g] = chi[g][g]\n sigma3:=List([1..rank-1],x->sigma3_1sigma1[x]chi[x][x]);\n sigma3_squared:=List(sigma3,x->x^2);\n sigma3_squared_trace:=Sum(sigma3);\n for g in [1..rank-1] do\n for h in [1..rank-1] do\n # group elements are invertible\n #S[g][h] := chi[g][h]chi[h][g]FPdim[g]FPdim[h];\n S[g][h] := chi[g][h]chi[h][g];\n od;\n #S[g][m] := sigma1[g]sigma2[g]FPdim[g]FPdim[rank];\n # group elements are invertible\n S[g][rank] := chi[g][g]FPdim[rank];\n S[rank][g] := S[g][rank];\n od;\n S[rank][rank] := sigma3_squared_traceFPdim[rank]FPdim[rank];\n Display(\"VERIFY S and T\\n\");\n return [Simples,S,T,N,FPdim,FPdimC];\n fi;\nend);\n#E near_group_data.gi . . . . . . . . . . . . . . . . . . . . . . . . ends here\n", "meta": {"hexsha": "19e6999dc875f63c493675658423d5f92c2f7ca8", "size": 5573, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "lib/near_group_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/near_group_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/near_group_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": 32.5906432749, "max_line_length": 138, "alphanum_fraction": 0.5420778755, "num_tokens": 1842, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7154240079185319, "lm_q2_score": 0.5774953651858118, "lm_q1q2_score": 0.4131540487156097}}
	{"text": "#############################################################################\n##\n#W mindeg.gi GAP 4 package SingerAlg Thomas Breuer\n##\n## This file contains the implementation for GAP functions related to\n## the numbers <M>m(q,e)</M>.\n##\n\n\n#############################################################################\n##\n#M SingerAlgE( <A> )\n#M SingerAlgE( <q>[, <n>], <z> )\n##\nInstallMethod( SingerAlgE,\n [ \"IsSingerAlgebra\" ],\n A -> CallFuncList( SingerAlgE, ParametersOfSingerAlgebra( A ) ) );\n\nInstallMethod( SingerAlgE,\n [ \"IsPosInt\", \"IsPosInt\", \"IsPosInt\" ],\n { q, n, z } -> (q^n-1) / z );\n\nInstallMethod( SingerAlgE,\n [ \"IsPosInt\", \"IsPosInt\" ],\n { q, z } -> (q^OrderMod( q, z )-1) / z );\n\n\n#############################################################################\n##\n#M MinimalDegreeOfSingerAlgebraGAP( <A> )\n#M MinimalDegreeOfSingerAlgebraGAP( <q>, <e> )\n#M MinimalDegreeOfSingerAlgebraGAP( <q>, <n>, <e> )\n##\n## If the <Ref Attr=\"LoewyStructureInfo\" Label=\"for a Singer algebra\"/>\n## value of the Singer algebra <A>A</A> is known then use it.\n## If the cheap criteria suffice then take their result.\n## Otherwise call the hard method for <A>q</A> and <A>e</A>;\n## if the dimension of the algebra is small then use the algebra\n## also if just the parameters <A>q</A> and <A>e</A> are given.\n##\nInstallMethod( MinimalDegreeOfSingerAlgebraGAP,\n [ \"IsSingerAlgebra and HasLoewyStructureInfoGAP\" ],\n A -> LoewyStructureInfoGAP( A ).m );\n\nInstallMethod( MinimalDegreeOfSingerAlgebraGAP,\n [ \"IsSingerAlgebra\" ],\n function( A )\n local paras, q, n, e;\n\n # Note that we cannot assume that the parameter 'n' is equal to\n # the multiplicative order of 'q' modulo 'e'.\n paras:= ParametersOfSingerAlgebra( A );\n q:= paras[1];\n n:= paras[2];\n e:= SingerAlgE( A );\n return MinimalDegreeOfSingerAlgebraGAP( q, OrderModExt( q, e, n ), e );\n end );\n\nInstallMethod( MinimalDegreeOfSingerAlgebraGAP,\n [ \"IsPosInt\", \"IsPosInt\" ],\n { q, e } -> MinimalDegreeOfSingerAlgebraGAP( q, OrderMod( q, e ), e ) );\n\nInstallMethod( MinimalDegreeOfSingerAlgebraGAP,\n [ \"IsPosInt\", \"IsPosInt\", \"IsPosInt\" ],\n function( q, n, e )\n local e_str, cache_e, m;\n\n q:= q mod e;\n e_str:= String( e ); # large integers cannot be record component names\n\n if not IsBound( MinimalDegreeOfSingerAlgebraCache.( e_str ) ) then\n cache_e:= rec();\n MinimalDegreeOfSingerAlgebraCache.( e_str ):= cache_e;\n else\n cache_e:= MinimalDegreeOfSingerAlgebraCache.( e_str );\n if IsBound( cache_e.( q ) ) then\n return cache_e.( q );\n fi;\n fi;\n\n m:= MinimalDegreeCheapGAP( q, n, e );\n if m = 0 then\n m:= MinimalDegreeHardGAP( q, n, e );\n fi;\n\n # Extend the cache.\n cache_e.( q ):= m;\n\n return m;\n end );\n\n\n#############################################################################\n##\n#F MinimalDegreeCheapGAP( <q>, <n>, <e> )\n##\n## Return either <C>0</C> or the number <M>m( <A>q</A>, <A>e</A> )</M>,\n## which is the smallest number of powers of <A>q</A>\n## such that <A>e</A> divides the sum of these powers.\n## <P/>\n## The return value <C>0</C> means that the cheap criteria from\n## the two papers <Cite Key=\"BHHK1\"/> and <Cite Key=\"BHHK2\"/>\n## do not suffice to determine <M>m( <A>q</A>, <A>e</A> )</M>.\n## <P/>\n## We assume that\n## <A>q</A> is smaller than <A>e</A>,\n## the argument <A>n</A> is\n## <C>OrderMod( </C><A>q</A><C>, </C><A>e</A><C> )</C>.\n## The function does not use cached values of <M>m( <A>q</A>, <A>e</A> )</M>\n## or values known via the database of low dimensional Singer algebras.\n##\nInstallGlobalFunction( MinimalDegreeCheapGAP, function( q, n, e )\n local e1, e2, m;\n\n if e = 1 then\n return 1;\n fi;\n\n Assert( 2, PowerMod( q, n, e ) = 1 and OrderModExt( q, e, n ) = n );\n\n if q = 1 then\n # Example I.6.1.\n return e;\n elif IsEvenInt( n ) and PowerModInt( q, n/2, e ) = e-1 then\n # Decide the case m = 2, see Lemma I.6.3.\n return 2;\n elif n = 2 then\n # Prop. II.2.7.\n e1:= Gcd( e, q-1 );\n e2:= Gcd( e, q+1 );\n if e2 <= e1 or ( IsEvenInt( e ) and IsEvenInt( (q^2-1)/e ) ) then\n return e1;\n else\n return 2 * e1;\n fi;\n fi;\n\n # Deal with those cases where e is a prime power,\n # and where we know the value of m(q,e).\n if IsPrimePowerInt( e ) then\n # Let e = p^k for a prime p.\n if e mod 2 = 0 then\n # see Prop. II.2.9, note that here we have e > 4 and q mod e <> q-1.\n if q mod 4 = 1 then\n return Gcd( e, q-1 );\n else\n Assert( 1, ( q+1 ) mod e <> 0 );\n return 4;\n fi;\n else\n # see Prop. II.2.10, note that q \\equiv 1 \\pmod{p}\n # if and only if \\gcd( e, q-1 ) \\not= 1 holds.\n m:= Gcd( e, q-1 );\n if m <> 1 then\n return m;\n elif n mod 3 = 0 then\n # Here we know that m(q,e) > 2 and thus p \\not= 3.\n # Hence \\gcd( e, q^{n/3}-1 ) = 1 holds,\n # because otherwise q^{n/3} would be a p-element in (Z/eZ)^.\n # Thus Lemma I.6.4 yields m(q,e) \\leq 3.\n # (This is a generalization of Cor. II.2.11.)\n return 3;\n elif 2 n = Phi( e ) then\n # Cor. II.2.14.\n return 3;\n elif e mod 11 = 0 then\n # Prop. II.2.16.\n return 5;\n fi;\n fi;\n fi;\n\n # Deal with those cases where e is twice an odd prime power,\n # and where we know the value of m(q,e).\n if IsEvenInt( e ) and IsPrimePowerInt( e/2 ) then\n # see Prop. II.2.17, note that the order of q mod e is a power of p\n # if and only if \\gcd( e/2, q-1 ) \\not= 1 holds.\n m:= Gcd( e, q-1 );\n if m > 2 then\n return m;\n fi;\n fi;\n\n # We give up.\n return 0;\n end );\n\n\n#############################################################################\n##\n#F VectorIterator( m, n, s )\n##\n## iterator for all vectors of length n\n## with entries in { 0, 1, 2, ... m }\n## and coefficient sum s, such that ...\n##\n## fill the first n positions in v with smallest partition of s into\n## numbers at most m\n## (we assume that s <= mn)\n##\nBindGlobal( \"VectorIterator_ResetPrefix\", function( v, m, n, s )\n local rest, i, j;\n\n rest:= s;\n i:= 1;\n while m < rest do\n v[i]:= m;\n rest:= rest - m;\n i:= i + 1;\n od;\n v[i]:= rest;\n for j in [ i+1 .. n ] do\n v[j]:= 0;\n od;\n\n return v;\n end );\n\nBindGlobal( \"VectorIterator\", function( m, n, s )\n local next;\n\n if s > mn then\n # The iterator is empty.\n next:= false;\n else\n # Initialize the coefficient vector.\n next:= VectorIterator_ResetPrefix( [], m, n, s );\n fi;\n\n return IteratorByFunctions( rec(\n NextIterator:= function( iter )\n local result, pos, succ;\n\n result:= iter!.next;\n # Find the first position with a nonzero value\n # such that the value on the right is smaller than m.\n pos:= First( [ 1 .. iter!.n - 1 ],\n i -> result[i] <> 0 and result[ i+1 ] < iter!.m );\n if pos = fail then\n succ:= false;\n else\n succ:= ShallowCopy( result );\n succ[ pos ]:= result[ pos ] - 1;\n succ[ pos + 1 ]:= result[ pos + 1 ] + 1;\n VectorIterator_ResetPrefix( succ, iter!.m, pos,\n Sum( succ{ [ 1 .. pos ] } ) );\n fi;\n iter!.next:= succ;\n return result;\n end,\n\n IsDoneIterator:= iter -> ( iter!.next = false ),\n\n ShallowCopy:= function( iter )\n end,\n\n m:= m,\n n:= n,\n s:= s,\n\n next:= next,\n ) );\n end );\n\n\n#############################################################################\n##\n#F MinimalDegreeHardGAP( <q>, <n>, <e> )\n##\n## - assume that the cheap criteria do not yield the result\n## (e.g., m = 2 cannot occur here)\n## - assume q < e\n## - assume that n equals OrderMod( q, e )\n## - do not use the cache\n## - do not create the monomials by computing all q-adic expansions at once,\n## but create these coefficient vectors one by one, using an iterator\n## - for increasing values of m, run over those coefficient vectors\n## of length n and with entries in \\{ 0, 1, \\ldots, m \\}\n## such that the coefficient sum is s\n## and such that a largest entry is in the first position.\n##\nInstallGlobalFunction( MinimalDegreeHardGAP, function( q, n, e )\n local z, e1, m, powers, a, v;\n\n Assert( 2, PowerMod( q, n, e ) = 1 and OrderModExt( q, e, n ) = n );\n\n # If A[q,n,z] has small dimension and e is not very small\n # then enumerate its basis.\n # (For small e, we known that the m values are small,\n # so it is cheaper not to enumerate.)\n if e > 100 then\n z:= ( q^n - 1 ) / e;\n if z <= 10^5 then\n return LoewyStructureInfoGAP( q, n, z ).m;\n fi;\n fi;\n\n # m(q,e) is divisible by \\gcd( e, q-1 ), and m(q,e) \\geq 3.\n e1:= Gcd( e, q-1 );\n if e1 = 1 then\n m:= 3;\n elif e1 = 2 then\n m:= 4;\n else\n m:= e1;\n fi;\n\n powers:= List( [ 1 .. n-1 ], i -> PowerModInt( q, i, e ) );\n\n while true do\n for a in [ 1 .. m ] do\n for v in VectorIterator( a, n-1, m-a ) do\n if ( a + v * powers ) mod e = 0 then\n return m;\n fi;\n od;\n od;\n m:= m + e1;\n od;\n end );\n\n\n#############################################################################\n##\n#M MinimalDegreeOfSingerAlgebraJulia( <A> )\n#M MinimalDegreeOfSingerAlgebraJulia( <q>, <e> )\n#M MinimalDegreeOfSingerAlgebraJulia( <q>, <n>, <e> )\n##\n## Use the same criteria as for the &GAP; variant.\n## These methods are available only if &Julia; is available.\n##\nif IsPackageMarkedForLoading( \"JuliaInterface\", \"\" ) then\n\nInstallMethod( MinimalDegreeOfSingerAlgebraJulia,\n [ \"IsSingerAlgebra and HasLoewyStructureInfoJulia\" ],\n A -> JuliaToGAP( IsInt,\n Julia.Base.get( LoewyStructureInfoJulia( A ),\n JuliaSymbol( \"m\" ), 0 ) ));\n\nInstallMethod( MinimalDegreeOfSingerAlgebraJulia,\n [ \"IsSingerAlgebra\" ],\n function( A )\n local paras, q, n, e;\n\n # Note that we cannot assume that the parameter 'n' is equal to\n # the multiplicative order of 'q' modulo 'e'.\n paras:= ParametersOfSingerAlgebra( A );\n q:= paras[1];\n n:= paras[2];\n e:= SingerAlgE( A );\n\n # Supply 'A' as an argument in order to set the GAP attribute.\n return JuliaToGAP( IsInt,\n Julia.SingerAlg.MinimalDegree( q, OrderModExt( q, e, n ), e,\n A ) );\n end );\n\nInstallMethod( MinimalDegreeOfSingerAlgebraJulia,\n [ \"IsPosInt\", \"IsPosInt\" ],\n { q, e } -> JuliaToGAP( IsInt,\n Julia.SingerAlg.MinimalDegree( q, GAPToJulia( e ) ) ) );\n\nInstallMethod( MinimalDegreeOfSingerAlgebraJulia,\n [ \"IsPosInt\", \"IsPosInt\", \"IsPosInt\" ],\n { q, n, e } -> JuliaToGAP( IsInt,\n Julia.SingerAlg.MinimalDegree( q, n, GAPToJulia( e ) ) ) );\n\nfi;\n\n\n#############################################################################\n##\n#E\n\n", "meta": {"hexsha": "c2162ad72bc30d4587b9d2cc1a5abfbb585ac241", "size": 11349, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "gap/mindeg.gi", "max_stars_repo_name": "oscar-system/SingerAlg", "max_stars_repo_head_hexsha": "7d303756163638d97fa3bc93dd3546b400a4122f", "max_stars_repo_licenses": ["Naumen", "Condor-1.1", "MS-PL"], "max_stars_count": 3, "max_stars_repo_stars_event_min_datetime": "2020-09-11T10:12:03.000Z", "max_stars_repo_stars_event_max_datetime": "2021-10-02T13:37:49.000Z", "max_issues_repo_path": "gap/mindeg.gi", "max_issues_repo_name": "oscar-system/SingerAlg", "max_issues_repo_head_hexsha": "7d303756163638d97fa3bc93dd3546b400a4122f", "max_issues_repo_licenses": ["Naumen", "Condor-1.1", "MS-PL"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2021-05-04T21:41:17.000Z", "max_issues_repo_issues_event_max_datetime": "2021-05-04T21:41:17.000Z", "max_forks_repo_path": "gap/mindeg.gi", "max_forks_repo_name": "oscar-system/SingerAlg", "max_forks_repo_head_hexsha": "7d303756163638d97fa3bc93dd3546b400a4122f", "max_forks_repo_licenses": ["Naumen", "Condor-1.1", "MS-PL"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 30.264, "max_line_length": 78, "alphanum_fraction": 0.5167856199, "num_tokens": 3457, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. 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	{"text": "#\n# walrus: Computational Methods for Finitely Generated Monoids and Groups\n#\n\nInstallGlobalFunction(NewPregroupWord,\nfunction(pg, word)\n local maxk, rel;\n maxk := MaxPowerK(word);\n return Objectify(IsPregroupRelatorType,\n rec( pregroup := pg\n , base := maxk[1]\n , exponent := maxk[2]\n , baselen := Length(maxk[1]) ) );\nend);\n\nInstallGlobalFunction(NewPregroupRelator,\nfunction(pres, word, id)\n local maxk, rel;\n maxk := MaxPowerK(word);\n rel := Objectify(IsPregroupRelatorType,\n rec( pres := pres\n , base := maxk[1]\n , exponent := maxk[2]\n , baselen := Length(maxk[1])\n , __ID := id)\n );\n return rel;\nend);\n\nInstallMethod(Base, \"for a pregroup relator\",\n [IsPregroupRelator and IsPregroupRelatorRep ],\n r -> r!.base);\n\nInstallMethod(Exponent, \"for a pregroup relator\",\n [IsPregroupRelator and IsPregroupRelatorRep ],\n r -> r!.exponent);\n\nInstallMethod(Inverse, \"for a pregroup relator\",\n [ IsPregroupRelator and IsPregroupRelatorRep ],\n r -> Objectify(IsPregroupRelatorType,\n rec( pres := r!.pres\n , base := List(Reversed(r!.base), PregroupInverse)\n , exponent := r!.exponent\n , baselen := r!.baselen\n , __ID := -r!.__ID)\n ));\nInstallMethod(PregroupPresentationOf,\n \"for pregroup relators\",\n [IsPregroupRelator],\n r -> r!.pres);\n\nInstallMethod(Locations, \"for a pregroup relator\",\n [IsPregroupRelator],\nfunction(r)\n return List([1..r!.baselen], i -> NewLocation(r, i));\nend);\n\nInstallMethod(\\[\\], \"for a pregroup relator\",\n [IsPregroupRelator and IsPregroupRelatorRep, IsInt],\nfunction(r, p)\n local i, l;\n i := RemInt(p - 1, r!.baselen);\n if i < 0 then\n i := i + r!.baselen;\n fi;\n return r!.base[i + 1];\nend);\n\nInstallMethod(Length, \"for a pregroup relator\",\n [ IsPregroupRelator and IsPregroupRelatorRep ],\nfunction(r)\n return r!.baselen * r!.exponent;\nend);\n\n# we could possibly store this on creation\n# But this is run at most once anyway\nInstallMethod(Places, \"for a pregroup relator\",\n [ IsPregroupRelator and IsPregroupRelatorRep ],\nfunction(r)\n local P, res;\n\n res := [];\n\n for P in Places(PregroupPresentationOf(r)) do\n if Relator(P) = r then\n Add(res, P);\n fi;\n od;\n return res;\nend);\n\nInstallMethod(ViewString, \"for a pregroup relator\",\n [IsPregroupRelator],\nfunction(r)\n if Exponent(r) > 1 then\n return STRINGIFY(\"<pregroup relator (\"\n , List(r!.base, ViewString)\n , \")^\", r!.exponent, \">\");\n else\n return STRINGIFY(\"<pregroup relator \"\n , List(r!.base, ViewString)\n , \">\");\n fi;\nend);\n\nInstallMethod(IsBound\\[\\], \"for a pregroup relator, and an position\",\n [IsPregroupRelator, IsInt], ReturnTrue );\n\n\nInstallMethod(\\=, \"for a pregroup relator, and a pregroup relator\",\n [IsPregroupRelator, IsPregroupRelator],\nfunction(l,r)\n # id is uniqe wrt pregroup presentation. We should probably\n # make a family of relators for each presentation etc\n return l!.__ID = r!.__ID;\n return (l!.exponent = r!.exponent)\n and (l!.base = r!.base);\nend);\n\nInstallMethod(\\in, \"for a generator and a pregroup relator\",\n [ IsElementOfPregroup, IsPregroupRelator and IsPregroupRelatorRep],\nfunction(e,r)\n return e in r!.base;\nend);\n\n#T redo and move to pregroup files\nInstallGlobalFunction(ReduceUPregroupWord,\nfunction(word)\n local rw, rw2, i, j, one;\n\n if Length(word) = 0 then\n return [];\n fi;\n\n one := PregroupOf(word[1])[1];\n rw := ShallowCopy(word);\n\n for i in [2..Length(rw)] do\n if rw[i-1] * rw[i] <> fail then\n rw[i] := rw[i-1] * rw[i];\n rw[i-1] := one;\n fi;\n od;\n\n i := 1; j := 1;\n rw2 := [];\n while i <= Length(rw) do\n if rw[i] <> one then\n rw2[j] := rw[i];\n j := j + 1;\n fi;\n i := i + 1;\n od;\n\n return rw2;\nend);\n\n\n", "meta": {"hexsha": "6c6c84d3a5ffc56e47950eb2fe19144738114982", "size": 4467, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "gap/relator.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/relator.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/relator.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": 28.0943396226, "max_line_length": 82, "alphanum_fraction": 0.5374972017, "num_tokens": 1195, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. 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	{"text": "MEMO_Base64Digits :=\n \"0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz-_\";\n\nInstallGlobalFunction(MEMO_Digits,\nfunction(n, base, args...)\n local minlen, len, digits, str;\n # Adapted from the DigitsNumber function in GAPDoc-1.6.1\n if Length(args) = 0 then\n minlen := 0;\n elif Length(args) = 1 then\n minlen := args[1];\n else\n return fail;\n fi;\n digits := MEMO_Base64Digits;\n str := \"\";\n while n <> 0 do\n Add(str, digits[(n mod base) + 1]);\n n := QuoInt(n, base);\n od;\n if Length(str) < minlen then\n # Pad with zeroes\n Append(str, ListWithIdenticalEntries(minlen - Length(str), digits[1]));\n fi;\n return Reversed(str);\nend);\n\nInstallGlobalFunction(MEMO_Hash,\nfunction(key)\n local str, ints, sum, i;\n IO_ClearPickleCache(); # In case IO_Pickle was recently interrupted\n str := IO_Pickle(key); # Pickle the key to a string\n ints := SHA256String(str); # Get the SHA-256 checksum in 32-bit chunks\n sum := 0; # Bring all 256 bits together into a single integer\n for i in [1..Length(ints)] do\n sum := sum + ints[i] * 2 ^ (32 * (i-1));\n od;\n str := MEMO_Digits(sum, 64, 43); # Make into a padded base-64 string\n return str;\nend);\n", "meta": {"hexsha": "6486b6644034bb56e30018e056958a561f2bc4f8", "size": 1187, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "gap/hashing.gi", "max_stars_repo_name": "gap-packages/Memoisation", "max_stars_repo_head_hexsha": "0b1c1c172d52d57376876fd345aaa7db81792df1", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 3, "max_stars_repo_stars_event_min_datetime": "2019-08-20T21:02:33.000Z", "max_stars_repo_stars_event_max_datetime": "2019-12-19T09:25:15.000Z", "max_issues_repo_path": "gap/hashing.gi", "max_issues_repo_name": "gap-packages/Memoisation", "max_issues_repo_head_hexsha": "0b1c1c172d52d57376876fd345aaa7db81792df1", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 7, "max_issues_repo_issues_event_min_datetime": "2018-08-06T11:56:51.000Z", "max_issues_repo_issues_event_max_datetime": "2020-02-04T15:04:36.000Z", "max_forks_repo_path": "gap/hashing.gi", "max_forks_repo_name": "gap-packages/Memoisation", "max_forks_repo_head_hexsha": "0b1c1c172d52d57376876fd345aaa7db81792df1", "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": 28.9512195122, "max_line_length": 75, "alphanum_fraction": 0.6663858467, "num_tokens": 369, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7025300573952054, "lm_q2_score": 0.5813030906443133, "lm_q1q2_score": 0.4083828936343597}}
	{"text": "\n# Copyright 2018-2019, Carnegie Mellon University\n# See LICENSE for details\n\nDeclare(OLCompose);\n\nClass(OLCompose, Compose, rec(\n printSeparationChar := \" o \",\n toOperator := self >> (vec -> Checked(Length(vec)=self.dims()[2], OLCompose(DropLast(self._children, 1)).toOperator()(Last(self._children).toOperator()(vec))))\n));\n\nClass(LinearSystem, BaseMat, rec(\n abbrevs := [ (A, b) -> [A, b] ],\n new := (self, A, b) >> SPL(WithBases(self, rec(\n mat := A, rhs := b, dimensions := [Rows(A), Cols(A)]))),\n print := (self, i, is) >> Print(\"LinearSystem(\", self.mat, \", \", self.rhs, \")\"),\n dims := self >> self.dimensions,\n rChildren := self >> [self.mat, self.rhs],\n rSetChild := rSetChildFields(\"mat\", \"rhs\"),\n isReal := True\n));\n\nClass(Reduction, BaseMat, rec(\n abbrevs := [ (N, op, idval, isSaturated) -> [N, op, idval, isSaturated] ],\n new := (self, N, op, idval, isSaturated) >> SPL(WithBases(self, rec(\n N := N, op := op, idval := idval, isSaturated := isSaturated, dimensions := [1, N]))),\n print := (self, i, is) >> Print(\"Reduction(\", self.N, \", \", self.op, \", \", self.idval, \", \", self.isSaturated, \")\"),\n dims := self >> self.dimensions,\n rChildren := self >> [self.N, self.op, self.idval, self.isSaturated],\n rSetChild := rSetChildFields(\"N\", \"op\", \"idval\", \"isSaturated\"),\n transpose := self >> self,\n isReal := True,\n toOperator := self >> (vec -> Checked(Length(vec)=self.dims()[2], [RulesStrengthReduce(FoldL(vec, self.op, self.idval)).v]))\n));\n\nClass(Induction, BaseMat, rec(\n abbrevs := [ (N, op, initval) -> [N, op, initval] ],\n new := (self, N, op, initval) >> SPL(WithBases(self, rec(\n N := N, op := op, initval := initval, dimensions := [N, 1]))),\n print := (self, i, is) >> Print(\"Induction(\", self.N, \", \", self.op, \", \", self.initval, \")\"),\n dims := self >> self.dimensions,\n rChildren := self >> [self.N, self.op, self.initval],\n rSetChild := rSetChildFields(\"N\", \"op\", \"initval\"),\n isReal := True,\n recurrence := self >> ((j,v)->When(j=0, self.initval, self.op.at(self.recurrence()(j-1,v),v))),\n toOperator := self >> (vec -> Checked(Length(vec)=self.dims()[2], List([0..self.N-1], i->_unwrap(RulesStrengthReduce(self.recurrence()(i,vec[1]))))))\n));\n\nClass(PointWise, BaseMat, rec(\n abbrevs := [ (N, op) -> [N, op] ],\n new := (self, N, op) >> SPL(WithBases(self, rec(\n N := N, op := op, dimensions := [N, N]))),\n print := (self, i, is) >> Print(\"PointWise(\", self.N, \", \", self.op, \")\"),\n dims := self >> self.dimensions,\n rChildren := self >> [self.N, self.op],\n rSetChild := rSetChildFields(\"N\", \"op\"),\n transpose := self >> self,\n isReal := True,\n toOperator := self >> (vec -> Checked(Length(vec)=self.dims()[2], List([0..Length(vec)-1], j->RulesStrengthReduce(self.op.at(vec[j+1], j)).v)))\n));\n\nClass(BinOp, BaseMat, rec(\n abbrevs := [ (N, op) -> [N, op] ],\n new := (self, N, op) >> SPL(WithBases(self, rec(\n N := N, op := op, dimensions := [N, 2N]))),\n print := (self, i, is) >> Print(\"BinOp(\", self.N, \", \", self.op, \")\"),\n dims := self >> self.dimensions,\n rChildren := self >> [self.N, self.op],\n rSetChild := rSetChildFields(\"N\", \"op\"),\n isReal := True,\n toOperator := self >> (vec -> Checked(Length(vec)=self.dims()[2], List([1..Length(vec)/2], j->RulesStrengthReduce(self.op.at(vec[j], vec[j+self.N])).v)))\n));\n\nClass(ScalarProd, BaseMat, rec(\n abbrevs := [ (N, scalars) -> [N, scalars] ],\n new := (self, N, scalars) >> SPL(WithBases(self, rec(\n N := N, scalars := scalars, dimensions := [1, N]))),\n print := (self, i, is) >> Print(\"ScalarProd(\", self.N, \", \", self.scalars, \")\"),\n dims := self >> self.dimensions,\n rChildren := self >> [self.N, self.scalars],\n rSetChild := rSetChildFields(\"N\", \"scalars\"),\n isReal := True,\n toOperator := self >>(vec -> Checked(Length(vec)=self.dims()[2], [_unwrapVec(self.scalars) vec]))\n));\n\nClass(Constant, BaseMat, rec(\n abbrevs := [ x -> [x]],\n new := (self, x) >> SPL(WithBases(self, rec(\n value := x, dimensions := [1,0]))),\n print := (self, i ,is) >> Print(\"Constant(\",self.value,\")\"),\n dims := self >> self.dimensions,\n rChildren := self >> [self.value],\n rSetChild := rSetChildFields(\"value\"),\n isReal := True\n));\t\t\n\nspiral.spl.IterVStack.toOperator := \n self >> (vec -> Checked(Length(vec)=self.dims()[2], \n Flat(List([0..self.var.range-1], \n j->RulesStrengthReduce(\n SubstVars(Copy(self._children[1]), \n rec((self.var.id):=V(j))\n )\n ).toOperator()(vec) )\n )\n )\n );\n\nspiral.spl.HStack.toOperator := \n self >> (vec -> Checked(Length(vec)=self.dims()[1]Length(self.children()), \n \t \t Sum(List([1..Length(self.children())], \n\t i->self.children()[i].toOperator()(vec{[(i-1)self.dims()[1] + 1..i*self.dims()[1]]})\n\t\t ))\n\t \t )\n );\n\nspiral.spl.DirectSum.toOperator := self >> (vec -> Checked(Length(vec)=Sum(List(self.children(), i->i.dims()[2])), \n ApplyFunc(Concat, List([1..Length(self.children())], \n i->self.children()[i].toOperator()(vec{\n [Sum(List(self.children(){[1..i-1]}, j->j.dims()[2]))+1..Sum(List(self.children(){[1..i]}, j->j.dims()[2]))]\n })))));\n\n\n\nspiral.spl.I.N := self >> self.params[1];\n", "meta": {"hexsha": "415716060653413e3b29aa137cee928de1a506cc", "size": 5515, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "spl.gi", "max_stars_repo_name": "spiral-software/spiral-package-hcol", "max_stars_repo_head_hexsha": "b4a0118382e3bba91ecd82a6c667f2cdb6389ceb", "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": "spl.gi", "max_issues_repo_name": "spiral-software/spiral-package-hcol", "max_issues_repo_head_hexsha": "b4a0118382e3bba91ecd82a6c667f2cdb6389ceb", "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": "spl.gi", "max_forks_repo_name": "spiral-software/spiral-package-hcol", "max_forks_repo_head_hexsha": "b4a0118382e3bba91ecd82a6c667f2cdb6389ceb", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2019-11-26T05:21:02.000Z", "max_forks_repo_forks_event_max_datetime": "2019-11-26T05:21:02.000Z", "avg_line_length": 43.7698412698, "max_line_length": 163, "alphanum_fraction": 0.5410698096, "num_tokens": 1673, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7025300573952054, "lm_q2_score": 0.5774953651858118, "lm_q1q2_score": 0.4057078520494534}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nImportAll(paradigms.smp); # for AParSMP\nImportAll(paradigms.vector); # for VRCLR\nImport(approx); # for CeilingRat.\n\n_swrap := (nt) -> let(t:=nt.firstTag(), ScratchWrap(t.size,t.nsgmts,t.linesize));\n\n_nodeFitsTensorDoesnt := (nt) -> let (\n k := nt.getTag(1).size,\n m := nt.params[1].dims()[2],\n n := nt.params[2],\n\n 2m <= k and mn >= k\n);\n\n_isALStoreTag := (nt) -> nt.isTag(1,ALStore) or nt.isTag(1,ALStoreCx);\n\nNewRulesFor(TTensorI, rec(\n# (In x Am)_{LS(<=k)} -> In x (Am)_{LS(<=k)} for m > k\n IxA_scratch_push := rec(\n forTransposition := false,\n applicable := nt -> nt.hasTags() \n and _isALStoreTag(nt)\n and IsParPar(nt.params) \n and nt.params[1].dims()[2] > nt.getTag(1).size,\n\n children := nt -> [[ nt.params[1].withTags(nt.getTags()) ]],\n apply := (nt, c, cnt) -> Tensor(I(nt.params[2]), c[1])\n ),\n \n AxI_scratch_push := rec(\n forTransposition := false,\n applicable := nt -> nt.hasTags()\n and _isALStoreTag(nt)\n and IsVecVec(nt.params)\n and nt.params[1].dims()[2] > nt.getTag(1).size,\n children := nt -> [[nt.params[1].withTags(nt.getTags())]],\n apply := (nt, c, cnt) -> Tensor(c[1], I(nt.params[2]))\n ),\n\n# ==========================================================\n# synchronous rules\n\n# (In x Am)_{LS(<=k)} -> Imn/k x (Ik/m x Am) for m\|k and k\|mn\n IxA_scratch := rec(\n forTransposition := false,\n applicable := nt -> nt.hasTags() \n and _isALStoreTag(nt)\n\t and IsParPar(nt.params)\n and IsPosInt(nt.getTag(1).size / nt.params[1].dims()[2])\n and IsPosInt(nt.params[1].dims()[2] * nt.params[2] / nt.getTag(1).size),\n\n children := nt -> [[ \n TTensorI(\n nt.params[1],\n nt.getTag(1).size / nt.params[1].dims()[2], \n APar, APar\n ).withTags(Drop(nt.getTags(),1)).setWrap(\n _swrap(nt)\n )\n ]],\n apply := (nt, c, cnt) -> let(k := nt.getTag(1).size, m := nt.params[1].dims()[2], n:= nt.params[2],\n DMAFence(Tensor(\n I(mn/k),\n LSKernel(c[1], nt.params[1].normalizedArithCost() k/m)\n )))\n ),\n\n# (Am x In)_{LS(<=k)} -> (L^m^2n/k_m x Ik/m) (Imn/k x (Am x Ik/m)) (L^m^2n/k_mn/k x Ik/m) for m\|k and k\|mn\n AxI_scratch := rec(\n forTransposition := false,\n applicable := nt -> nt.hasTags() \n and _isALStoreTag(nt)\n\t and IsVecVec(nt.params) \n and IsPosInt(nt.getTag(1).size / nt.params[1].dims()[2])\n and IsPosInt(nt.params[1].dims()[2]nt.params[2] / nt.getTag(1).size),\n\n children := nt -> [[ let(t := nt.firstTag(),\n TTensorI(\n nt.params[1], \n t.size / nt.params[1].dims()[2], \n AVec, AVec\n ).withTags(Drop(nt.getTags(),1)).setWrap(_swrap(nt))\n ) ]],\n\n apply := (nt, c, cnt) -> let(\n k := nt.getTag(1).size, \n m := nt.params[1].dims()[2], \n n:= nt.params[2],\n\n DMAFence(Prm(fTensor(L(m^2n/k, m), fId(k/m))) \n Tensor(\n I(mn/k),\n LSKernel(c[1], nt.params[1].normalizedArithCost() * k/m)\n ) \n Prm(fTensor(L(m^2n/k, mn/k), fId(k/m))))\n )\n ),\n\n IxAL_scratch := rec(\n forTransposition := false,\n applicable := nt -> nt.hasTags()\n and _isALStoreTag(nt)\n and IsParVec(nt.params)\n and IsPosInt(nt.getTag(1).size/ nt.params[1].dims()[2])\n and IsPosInt(nt.params[1].dims()[2]nt.params[2]/nt.getTag(1).size),\n children := nt -> let(\n k := nt.firstTag().size,\n m := nt.params[1].dims()[2],\n\n [[ TTensorI(\n nt.params[1], \n k/m, \n APar,AVec\n ).withTags(Drop(nt.getTags(),1)).setWrap(_swrap(nt)) \n ]]),\n\n apply := (self, nt, c, cnt) >> let(\n k := nt.getTag(1).size, \n m := nt.params[1].dims()[2], \n n := nt.params[2],\n\n DMAFence(\n Tensor(\n I(mn/k),\n LSKernel(c[1],nt.normalizedArithCost() k/m)\n ) \n Prm(fTensor(L(m^2n/k,mn/k),fId(k/m)))\n )\n ),\n ),\n\n L_IxA_scratch := rec(\n forTransposition := false,\n applicable := nt -> nt.hasTags() \n and _isALStoreTag(nt) \n\t and IsVecPar(nt.params),\n\n children := nt -> [[ \n TTensorI(\n nt.params[1], \n nt.getTag(1).size / nt.params[1].dims()[2], \n AVec, APar\n ).withTags(Drop(nt.getTags(),1)).setWrap(\n _swrap(nt)\n )\n ]],\n\n apply := (self, nt, c, cnt) >> let(\n k := nt.getTag(1).size,\n m := nt.params[1].dims()[2], \n n:= nt.params[2],\n\n DMAFence( \n Prm(fTensor(L(m^2n/k, mn/k), fId(k/m))\n ) Tensor(LSKernel(\n c[1], nt.normalizedArithCost() * k/m\n ), I(mn/k))\n )\n )\n ),\n#====================================================================\n# SWP Rules - double buffering is applied\n IxA_scratch_swp := rec(\n forTransposition := false,\n applicable := nt -> nt.hasTags() \n and _isALStoreTag(nt)\n\t and IsParPar(nt.params)\n and IsPosInt(nt.getTag(1).size / (2 nt.params[1].dims()[2]))\n and IsPosInt(2 * nt.params[1].dims()[2] * nt.params[2] / nt.getTag(1).size),\n\n children := nt -> [[ \n TTensorI(\n nt.params[1],\n nt.getTag(1).size / (2 * nt.params[1].dims()[2]), \n APar, APar\n ).withTags(Drop(nt.getTags(),1)).setWrap(\n _swrap(nt)\n )\n ]],\n apply := (nt, c, cnt) -> let(k := nt.getTag(1).size, m := nt.params[1].dims()[2], n:= nt.params[2],\n DMAFence(Tensor(\n I(2mn/k),\n LSKernel(c[1], nt.params[1].normalizedArithCost() * k/(2m))\n )))\n ),\n\n AxI_scratch_swp := rec(\n forTransposition := false,\n applicable := nt -> nt.hasTags() \n and _isALStoreTag(nt)\n\t and IsVecVec(nt.params) \n and IsPosInt(nt.getTag(1).size / (2nt.params[1].dims()[2]))\n and IsPosInt(2nt.params[1].dims()[2]nt.params[2] / nt.getTag(1).size),\n\n children := nt -> [[ let(t := nt.firstTag(),\n TTensorI(\n nt.params[1], \n t.size / (2nt.params[1].dims()[2]), \n AVec, AVec\n ).withTags(Drop(nt.getTags(),1)).setWrap(_swrap(nt))\n ) ]],\n\n apply := (nt, c, cnt) -> let(\n k := nt.getTag(1).size, \n m := nt.params[1].dims()[2], \n n:= nt.params[2],\n\n DMAFence(Prm(fTensor(L(2m^2n/k, 2m), fId(k/(2m)))) \n Tensor(\n I(2mn/k),\n LSKernel(c[1], nt.params[1].normalizedArithCost() * k/(2m))\n ) \n Prm(fTensor(L(2m^2n/k, 2mn/k), fId(k/(2m)))))\n )\n ),\n\n IxAL_scratch_swp := rec(\n forTransposition := false,\n applicable := nt -> nt.hasTags()\n and _isALStoreTag(nt)\n and IsParVec(nt.params)\n and IsPosInt(nt.getTag(1).size/ (2nt.params[1].dims()[2]))\n and IsPosInt(2nt.params[1].dims()[2]nt.params[2]/nt.getTag(1).size),\n children := nt -> let(\n k := nt.firstTag().size,\n m := nt.params[1].dims()[2],\n\n [[ TTensorI(\n nt.params[1], \n k/(2m), \n APar,AVec\n ).withTags(Drop(nt.getTags(),1)).setWrap(_swrap(nt)) \n ]]),\n\n apply := (self, nt, c, cnt) >> let(\n k := nt.getTag(1).size, \n m := nt.params[1].dims()[2], \n n := nt.params[2],\n\n DMAFence(\n Tensor(\n I(2mn/k),\n LSKernel(c[1],nt.normalizedArithCost() k/(2m))\n ) \n Prm(fTensor(L(2m^2n/k,2mn/k),fId(k/(2m))))\n )\n ),\n ),\n\n L_IxA_scratch_swp := rec(\n forTransposition := false,\n applicable := nt -> nt.hasTags() \n and _isALStoreTag(nt) \n\t and IsVecPar(nt.params)\n and IsPosInt(nt.getTag(1).size/ (2nt.params[1].dims()[2]))\n and IsPosInt(2nt.params[1].dims()[2]nt.params[2]/nt.getTag(1).size),\n\n children := nt -> [[ \n TTensorI(\n nt.params[1], \n nt.getTag(1).size / (2nt.params[1].dims()[2]), \n AVec, APar\n ).withTags(Drop(nt.getTags(),1)).setWrap(\n _swrap(nt)\n )\n ]],\n\n apply := (self, nt, c, cnt) >> let(\n k := nt.getTag(1).size,\n m := nt.params[1].dims()[2], \n n:= nt.params[2],\n\n DMAFence( \n Prm(fTensor(L(2m^2n/k, 2mn/k), fId(k/(2m)))\n ) * Tensor(LSKernel(\n c[1], nt.normalizedArithCost() * k/(2m)\n ), I(2m*n/k))\n )\n )\n )\n));\n", "meta": {"hexsha": "30680d70d4a8a18801d2f33da0edacb57129f681", "size": 9722, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/scratchpad/breakdown.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/scratchpad/breakdown.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/scratchpad/breakdown.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": 33.8745644599, "max_line_length": 108, "alphanum_fraction": 0.4279983542, "num_tokens": 2720, "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\nNewRulesFor(TRaderMid, rec(\n Pad_vec := rec(\n applicable := (self, t) >> t.isTag(1, AVecReg) or t.isTag(1, AVecRegCx),\n forTransposition := false,\n apply := (t, C, Nonterms) -> let(\n v := t.firstTag().v,\n ds := Rows(t)-1,\n When(IsInt(ds/v),\n DelayedDirectSum(VScat_sv(fId(1), v , 1), I(ds))\n * VecRaderMid(t.params[1], t.params[2], t.params[3], v)\n * DelayedDirectSum(VGath_sv(fId(1), v , 1), I(ds)),\n DelayedDirectSum(VScat_sv(fId(1), v , 1), VScat_sv(fId(ds), v, 1))\n * VecRaderMid(t.params[1], t.params[2], t.params[3], v)\n * DelayedDirectSum(VGath_sv(fId(1), v , 1), VGath_sv(fId(ds), v, 1))\n )\n )\n )\n));\n", "meta": {"hexsha": "fc452e6cddff6bf6917c5eb061d675215195ec82", "size": 860, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/vector/breakdown/tradermid.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/tradermid.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/breakdown/tradermid.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": 35.8333333333, "max_line_length": 84, "alphanum_fraction": 0.511627907, "num_tokens": 276, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7490872131147275, "lm_q2_score": 0.5389832206876841, "lm_q1q2_score": 0.4037454387005374}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nClass(UTwid, DiagFunc, rec(\n def := (N, n, k, a, b, i) -> rec(size:=n),\n lambda := self >> let(N:=self.params[1], n:=self.size, k:=self.params[3],\n\ta := self.params[4], b := self.params[5], i := self.params[6],\n\tna := Numerator(a), nb := Numerator(b),\n\tda := Denominator(a), db := Denominator(b),\n\tw := E(Ndadb)^k, j := Ind(n),\n\tLambda(j, cond(eq(j,n/2), omega(dadb,k), omega(Ndadb, k(ida+na)(jdb+nb)))))\n));\nClass(UTwid1, DiagFunc, rec(\n def := (N, n, k, a, b, i) -> rec(size:=n),\n lambda := self >> let(N:=self.params[1], n:=self.size, k:=self.params[3],\n\ta := self.params[4], b := self.params[5], i := self.params[6],\n\tna := Numerator(a), nb := Numerator(b),\n\tda := Denominator(a), db := Denominator(b),\n\tw := E(Ndadb)^k, j := Ind(n),\n\tLambda(j, cond(eq(j,n/2), 1, omega(Ndadb, k(ida+na)(jdb+nb)))))\n));\n\nClass(UDFT_NonTerm, DFT_NonTerm, rec(\n isReal := False,\n));\n\nClass(UDFT, UDFT_NonTerm, rec(\n abbrevs := [ \n (n) -> Checked(IsPosIntSym(n), AnySyms(n) or (n mod 2=0), [n, 1]),\n (n,k) -> Checked(IsPosIntSym(n), AnySyms(n) or (n mod 2=0), \n\t IsIntSym(k), AnySyms(n,k) or Gcd(n,k)=1, \n\t\t [n, When(AnySyms(n,k), k, k mod n)]) ],\n omega4pow := (r,c)->4rc,\n terminate := self >> let(\n\tn:=self.params[1], k:=self.params[2], m:=MatSPL(DFT(2))^-1,\n\tDirectSum(Mat(m), I(n-2))^L(n,n/2) \n\tDFT(n,k).terminate()),\n\n conjTranspose := self >> ObjId(self)(self.params[1], -self.params[2]).transpose()\n));\nUDFT1 := UDFT;\n\nClass(UDFT2, UDFT_NonTerm, rec(\n abbrevs := [ \n (n) -> Checked(IsPosIntSym(n), AnySyms(n) or (n mod 2=0), [n, 1]),\n (n,k) -> Checked(IsPosIntSym(n), AnySyms(n) or (n mod 2=0), \n\t IsIntSym(k), AnySyms(n,k) or Gcd(n,k)=1, \n\t\t [n, When(AnySyms(n,k), k, k mod (2n))]) ],\n omega4pow := (r,c)->2r(2c+1),\n terminate := self >> let(\n\tn:=self.params[1], k:=self.params[2], m:=MatSPL(DFT2(2,k))^-1,\n\tDirectSum(Mat(m), I(n-2))^L(n,n/2) \n\tDFT2(n,k).terminate()),\n));\n\nClass(UUDFT, UDFT_NonTerm, rec(\n abbrevs := [ \n (n) -> Checked(IsPosIntSym(n), AnySyms(n) or (n mod 4=0), [n, 1]),\n (n,k) -> Checked(IsPosIntSym(n), AnySyms(n) or (n mod 4=0), \n\t IsIntSym(k), AnySyms(n,k) or Gcd(n,k)=1, \n\t\t [n, When(AnySyms(n,k), k, k mod n)]) ],\n omega4pow := (r,c)->4rc,\n terminate := self >> let(\n\tn:=self.params[1], k:=self.params[2], m:=MatSPL(DFT(2))^-1,\n\tDirectSum(Mat(m), I((n-4)/2), Mat(m), I((n-4)/2))^L(n,n/2) \n\tDFT(n,k).terminate()),\n));\nUUDFT1 := UUDFT;\n\nClass(UUDFT2, UDFT_NonTerm, rec(\n abbrevs := [ \n (n) -> Checked(IsPosIntSym(n), AnySyms(n) or (n mod 4=0), [n, 1]),\n (n,k) -> Checked(IsPosIntSym(n), AnySyms(n) or (n mod 4=0), \n\t IsIntSym(k), AnySyms(n,k) or Gcd(n,k)=1, \n\t\t [n, When(AnySyms(n,k), k, k mod (2n))]) ],\n omega4pow := (r,c)->2r(2c+1),\n terminate := self >> let(\n\tn:=self.params[1], k:=self.params[2], m:=MatSPL(DFT2(2,k))^-1,\n\tDirectSum(Mat(m), I((n-2)/2), Mat(m), I((n-2)/2))^L(n,n/2) *\n\tDFT2(n,k).terminate()),\n));\n", "meta": {"hexsha": "0f61c691bb7e9a2e56a15a697cbd3f0d38d9256b", "size": 3168, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/dft/udft.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/udft.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/udft.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": 37.7142857143, "max_line_length": 84, "alphanum_fraction": 0.5299873737, "num_tokens": 1233, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.757794360334681, "lm_q2_score": 0.5312093733737563, "lm_q1q2_score": 0.4025474672995523}}
	{"text": "#!/usr/bin/gap\n\n# time gap -o 8g clifford.gap\n\n# Build clifford groups, up to 3 qubits, and\n# search for T operators defined by field extensions......\n\n\nPrint(\"running clifford.gap\\n\");;\n\n# See:\n# https://www.mathstat.dal.ca/~selinger/papers/clifford.pdf\n\nr2 := Sqrt(2);;\nir2 := 1/r2;;\n\ni := [[1, 0], [0, 1]];;\nw := [[E(4), 0], [0, E(4)]];;\nx := [[0, 1], [1, 0]];;\nz := [[1, 0], [0, -1]];;\ns := [[1, 0], [0, E(4)]];;\nh := [[ir2, ir2], [ir2, -ir2]];;\n\nCliff1 := Group(w, s, h);; # Order 192\nPauli1 := Group(w, x, z);; # Order 32\n\nfor U in Cliff1 do\n found := false;;\n #Udag := Inverse(U);\n #Print(\"found? \");\n for g in Pauli1 do\n if (UgInverse(U)Inverse(g) in Pauli1) then found:=true; break; fi;\n od;\n if not found then Print(\"Not found\\n\"); fi;\nod;\n\nxi := KroneckerProduct(x, i);;\nix := KroneckerProduct(i, x);;\nzi := KroneckerProduct(z, i);;\niz := KroneckerProduct(i, z);;\nsi := KroneckerProduct(s, i);;\nis := KroneckerProduct(i, s);;\nhi := KroneckerProduct(h, i);;\nih := KroneckerProduct(i, h);;\nwi := KroneckerProduct(w, i);;\n\n\ncz := [\n [1, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, -1]];;\n\nCliff2 := Group(si, is, hi, ih, wi, cz);; # Order 92160\n#for g in Cliff2 do Print(g, \"\\n\"); od;\nPauli2 := Group(wi, xi, ix, zi, iz);;\n\n# Works:\nfor U in Cliff2 do\n found := false;;\n #Udag := Inverse(U);\n #Print(\"found? \");\n for g in Pauli2 do\n if (UgInverse(U)Inverse(g) in Pauli2) then found:=true; break; fi;\n od;\n if not found then Print(\"Not found\\n\"); fi;\nod;\n\na := [\n [0, 1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n [-1, 0, 0, 0]];; # a in G2 = true\n\n#Print(aa, \"\\n\");\n#Print(aaa, \"\\n\");\n#Print(aaaa, \"\\n\");\n\n# Print(Order(G2));\n\n\nxii := KroneckerProduct(xi, i);;\nixi := KroneckerProduct(i, xi);;\niix := KroneckerProduct(i, ix);;\n\nzii := KroneckerProduct(zi, i);;\nizi := KroneckerProduct(i, zi);;\niiz := KroneckerProduct(i, iz);;\n\nsii := KroneckerProduct(si, i);;\nisi := KroneckerProduct(i, si);;\niis := KroneckerProduct(i, is);;\n\nhii := KroneckerProduct(hi, i);;\nihi := KroneckerProduct(i, hi);;\niih := KroneckerProduct(i, ih);;\n\nwii := KroneckerProduct(wi, i);;\n\nicz := KroneckerProduct(i, cz);;\nczi := KroneckerProduct(cz, i);;\n\nca := [\n [1, 0, 0, 0, 0, 0, 0, 0],\n [0, 1, 0, 0, 0, 0, 0, 0],\n [0, 0, 1, 0, 0, 0, 0, 0],\n [0, 0, 0, 1, 0, 0, 0, 0],\n [0, 0, 0, 0, 0, 1, 0, 0],\n [0, 0, 0, 0, 0, 0, 1, 0],\n [0, 0, 0, 0, 0, 0, 0, 1],\n [0, 0, 0, 0, -1, 0, 0, 0]];;\n\ncb := [\n [1, 0, 0, 0, 0, 0, 0, 0],\n [0, 1, 0, 0, 0, 0, 0, 0],\n [0, 0, 1, 0, 0, 0, 0, 0],\n [0, 0, 0, 1, 0, 0, 0, 0],\n [0, 0, 0, 0, 0, 0, 1, 0],\n [0, 0, 0, 0, 0, 0, 0, 1],\n [0, 0, 0, 0, -1, 0, 0, 0],\n [0, 0, 0, 0, 0, -1, 0, 0]];;\n\ncc := [\n [1, 0, 0, 0, 0, 0, 0, 0],\n [0, 1, 0, 0, 0, 0, 0, 0],\n [0, 0, 1, 0, 0, 0, 0, 0],\n [0, 0, 0, 1, 0, 0, 0, 0],\n [0, 0, 0, 0, 0, 0, 0, 1],\n [0, 0, 0, 0, -1, 0, 0, 0],\n [0, 0, 0, 0, 0, -1, 0, 0],\n [0, 0, 0, 0, 0, 0, -1, 0]];;\n\n\nTofolli := [\n [1, 0, 0, 0, 0, 0, 0, 0],\n [0, 1, 0, 0, 0, 0, 0, 0],\n [0, 0, 1, 0, 0, 0, 0, 0],\n [0, 0, 0, 1, 0, 0, 0, 0],\n [0, 0, 0, 0, 1, 0, 0, 0],\n [0, 0, 0, 0, 0, 1, 0, 0],\n [0, 0, 0, 0, 0, 0, 0, 1],\n [0, 0, 0, 0, 0, 0, 1, 0]];;\n\n\nCliff3 := Group(sii, isi, iis, hii, ihi, iih, wii, icz, czi);; # Order 743178240\nPauli3 := Group(wii, xii, ixi, iix, zii, izi, iiz);; # Order 256\n\n# Print(Order(Pauli3), \"\\n\");;\n\n# ca in Cliff3 = false\n# ca in third level of clifford hierarchy = true\n\n\nCliff3_12 := Group(sii, isi, hii, ihi, wii, czi);;\nCliff3_13 := Group(sii, iis, hii, iih, wii);; # cz on 1&3 ??\nCliff3_23 := Group(isi, iis, ihi, iih, wii, icz);;\n\n#SmCliff3 := Group(sii, isi, iis, hii, ihi, iih, icz, czi);; # Order 743178240\n\nPrint(\"warming up...\\n\");\nOrder(Cliff3);; # need this line otherwise membership test eats all memory...!\nPrint(\"Ok\\n\");\n\nin_third_level := function(U)\n # Is U in the third level of the clifford hierarchy ?\n local A;\n for g in Pauli3 do\n A := UgInverse(U)Inverse(g);\n if A in Cliff3_12 then continue; fi;\n if A in Cliff3_13 then continue; fi;\n if A in Cliff3_23 then continue; fi;\n if A in Cliff3 then continue; fi;\n return false; # no\n od;\n return true; # yes\nend;;\n\n\nPrint(\"in_third_level(ca):\", in_third_level(ca), \"\\n\"); # true\nPrint(\"in_third_level(cb):\", in_third_level(cb), \"\\n\"); # true\nPrint(\"in_third_level(cc):\", in_third_level(cc), \"\\n\"); # true\nPrint(\"in_third_level(Tofolli):\", in_third_level(Tofolli), \"\\n\"); # true\nPrint(\"in_third_level(Tofollica):\", in_third_level(Tofolli*ca), \"\\n\"); # false\n\nU3 := [ \n [1, 0, 0, 0, 0, 0, 0, 0],\n [0, 1, 0, 0, 0, 0, 0, 0],\n [0, 0, 1, 0, 0, 0, 0, 0],\n [0, 0, 0, 1, 0, 0, 0, 0],\n [0, 0, 0, 0, 1, 0, 0, 0],\n [0, 0, 0, 0, 0, 1, 0, 0],\n [0, 0, 0, 0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0, 0, 0, 0]];\n\nPrint(\"# Where do control control 1-qubit Pauli gates live ?\\n\");\nfor g in Pauli1 do \n #Print(g, \"\\n\");\n U3{[7,8]}{[7,8]} := g;\n if U3 in Pauli3 then Print(\"1\\c\"); continue; fi;\n if U3 in Cliff3 then Print(\"2\\c\"); continue; fi;\n if in_third_level(U3) then Print(\"3\\c\"); else Print(\".\\c\"); fi;\nod;\nPrint(\"\\n\");\n\nPrint(\"# Where do control control 1-qubit clifford gates live ?\\n\");\nfor g in Cliff1 do \n #Print(g, \"\\n\");\n U3{[7,8]}{[7,8]} := g;\n if U3 in Pauli3 then Print(\"1\\c\"); continue; fi;\n if U3 in Cliff3 then Print(\"2\\c\"); continue; fi;\n if in_third_level(U3) then Print(\"3\\c\"); else Print(\".\\c\"); fi;\nod;\nPrint(\"\\n\");\n\nPrint(\"# Where do control 2-qubit Pauli gates live ?\\n\");\nfor g in Pauli2 do \n #Print(g, \"\\n\");\n U3{[5,6,7,8]}{[5,6,7,8]} := g;\n if U3 in Pauli3 then Print(\"1\\c\"); continue; fi;\n if U3 in Cliff3 then Print(\"2\\c\"); continue; fi;\n if in_third_level(U3) then Print(\"3\\c\"); else Print(\".\\c\"); fi;\nod;\nPrint(\"\\n\");\n\nPrint(\"# Where do control 2-qubit clifford gates live ?\\n\");\nfor g in Cliff2 do \n #Print(g, \"\\n\");\n U3{[5,6,7,8]}{[5,6,7,8]} := g;\n if U3 in Pauli3 then Print(\"1\\c\"); continue; fi;\n if U3 in Cliff3 then Print(\"2\\c\"); continue; fi;\n if in_third_level(U3) then Print(\"3\\c\"); else Print(\".\\c\"); fi;\nod;\n\nPrint(\"\\n\");\n\nPrint(\"Done.\\n\");\n\n\n", "meta": {"hexsha": "99b868878e0cf5e0ad4958cda6de0234c36a9d5d", "size": 6194, "ext": "gap", "lang": "GAP", "max_stars_repo_path": "bruhat/dev/clifford.gap", "max_stars_repo_name": "punkdit/bruhat", "max_stars_repo_head_hexsha": "3231eacc49fd3464542f7eb72684751371d9876c", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 3, "max_stars_repo_stars_event_min_datetime": "2020-04-07T13:21:30.000Z", "max_stars_repo_stars_event_max_datetime": "2020-07-15T02:07:20.000Z", "max_issues_repo_path": "bruhat/dev/clifford.gap", "max_issues_repo_name": "punkdit/bruhat", "max_issues_repo_head_hexsha": "3231eacc49fd3464542f7eb72684751371d9876c", "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": "bruhat/dev/clifford.gap", "max_forks_repo_name": "punkdit/bruhat", "max_forks_repo_head_hexsha": "3231eacc49fd3464542f7eb72684751371d9876c", "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": 25.9163179916, "max_line_length": 80, "alphanum_fraction": 0.5182434614, "num_tokens": 2859, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. NO", "lm_q1_score": 0.8221891392358015, "lm_q2_score": 0.48828339529583464, "lm_q1q2_score": 0.40146130448141687}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nDeclare(GT);\nDeclare(ListProduct);\n\nListProduct := function(l)\n local prod, i;\n if Length(l) <=0 then return 0; fi;\n prod := 1;\n for i in l do\n prod := prod * i;\n od;\n return(prod);\nend;\n\nGTVec := XChain([0,1]);\nGTPar := XChain([1,0]);\n\nTTensorI_GT := function(gt)\n local spl, g, s, v, tags;\n [spl,g,s,v] := gt.params;\n tags := gt.getTags();\n Constraint(IsList(v) and Length(v)=1 and IsPosInt(v[1]));\n g := When(g=XChain([0,1]), AVec, APar);\n s := When(s=XChain([0,1]), AVec, APar);\n return TTensorI(spl, v[1], s, g).withTags(tags);\nend;\n\nGT_TTensorI := function(tt)\n local spl, g, s, v, tags;\n [spl,v,s,g] := tt.params;\n tags := tt.getTags();\n g := When(g=AVec, GTVec, GTPar);\n s := When(s=AVec, GTVec, GTPar);\n return GT(spl, g, s, [v]).withTags(tags);\nend;\n\nIsGT := x -> IsRec(x) and IsBound(x.isGT) and x.isGT;\n\nClass(GTBase, rec(\n isGT := true,\n\n freeTags := self >> Filtered(self.tags, x -> not x.isSticky),\n stickyTags := self >> Filtered(self.tags, x -> x.isSticky),\n\n stickyRank := self >> Length(self.stickyTags()),\n freeRank := self >> self.rank() - self.stickyRank(),\n freeLoops := self >> [self.stickyRank()+1 .. self.rank()],\n\n transposedTags := self >> List(self.tags, x->x.transpose()),\n\n getSpl := self >> self.params[1],\n setSpl := (self, spl) >> ApplyFunc(ObjId(self), Concatenation([spl], Drop(self.params, 1)))\n .withTags(self.tags),\n\n # need setIts(its) and getIts()\n _fmanip := meth(self, func_manip, gt_manip, newits) \n local cpy, z;\n\t cpy := Copy(self);\n \t z := SubstTopDownNR_named(cpy, @.cond(x -> (not Same(x, cpy) and IsGT(x)) or IsFunction(x) or IsFuncExp(x) or ObjId(x)=ind), \n\t e -> When(IsGT(e), gt_manip(e), func_manip(e)), \"__GT._fmanip\");\n return z.setIts(newits);\n end,\n\n bodyRank := self >> Maximum( [0] ::\n\tList(Collect(self.getSpl(), @.cond(e->IsFunction(e) or IsFuncExp(e))), _rank)),\n\n downRankFull := (self, inds) >> let(thisrank := self.rank(), \n\tself._fmanip(f -> f.downRankFull(inds), \n\t e -> Cond(e.bodyRank()=0, e, Error(\".downRankFull does not work with nested GTs\")),\n\t\t [])),\n\n\n downRank := (self, loopid, ind) >>\n self._fmanip(f -> f.downRank(loopid, ind), \n\t e -> e.downRankOuter(loopid + e.rank(), ind), \n\t ListWithout(self.getIts(), loopid)),\n # downRankOuter: notification that downRank performed on some outer GT, \n # so that this GT can update its functions and notify children.\n downRankOuter := (self, loopid, ind) >>\n self._fmanip(f -> f.downRank(loopid + self.rank(), ind), \n\t e -> e.downRankOuter(loopid + e.rank(), ind), \n\t self.getIts()),\n\n rotate := (self, n) >> When(n=1, self, let(\n\tits := self.getIts(), \n\ttags := self.getTags(),\tstags := self.stickyTags(), ftags := self.freeTags(),\n res := self._fmanip(\n\t f -> f.rotate(n), \n\t e -> Cond(e.bodyRank() <= e.rank(), e, \n\t\t Error(\".rotate() doesn't support nested GTs where inner GTs depend on outer indices\")),\n\t [its[n]] :: its{[1..n-1]} :: its{[n+1..Length(its)]}),\n\tCond(self.stickyRank() = 0, \n\t res,\n\t n <= self.stickyRank(),\n\t res.setTags( ftags :: [stags[n]] :: stags{[1..n-1]} :: stags{[n+1..Length(stags)]}),\n\t # else, n > self.stickyRank(),\n \t Error(\"Can't make non-sticky rank <n> an inner loop, because sticky tags exist\")\n # it could look like this instead: res.setTags( [ANoTag] :: tags )\n\t))),\n\n rotateIntoSticky := (self, n, newtag) >> let(\n\tits := self.getIts(), \n\ttags := self.getTags(),\tstags := self.stickyTags(), ftags := self.freeTags(),\n res := self._fmanip(\n\t f -> f.rotate(n),\n\t e -> Cond(e.bodyRank() <= e.rank(), e, \n\t\t Error(\".rotate() doesn't support nested GTs where inner GTs depend on outer indices\")),\n\t [its[n]] :: its{[1..n-1]} :: its{[n+1..Length(its)]}),\n\tCond(self.stickyRank() = 0, \n\t res.setTags(tags :: [newtag]),\n\t n <= self.stickyRank(),\n\t res.setTags( ftags :: [newtag] :: stags{[1..n-1]} :: stags{[n+1..Length(stags)]}),\n\t # else, n > self.stickyRank(),\n res.setTags( ftags :: [newtag] :: stags )\n\t)),\n\n # NOTE: upRank() leaves GT in inconsistent state, because sticky tags still need to be shifted\n upRank := self >> self._fmanip(\n\tf -> f.upRank(), \n\te -> Cond(e.bodyRank() <= e.rank(), e, \n\t Error(\".upRank() doesn't support nested GTs where inner GTs depend on outer indices\")),\n\tConcatenation([0], self.getIts())),\n\n # NOTE: upRank() leaves GT in inconsistent state, because sticky tags still need to be shifted\n upRankBy := (self, n) >> self._fmanip(\n\tf -> f.upRankBy(n), \n\te -> Cond(e.bodyRank() <= e.rank(), e, \n\t Error(\".upRankBy() doesn't support nested GTs where inner GTs depend on outer indices\")),\n\tConcatenation(Replicate(n, 0), self.getIts())),\n\n split := (self, loopid, inner_its, outer_its) >> let(its := self.getIts(),\n self._fmanip(\n\t f -> f.split(loopid, inner_its, outer_its),\n\t e -> e.splitOuter(loopid + e.rank(), inner_its, outer_its), \n Concatenation(its{[1..loopid-1]}, [inner_its, outer_its], its{[loopid+1..Length(its)]}))),\n # splitOuter: notification that some outer GT is splitting loop, \n # so that this GT can update its functions and notify children.\n splitOuter := (self, loopid, inner_its, outer_its) >> let(its := self.getIts(),\n self._fmanip(\n\t f -> f.split(loopid + self.rank(), inner_its, outer_its),\n\t e -> e.splitOuter(loopid + e.rank(), inner_its, outer_its), \n its)),\n\n getGath := self >> Error(\"Must be implemented in a subclass\"),\n\n getScat := self >> Error(\"Must be implemented in a subclass\"),\n\n isReal := self >> self.params[1].isReal(),\n toAMat := self >> self.toSpl().toAMat(),\n # when self.getIts() returns empty list it actually means single iteration,\n # that's why [1] appended to the list\n normalizedArithCost := self >> self.getSpl().normalizedArithCost() * ListProduct(self.getIts() :: [1]),\n\n children := self >> [self.params[1]],\n child := (self, n) >> Checked( n = 1, self.params[1] ),\n\n # overrideing withTags() to make sure non-sticky/sticky tags order is preserved\n # returns a copy of the object with 'tags' added on to any existing tags.\n withTags := (self, tags) >> self.setTags(Flat(TransposedMat(\n List([self.tags, tags], t -> SplitBy(t, e -> not e.isSticky))))),\n));\n\n# GT(<spl>, <gath>, <scat>, <v>) - generalized problem spec\n#\n# NOTE: assumes tightly packed data, i.e. Dims(GT(spl)) = Dims(spl) * Product(v)\n# (if gath/scat functions have domain&range == 0)\nClass(GT, GTBase, Tagged_tSPL, rec(\n abbrevs := [\n (spl, gath, scat, v) -> Checked(\n IsSPL(spl), IsIndexMapping(gath), IsIndexMapping(scat), IsList(v),\n ForAll(v, IsPosInt0Sym),\n [spl, gath, scat, v]\n ) ],\n\n dims := self >> let(p := self.params, r := range(p[3]), c := range(p[2]), d := p[1].dims(),\n When(r<>0 and c<>0,\n [r, c],\n let(prod := Product(p[4]), [d[1]prod, d[2]prod]))), # NOTE: assumes XChain.\n\n advdims := self >> let(p := self.params, [p[3].advrange(), p[2].advrange()]),\n\n getIts := self >> self.params[4],\n setIts := (self,its) >> ObjId(self)(self.params[1], self.params[2], self.params[3], its).withTags(self.tags),\n getGath := self >> self.params[2],\n getScat := self >> self.params[3],\n\n rank := self >> Length(self.params[4]),\n\n _scat := Scat,\n _gath := Gath,\n\n # NOTE: toSpl doesn't work with nested GTs. It should use downRank method for function manipulations\n toSpl := self >> self.toSplCx([]),\n toSplCx := (self, outer_inds) >> let(\n p := self.params, spl := Copy(p[1]), g := Copy(p[2]), s := Copy(p[3]), dims := p[4],\n inds := List(dims, Ind), allinds := Concatenation(inds, outer_inds),\n kernel := self._scat(s.toSpl(allinds, Rows(spl))) * spl * self._gath(g.toSpl(allinds, Cols(spl))),\n kerneld := Cond(inds=[], kernel, # downRank only if not rank-0\n SubstTopDownNR(kernel, @.cond(e->IsFunction(e) or IsFuncExp(e)), e->e.downRankFull(allinds))),\n FoldL(inds, (ker, idx) -> ISum(idx.setAttr(\"GT\"), ker), kerneld)\n ),\n\n toISums := self >> let(\n inds := List(self.getIts(), Ind),\n kernel := self._scat(self.getScat()) * self.params[1] * self._gath(self.getGath()),\n FoldL(inds, (ker, idx) -> ISum(idx.setAttr(\"GT\"), ker), kernel)\n ),\n\n transpose := self >> let(p:=self.params,\n GT(p[1].transpose(), p[3], p[2], p[4]).withTags(self.transposedTags())),\n\n conjTranspose := self >> let(p:=self.params,\n GT(p[1].conjTranspose(), p[3], p[2], p[4]).withTags(self.transposedTags())),\n\n hashAs := self >> let(p:=self.params,\n ObjId(self)(HashAsSPL(p[1]), p[2], p[3], p[4]).withTags(self.tags)),\n));\n\nDeclare(GTAccT, GTAcc0T);\n\n# GTAcc(<spl>, <gath>, <scat>, <v>) - generalized problem spec with accumulation on output side\n#\nClass(GTAcc, GT, rec(\n transpose := self >> let(p:=self.params,\n GTAccT(p[1].transpose(), p[3], p[2], p[4]).withTags(self.transposedTags())),\n _scat := ScatAcc\n));\n\nClass(GTAcc0, GT, rec(\n transpose := self >> let(p:=self.params,\n GTAcc0T(p[1].transpose(), p[3], p[2], p[4]).withTags(self.transposedTags())),\n _scat := ScatAcc,\n\n toSplCx := (self, outer_inds) >> Checked(self.rank()=1, let( # NOTE: works only for rank-1\n dims := self.getIts(),\n inds0 := Concatenation(List(DropLast(dims,1), Ind), [0]),\n inds := Concatenation(List(DropLast(dims,1), Ind), [Ind(Last(dims)-1)]),\n inds_shft := Concatenation(DropLast(inds,1), [Last(inds)+1]),\n\n dr0 := self.downRankFull(Concatenation(inds0, outer_inds)),\n dr := self.downRankFull(Concatenation(inds_shft, outer_inds)),\n kernel0 := Scat(dr0.getScat()) * dr0.params[1] * self._gath(dr0.getGath()),\n kernel := ScatAcc(dr.getScat()) * dr .params[1] * self._gath(dr .getGath()),\n When(Last(dims)=1,\n kernel0,\n SUM(kernel0, FoldL(inds, (ker, idx) -> ISum(idx.setAttr(\"GT\"), ker), kernel))))\n ),\n));\n\n# GTAccT == GTAcc.transpose(), even though semantically GTAccT == GT, we need a separate object, so that\n# GTAccT.transpose() is back to GTAcc itself.\nClass(GTAccT, GT, rec(\n transpose := self >> let(p:=self.params,\n GTAcc(p[1].transpose(), p[3], p[2], p[4]).withTags(self.transposedTags())),\n));\n\nClass(GTAcc0T, GT, rec(\n transpose := self >> let(p:=self.params,\n GTAcc0(p[1].transpose(), p[3], p[2], p[4]).withTags(self.transposedTags())),\n));\n\nDeclare(GTInplace);\n\nClass(GTInplace, GTBase, Tagged_tSPL, rec(\n abbrevs := [ (spl, gathscat, v) -> Checked(\n IsSPL(spl), IsIndexMapping(gathscat), IsList(v), ForAll(v, IsPosInt0Sym),\n [spl, gathscat, v]) ],\n\n dims := self >> let(p := self.params, rc := range(p[2]), d := p[1].dims(),\n When(rc<>0,\n [rc, rc],\n let(prod:=Product(p[3]), [d[1]prod, d[2]prod]))), # NOTE: assumes XChain.\n\n getIts := self >> self.params[3],\n setIts := (self,its) >> GTInplace(self.params[1], self.params[2], its).withTags(self.tags),\n\n getGath := self >> self.params[2],\n getScat := self >> self.params[2],\n\n rank := self >> Length(self.params[3]),\n toGT := self >> let(p:=self.params, GT(p[1], p[2], p[2], p[3]).withTags(self.tags)),\n toNonInplace := self >> self.toGT(),\n toSpl := self >> Inplace(self.toGT().toSpl()),\n isInplace := self >> true,\n\n conjTranspose := self >> let(p:=self.params,\n GTInplace(p[1].conjTranspose(), p[2], p[3]).withTags(self.transposedTags())),\n\n transpose := self >> let(p:=self.params,\n GTInplace(p[1].transpose(), p[2], p[3]).withTags(self.transposedTags())),\n\n hashAs := self >> let(p:=self.params,\n ObjId(self)(HashAsSPL(p[1]), p[2], p[3]).withTags(self.tags))\n));\n\n\n#\n# NOTE: what if there is no SUM scatters or gathers\n#\n\nClass(GTPS, GTBase, Tagged_tSPL, rec(\n abbrevs := [\n (spl, fb_cnt, gath, scat, v) -> Checked(\n IsSPL(spl), IsPosInt(fb_cnt), IsIndexMapping(gath), IsIndexMapping(scat), IsList(v),\n ForAll(v, IsPosInt0Sym),\n [spl, fb_cnt, gath, scat, v]\n ) ],\n\n dims := self >> let( p := self.params, r := range(p[4]), c := range(p[3]), \n d := p[1].dims(), \n [ StripList(Flat([d[1]]){[1..p[2]]} :: Flat([r])), \n StripList(Flat([d[2]]){[1..p[2]]} :: Flat([c])) ]),\n\n advdims := self >> let(p := self.params, r := p[4].advrange(), c := p[3].advrange(), \n d := p[1].advdims(), \n [ StripList(Flat([d[1]]){[1..p[2]]} :: Flat([r])), \n StripList(Flat([d[2]]){[1..p[2]]} :: Flat([c])) ]),\n\n getIts := self >> self.params[5],\n setIts := (self,its) >> ObjId(self)(self.params[1], self.params[2], self.params[3], self.params[4], its).withTags(self.tags),\n getGath := self >> fCross(List(Flat([self.params[1].advdims()[1]]){[1..self.params[2]]}, e -> fId(e)) :: [self.params[3]]),\n getScat := self >> fCross(List(Flat([self.params[1].advdims()[2]]){[1..self.params[2]]}, e -> fId(e)) :: [self.params[4]]),\n\n rank := self >> Length(self.params[5]),\n\n toSpl := self >> let(\n inds := List(self.params[5], Ind),\n kernel := FoldR([1..self.rank()], (ker, i) -> ker.downRank(i, inds[i]), Copy(self)),\n spl := Scat(kernel.getScat()) * kernel.child(1) * Gath(kernel.getGath()),\n FoldL(inds, (ker, idx) -> IParSeq(idx.setAttr(\"GT\"), kernel.params[2], ker), spl)),\n\n hashAs := self >> let(p:=self.params,\n ObjId(self)(HashAsSPL(p[1]), p[2], p[3], p[4], p[5]).withTags(self.tags)),\n \n));\n\n# Useful identities:\n#\n# Tr(m,n) = GT(I(m), XChain([0,1]), XChain([1,0]), [n]) =\n# GT(I(n), XChain([1,0]), XChain([0,1]), [m]) = L(mn, n)\nGT_Tr1 := (m,n) -> GT(I(m), XChain([0,1]), XChain([1,0]), [n]);\nGT_Tr2 := (m,n) -> GT(I(n), XChain([1,0]), XChain([0,1]), [m]);\n\nGT_Tr1u := (m,n,u) -> let(uu:=When(m mod u = 0, u, 1),\n GT(BB(I(uu)), XChain([1,0,2]), XChain([2,1,0]), [m/uu, n]));\n\nGT_Tr2u := (m,n,u) -> let(uu:=When(n mod u = 0, u, 1),\n GT(BB(I(uu)), XChain([2,1,0]), XChain([1,0,2]), [n/uu, m]));\n\n\nNewRulesFor(GT, rec(\n GT_Base := rec(\n\tswitch := false,\n\ta := rec(maxSize := false),\n # requiredFirstTag := ANoTag,\n\tapplicable := (self, t) >> let(rank := Length(t.params[4]), spl := t.params[1],\n rank = 0 and (self.a.maxSize=false\n\t\tor Rows(spl) <= self.a.maxSize or Cols(spl) <= self.a.maxSize)),\n freedoms := (self, t) >> [],\n\tchild := (t, fr) -> [ t.params[1].withTags(t.getTags()) ],\n\tapply := (t, C, Nonterms) -> let(\n g := t.params[2], s := t.params[3],\n Scat(s.toSpl([], Rows(C[1]))) C[1] * Gath(g.toSpl([], Cols(C[1])))\n )\n ),\n\n GT_NthLoop := rec(\n\t requiredFirstTag := [ANoTag, ALimitNthLoop],\n\t applicable := t -> let(rank := Length(t.params[4]), rank > 0), \n\n # restrict to innermost first (i.e. loop interchange)\n\t # to search over loop orders use [1..nloops]\n\n # Limit tag reduces the number of loop interchanges.\n # it is useful when you don't want the number of potential\n # ruletrees to explode, and you are not overtly concerned\n # with having access to all the potential ones.\n freedoms := t -> let(\n fr := [1..Length(t.params[4])], \n When(t.hasTag(ALimitNthLoop),\n [[1]],\n [fr]\n )\n ),\n\n\t child := (t, fr) -> let(\n\t spl := t.params[1], \n g := t.params[2], \n s := t.params[3], \n loopid := fr[1],\n\t [ \n GT(spl, g.without(loopid), \n s.without(loopid), ListWithout(t.params[4], loopid)), \n InfoNt(loopid) \n ]\n ),\n\n\t apply := (t, C, Nonterms) -> let(\n\t loopid := Nonterms[2].params[1], \n dft := Nonterms[1].params[1], \n\t g := t.params[2], \n s := t.params[3],\n\t loop_dims := t.params[4],\n\t i := Ind(loop_dims[loopid]),\n\n\t ISum(i, Scat(s.part(loopid, i, Rows(dft), loop_dims)) \n * C[1] \n * Gath(g.part(loopid, i, Cols(dft), loop_dims)))\n )\n ),\n\n GT_BufReshape := rec(\n bufIters := [2, 4, 8, 16, 32],\n requiredFirstTag := ANoTag,\n\n applicable := (self, t) >> Length(t.params[4])=1 and let(\n N := Minimum(t.params[1].dimensions), its := t.params[4][1],\n PatternMatch(t, [GT, @, @(2,XChain), @(3,XChain), ...], empty_cx()) and\n (@(2).val.params[1] = [0,1] or @(3).val.params[1] = [0,1]) and\n ForAny(self.bufIters, bi -> bi < its and IsInt(its/bi))),\n\n u := [2,4,8,16],\n\n children := (self, t) >> let(\n spl := t.params[1], its := t.params[4][1],\n bufiters := Filtered(self.bufIters, bi -> (bi < its) and IsInt(its/bi)),\n Map2(Cartesian(bufiters, self.u), (bi, u) ->\n [ GT(spl, XChain([1,0]), XChain([1,0]), [bi]),\n InfoNt(u) ])),\n\n apply := (self, t, C, Nonterms) >> let(\n g := t.params[2].params[1], s := t.params[3].params[1],\n gg := When(g=[0,1], XChain([0,1,2]), XChain([1,2,0])),\n ss := When(s=[0,1], XChain([0,1,2]), XChain([1,2,0])),\n spl := t.params[1], its := t.params[4][1], inner := Nonterms[1].params[4][1],\n i := Ind(its / inner),\n u := When(IsBound(Nonterms[2]), Nonterms[2].params[1], 4),\n\n ISum(i, Scat(ss.part(1, i, Rows(spl), [i.range, inner])) \n When(s=[0,1], GT_Tr2u(inner, Rows(spl), u).toSpl(), I(Rows(spl)inner)) \n C[1] \n When(g=[0,1], GT_Tr1u(Cols(spl), inner, u).toSpl(), I(Cols(spl)inner)) \n Gath(gg.part(1, i, Cols(spl), [i.range, inner]))\n )\n )\n )\n));\n", "meta": {"hexsha": "96647f9fa2ada3b111abfb5b8f18a7e91e0d4333", "size": 17897, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/common/gt.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/common/gt.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/common/gt.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": 39.5951327434, "max_line_length": 129, "alphanum_fraction": 0.5567413533, "num_tokens": 5721, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. 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	{"text": "IsSymInf := x -> IsSymbolic(x) and IsBound(x.isSymInf) and x.isSymInf;\n\nClass(SymInf, Symbolic, rec(\n __call__ := (self, t) >> WithBases(self, rec(\n t := Checked(IsType(t), t),\n operations := rec(Print := x-> When(IsBound(x.print), x.print(), Print(x.__name__)))\n )),\n print := self >> Print(self.__name__, \"(\", self.t, \")\"),\n isSymInf := true,\n isValue := true,\n ev := self >> self,\n computeType := self >> self.t\n));\n\n# ==========================================================================\n# Semiring\n# ==========================================================================\n\nIsSemiring := x -> IsType(x) and IsBound(x.isSemiring) and x.isSemiring;\n\nIsSemiring_Arithmetic := x -> IsSemiring(x) and IsBound(x.isSemiring_Arithmetic) and x.isSemiring_Arithmetic;\n\nIsSemiring_MinPlus := x -> IsSemiring(x) and IsBound(x.isSemiring_MinPlus) and x.isSemiring_MinPlus;\n\nIsSemiring_MinTimes := x -> IsSemiring(x) and IsBound(x.IsSemiring_MinTimes) and x.isSemiring_MinTimes;\n\nisSemiring_Boolean := x -> IsSemiring(x) and IsBound(x.isSemiring_Boolean) and x.isSemiring_Boolean;\n\nClass(TSemiring, CompositeTyp, rec(\n __call__ := (self, t) >> WithBases(self, rec(\n t := Checked(IsType(t), t),\n operations := TypOps\n )),\n base_t := self >> self.t,\n isSemiring := true,\n\n print := self >> Print(self.__name__, \"(\", self.t, \")\"),\n\n check := (self, v) >> Cond(\n UnifyTypes([self.t, InferType(v)]) = self.t,\n v,\n Error(\"type mismatch: semiring is type \", self.t)\n ),\n\n rChildren := self >> [self.t],\n rSetChild := rSetChildFields(\"t\"),\n from_rChildren := (self, rch) >> self,\n\n zero := self >> Error(\"method on undefined semiring\"),\n one := self >> Error(\"method on undefined semiring\"),\n\n sum := self >> Error(\"method on undefined semiring\"),\n product := self >> Error(\"method on undefined semiring\")\n));\n\nClass(TSemiring_Arithmetic, TSemiring, rec(\n zero := self >> self.t.zero(),\n one := self >> self.t.one(),\n\n sum := (self, v1, v2) >> Cond(\n UnifyTypes([self.t, InferType(v1), InferType(v2)]) = self.t,\n self.t.sum(v1, v2),\n Error(\"type mismatch: semiring is type \", self.t)\n ),\n product := (self, v1, v2) >> Cond(\n UnifyTypes([self.t, InferType(v1), InferType(v2)]) = self.t,\n self.t.product(v1, v2),\n Error(\"type mismatch: semiring is type \", self.t)\n ),\n\n OpenMP_sum := \"+\",\n OpenMP_product := \"\",\n\n isSemiring_Arithmetic := true\n));\n\nClass(TSemiring_MinPlus, TSemiring, rec(\n zero := self >> SymInf(self.t),\n one := self >> self.t.zero(),\n\n sum := (self, v1, v2) >> Cond(\n IsSymInf(v1) and IsSymInf(v2),\n SymInf(self.t),\n IsSymInf(v1) and UnifyTypes([self.t, v2.t]) = self.t,\n v2,\n IsSymInf(v2) and UnifyTypes([self.t, v1.t]) = self.t,\n v1,\n UnifyTypes([self.t, InferType(v1), InferType(v2)]) = self.t,\n min(v1, v2),\n Error(\"type mismatch: semiring is type \", self.t)\n ),\n product := (self, v1, v2) >> Cond(\n IsSymInf(v1) or IsSymInf(v2),\n SymInf(self.t),\n UnifyTypes([self.t, InferType(v1), InferType(v2)]) = self.t,\n self.t.sum(v1, v2),\n Error(\"type mismatch: semiring is type \", self.t)\n ),\n\n OpenMP_sum := \"min\",\n OpenMP_product := \"+\",\n\n isSemiring_MinPlus := true\n));\n\n\nClass(TSemiring_MinTimes, TSemiring, rec(\n zero := self >> SymInf(self.t),\n one := self >> self.t.zero(),\n\n sum := (self, v1, v2) >> Cond(\n IsSymInf(v1) and IsSymInf(v2),\n SymInf(self.t),\n IsSymInf(v1) and UnifyTypes([self.t, v2.t]) = self.t,\n v2,\n IsSymInf(v2) and UnifyTypes([self.t, v1.t]) = self.t,\n v1,\n UnifyTypes([self.t, InferType(v1), InferType(v2)]) = self.t,\n min(v1, v2),\n Error(\"type mismatch: semiring is type \", self.t)\n ),\n product := (self, v1, v2) >> Cond(\n UnifyTypes([self.t, InferType(v1), InferType(v2)]) = self.t,\n self.t.product(v1, v2),\n Error(\"type mismatch: semiring is type \", self.t)\n ),\n\n OpenMP_sum := \"min\",\n OpenMP_product := \"\",\n\n isSemiring_MinTimes := true\n));\n\n\nClass(TSemiring_Boolean, TSemiring, rec(\n zero := self >> self.t.zero(),\n one := self >> self.t.one(),\n\n sum := (self, v1, v2) >> Cond(let(\n l := UnifyTypes([self.t, InferType(v1), InferType(v2)]), Cond(IsArrayT(l), l.t = self.t, l = self.t)),\n logic_or(v1, v2),\n Error(\"type mismatch: semiring is type \", self.t)\n ),\n product := (self, v1, v2) >> Cond(let(\n l := UnifyTypes([self.t, InferType(v1), InferType(v2)]), Cond(IsArrayT(l), l.t = self.t, l = self.t)),\n logic_and(v1,v2),\n Error(\"type mismatch: semiring is type \", self.t)\n ),\n\n OpenMP_sum := \"\|\|\",\n OpenMP_product := \"&&\",\n\n isSemiring_Boolean := true\n));", "meta": {"hexsha": "3c71b4c37e44edc5087c34108be0e49e1848c05e", "size": 4619, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/packages/graph/semiring.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": 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	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n_DHT_CONST := 2.5;\n\n#F TDHT(<n>, <k>) - RDFT Nonterminal\nClass(TDHT, TaggedNonTerminal, rec(\n abbrevs := [ (n) -> Checked(IsPosInt(n), [n]) ],\n dims := self >> [self.params[1], self.params[1]],\n isReal := True,\n terminate := self >> PkDHT1(self.params[1]).terminate(),\n SmallRandom := () -> Random([2,4,6,8,10,12,16,18,24,30,32]),\n normalizedArithCost := (self) >> let(n := self.params[1], IntDouble(_DHT_CONST * n * d_log(n) / d_log(2)))\n));\n\n\n_DHTtoRDFT := N -> DirectSum(I(2), Tensor(I(N/2-1), F(2)));\n\n#F TXMatDHT(<n>) - X-matrix to translate a RC(DFT(N)) -> DHT(2N)\nClass(TXMatDHT, TaggedNonTerminal, rec(\n abbrevs := [ (n) -> Checked(IsPosIntSym(n), [n]) ],\n dims := self >> [self.params[1], self.params[1]],\n isReal := True,\n terminate := self >> _DHTtoRDFT(self.params[1]) TConjEven(self.params[1]).terminate(),\n SmallRandom := () -> Random([2,4,6,8,10,12,16,18,24,30,32]),\n doNotMeasure := true\n));\n\n\n#F Translate DHT into RDFT\nNewRulesFor(TDHT, rec(\n DHT_DFT_tSPL := rec(\n switch := true,\n applicable := (self, t) >> IsEvenInt(t.params[1]), # and t.hasTags(),\n children := (self, t) >> let(N := t.params[1], tags := t.getTags(),\n [[\n TXMatDHT(N).withTags(tags),\n TRC(DFT(N/2)).withTags(tags)\n ]]),\n apply := (self, t, C, Nonterms) >> C[1] * C[2]\n )\n));\n\n\nNewRulesFor(TXMatDHT, rec(\n TXMatDHT_TConjEven := rec(\n switch := true,\n applicable := (self, t) >> IsEvenInt(t.params[1]),\n children := (self, t) >> let(N := t.params[1], tags := t.getTags(),\n [[\n TConjEven(N).withTags(tags),\n ]]),\n apply := (self, t, C, Nonterms) >> _DHTtoRDFT(t.params[1]) * C[1]\n )\n));\n", "meta": {"hexsha": "b626b4696baa437164bd9deee9c8d31510211121", "size": 1854, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/common/dht.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/common/dht.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/common/dht.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": 31.9655172414, "max_line_length": 110, "alphanum_fraction": 0.5469255663, "num_tokens": 619, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7341195152660687, "lm_q2_score": 0.6076631698328916, "lm_q1q2_score": 0.44609739168276513}}
	{"text": "\nInstallMethod(NilpotentChv,\n \"NilpotentChv element in simple Lie type\",\n [IsChevalleyAdj,IsList],\n function(sys,coeffs)\n local object,\n B,admat,l;\n \n if Filtered(coeffs,i->not i[2] in Integers)=[] then\n coeffs:=List(coeffs,i->[i[1],One(ring(sys))i[2]]);\n elif Filtered(coeffs,i->not i[2] in ring(sys))<>[] then\n Error(\"NilpotentChv: The coefficients ar not in indicated ring.\");\n fi;\n\n object:=Objectify(NewType(NewFamily(\"NilpotentChvFamily\"),\n IsAttributeStoringRep and\n IsNilpotentChv and\n IsAdditiveElementWithInverse and\n IsAdditiveElementWithZero),\n rec());\n\n SetchevalleyAdj(object,sys);\n\n # Simplified form of the element (negative root vectors are also allowd \"2Len..\")\n coeffs:=Filtered(List([1..2Length(positiveRoots(sys))],\n i->[i,One(ring(sys))Sum(List(Filtered(coeffs,\n j->j[1]=i),\n k->k[2]))]),\n l->l[2]<>Zero(ring(sys)));\n\n Setcoefficients(object,coeffs);\n\n B:=Basis(lieAlgebra(sys));\n if coeffs<>[] then SetLieAlgebraElement(object,Sum(coeffs,i->i[2]B[i[1]]));\n else SetLieAlgebraElement(object,Zero(lieAlgebra(sys))); fi;\n SetLieAlgebraCoeffs(object,Coefficients(B,LieAlgebraElement(object)));\n\n# l:=Length(PRoots(R));\n# admat:=AdjointMatrix(B,LieAlgebraElement(e));\n# SetPositiveAde(object,List([1..l],i->admat[i]{[1..l]}));\n \n SetName(object,Concatenation(\"<nilpotent element for \",\n type(sys),String(rank(sys)),\n \" in characteristic \",String(Characteristic(sys)),\">\"));\n return object;\nend);\n\nInstallMethod(Ascend,\n \"If possible embed the parameters in a polynomial ring with coefficients ring the base ring\",\n [IsNilpotentChv,IsPolynomialRing],\n function(e,inel)\n local sys,\n check;\n\n sys:=chevalleyAdj(e);\n\n if not IsPolynomialRing(inel) then\n Error(\"Ascend NilpotentChv: The new ring is not a polynomial ring to embed in!\\n\");\n elif CoefficientsRing(inel)<>ring(sys) then\n Error(\"Ascend NilpotentChv: CoefficientsRing and ring(sys) do not coincide!\\n\");\n fi;\n \n return NilpotentChv(ChevalleyAdj(sys,inel),List(coefficients(e),i->[i[1],One(inel)i[2]]));\nend);\n\nInstallMethod(Ascend,\n \"If possible embed the parameters in a polynomial ring with coefficients ring the base ring\",\n [IsNilpotentChv,IsChevalleyAdj],\n function(e,sys)\n local syse,\n check;\n\n syse:=chevalleyAdj(e);\n\n if not IsPolynomialRing(ring(sys)) then\n Error(\"The new ring is not a polynomial ring to embed in.\");\n elif CoefficientsRing(ring(sys))<>ring(syse) then\n Error(\"CoefficientsRing and ring(syse) do not coincide.\");\n fi;\n \n return NilpotentChv(sys,List(coefficients(e),i->[i[1],One(ring(sys))i[2]]));\nend);\n\nInstallMethod(\\,\n \"multiplication by scalar for nilpotent elements se\",\n [IsRingElement,IsNilpotentChv],\n function(s,e)\n local sys;\n\n sys:=chevalleyAdj(e);\n if not s in ring(sys) then\n Error(\"ScalarNilpotentChv: Scalar not in ring of nilpotent!\\n\");\n fi;\n \n return NilpotentChv(sys,List(coefficients(e),i->[i[1],s*i[2]]));\nend);\n\nInstallMethod(\\+,\n \"addition for nilpotent elements e1+e2\",\n [IsNilpotentChv,IsNilpotentChv],\n function(e1,e2)\n local sys1,sys2;\n\n sys1:=chevalleyAdj(e1);\n sys2:=chevalleyAdj(e2);\n if type(sys1)<>type(sys2) or\n rank(sys1)<>rank(sys2) or\n ring(sys1)<>ring(sys2) then\n Error(\"NilpotentChv+NilpotentChv: Not in the same family!\\n\");\n fi;\n \n return NilpotentChv(sys1,Concatenation(coefficients(e1),coefficients(e2)));\nend);\n\nInstallMethod(AdditiveInverseMutable,\n \"additive inverse for nilpotent elements -e1\",\n [IsNilpotentChv],\n function(e)\n local sys;\n\n sys:=chevalleyAdj(e);\n \n return NilpotentChv(sys,List(coefficients(e),i->[i[1],-i[2]]));\nend);\n\nInstallMethod(ZeroMutable,\n \"Zero vector of the Lie algebra\",\n [IsNilpotentChv],\n function(e)\n local sys;\n \n return NilpotentChv(chevalleyAdj(e),[]);\nend);\n", "meta": {"hexsha": "6d404a60c279bdce9dfef43290f6db8c8ea38821", "size": 5268, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "lib/nilchv.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/nilchv.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/nilchv.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": 39.3134328358, "max_line_length": 107, "alphanum_fraction": 0.5034168565, "num_tokens": 1199, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.7279754489059774, "lm_q2_score": 0.6113819732941511, "lm_q1q2_score": 0.445071066461832}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n# ==========================================================================\n# ColDirectSum\n# ==========================================================================\nClass(ColDirectSum, BaseOverlap, rec(\n #-----------------------------------------------------------------------\n abbrevs := [ \n function(arg) \n arg:=Flat(arg); \n return [arg[1], arg{[2..Length(arg)]}];\n end ],\n #-----------------------------------------------------------------------\n new := meth(self, overlap, spls)\n return self._new(0, overlap, spls);\n end,\n #-----------------------------------------------------------------------\n dims := meth(self)\n local ovdim;\n\tovdim := self.ovDim(self.overlap,\n\t List(self._children, t -> t.dimensions[1]));\n\treturn [ ovdim[3] - ovdim[2] + 1, # max - min + 1\n\t Sum(self._children, t -> t.dimensions[2]) ];\n end,\n #-----------------------------------------------------------------------\n toAMat := meth(self) \n return \n\t AMatSPL(\n\t Sparse(\n\t\t self._coloverlap(\n\t\t List(self._children, t -> t.dimensions[1]),\n\t\t self.overlap\n\t\t )\n\t )\n\t ) *\n\t DirectSumAMat(List(self._children, AMatSPL));\n end,\n));\n\nColDirectSum._transpose_class := RowDirectSum;\nRowDirectSum._transpose_class := ColDirectSum;\n", "meta": {"hexsha": "9fc6e37d40ad33c6edf2e565ffdd544f9a729ec0", "size": 1432, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/spl/ColDirectSum.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/ColDirectSum.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/ColDirectSum.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": 31.8222222222, "max_line_length": 76, "alphanum_fraction": 0.3868715084, "num_tokens": 295, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7279754371026368, "lm_q2_score": 0.6113819732941511, "lm_q1q2_score": 0.4450710592454823}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n#P Permutations\n#P ------------\n#P\n#P Under different circumstances different objects are called permutations,\n#P even in the context of linear algrebra.\n#P\n#P Following list describes these objects and their representation in SPIRAL:\n#P\n#P 1. Regular permutations\n#P (a) in cycle notation : (1,2)(3,4)\n#P (b) as lists : [2,1,4,3]\n#P (c) as index space mapping function: i -> i+1 mod N\n#P\n#P 2. Parametrized permutation classes\n#P [For example stride permutations L(size,str) \| size mod str = 0]\n#P Represented as a construction function, which returns an index mapping\n#P function - (c) above.\n#P\n#P Conversions: ListPerm (b) <- (a) [gap.perm]\n#P PermList (a) <- (b) [gap.perm]\n#P PermFunc (a) <- (c) [spiral.spl.perm]\n#P ListPermFunc (b) <- (c) [spiral.spl.perm]\n#P\n#P -------------------\n\n#F PermFunc(<func>, <size>) . . . . . convert perm. function into explicit GAP perm.\n#F\n#F PermFunc converts a 0-based permutation function used in SPLs, into an explicit\n#F GAP permutation. Recall that GAP permutations are 1-based, and are in cycle\n#F representation.\n#F\nPermFunc := (func, size) ->\n PermList( List([0..size-1], func) + 1 );\n\n#F PermFunc(<func>, <size>) . . . . . convert perm. function into explicit list perm.\n#F\n#F PermFunc converts a 0-based permutation function used in SPLs, into an explicit\n#F 1-based list permutation. List permutations can be converted to GAP permutations\n#F using PermList. Alternatively PermFunc can be used, wihch returns GAP permutation.\n#F\nListPermFunc := (func, size) ->\n List([0..size-1], func) + 1;\n\n# ==========================================================================\n# FuncClass\n#\n# Base class for symbolic functions\n# ==========================================================================\nClass(FuncClass, BaseMat, Function, rec(\n #-----------------------------------------------------------------------\n # Must be implemented in subclasses\n #-----------------------------------------------------------------------\n lambda := self >> Error(\"not implemented\"), \n domain := self >> Error(\"not implemented\"), \n range := self >> Error(\"not implemented\"), \n\n #-----------------------------------------------------------------------\n _perm := true,\n isReal := True,\n isPermutation := self >> false,\n perm := self >> Checked(self.isPermutation(), PermFunc(x->self.lambda().at(x), self.range())),\n\n #-----------------------------------------------------------------------\n print := (self,i,is) >> Print(\n\tself.name, \"(\", PrintCS(self.params), \")\", When(self.transposed, \".transpose()\")),\n #-----------------------------------------------------------------------\n equals := (self, other) >> ObjId(other) = ObjId(self) and self.params=other.params,\n dims := self >> [self.range(), self.domain()],\n\n advdims := self >> [ [[ self.range() ]], [[ self.domain() ]] ],\n\n # size along each dimension, for a multidimensional range\n # for compatibility with ClassSPL, we wrap this into another list \n # (list of outputs, since ClassSPL can have >1 output)\n advrange := self >> [[ self.range() ]],\n\n # size along each dimension, for a multidimensional domain\n # for compatibility with ClassSPL, we wrap this into another list \n # (list of outputs, since ClassSPL can have >1 output)\n advdomain := self >> [[ self.domain() ]],\n\n # dimensionality of range (1-d, 2-d, etc)\n advrangeDim := self >> Length(self.advrange()[1]),\n # dimensionality of domain (1-d, 2-d, etc)\n advdomainDim := self >> Length(self.advdomain()[1]),\n #-----------------------------------------------------------------------\n toAMat := self >> Gath(self).toAMat(),\n #-----------------------------------------------------------------------\n arithmeticCost := (self, costMul, costAddMul) >> costMul(0) - costMul(0),\n #-----------------------------------------------------------------------\n transpose := self >> CopyFields(self, rec(transposed := not self.transposed )),\n #-----------------------------------------------------------------------\n conjTranspose := self >> self.transpose(),\n #-----------------------------------------------------------------------\n normalizedArithCost := self >> 0,\n #-----------------------------------------------------------------------\n free := self >> Union(List(self.params, FreeVars)),\n #-----------------------------------------------------------------------\n # Rewrite rules support \n #\n from_rChildren := (self, rch) >> CopyFields(ApplyFunc(ObjId(self), rch), \n\trec(transposed:=self.transposed)),\n\n # NOTE: self.transposed not exposed\n rChildren := self >> self.params, \n\n rSetChild := meth(self, n, newChild)\n self.params[n] := newChild;\n # self.canonizeParams(); ??\n\tself.dimensions := self.dims();\n end,\n # ----------------------------------------------------------------------\n checkParams := meth(self, params)\n local nargs, nump;\n\tnargs := NumArgs(self.def);\n\tnump := Length(params);\n\tif nargs <> -1 and nargs <> nump then\n Error(self.name, \" needs \", NumArgs(self.def), \" parameters: \",\n\t\tParamsFunc(self.def), \"\\n\");\n\tfi;\n end,\n #-----------------------------------------------------------------------\n canonizeParams := meth(self, params)\n local A, nump;\n\tnump := Length(params);\n\tif IsBound(self.abbrevs) then\n for A in self.abbrevs do\n if NumArgs(A) = -1 or NumArgs(A) = nump then\n\t\t return ApplyFunc(A, params);\n\t\tfi;\n\t od;\n return params;\n\telse\n return params;\n\tfi;\n end,\n #-----------------------------------------------------------------------\n __call__ := meth(arg)\n local result, self, params, lkup, h;\n self := arg[1];\n params := arg{[2..Length(arg)]};\n params := self.canonizeParams(params);\n self.checkParams(params);\n\n h := self.hash;\n if h<>false then\n lkup := h.objLookup(self, params);\n if lkup[1] <> false then return lkup[1]; fi;\n fi;\n \n result := SPL(WithBases(self, rec(params := params, transposed := false)));\n result := Inherit(result, ApplyFunc(result.def, params));\n\tresult.dimensions := result.dims();\n \n if h<>false then return h.objAdd(result, lkup[2]);\n else return result;\n fi;\n end,\n\n# obsolete\n# checkInverse := self >> Checked(self.isPermutation(),\n# PermFunc(self.direct, self.range()) * PermFunc(self.inverse, self.domain())),\n));\n\nClass(PermClass, FuncClass, rec(\n isPermutation := self >> true,\n toAMat := self >> Gath(self).toAMat(),\n equals := (self, other) >> ObjId(other) = ObjId(self) and self.params=other.params\n));\n", "meta": {"hexsha": "5eeb94fc7b4ab3f15f8391facbe6595d572a87ba", "size": 6927, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/spl/PermClass.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/PermClass.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/PermClass.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": 39.5828571429, "max_line_length": 98, "alphanum_fraction": 0.5006496319, "num_tokens": 1589, "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# Radix n kernel for FFTE, targeting ARM SVE\n\nbuildSVEKernel_a := function(n, kk, conf, opts)\n local vlen, name, suffix, filesuffix, t, j, k, l, m, tmp1, tmp2, tmp3,\n gi, g, gc, si, ss, s, sc, dft, rts, rt, opcnts, dfts, dftc, i, twt, twf, twl, tws, twc,\n cl, cc, c, clp, useFMA, _FMA, lp;\n\n name := DFTnameStr(n, kk);\n suffix := \"a\";\n filesuffix := \"sve_\";\n# suffix := \"_j\";\n Print(\"\\n\\n// == Generating \\\"\", name, \"\\\" ==================================================\\n\\n\"); \n\n vlen := TInt;\n useFMA := When(IsBound(conf.useFMA), conf.useFMA, true);\n _FMA := When(useFMA, FMA, p -> p);\n\n # variables\n t := var.fresh_t(\"t\", TInt);\n j := var.fresh_t(\"j\", TInt);\n k := V(0);\n l := var.fresh_t(\"l\", TInt);\n m := V(1);\n lp := var.fresh_t(\"lp\", TPtr(TInt));\n# mp := var.fresh_t(\"mp\", TPtr(TInt));\n\n\n # temp arrays\n tmp1 := var.fresh_t(\"R\", TArray(TVectSVE, 2n));\n tmp2 := var.fresh_t(\"S\", TArray(TVectSVE, 2n));\n tmp3 := var.fresh_t(\"T\", TArray(TVectSVE, 2n));\n\n # gather\n gi := _i -> VGath_L(1, vlen, 2(k + jm + _ilm));\n g := RulesSums(SumsSPL(VStack(List([0..n-1], gi)), opts));\n gc := Compile(opts.codegen(g, tmp1, X, opts), opts);\n \n # scatter\n si := _i -> ScatH(1, 1, 2nj+_i, 2n);\n ss := SumsSPL(HStack(List([0..2n-1], si)), opts);\n s := RulesSums(SubstTopDown(ss, @(1, ScatAcc), e->Scat(@(1).val.func)));\n sc := Compile(opts.codegen(s, 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 i := var.fresh_t(\"i\", 2n);\n twt := var.fresh_t(\"TW\", TPtr(TReal)); \n twf := Lambda(i, cond(\n eq(i, 0), 1, \n eq(i, 1), 0, \n sve_gath(nth(twt, 2((n-1)j) + 2 * idiv(i, 2) + (imod(i, 2) - 2)).toPtr(TReal), TInt, opts.pg, 2*(n-1))\n ));\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 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, opts.pg], \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, l, opts.pg], \n decl(cc.vars, _FMA(cc.cmd.cmds[1].cmd)));\n \n # print Radix N FFTE kernel as function\n #PrintCode(name, c, opts);\n #PrintTo(name::\".c\", PrintCode(name, c, opts));\n \n ########################################################\n # version with j loop vectorized as m == 1, k == 0\n clp := func(TVoid, \"transform\", [Y, X, twt, lp], \n decl(c.cmd.vars::c.free()::[opts.pg, l], \n chain(\n assign(l, deref(lp)),\n sve_loopn(j, l, \n c.cmd.cmd\n )\n )\n )\n );\n\n # print Radix N FFTE kernel as function\n PrintCode(opts.FortranIze(name::suffix), clp, opts);\n PrintTo(name::filesuffix::suffix::\".c\", PrintCode(opts.FortranIze(name::suffix), clp, opts));\nend;\n\n\n\n\n", "meta": {"hexsha": "012d60ac9fe916cf3f0783131e46200063b8a9e6", "size": 3576, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "kernelgen/sve_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/sve_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/sve_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": 34.3846153846, "max_line_length": 112, "alphanum_fraction": 0.5212527964, "num_tokens": 1246, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7549149868676283, "lm_q2_score": 0.588889130767832, "lm_q1q2_score": 0.44456123042008694}}
	{"text": "#############################################################################\n##\n#W listops.gi automgrp package Yevgen Muntyan\n#W Dmytro Savchuk\n##\n#Y Copyright (C) 2003 - 2018 Yevgen Muntyan, Dmytro Savchuk\n##\n\n\n###############################################################################\n##\n## AG_IsCorrectAutomatonList( <list>, <invertible> )\n##\nInstallGlobalFunction(AG_IsCorrectAutomatonList,\nfunction(list, invertible)\n local len, deg, i, j, sym, semi;\n\n if not IsDenseList(list) then\n return false;\n fi;\n\n len := Length(list);\n if len = 0 then\n return false;\n fi;\n\n for i in [1..len] do\n if not IsDenseList(list[i]) then\n return false;\n fi;\n if Length(list[i]) <> Length(list[1]) then\n return false;\n fi;\n od;\n\n deg := Length(list[1]) - 1;\n if deg < 1 then\n return false;\n fi;\n\n sym := SymmetricGroup(deg);\n semi := FullTransformationSemigroup(deg);\n\n for i in [1..len] do\n for j in [1..deg] do\n if not IsInt(list[i][j]) then\n return false;\n fi;\n if list[i][j] > len or list[i][j] < 1 then\n return false;\n fi;\n od;\n\n if not list[i][deg + 1] in sym then\n if not list[i][deg + 1] in semi then\n return false;\n fi;\n if invertible and list[i][deg + 1]^-1=fail then\n return false;\n fi;\n fi;\n od;\n\n return true;\nend);\n\n\n###############################################################################\n##\n## AG_IsCorrectRecurList( <list>, <invertible> )\n##\nInstallGlobalFunction(AG_IsCorrectRecurList,\nfunction(list, invertible)\n local len, deg, i, j, k, sym, semi, inv_states;\n\n if not IsDenseList(list) then\n return false;\n fi;\n\n len := Length(list);\n if len = 0 then\n return false;\n fi;\n\n for i in [1..len] do\n if not IsDenseList(list[i]) then\n return false;\n fi;\n if Length(list[i]) <> Length(list[1]) then\n return false;\n fi;\n od;\n\n deg := Length(list[1]) - 1;\n if deg < 2 then\n return false;\n fi;\n\n sym := SymmetricGroup(deg);\n semi := FullTransformationSemigroup(deg);\n\n for i in [1..len] do\n for j in [1..deg] do\n if IsInt(list[i][j]) then\n if list[i][j] > len or list[i][j] < -len or list[i][j] = 0 then\n return false;\n fi;\n elif IsList(list[i][j]) then\n if not IsDenseList(list[i][j]) then\n return false;\n fi;\n for k in list[i][j] do\n if (not IsInt(k)) or k > len or k < -len or k = 0 then\n return false;\n fi;\n od;\n else\n return false;\n fi;\n od;\n\n\n # Check that everything is correct here\n if (not IsPerm(list[i][deg + 1])) and (not IsTransformation(list[i][deg + 1])) then\n return false;\n elif LargestMovedPoint(list[i][deg + 1]) > deg then\n return false;\n elif IsTransformation(list[i][deg + 1]) and invertible and list[i][deg + 1]^-1=fail then\n return false;\n fi;\n od;\n\n\n# check if there is x^-1 in the list, while x is not invertible\n inv_states:=[];\n for i in [1..len] do\n if AG_IsInvertibleStateInList(i,list) then Add(inv_states,i); fi;\n od;\n\n for i in [1..len] do\n for j in [1..deg] do\n if IsInt(list[i][j]) then\n if list[i][j]<0 and not -list[i][j] in inv_states then\n return false;\n fi;\n else\n for k in list[i][j] do\n if k<0 and not -k in inv_states then\n return false;\n fi;\n od;\n fi;\n od;\n od;\n\n return true;\nend);\n\n\n###############################################################################\n##\n## AG_ConnectedStatesInList(state, list)\n##\n## Returns list of states which are reachable from given state,\n## it does not check correctness of arguments\n##\nInstallGlobalFunction(AG_ConnectedStatesInList,\nfunction(state, list)\n local i, j, s, d, to_check, checked;\n\n d := Length(list[1]) - 1;\n\n to_check := [state];\n checked := [];\n\n while Length(to_check) <> 0 do\n for s in to_check do\n for i in [1..d] do\n if IsList(list[s][i]) then\n for j in AsSet(List(list[s][i],AbsInt)) do\n if (not j in checked) and (not j in to_check) then\n to_check := Union(to_check, [j]);\n fi;\n od;\n else\n if (not AbsInt(list[s][i]) in checked) and (not AbsInt(list[s][i]) in to_check) then\n to_check := Union(to_check, [AbsInt(list[s][i])]);\n fi;\n fi;\n od;\n checked := Union(checked, [s]);\n to_check := Difference(to_check, [s]);\n od;\n od;\n\n return checked;\nend);\n\n\n###############################################################################\n##\n## AG_IsTrivialStateInList( <state>, <list>)\n##\n## Checks whether given state is trivial.\n## Does not check correctness of arguments.\n##\nInstallGlobalFunction(AG_IsTrivialStateInList,\nfunction(state, list)\n local deg;\n deg := Length(list[1]) - 1;\n # IsOne works for Transformation's\n return ForAll(AG_ConnectedStatesInList(state, list),\n s -> IsOne(list[s][deg+1]));\nend);\n\n\n###############################################################################\n##\n## AG_IsObviouslyTrivialStateInList( <state>, <list>)\n##\n## Checks whether given state is obviously trivial.\n## Works for lists generating self-similar groups.\n## Returns `true' if <state>=(,...,)(), where\n## * could be either +-<state> or [+-<state>], or [].\n##\nInstallGlobalFunction(AG_IsObviouslyTrivialStateInList,\nfunction(state, list)\n local deg, check;\n\n check := function(s)\n if IsInt(s) then return state=AbsInt(s);\n else return s=[] or (Length(s)=1 and state=AbsInt(s[1]));\n fi;\n end;\n\n\n deg := Length(list[1]) - 1;\n if not IsOne(list[state][deg+1]) then return false; fi;\n # IsOne works for Transformation's\n return ForAll(list[state]{[1..deg]}, check);\nend);\n\n\n\n###############################################################################\n##\n## AG_IsInvertibleStateInList( <state>, <list> )\n##\n## Checks whether given state is invertible.\n## Does not check correctness of arguments.\n##\nInstallGlobalFunction(AG_IsInvertibleStateInList,\nfunction(state, list)\n local deg;\n deg := Length(list[1]) - 1;\n return ForAll(AG_ConnectedStatesInList(state, list),\n s -> (list[s][deg+1]^-1<>fail));\nend);\n\n\n###############################################################################\n##\n## AG_AreEquivalentStatesInList( <state1>, <state2>, <list> )\n##\n## Checks whether two given states are equivalent.\n## Does not check correctness of arguments.\n##\nInstallGlobalFunction(AG_AreEquivalentStatesInList,\nfunction(state1, state2, list)\n local d, checked_pairs, pos, s1, s2, np, i;\n\n d := Length(list[1]) - 1;\n checked_pairs := [[state1, state2]];\n pos := 0;\n\n while Length(checked_pairs) <> pos do\n pos := pos + 1;\n s1 := checked_pairs[pos][1];\n s2 := checked_pairs[pos][2];\n\n if list[s1][d+1] <> list[s2][d+1] then\n return false;\n fi;\n\n for i in [1..d] do\n np := [list[s1][i], list[s2][i]];\n if not np in checked_pairs then\n checked_pairs := Concatenation(checked_pairs, [np]);\n fi;\n od;\n od;\n\n return true;\nend);\n\n\n###############################################################################\n##\n## AG_AreEquivalentStatesInLists( <state1>, <state2>, <list1>, <list2>)\n##\n## Checks whether two given states in different lists are equivalent.\n## Does not check correctness of arguments.\n##\nInstallGlobalFunction(AG_AreEquivalentStatesInLists,\nfunction(state1, state2, list1, list2)\n local d, checked_pairs, pos, s1, s2, np, i;\n\n d := Length(list1[1]) - 1;\n checked_pairs := [[state1, state2]];\n pos := 0;\n\n while Length(checked_pairs) <> pos do\n pos := pos + 1;\n s1 := checked_pairs[pos][1];\n s2 := checked_pairs[pos][2];\n\n if list1[s1][d+1] <> list2[s2][d+1] then\n return false;\n fi;\n\n for i in [1..d] do\n np := [list1[s1][i], list2[s2][i]];\n if not np in checked_pairs then\n checked_pairs := Concatenation(checked_pairs, [np]);\n fi;\n od;\n od;\n\n return true;\nend);\n\n\n###############################################################################\n##\n## AG_ReducedAutomatonInList( <list> )\n##\n## Returns [new_list, list_of_states, old_states] where new_list is a new list\n## which represents reduced form of given automaton, i-th elmt of list_of_states\n## is the number of i-th state of new automaton in the old one.\n## old_states[i] is the number of state which corresponds to the i-th state\n## of the original automaton.\n##\n## First state of returned list is always first state of given one.\n## It does not remove trivial state, so it's not really \"reduced automaton\",\n## it just removes equivalent states.\n## TODO: write such function which removes trivial state\n##\n## Does not check correctness of list.\n##\n## WARNING: do NOT change it.\n##\nInstallGlobalFunction(AG_ReducedAutomatonInList,\nfunction(list)\n local i, n, triv_states, equiv_classes, checked_states, s, s1, s2,\n eq_cl, eq_cl_1, eq_cl_2, are_equiv, eq_cl_reprs,\n new_states, new_list, deg,\n reduced_automaton, state, states_reprs;\n\n n := Length(list);\n triv_states := [];\n equiv_classes := [];\n checked_states := [];\n deg := Length(list[1]) - 1;\n\n for s in [1..n] do\n if AG_IsTrivialStateInList(s, list) then\n triv_states := Union(triv_states, [s]);\n fi;\n od;\n\n equiv_classes:=[triv_states];\n for s1 in Difference([1..n], triv_states) do\n for s2 in Difference([s1+1..n], triv_states) do\n are_equiv := AG_AreEquivalentStatesInList(s1, s2, list);\n\n if s1 in checked_states then\n for eq_cl in equiv_classes do\n if s1 in eq_cl then\n eq_cl_1 := StructuralCopy(eq_cl);\n break; fi; od;\n else\n equiv_classes := Union(equiv_classes, [[s1]]);\n eq_cl_1 := [s1];\n checked_states := Union(checked_states, [s1]);\n fi;\n if s2 in checked_states then\n for eq_cl in equiv_classes do\n if s2 in eq_cl then\n eq_cl_2 := StructuralCopy(eq_cl);\n break; fi; od;\n else\n equiv_classes := Union(equiv_classes, [[s2]]);\n eq_cl_2 := [s2];\n checked_states := Union(checked_states, [s2]);\n fi;\n\n if are_equiv then\n equiv_classes := Difference(equiv_classes, [eq_cl_1, eq_cl_2]);\n equiv_classes := Union(equiv_classes, [Union(eq_cl_1, eq_cl_2)]);\n fi;\n od;\n od;\n states_reprs := [1..n];\n for eq_cl in equiv_classes do\n for s in eq_cl do\n states_reprs[s] := Minimum(eq_cl);\n od;\n od;\n\n\n new_states := Set(states_reprs);\n new_list := [];\n\n for s in new_states do\n state := [];\n state[deg+1] := list[s][deg+1];\n for i in [1..deg] do\n state[i] := Position(new_states, states_reprs[list[s][i]]);\n od;\n new_list := Concatenation(new_list, [state]);\n od;\n\n return [new_list, new_states, List([1..n], i -> Position(new_states, states_reprs[i]))];\nend);\n\n\n###############################################################################\n##\n## AG_MinimalSubAutomatonInlist(<states>, <list>)\n##\n## Returns list representation of automaton given by <list> which is minimal\n## subatomaton of automaton containing states <states>.\n##\n## Does not check correctness of list.\n##\nInstallGlobalFunction(AG_MinimalSubAutomatonInlist,\nfunction(states, list)\n local s, new_states, state, new_list, i, deg;\n\n new_states := [];\n for s in states do\n new_states := Union(new_states, AG_ConnectedStatesInList(s, list));\n od;\n\n new_list := [];\n deg := Length(list[1]) - 1;\n\n for s in new_states do\n state := [];\n for i in [1..deg] do\n state[i] := Position(new_states, list[s][i]);\n od;\n state[deg+1] := list[s][deg+1];\n new_list := Concatenation(new_list, [state]);\n od;\n\n return [new_list, new_states];\nend);\n\n\n###############################################################################\n##\n## AG_PermuteStatesInList(<list>, <perm>)\n##\n## Does not check correctness of arguments.\n##\nInstallGlobalFunction(AG_PermuteStatesInList,\nfunction(list, perm)\n local new_list, i, j, deg;\n\n deg := Length(list[1]) - 1;\n new_list := [];\n for i in [1..Length(list)] do\n new_list[i^perm] := [];\n for j in [1..deg] do\n new_list[i^perm][j] := list[i][j]^perm;\n od;\n new_list[i^perm][deg+1] := list[i][deg+1];\n od;\n\n return new_list;\nend);\n\n\n###############################################################################\n##\n## AG_WordStateInList(<w>, <s>, <list>, <reduce>, <trivstate>)\n##\n## It's ProjectWord from selfs.g\n## Does not check correctness of arguments.\n##\nInstallGlobalFunction(AG_WordStateInList,\nfunction(w, s, list, reduce, trivstate)\n local i, perm, d, proj, red, reduce_word;\n\n reduce_word := function(v)\n local len, red, x;\n len := 0;\n red := [];\n for x in v do\n if x <> trivstate then\n if len <> 0 and x = -red[len] then\n Remove(red, len);\n len := len - 1;\n else\n Add(red, x);\n len := len + 1;\n fi;\n fi;\n od;\n return red;\n end;\n\n d := Length(list[1])-1;\n proj := [];\n perm := ();\n for i in [1..Length(w)] do\n Add(proj, list[w[i]][s^perm]);\n perm := perm * list[w[i]][d+1];\n od;\n if reduce then\n return reduce_word(proj);\n else\n return proj;\n fi;\nend);\n\n\n###############################################################################\n##\n## AG_WordStateAndPermInList(<w>, <s>, <list>)\n##\n## Does not check correctness of arguments.\n##\nInstallGlobalFunction(AG_WordStateAndPermInList,\nfunction(w, s, list)\n local i, perm, perm_res, new_state, d, proj;\n d := Length(list[1])-1;\n proj := [];\n perm := ();\n perm_res := ();\n for i in [1..Length(w)] do\n new_state := list[w[i]][s^perm];\n Add(proj, new_state);\n perm := perm * list[w[i]][d+1];\n perm_res := perm_res * list[new_state][d+1];\n od;\n return [proj, perm_res];\nend);\n\n\n###############################################################################\n##\n## AG_ImageOfVertexInList(<list>, <init>, <vertex>)\n##\n## Does not check correctness of arguments.\n##\nInstallGlobalFunction(AG_ImageOfVertexInList,\nfunction(list, s, seq)\n local deg, img, x;\n\n deg := Length(list[1]) - 1;\n img := [];\n for x in seq do\n Add(img, x^list[s][deg+1]);\n s := list[s][x];\n od;\n\n return img;\nend);\n\n\n###############################################################################\n##\n## AG_DiagonalPowerInList(<list>, <n>)\n##\nInstallGlobalFunction(AG_DiagonalPowerInList,\nfunction(list, n, names)\n local d, nlist, nd, nalph, nstates, nperm,\n i, j, k, letter, n_letter, n_state, state,\n nnames;\n\n d := Length(list[1]) - 1;\n nd := d ^ n;\n nalph := Tuples([1..d], n);\n nstates := Tuples([1..Length(list)], n);\n nlist := List([1..Length(nstates)], i -> []);\n nnames := List(nstates, s->List(s, i->names[i]));\n\n for i in [1..Length(nlist)] do\n nperm := [];\n state := nstates[i];\n for j in [1..nd] do\n letter := nalph[j];\n n_letter := [];\n n_state := [];\n for k in [1..n] do\n n_letter[k] := letter[k]^list[state[k]][d+1];\n n_state[k] := list[state[k]][letter[k]];\n od;\n nperm[j] := n_letter;\n nlist[i][j] := Position(nstates, n_state);\n od;\n nlist[i][nd+1] := PermListList(nalph, nperm);\n od;\n\n nnames := List(nnames, l->Concatenation(l));\n return [nlist, nnames];\nend);\n\n\n###############################################################################\n##\n## AG_MultAlphabetInList(<list>, <n>)\n##\nInstallGlobalFunction(AG_MultAlphabetInList,\nfunction(list, n)\n local d, nlist, nd, nalph, nperm,\n i, j, k, letter, n_letter, st;\n\n d := Length(list[1]) - 1;\n nd := d ^ n;\n nalph := Tuples([1..d], n);\n nlist := List(list, i -> []);\n\n for i in [1..Length(nlist)] do\n nperm := [];\n for j in [1..Length(nalph)] do\n letter := nalph[j];\n n_letter := [];\n st := i;\n for k in [1..n] do\n Add(n_letter, letter[k]^list[st][d+1]);\n st := list[st][letter[k]];\n od;\n nlist[i][j] := st;\n nperm[j] := n_letter;\n od;\n nlist[i][nd+1] := PermListList(nalph, nperm);\n od;\n\n return nlist;\nend);\n\n\n###############################################################################\n##\n## AG_HasDualInList(<list>)\n##\nInstallGlobalFunction(AG_HasDualInList,\nfunction(list)\n local i, j, p, d, n;\n d := Length(list[1]) - 1;\n n := Length(list);\n for i in [1..d] do\n p := [];\n for j in [1..n] do\n p[j] := list[j][i];\n od;\n if PermListList([1..n], p) = fail then\n return false;\n fi;\n od;\n return true;\nend);\n\n\n###############################################################################\n##\n## AG_DualAutomatonList(<list>)\n##\nInstallGlobalFunction(AG_DualAutomatonList,\nfunction(list)\n local dual, d, n;\n d := Length(list[1]) - 1;\n n := Length(list);\n return List([1..d], i -> Concatenation(List([1..n], j -> i^list[j][d+1]),\n [PermList(List([1..n], j -> list[j][i]))]));\nend);\n\n\n###############################################################################\n##\n## AG_HasDualOfInverseInList(<list>)\n##\nInstallGlobalFunction(AG_HasDualOfInverseInList,\nfunction(list)\n return AG_HasDualInList(AG_InverseAutomatonList(list));\nend);\n\n\n###############################################################################\n##\n## AG_InverseAutomatonList(<list>)\n##\nInstallGlobalFunction(AG_InverseAutomatonList,\nfunction(list)\n local inv, d, i;\n d := Length(list[1]) - 1;\n inv := List(list, l -> Permuted(l, l[d+1]));\n for i in [1..Length(list)] do inv[i][d+1] := inv[i][d+1]^-1; od;\n return inv;\nend);\n\n\n#E\n", "meta": {"hexsha": "46feabccc68565e100d50b9c2a580f8cb234374a", "size": 17625, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "gap/listops.gi", "max_stars_repo_name": "gap-packages/automgrp", "max_stars_repo_head_hexsha": "1beb0cbc96c9748cf912433c27c661e1f87ef5dc", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-10-02T15:00:11.000Z", "max_stars_repo_stars_event_max_datetime": "2021-10-02T15:00:11.000Z", "max_issues_repo_path": "gap/listops.gi", "max_issues_repo_name": "gap-packages/automgrp", "max_issues_repo_head_hexsha": "1beb0cbc96c9748cf912433c27c661e1f87ef5dc", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 9, "max_issues_repo_issues_event_min_datetime": "2019-09-21T22:10:40.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-26T23:51:41.000Z", "max_forks_repo_path": "gap/listops.gi", "max_forks_repo_name": "gap-packages/automgrp", "max_forks_repo_head_hexsha": "1beb0cbc96c9748cf912433c27c661e1f87ef5dc", "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": 24.9292786421, "max_line_length": 94, "alphanum_fraction": 0.5400283688, "num_tokens": 4920, "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(TDCT2, TDCT3, TDCT4);\n\n_DCT_CONST := 2.5;\n\n#######################################################################################\n# tSPL DCT rules\n\n\n# PDCT4_CT_SPL := rec(\n# isApplicable := P -> P > 2 and ForAny(DivisorPairs(2P), d->IsEvenInt(d[1]) and IsEvenInt(d[2])),\n# forTransposition := false,\n#\n# allChildren := P -> let(N := P,\n# Map2(Filtered(DivisorPairs(2N), d -> IsEvenInt(d[1]) and IsEvenInt(d[2])),\n# (m,n) -> [ PRDFT3(m,-1).transpose(), PRDFT3(n) ])),\n#\n# rule := (P,C) -> let(N := P, m := Rows(C[1]), n := Cols(C[2]),\n# j := Ind(n/2),\n# T := Diag(Twid(2N, m/2, 1, 1/2, 1/2, j)),\n#\n# Prm(Refl(N, 2N-1, N, L(mn, m))) \n# IterDirectSum(j, j.range, Diag(BHN(m)) * C[1] * RC(T)) \n# RC(L(mn/4, n/2)) \n# Tensor(I(m/2), C[2] Diag(BHN(n))) \n# Prm(Refl(N, 2N-1, N, L(mn, m)))\n# )\n# )\n#\n\n\n#F TDCT4(<size>, tags) - Discrete Cosine Transform, Type IV, non-terminal\n#F Definition: (n x n)-matrix [ cos((k+1/2)(l+1/2)pi/n) \| k,l = 0...n-1 ]\n#F Note: DCT4 is symmetric\n#F Example: DCT4(8)\nClass(TDCT4, TaggedNonTerminal, rec(\n abbrevs := [ N -> Checked(IsInt(N), N >= 1, [N]) ] ,\n dims := self >> [self.params[1], self.params[1]],\n isReal := True,\n terminate := self >> Mat(DCT_IVunscaled(self.params[1])),\n transpose := self >> Copy(self),\n SmallRandom := () -> Random([2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32]),\n normalizedArithCost := (self) >> let(n := self.params[1], IntDouble(_DCT_CONST n * d_log(n) / d_log(2)))\n));\n\n\nNewRulesFor(TDCT4, rec(\n# DCT4_CT_tSPL := rec(\n# switch := false,\n#\n# applicable := (self, t) >> let(P:=t.params, P[1] > 2 and ForAny(DivisorPairs(2P[1]), d->IsEvenInt(d[1]) and IsEvenInt(d[2])) and HasTags(t)),\n#\n# children := (self, t) >> let(tags := GetTags(t), N := t.params[1],\n# Map2(Filtered(DivisorPairs(2N), d -> IsEvenInt(d[1]) and IsEvenInt(d[2])),\n# (m,n) -> [\n# SetTag(TCompose([\n# TScat(Refl(N, 2N-1, N, L(mn, m))),\n# TTensorI(Diag(BHN(m)) * PRDFT3(m,-1).transpose(), n/2, APar, APar),\n# TRC(TDiag(fPrecompute(\n# fCompose(dOmega(8 * N, 1), diagTensor(dLin(N/m, 2, 1, TInt), dLin(m/2, 2, 1, TInt)))\n# ))),\n# TRC(TL(mn/4, n/2, 1, 1)),\n# TTensorI(PRDFT3(n) Diag(BHN(n)), m/2, APar, APar),\n# TGath(Refl(N, 2N-1, N, L(mn, m))) ]),\n# tags)\n# ])),\n#\n# apply := (self, t, C, Nonterms) >> C[1]\n# ),\n#\n# # Variant better suited for vectorization\n# PDCT4_CT_SPL_Vec := rec(\n# isApplicable := P -> P > 2 and (P mod 2) = 0,\n# forTransposition := false,\n#\n# allChildren := P -> let(N := P,\n# Map2(Filtered(DivisorPairs(2N), d -> IsEvenInt(d[1]) and IsEvenInt(d[2])),\n# (m,n) -> [ PRDFT3(m,-1).transpose(), PRDFT3(n) ])),\n#\n# rule := (P,C) -> let(N := P, m := Rows(C[1]), n := Cols(C[2]),\n# TT := Diag(fPrecompute(fCompose(dOmega(8 N, 1),\n# diagTensor(dLin(N/m, 2, 1, TInt), dLin(m/2, 2, 1, TInt))))),\n#\n# IJ(N, n/2) \n# L(N, m) \n# Tensor(I(n/2),\n# M(m,m/2) * Diag(BHN(m)) * C[1]) \n# RC(TT) \n# L(N, n/2) \n# Tensor(I(m/2),\n# L(n, 2) C[2] * Diag(BHN(n)) * K(n, 2)) \n# L(N, m/2) \n# IJ(N, m/2)\n# )\n# )\n\n\n DCT4_CT_tSPL := rec(\n switch := false,\n\n applicable := (self, t) >> let(\n P:=t.params,\n P[1] > 2\n and ForAny(DivisorPairs(2P[1]), d ->\n IsEvenInt(d[1]) and IsEvenInt(d[2])\n )\n and t.hasTags()\n ),\n\n children := (self, t) >> let(\n tags := t.getTags(),\n N := t.params[1],\n Map2(\n Filtered(DivisorPairs(2N), d -> IsEvenInt(d[1]) and IsEvenInt(d[2])),\n (m,n) -> List([\n TPrm(IJ(N, n/2)),\n TTensorI(condM(m,m/2) * Diag(BHN(m)) * PRDFT3(m,-1).transpose(), n/2, AVec, AVec),\n TTensorI(L(n, 2) * PRDFT3(n) * Diag(BHN(n)) * condK(n, 2), m/2, APar, AVec),\n TPrm(IJ(N, m/2))\n ], i -> i.setTags(tags))\n )\n ),\n\n apply := (self, t, C, Nonterms) >> let(\n N:=t.params[1],\n n:=2Rows(Nonterms[1].params[1].params[2]),\n m:=2Rows(Nonterms[4].params[1].params[2]),\n Grp(\n C[1] * C[2]\n * ConjDiag(RC(Diag(fPrecompute(\n fCompose(dOmega(8 * N, 1), diagTensor(dLin(N/m, 2, 1, TInt), dLin(m/2, 2, 1, TInt)))\n ))), L(N, m), L(N, n/2))\n )\n * C[3] * C[4]\n )\n )\n));\n\n\n#F TDCT2(<n>) - Discrete Cosine Transform, Type II, non-terminal\n#F Definition: (n x n)-matrix [ cos(k(l+1/2)pi/n) \| k,l = 0...n-1 ]\n#F Note: DCT2 is the transpose of DCT3\n#F Example: DCT2(8)\nClass(TDCT2, TaggedNonTerminal, rec(\n abbrevs := [ N -> Checked(IsInt(N), N >= 1, [N]) ] ,\n dims := self >> [self.params[1], self.params[1]],\n isReal := True,\n terminate := self >> Mat(DCT_IIunscaled(self.params[1])),\n transpose := self >> TDCT3(self.params[1]),\n SmallRandom := () -> Random([2,3,4,5,6,8,9,10,12,15,16,18,24,27,30,32]),\n normalizedArithCost := (self) >> let(n := self.params[1], IntDouble(_DCT_CONST * n * d_log(n) / d_log(2)))\n));\n\n\nNewRulesFor(TDCT2, rec(\n DCT2_DCT4_tSPL := rec(\n switch := false,\n applicable := (self, t) >> true,\n children := (self, t) >> [[ TS(t.params[1]).withTags(t.getTags()), TDCT4(t.params[1]).withTags(t.getTags()) ]],\n apply := (self, t, C, Nonterms) >> let(P := t.params[1],\n Diag(Concat([V(2.0)], List([1..P-1], i->V(1.0)))) \n C[1].transpose() C[2] \n Diag(List([0..P - 1], i -> 1/(2 CosPi((2i + 1)/(4P))))))\n ))\n);\n\n\n\n#F TDCT3(<n>) - Discrete Cosine Transform, Type III, non-terminal (unscaled)\n#F Definition: (n x n)-matrix [ cos((k+1/2)lpi/n) \| k,l = 0...n-1 ]\n#F [scaled] (n x n)-matrix [ a_lcos((k+1/2)lpi/n) \| k,l = 0...n-1 ]\n#F a_j = 1/sqrt(2) for j = 0 and = 1 else\n#F Note: DCT3 is the transpose of DCT2, scaled NOT supported yet\n#F Example: DCT3(8)\nClass(TDCT3, TaggedNonTerminal, rec(\n abbrevs := [ N -> Checked(IsInt(N), N >= 1, [N]) ] ,\n dims := self >> [self.params[1], self.params[1]],\n isReal := True,\n terminate := self >> Mat(DCT_IIIunscaled(self.params[1])),\n transpose := self >> TDCT2(self.params[1]),\n SmallRandom := () -> Random([2,3,4,5,6,8,9,10,12,15,16,18,24,27,30,32]),\n normalizedArithCost := (self) >> let(n := self.params[1], IntDouble(_DCT_CONST n * d_log(n) / d_log(2)))\n));\n\n\nNewRulesFor(TDCT3, rec(\n DCT3_DCT2_tSPL := rec(\n switch := false,\n applicable := (self, t) >> true,\n children := (self, t) >> [[ TDCT2(t.params[1]).withTags(t.getTags()) ]],\n apply := (self, t, C, Nonterms) >> C[1].transpose()\n ),\n DCT3_DCT4_tSPL := rec(\n switch := false,\n applicable := (self, t) >> true,\n children := (self, t) >> [[ TDCT4(t.params[1]).withTags(t.getTags()), TS(t.params[1]).withTags(t.getTags()) ]],\n apply := (self, t, C, Nonterms) >> let(P := t.params[1],\n Diag(List([0..P - 1], i -> 1/(2 * CosPi((2i + 1)/(4P))))) \n C[1] C[2] *\n Diag(Concat([V(2.0)], List([1..P-1], i->V(1.0)))))\n )\n));\n", "meta": {"hexsha": "49dad3b65443d73e410b28749144292e1e9502fd", "size": 8093, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/common/dct.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/common/dct.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/common/dct.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": 39.0966183575, "max_line_length": 151, "alphanum_fraction": 0.4470530088, "num_tokens": 2768, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. 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	{"text": "\n#\n# ---------- Constructors ----------\n#\n\nInstallMethod(UnipotentMod,\n \"Unipotent element in simple adjoint type\",\n [IsChevalleyAdj,IsList,IsList,IsInt,IsPosInt],\n function(sys,coeffs,ordering,order,root)\n local object;\n \n if Filtered(coeffs,i->not i[2] in Integers)=[] then coeffs:=List(coeffs,i->[i[1],One(ring(sys))i[2]]);\n elif Filtered(coeffs,i->not i[2] in ring(sys))<>[] then Error(\"The coefficients ar not in indicated ring.\"); fi;\n\n object:=Objectify(NewType(NewFamily(\"UnipotentFamily\"),\n IsAttributeStoringRep and\n IsUnipotent and\n IsMultiplicativeElementWithInverse),\n rec());\n\n SetchevalleyAdj(object,sys);\n SetOrdering(object,ordering);\n\n Setcoefficients(object,CanonicMod(sys,coeffs,ordering,root));\n# SetInverse(object,InverseOp(object)); This is set at the first call Inverse(obj);\n\n if order = -1 and Characteristic(sys)>0 then\n SetOrder(object,OrderOp(object));\n elif order > -1 then\n SetOrder(object,order);\n fi;\n \n SetName(object,Concatenation(\"<unipotent element for \",\n type(sys),String(rank(sys)),\n \" in characteristic \",String(Characteristic(sys)),\">\"));\n return object;\nend);\n\nInstallMethod(UnipotentMod,\n \"Unipotent element in simple adjoint type\",\n [IsChevalleyAdj,IsList,IsList,IsPosInt],\n function(sys,coeffs,ordering,root)\n\n return UnipotentMod(sys,coeffs,ordering,-2,root);\nend);\n\n\n#\n# ---------- Canonic form of element modulo some roots ----------\n#\n\nInstallMethod(CanonicMod,\n \"Canonic form of coefficients of unipotent element in given ordering modulo some roots\",\n [IsChevalleyAdj,IsList,IsList,IsPosInt],\n function(sys,coeffs,Ordering,root)\n local lista,\n pr,Cijrs,\n flag,i,temp,suma,param,cc,k,pos;\n \n lista:=[];\n for i in coeffs do\n if Ordering[i[1]]<=Ordering[root] then\n Add(lista,ShallowCopy(i));\n fi;\n od;\n \n pr:=positiveRoots(sys);\n\n Cijrs:=C(sys);\n flag:=true;\n while flag do\n flag:=false;\n i:=Length(lista);\n while 0 < i do\n if lista[i][2] = Zero(ring(sys)) then \n Remove(lista,i);\n flag:=true;\n elif 1 < i and lista[i][1] = lista[i-1][1] then\n lista[i-1][2]:=lista[i-1][2]+lista[i][2];\n Remove(lista,i);\n flag:=true;\n elif 1 < i and Ordering[lista[i][1]] < Ordering[lista[i-1][1]] then\n temp:=lista[i]; lista[i]:=lista[i-1]; lista[i-1]:=temp;\n \n #aici r si s sunt pe pozitia i-1 si repsectiv i\n k:=1;\n for cc in Cijrs[lista[i-1][1]][lista[i][1]] do\n suma:=cc[1]pr[lista[i-1][1]]+cc[2]pr[lista[i][1]];\n pos:=Position(pr,suma);\n if Ordering[pos]<=Ordering[root] then\n param:=cc[3]((-1)^cc[1])(lista[i-1][2]^cc[1])(lista[i][2]^cc[2]);\n Add(lista,[pos,param],i+k);\n k:=k+1;\n fi;\n od;\n flag:=true;\n fi;\n i:=i-1;\n od;\n od;\n\n return Immutable(lista);\nend);\n\n\n#\n# ---------- Arithmetic Operations modulo some roots ----------\n#\n\nInstallMethod(MMod,\n \"Multiplication for unipotent elements a*b modulo some roots and with the ordering of b\",\n [IsUnipotent,IsUnipotent,IsPosInt],\n function(u1,u2,root)\n local sys1,sys2,\n generic,result,coeffs1,coeffs2,\n APR,avars,pr_len,\n i;\n\n sys1:=chevalleyAdj(u1);\n sys2:=chevalleyAdj(u2);\n if type(sys1)<>type(sys2) or\n rank(sys1)<>rank(sys2) or\n ring(sys1)<>ring(sys2) then Error(\"Not in the same family.\"); fi;\n \n return UnipotentMod(sys2,Concatenation(coefficients(u1),coefficients(u2)),Ordering(u2));\nend);\n\nInstallMethod(CommMod,\n \"Commutator for unipotent elements a^-1b^-1ab with the ordering of b\",\n [IsUnipotent,IsUnipotent,IsPosInt],\n function(u1,u2,root)\n local sys1,sys2;\n\n sys1:=chevalleyAdj(u1);\n sys2:=chevalleyAdj(u2);\n if type(sys1)<>type(sys2) or\n rank(sys1)<>rank(sys2) or\n ring(sys1)<>ring(sys2) then Error(\"Not in the same family.\"); fi;\n return UnipotentMod(sys2,\n Concatenation(coefficients(u1^-1),coefficients(u2^-1),\n coefficients(u1),coefficients(u2)),\n Ordering(u2),\n root);\nend);\n\nInstallMethod(ConjMod,\n \"Conjugation for unipotent elements b^-1ab with the ordering of b\",\n [IsUnipotent,IsUnipotent,IsPosInt],\n function(u1,u2,root)\n local sys1,sys2;\n\n sys1:=chevalleyAdj(u1);\n sys2:=chevalleyAdj(u2);\n if type(sys1)<>type(sys2) or\n rank(sys1)<>rank(sys2) or\n ring(sys1)<>ring(sys2) then Error(\"Not in the same family.\"); fi;\n return Unipotent(sys2,\n Concatenation(coefficients(u2^-1),coefficients(u1),coefficients(u2)),\n Ordering(u2),\n root);\nend);\n\n", "meta": {"hexsha": "9af598ddff039e009eef1547af0c2410e4e2c03e", "size": 6478, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "lib/unimod.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/unimod.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/unimod.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": 39.7423312883, "max_line_length": 126, "alphanum_fraction": 0.4487496141, "num_tokens": 1400, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7606506526772884, "lm_q2_score": 0.5774953651858118, "lm_q1q2_score": 0.4392722264466967}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nsetLeft := function(tags)\n local i, retval;\n retval := Copy(tags);\n for i in retval do\n i.isLeftChild := true;\n i.isRightChild := false;\n od;\n return(retval);\nend; \n\nsetRight := function(tags)\n local i, retval;\n retval := Copy(tags);\n for i in retval do\n i.isLeftChild := false;\n i.isRightChild := true;\n od;\n return(retval);\nend; \n\n\nNewRulesFor(WHT, rec(\n WHT_GT := rec(\n switch := false,\n maxSize := false,\n minSize := false,\n codeletSize := false,\n inplace := false,\n\n applicable := (self, t) >> let(n := Rows(t),\n n > 2 and\n (self.maxSize=false or n <= self.maxSize) and\n (self.minSize=false or n >= self.minSize) and\n not IsPrime(n)),\n\n children := (self, t) >> Map2(Filtered(DivisorPairs(Rows(t)), d->When(IsInt(self.codeletSize), d[1]<=self.codeletSize, true)),\n (m,n) -> [\n GT(WHT(LogInt(m, 2)), XChain([0, 1]), XChain([0, 1]), [n]).withTags(t.getTags()),\n GT(WHT(LogInt(n, 2)), XChain([1, 0]), XChain([1, 0]), [m]).withTags(t.getTags()),\n #GT(WHT(LogInt(m, 2)), XChain([0, 1]), XChain([0, 1]), [n]).withTags( let(ts := t.getTags(), setLeft(ts)) ),\n #GT(WHT(LogInt(n, 2)), XChain([1, 0]), XChain([1, 0]), [m]).withTags( let(ts := t.getTags(), setRight(ts)) ),\n ]),\n\n apply := (self, t, C, Nonterms) >> C[1] * C[2]\n )\n));\n\nNewRulesFor(DFT, rec(\n DFT_GT_CT := rec(\n switch := false,\n maxSize := false,\n minSize := 2,\n codeletSize := false,\n inplace := false,\n\n a := rec(\n precompute := true\n ),\n\n applicable := (self, t) >> let(n := Rows(t),\n n > 2 and\n (self.maxSize=false or n <= self.maxSize) and\n (self.minSize=false or n >= self.minSize) and\n not IsPrime(n)),\n\n #GT(DFT(m, t.params[2] mod m), XChain([0, 1]), XChain([0, 1]), [n]).withTags( let(a := t.getTags(), ),\n #GT(DFT(n, t.params[2] mod n), XChain([0, 1]), XChain([1, 0]), [m]).withTags( t.getTags())\n\n #GT(DFT(m, t.params[2] mod m), XChain([0, 1]), XChain([0, 1]), [n]).withTags(t.getTags()),\n #GT(DFT(n, t.params[2] mod n), XChain([0, 1]), XChain([1, 0]), [m]).withTags(t.getTags())\n\n children := (self, t) >> Map2(Filtered(DivisorPairs(Rows(t)), d->When(IsInt(self.codeletSize), d[1]<=self.codeletSize, true)),\n (m,n) -> [\n GT(DFT(m, t.params[2] mod m), XChain([0, 1]), XChain([0, 1]), [n]).withTags(t.getTags()),\n GT(DFT(n, t.params[2] mod n), XChain([0, 1]), XChain([1, 0]), [m]).withTags(t.getTags()),\n #GT(DFT(m, t.params[2] mod m), XChain([0, 1]), XChain([0, 1]), [n]).withTags( let(ts := t.getTags(), setLeft(ts)) ),\n #GT(DFT(n, t.params[2] mod n), XChain([0, 1]), XChain([1, 0]), [m]).withTags( let(ts := t.getTags(), setRight(ts)) ),\n ]),\n\n apply := (self, t, C, Nonterms) >> let(\n inplace := When(self.inplace, Inplace, Grp),\n n := Rows(Nonterms[2].params[1]),\n rot := t.params[2],\n compute := When(self.a.precompute, fPrecompute, fComputeOnline),\n\n inplace(Buf(C[1] * Diag(compute(Tw1(Rows(t), n, rot))))) * C[2])\n )\n));\n\n# GT(DFT(), ...) rules\n#\nNewRulesFor(GT, rec(\n GT_DFT_Base2 := rec(\n applicable := (self, t) >> let(rank := Length(t.params[4]),\n rank = 0 and PatternMatch(t, [GT, DFT, @, @, @, @, @], empty_cx()) and Rows(t.params[1])=2),\n apply := (t, C, Nonterms) -> F(2)\n ),\n\n GT_DFT_CT := rec(\n maxSize := false,\n minSize := false,\n minRank := 0,\n maxRank := 1,\n codeletSize := 32,\n inplace := true,\n\n a := rec(\n precompute := true\n ),\n\n applicable := (self, t) >> let(\n rank := Length(t.params[4]), \n dft := t.params[1],\n\n rank >= self.minRank \n and rank <= self.maxRank \n and When(rank>0, t.getTags()=[], true) \n and (self.maxSize=false or Rows(dft) <= self.maxSize) \n and (self.minSize=false or Rows(dft) >= self.minSize) \n and PatternMatch(t, [GT, DFT, XChain, XChain, @, @, @], empty_cx()) \n and DFT_GT_CT.applicable(dft)\n ),\n \n children := (self, t) >> let(\n dft := t.params[1], \n g := t.params[2], s := t.params[3], \n rot := dft.params[2],\n loop_dims := t.params[4],\n nloops := Length(loop_dims),\n tags := t.getTags(),\n \n Map2( Filtered(DivisorPairs(Rows(dft)), d->d[1]<=self.codeletSize),\n (m,n) -> [\n GT(DFT(m, rot mod m),\n s.composeWith(XChain([0, 1])), s.composeWith(XChain([0, 1])),\n Concatenation([n], loop_dims)\n ).withTags(tags),\n \n GT(DFT(n, rot mod n),\n g.composeWith(XChain([0, 1])), s.composeWith(XChain([1, 0])),\n Concatenation([m], loop_dims)\n ).withTags(tags)\n ]\n )\n ),\n \n apply := (self, t, C, Nonterms) >> let(\n loop_dims := t.params[4], \n s := t.params[3],\n N := Rows(t.params[1]), \n k := t.params[1].params[2], \n n := Rows(Nonterms[2].params[1]),\n\n inplace := When(self.inplace, Inplace, Grp),\n compute := When(self.a.precompute, fPrecompute, fComputeOnline),\n \n inplace(Buf(C[1] * Diag(compute(s.toDiag(loop_dims, Tw1(N,n,k)))))) * C[2]\n )\n )\n));\n", "meta": {"hexsha": "8143b5639a5d6d718360508d22938100c2b64e19", "size": 5653, "ext": "gi", "lang": "GAP", 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YES\n2. YES", "lm_q1_score": 0.7248702642896702, "lm_q2_score": 0.6039318337259584, "lm_q1q2_score": 0.4377722279258806}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nIsIntSym := x -> (IsSymbolic(x) and IsOrdT(x.t)) or (IsValue(x) and IsOrdT(x.t)) or IsInt(x);\nIsPosIntSym := x -> (IsSymbolic(x) and IsOrdT(x.t)) or (IsValue(x) and IsOrdT(x.t) and x.v > 0) or (IsInt(x) and x > 0);\nIsPosInt0Sym := x -> (IsSymbolic(x) and IsOrdT(x.t)) or (IsValue(x) and IsOrdT(x.t) and x.v >= 0) or (IsInt(x) and x >= 0);\nIsRatSym := x -> (IsSymbolic(x) and (IsOrdT(x.t) or IsRealT(x.t) or x.t=TUnknown)) or IsRat(x) or (IsValue(x) and (IsOrdT(x.t) or IsRealT(x.t)));\nIsBoolSym := x -> x.t=TBool and (IsSymbolic(x) or IsValue(x));\n\nAnySyms := arg -> ForAny(arg, IsSymbolic);\n\n_ev := x->When(IsRec(x) and IsBound(x.ev), x.ev(), x);\n\n# in functions below\n# vec elements could be non-values (i.e. symbolic == expressions)\n\nisValueZero := e ->\n (e.v=0 or IsDouble(e.v) and AbsFloat(e.v)<TReal.cutoff) or\n (IsVecT(e.t) and ForAll(e.v, x->not IsSymbolic(x) and AbsFloat(_ev(x)) < TDouble.cutoff));\n\nisValueOne := e ->\n (e.v=1 or IsDouble(e.v) and AbsFloat(e.v-1)<TReal.cutoff) or\n (IsVecT(e.t) and ForAll(e.v, x->not IsSymbolic(x) and AbsFloat(_ev(x)-1) < TDouble.cutoff));\n\nisValueNegOne := e ->\n (e.v=-1 or IsDouble(e.v) and AbsFloat(e.v+1)<TReal.cutoff) or\n (IsVecT(e.t) and ForAll(e.v, x->not IsSymbolic(x) and AbsFloat(_ev(x)+1) < TReal.cutoff));\n\n_is0none := e -> Cond(IsValue(e), isValueZero(e), ObjId(e)=noneExp or e=0); \n_is1 := e -> Cond(IsValue(e), isValueOne(e), e=1);\n\n# in the patterns below 'e' could be a plan GAP integer or other non-class GAP object\n_0 := @(0).cond(e -> Cond(IsValue(e), isValueZero(e), e=0)); \n_0none:= @(0).cond(_is0none); \n_1 := @(0).cond(_is1);\n_2 := @(0).cond(x -> x=2);\n_neg1 := @(0).cond(e -> Cond(IsValue(e), isValueNegOne(e), e=-1)); \n\n_v0 := @(0, Value, isValueZero); \n_v0none:= @(0, [Value, noneExp], e -> Cond(ObjId(e)=noneExp, true, isValueZero(e))); \n_v1 := @(0, Value, isValueOne); \n_vneg1 := @(0, Value, isValueNegOne); \n\n_vtrivial := @(0, Value, e->isValueZero(e) or isValueOne(e) or isValueNegOne(e));\n\n\n_vtrue := @(0, Value, e -> e.v=true); \n_vfalse := @(0, Value, e -> e.v=false); \n\n\nDeclare(_divides_rec);\n\n_divides_rec := (d,n) -> Cond(\n ObjId(n) = add and ForAll( n.args, e -> _divides_rec(d, e) ), true,\n ObjId(n) = mul and ForAny( n.args, e -> _divides_rec(d, e) ), true,\n IsSymbolic(d) or IsSymbolic(n), d=n or n=0,\n (EvalScalar(n) mod EvalScalar(d)) = 0);\n\n_divides := (d,n) -> CondPat( d, \n [mul, param, param, ...], # product of distinct params\n ForAll( d.args, p -> IsParam(p) and _divides_rec(p,n) ) and Length(Set(d.args))=Length(d.args),\n [mul, Value, param],\n _divides_rec(d.args[1], n) and _divides_rec(d.args[2], n),\n # else\n _divides_rec(d,n));\n\n_isEven := x -> _divides(2, x);\n\n# We can't know for sure that d\|n, because _dividesUnsafe returns true if either d or n is a variable\n_dividesUnsafe := (d,n) -> Cond(IsSymbolic(d) or IsSymbolic(n), true,\n (EvalScalar(n) mod EvalScalar(d)) = 0);\n\n\n_unwrap := n -> Cond(IsValue(n), n.v, n);\nDeclare(_stripval);\n_stripval := n -> Cond( IsValue(n), _stripval(n.v),\n IsList(n), List(n, _stripval),\n n );\n\n_unwrapV := (n) -> let(_n := EvalScalar(n), Cond(IsValue(_n), n.v, _n));\n", "meta": {"hexsha": "ff4735bdb74df7c5cf486bd25f7289a3742eadb5", "size": 3327, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/code/constraints.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/code/constraints.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/code/constraints.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": 40.0843373494, "max_line_length": 149, "alphanum_fraction": 0.6086564472, "num_tokens": 1181, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7577943712746406, "lm_q2_score": 0.5774953651858117, "lm_q1q2_score": 0.4376227371750011}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nClass(PDTT_Base, TaggedNonTerminal, rec(\n abbrevs := [ n -> Checked(IsPosIntSym(n), [n]) ],\n dims := self >> [self.params[1], self.params[1]],\n isReal := True,\n print := (self,i,is) >> Print(self.__name__, \"(\", PrintCS(self.params), \")\", \n\tWhen(self.transposed, Print(\".transpose()\")),\n When(self.tags<>[], Print(\".withTags(\", self.tags, \")\"))),\n\n normalizedArithCost := self >> let(n := self.params[1],\n\tfloor(2.5 * n * log(n) / log(2.0)) )\n));\n\n#\n# Discrete Trigonometric Transforms (DTTs) via PRF\n# \nDeclare(PDST3, PDCT3);\n\nClass(PDST4, PDTT_Base, rec(\n transpose := self >> Copy(self),\n terminate := self >> Mat(DST_IVunscaled(EvalScalar(self.params[1]))),\n));\n\nClass(PDCT4, PDTT_Base, rec(\n transpose := self >> Copy(self),\n terminate := self >> Mat(DCT_IVunscaled(EvalScalar(self.params[1]))),\n));\n\nClass(PDCT2, PDTT_Base, rec(\n terminate := self >> Mat(DCT_IIunscaled(EvalScalar(self.params[1]))), \n transpose := self >> PDCT3(self.params[1])\n));\n\nClass(PDST2, PDTT_Base, rec(\n terminate := self >> Mat(DST_IIunscaled(EvalScalar(self.params[1]))), \n transpose := self >> PDST3(self.params[1])\n));\n\nClass(PDCT3, PDTT_Base, rec(\n terminate := self >> Mat(DCT_IIIunscaled(EvalScalar(self.params[1]))), \n transpose := self >> PDCT2(self.params[1])\n));\n\nClass(PDST3, PDTT_Base, rec(\n terminate := self >> Mat(DST_IIIunscaled(EvalScalar(self.params[1]))), \n transpose := self >> PDST2(self.params[1])\n));\n\nRulesFor(PDST4, rec(\n PDST4_Base2 := DST4_Base, #BaseRule(PDST4, 2),\n PDST4_CT := rec(\n\tisApplicable := P -> P[1] > 2, #not IsPrime(P),\n\tforTransposition := false,\n\tallChildren := P -> let(N := P[1], Map2(DivisorPairs(2N), (m,n) -> Cond(\n\t\tIsEvenInt(m) and IsEvenInt(n), [ PRDFT3(m,-1).transpose(), PRDFT3(n) ],\n\t\t#IsEvenInt(m) and IsEvenInt(n), [ PDHT3(m).transpose(), PDHT3(n) ],\n\t\tIsEvenInt(m) and IsOddInt(n), [ PRDFT3(m,-1).transpose(), PRDFT3(n), PDST4(m/2) ],\n\t\tIsOddInt(m) and IsEvenInt(n), [ PRDFT3(m,-1).transpose(), PRDFT3(n), PDST4(n/2) ],\n\t\tIsOddInt(m) and IsOddInt(n), Error(\"This can't happen\")))),\n\n\trule := (P,C) -> let(N := P[1], m := Rows(C[1]), n := Cols(C[2]),\n\t nf:=Int(n/2), nc:=Int((n+1)/2), mf:=Int(m/2), mc:=Int((m+1)/2), j:=Ind(nf), i:=Ind(mf), \n\t # mult twid by -E(4) for RDFT, by 1/2 for DHT\n\t t := ScaledTwid(2N, mf, 1, 1/2, 1/2, j, -E(4)),\n\t T := When(IsOddInt(m), Diag(diagDirsum(t,fConst(1,1))), Diag(t)), \n\t Et := Tensor(I(mf),Mat([[0,-1],[-1,0]])),\n\t Ett := Tensor(I(mf),Mat([[0,-1],[1,0]])),\n\t SUM(\n\t\tISum(j, \n\t\t Scat(BH(N, 2N-1, m, j, n)) C[1] * #Ett \n\t\t RC(T) \n\t\t #Et * # DHT only\n\t\t RC(Gath(H(mcnc, mc, j, nc)))\n\t\t),\n\t\tWhen(IsEvenInt(n), [], Scat(H(N,m/2,nf,n))C[3]Gath(H(2mcnc, m/2, 2nf, 2nc)))\n\t ) \n\t SUM(\n\t\tISum(i, RC(Scat(H(mcnc, nc, inc, 1))) * C[2] * Gath(BH(N, 2N-1, n, i, m))),\n # output is imaginary, but we output into real slot, because subseq transform\n\t\t# is jIR2, which we implement as IR2 (-j)\n\t\tWhen(IsEvenInt(m), [], Scat(H(2mcnc, nc, 2mfnc, 2))C[3]Gath(H(N,n/2,mf,m)))\n\t ))),\n\n PDST4_CT_SPL := rec(\n\tisApplicable := P -> P[1] > 2 and ForAny(DivisorPairs(2P[1]), d->IsEvenInt(d[1]) and IsEvenInt(d[2])), \n\tforTransposition := false,\n\n\tallChildren := P -> let(N := P[1], \n\t Map2(Filtered(DivisorPairs(2N), d -> IsEvenInt(d[1]) and IsEvenInt(d[2])),\n\t\t(m,n) -> [ PRDFT3(m,-1).transpose(), PRDFT3(n) ])),\n\n\trule := (P,C) -> let(N := P[1], m := Rows(C[1]), n := Cols(C[2]),\n TT := Diag(fPrecompute(diagMul(fConst(N/2, -E(4)), \n fCompose(dOmega(8 * N, 1), \n diagTensor(dLin(N/m, 2, 1, TInt), dLin(m/2, 2, 1, TInt)))))),\n\n\t Prm(Refl(N, 2N-1, N, L(mn, m))) \n\t Tensor(I(n/2), C[1]) \n RC(TT) * \n RC(L(mn/4, n/2)) \n\t Tensor(I(m/2), C[2]) \n\t Prm(Refl(N, 2N-1, N, L(mn, m)))\n\t)\n )\n));\n\nRulesFor(PDCT4, rec(\n PDCT4_Base2 := rec(isApplicable:=P->P[1]=2, rule:=(P,C)->DCT4(2).terminate()),\n PDCT4_Base4 := rec(isApplicable:=P->P[1]=4, \n\t allChildren := P -> [[ DCT4(4) ]], \n\t\t rule:=(P,C)->C[1]),\n\n PDCT4_CT := rec(\n\tisApplicable := P -> P[1] > 2, #not IsPrime(P),\n\tforTransposition := false,\n\tallChildren := P -> let(N := P[1], Map2(DivisorPairs(2N), (m,n) -> Cond(\n\t\tIsEvenInt(m) and IsEvenInt(n), [ PRDFT3(m,-1).transpose(), PRDFT3(n) ],\n\t\t#IsEvenInt(m) and IsEvenInt(n), [ PDHT3(m).transpose(), PDHT3(n) ],\n\t\tIsEvenInt(m) and IsOddInt(n), [ PRDFT3(m,-1).transpose(), PRDFT3(n), PDCT4(m/2) ],\n\t\tIsOddInt(m) and IsEvenInt(n), [ PRDFT3(m,-1).transpose(), PRDFT3(n), PDCT4(n/2) ],\n\t\tIsOddInt(m) and IsOddInt(n), Error(\"This can't happen\")))),\n\n\trule := (P,C) -> let(N := P[1], m := Rows(C[1]), n := Cols(C[2]),\n\t nf:=Int(n/2), nc:=Int((n+1)/2), mf:=Int(m/2), mc:=Int((m+1)/2), j:=Ind(nf), i:=Ind(mf), \n\t t := fPrecompute(Twid(2N, mf, 1, 1/2, 1/2, j)),\n\t T := When(IsOddInt(m), Diag(diagDirsum(t,fConst(1,1))), Diag(t)), \n\t Et := Tensor(I(mf),Mat([[0,1],[1,0]])),\n\t SUM(\n\t\tISum(j, \n\t\t Scat(BH(N, 2N-1, m, j, n)) * Diag(BHN(m)) * C[1] \n\t\t # mult twid by 1/2 for DHT\n\t\t RC(T) \n\t\t #Et * # DHT only\n\t\t RC(Gath(H(mcnc, mc, j, nc)))\n\t\t),\n\t\tWhen(IsEvenInt(n), [], Scat(H(N,m/2,nf,n))C[3]Gath(H(2mcnc, m/2, 2nf, 2nc)))\n\t ) \n\t SUM(\n\t\tISum(i, RC(Scat(H(mcnc, nc, inc, 1))) * C[2] * Diag(BHN(n)) * Gath(BH(N, 2N-1, n, i, m))),\n\t\tWhen(IsEvenInt(m), [], Scat(H(2mcnc, nc, 2mfnc, 2))C[3]Gath(H(N,n/2,mf,m)))\n\t ))),\n));\n\nNewRulesFor(PDCT4, rec(\n PDCT4_CT_SPL := rec(\n libApplicable := t -> eq(imod(t.params[1], 2), 0),\n\tapplicable := t -> IsSymbolic(t.params[1]) or (t.params[1] > 2 and (t.params[1] mod 4) = 0), \n extraLeftTags := [],\n\tforTransposition := false,\n\n freedoms := t -> [ divisorsIntNonTriv(t.params[1]/2) ], \n\n\tchild := (self, t, fr) >> let(N := t.params[1], f := fr[1], \n\t [ spiral.sym.ASP(-1).RDFT3(2f).withTags(self.extraLeftTags).transpose(), \n\t spiral.sym.ASP.RDFT3(div(N,f)) ]),\n\n\tapply := (t,C,Nonterms) -> let(N := t.params[1], m := Rows(C[1]), n := Cols(C[2]),\n mh := Rows(C[1])/2, nh := Cols(C[2])/2,\n D := RC(Diag(fPrecompute(fCompose(dOmega(8 * N, 1), \n diagTensor(dLin(N/m, 2, 1, TInt), dLin(m/2, 2, 1, TInt)))))),\n\n Grp(Scat(Refl1(nh, m)) * \n Tensor(I(nh), Diag(BHN(m)) * C[1]) * \n D \n Tensor(I(nh), Tr(2, mh))) \n #RC(Tr(mh, nh)) \n Grp(Tr(mh, n) \n Tensor(I(mh), C[2] * Diag(BHN(n))) \n Gath(Refl1(mh, n)))\n\t)\n )\n));\n\nRulesFor(PDCT4, rec(\n # Variant better suited for vectorization\n PDCT4_CT_SPL_Vec := rec(\n\tisApplicable := P -> P[1] > 2 and (P[1] mod 2) = 0, \n\tforTransposition := false,\n\n\tallChildren := P -> let(N := P[1], \n\t Map2(Filtered(DivisorPairs(2N), d -> IsEvenInt(d[1]) and IsEvenInt(d[2])),\n\t\t(m,n) -> [ PRDFT3(m,-1).transpose(), PRDFT3(n) ])),\n\n\trule := (P,C) -> let(N := P[1], m := Rows(C[1]), n := Cols(C[2]),\n TT := Diag(fPrecompute(fCompose(dOmega(8 * N, 1), \n diagTensor(dLin(N/m, 2, 1, TInt), dLin(m/2, 2, 1, TInt))))),\n\n Prm(condIJ(N, n/2)) * \n Prm(L(N, m)) * \n\t Tensor(I(n/2), \n condM(m,m/2) * Diag(BHN(m)) * C[1]) * \n RC(TT) * \n Prm(L(N, n/2)) \n\t Tensor(I(m/2), \n L(n, 2) C[2] * Diag(BHN(n)) * condK(n, 2)) \n Prm(L(N, m/2)) \n Prm(condIJ(N, m/2))\n\t)\n )\n\n));\n\ntestPDCT4 := function(n)\n local opts, r, s;\n opts := CopyFields(SpiralDefaults, rec(\n breakdownRules := rec(\n PDCT4 := [PDCT4_Base2, PDCT4_CT_SPL_Vec],\n PRDFT1 := [PRDFT1_Base1, PRDFT1_Base2, PRDFT1_CT],\n PRDFT3 := [PRDFT3_Base1, PRDFT3_Base2, PRDFT3_CT],\n DFT := [DFT_Base, DFT_CT]\n )));\n r := RandomRuleTree(PDCT4(n), opts);\n s := SumsRuleTree(r, opts);\n return [opts,r,s];\nend;\n\n \nNewRulesFor(PDCT2, rec(\n PDCT2_Base2 := rec(\n\tforTransposition := true,\n applicable := t -> t.params[1] = 2, \n apply := (t, C, Nonterms) -> DCT2(2).terminate()\n ),\n\n PDCT2_Base4 := rec(\n\tforTransposition := true,\n applicable := t -> t.params[1] = 4, \n apply := (t, C, Nonterms) -> \n LIJ(4) * \n DirectSum(\n Diag(FList(TReal, [ 1, 0.70710678118654757 ])) * F(2),\n Rot(cospi(13/8), sinpi(13/8)) * J(2)) * \n (Tensor(I(2), F(2))) ^ LIJ(4)\n ),\n\n PDCT2_CT_SPL := rec(\n\tforTransposition := true,\n libApplicable := t -> eq(imod(t.params[1], 2), 0),\n extraLeftTags := [],\n\n\tapplicable := t -> let(N:=t.params[1], \n IsSymbolic(N) or \n (N > 2 and IsEvenInt(N) and (N mod 4) = 0)),\n\n\tfreedoms := t -> [ divisorsIntNonTriv(t.params[1]/2) ], \n\n # N/2 = km\n child := (self, t, fr) >> let(N:=t.params[1], k:=fr[1], m:=N/2/k, \n [ PDCT2(2k).withTags(self.extraLeftTags), \n spiral.sym.ASP(-1).RDFT3(2k).transpose().withTags(self.extraLeftTags), \n spiral.sym.ASP(+1).URDFT(2m) ]), \n\n\tapply := (t,C,Nonterms) -> let(N:=t.params[1], k:=Rows(C[1])/2, m:=Cols(C[3])/2,\n D := RC(Diag(fPrecompute(fCompose(dOmega(4 * N, 1), \n diagTensor(dLin(m-1, 1, 1, TInt), dLin(k, 2, 1, TInt)))))),\n Grp(\n Scat(Refl0_u(m, 2k)) \n DirectSum(\n C[1] * KK(k, 2), \n Tensor(I(m-1), Diag(BHN(2k)) C[2]) * D\n )) \n Grp(\n RC(Tr(k, m)) \n Tensor(I(k), C[3]) \n Gath(Refl1(k, 2m))\n )\n\t)\n )\n));\n\nNewRulesFor(PDST2, rec(\n PDST2_Base2 := rec(\n applicable := t -> t.params[1] = 2, \n apply := (t, C, Nonterms) -> DST2(2).terminate()\n ),\n\n PDST2_CT_SPL := rec(\n\tforTransposition := true,\n\tapplicable := t -> let(N:=t.params[1], N > 2 and IsEvenInt(N) and (N mod 4) = 0),\n\tfreedoms := t -> [ DivisorsIntNonTriv(t.params[1]/2) ], \n\n # N/2 = km\n child := (t, fr) -> let(N:=t.params, k:=fr[1], m:=N/2/k, \n [ DST2(2k), PRDFT3(2k,-1).transpose(), URDFT(2m) ]), \n\n\tapply := (t,C,Nonterms) -> let(N:=t.params[1], k:=Rows(C[1])/2, m:=Cols(C[3])/2,\n TT := Diag(fPrecompute(fCompose(dOmega(4 * N, 1), \n # ie multiply all twiddles by -E(4)\n diagAdd(diagDirsum(fConst(k, 0), fConst(k(m-1), 3N)), \n diagTensor(dLin(m, 1, 0, TInt), dLin(k, 2, 1, TInt)))))),\n\n J(N) * \n Kp(N, 2k) \n\t DirectSum(\n J(2k) C[1] * Diag(BHN(2k)) K(2k, 2), \n Tensor(I(m-1), J(2k) * M(2k, k) C[2])\n ) * \n RC(TT) * \n RC(L(N/2, m)) \n\t Tensor(I(k), C[3] Diag(BHN(2m))) \n\t Prm(Refl(N, 2N-1, N, L(2N, 2k)))\n\t)\n )\n\n));\n\nRulesFor(DCT5, rec(\n DCT5_Rader := rec(\n\tforTransposition := false,\n\tisApplicable := P -> P > 2 and IsPrime(2P-1),\n\tallChildren := P -> [[ IPRDFT(P-1,-1), PRDFT(P-1,-1) ]],\n\n\tdiag := N -> Sublist(\n\t DFT_Rader.raderDiag(2N-1,1,PrimitiveRootMod(2N-1)), \n\t [1..Int((N-1)/2)]2),\n\n\t# 3rd col with 0's is for PRDFT, not necessary for (non-packed) RDFT\n\traderMid := (self, N) >> let(Fsize := 2N-1, \n\t DirectSum(Mat([[1, 1, 0], [1, -1/(Fsize-1), 0], [0,0,0]]),\n\t\t\t RC(Diag(FData(self.diag(N)))))),\n\n\t# NOTE, special case for even P-1\n\trule := (self,P,C) >> let(N := P, \n\t #RealRR(N).transpose() * \n\t\t\n\t Gath(H(2P-1, P, 0, 1)) \n\t RR(2P-1).transpose() \n\t DirectSum(I(1), VStack(I(P-1), I(P-1))) \n\n\t DirectSum(I(1), C[1]) \n#\t\tC[1]Diag(1,1, Replicate(2Int((P-2)/2), 2), \n#\t\t When(IsEvenInt(P-1), [1,1],[]))) * \n\t self.raderMid(N) \n\t DirectSum(I(1), C[2]) \n\n # replace by RealRR\n\t Gath(H(2P-1, P, 0, 1)) \n\t RR(2P-1) DirectSum(I(1), VStack(I(P-1), J(P-1)))\n ))\n));\n\n#q:=ExpandSPL(DCT5(6))[1];\n#s:=SPLRuleTree(q);\n#me := MatSPL(s);\n#them := remat(MatSPL(q.node));\n\n#RDFT-11, DCT5(6) 15(6/9 rots) + 19(12/7 irdft) + 17(12/5 rdft) = 30/21 = 51\n# DST5(5)\n# 10(blk) \n# fftw 60/50\n\n# RDFT-13\n# DCT5(7) 18(8/10=4/8+0/1+2/1 rots) + 18(14/4 irdft) + 18(14/4 rdft) = 36/18=54\n# DST5(6) \n# 12(blk)\n# fftw 76/34=110\n\n# DFT-13\n# fftw 176+68=244\n# us = 542 (dct5) + 24(blk)2 + dst5 \n", "meta": {"hexsha": "7dc3b1b35016bdd470a04dd8f5ad0ea1b9698020", "size": 12631, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/realdft/pdtt4.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/pdtt4.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/pdtt4.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": 34.6054794521, "max_line_length": 109, "alphanum_fraction": 0.4979811575, "num_tokens": 4901, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7634837635542924, "lm_q2_score": 0.5698526514141571, "lm_q1q2_score": 0.4350732469730729}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n# input: imaginary, output: co1 (?)\n_j := N -> Tensor(I(approx.CeilingRat(N/2)),J(2)Diag(-1,1));\n\nRealRR_Out := (N, root) -> let(\n rrind := RR(N, 1, root).tolist(),\n outind := List(rrind{[1..(N+1)/2]}, x->When(x.v >= (N+1)/2, N-x.v, x.v)),\n #same as Refl((N+1)/2, N, (N+1)/2, RR(N,1,root)).tolist(),\n\n # Reflective RR\n Scat(fTensor(FList((N+1)/2, outind), fId(2))) \n # Conjugate complex elements that will be reflected\n Diag(ConcatList([0..(N-1)/2], x->When(rrind[x+1].v >= (N+1)/2, [1,-1], [1,1])))\n);\n\nRulesFor(PRDFT, rec(\n\n # PRDFT_PD : Projection of complex DFT partial diagonalization rule to real DFT \n # See also : PRDFT_Rader\n #\n PRDFT_PD := rec(\n\tforTransposition := true,\n\tmaxSize := 13,\n\tisApplicable := (self, P) >> P[1] > 2 and P[1] <= self.maxSize and IsPrime(P[1]),\n\t\n\trule := (self,P,C) >> let(N:=P[1], n:=N-1, k:=P[2], root:=PrimitiveRootMod(N),\n\t BB(RealRR_Out(N, root) \n\t DirectSum(Mat([[1],[0]]), L(n, n/2)) \n\t Mat(MatSPL(DFT_PD.core(N, k, root, true) * DFT_PD.A(N))) \n\t DirectSum(I(1), Tensor(F(2), I(n/2))) \n\t DirectSum(I(1), OS(n, -1)) \n\t Gath(RR(N, 1, root)))\n\t)\n ),\n\n # PRDFT_Rader : Projection of complex DFT Rader rule to real DFT \n #\n # Note: PRDFT of types 2--4 of odd size (which includes all primes > 2)\n # can be converted without arithmetic cost to PRDFT1,\n # which means that this rule enables implementation of a prime \n # size PRDFT of any type.\n PRDFT_Rader := rec(\n\tisApplicable := (self, P) >> P[1] > 3 and IsPrime(P[1]),\n\t\n\tdiag := (N, k, root) -> let(fulldiag := DFT_Rader.raderDiag(N,k,root),\n\t last := Int((N-1)/2),\n\t Concatenation(2fulldiag{[1..last-1]}, [fulldiag[last]])),\n\n\t# 3rd col with 0's is for padding used by PRDFT\n\traderMid := (self, N, k, root) >> let(n:=N-1,\n\t DirectSum(Mat([[1, 1, 0], [1, -1/n, 0], [0,0,0]]),\n\t\t RCDiag(RCData(FData(self.diag(N, k, root)))))),\n\n\tallChildren := P -> let(n:=P[1]-1,\n\t [[ PRDFT(n/2).transpose(), PRDFT3(n/2).transpose(), PRDFT(n, -1) ]]),\n\n\trule := (self,P,C) >> let(N:=P[1], n:=N-1, k:=P[2], root:=PrimitiveRootMod(N),\n\t RealRR_Out(N, root) \n\t DirectSum(Mat([[1],[0]]), ##\n\t\t L(n, n/2) \n\t\t DirectSum(C[1], C[2] * _j(n/2)) \n\t\t RC(L_or_OS(n/2+1, 2))) \n\t self.raderMid(N, k, root) \n\t DirectSum(I(1), C[3]) \n\t Gath(RR(N, 1, root))\n\t)\n )\n));\n\nRulesFor(IPRDFT, rec(\n\n # IPRDFT_PD : Projection of complex DFT partial diagonalization rule to inverse real DFT \n # See also : IPRDFT_Rader\n #\n IPRDFT_PD := rec(\n\tforTransposition := true,\n\tmaxSize := 13,\n\tisApplicable := (self, P) >> P[1] > 2 and P[1] <= self.maxSize and IsPrime(P[1]),\n\trule := (self,P,C) >> let(N:=P[1], n:=N-1, k:=P[2], root:=PrimitiveRootMod(N),\n\t BB(Scat(RR(N, 1, root)) \n\t DirectSum(I(1), OS(n, -1)) \n\t DirectSum(I(1), Tensor(F(2), I(n/2))) * \n\t Mat(MatSPL(TransposedSPL(DFT_PD.core(N, -k, root, true) * DFT_PD.A(N)) * DirectSum(I(1), 2I(n)))) \n\t DirectSum(Mat([[1,0]]), L(n, 2)) * \n\t RealRR_Out(N, root).transpose())\n\t)\n ),\n\n # IPRDFT_Rader : Projection of complex DFT Rader rule to inverse real DFT \n #\n # Note: IPRDFT of types 2--4 of odd size (which includes all primes > 2)\n # can be converted without arithmetic cost to IPRDFT1,\n # which means that this rule enables implementation of a prime \n # size IPRDFT of any type.\n IPRDFT_Rader := CopyFields(PRDFT_Rader, rec(\n\t# 3rd col with 0's is for padding, we also scale everything but 1st elt by 2,\n\t# as IPRDFT requires. \n\traderMid := (self, N, k, root) >> let(n:=N-1,\n\t DirectSum(Mat([[1, 2, 0], [1, -2/n, 0], [0,0,0]]),\n\t\t RCDiag(RCData(FConj(FData(2self.diag(N, -k, root))))))),\n\n\tallChildren := P -> let(n:=P[1]-1,\n\t [[ PRDFT(n/2), PRDFT3(n/2), PRDFT(n,-1).transpose() ]]),\n\n\trule := (self,P,C) >> let(N:=P[1], n:=N-1, k:=P[2], root:=PrimitiveRootMod(N),\n\t Scat(RR(N, 1, root)) \n\t DirectSum(I(1), C[3]) \n\t self.raderMid(N, k, root) \n\t DirectSum(Mat([[1,0]]), ##\n\t\t RC(L_or_OS(n/2+1, 2).transpose()) \n\t\t DirectSum(C[1], _j(n/2).transpose() C[2]) \n\t\t L(n, 2)) \n\t RealRR_Out(N, root).transpose()\n\t)\n ))\n));", "meta": {"hexsha": "d6ff32d471f83a5c606986e74dd4b8d89f2a0905", "size": 4303, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/realdft/rpd.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/rpd.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/rpd.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": 35.8583333333, "max_line_length": 105, "alphanum_fraction": 0.5596095747, "num_tokens": 1623, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7520125737597972, "lm_q2_score": 0.5774953651858117, "lm_q1q2_score": 0.43428377590773626}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n# NOTE: MISSING (YV)\nClass(VScat_red);\n\nClass(BaseVScat, BaseMat, SumsBase, rec(\n isVScat := true,\n sums := self >> self,\n dims := self >> self.dimensions,\n isReal := self >> true,\n needInterleavedLeft := False,\n needInterleavedRight := False,\n area := self >> self.transpose().area(),\n toAMat := self >> TransposedAMat(self.transpose().toAMat()),\n conjTranspose := self >> self.transpose(), \n));\n\nClass(BaseSVScat, BaseMat, SumsBase, rec(\n isVScat := true,\n isSVScat := true,\n #-----------------------------------------------------------------------\n abbrevs := BaseSVGath.abbrevs, \n new := BaseSVGath.new, \n print := BaseSVGath.print,\n getConstantRem := BaseSVGath.getConstantRem,\n #-----------------------------------------------------------------------\n dims := self >> Error(ObjId(self), \".dims() is undefined\"),\n #-----------------------------------------------------------------------\n sums := self >> self,\n isReal := self >> true,\n needInterleavedLeft := True,\n needInterleavedRight := False,\n #-----------------------------------------------------------------------\n conjTranspose := self >> self.transpose(), \n area := self >> self.transpose().area(),\n toAMat := self >> TransposedAMat(self.transpose().toAMat())\n));\n\nIsVScat := x -> IsRec(x) and IsBound(x.isVScat) and x.isVScat;\nIsSVScat := x -> IsRec(x) and IsBound(x.isSVScat) and x.isSVScat;\n\n# ==========================================================================\n# VScat(<func>, <v>) - vector scatter (write) matrix, assumes aligned output\n# ==========================================================================\nClass(VScat, BaseVScat, rec(\n #-----------------------------------------------------------------------\n rChildren := self >> [self.func],\n rSetChild := rSetChildFields(\"func\"),\n from_rChildren := (self, rch) >> ObjId(self)(rch[1], self.v),\n #-----------------------------------------------------------------------\n new := (self, func, v) >> SPL(WithBases(self, \n rec(func := func, v := v))).setDims(),\n #-----------------------------------------------------------------------\n dims := self >> [self.v * self.func.range(), self.v * self.func.domain()],\n #-----------------------------------------------------------------------\n transpose := self >> VGath(self.func, self.v),\n #-----------------------------------------------------------------------\n print := (self,i,is) >> Print(self.__name__, \"(\", self.func, \", \", self.v, \")\", self.printA()),\n ));\n\n# ==========================================================================\n# VScat_u(<func>, <v>) -- same as VScat but assumes that output is unaligned\n# ==========================================================================\nClass(VScat_u, VScat, rec(\n dims := self >> [ self.func.range(), self.v * self.func.domain()],\n transpose := self >> VGath_u(self.func, self.v)\n));\n\n# ==========================================================================\n# VScat_zero(N, n, <v>) - vector scatter (write) matrix\n# ==========================================================================\nClass(VScat_zero, BaseVScat, rec(\n #-----------------------------------------------------------------------\n rChildren := self >> [],\n rSetChild := rSetChildFields(),\n from_rChildren := (self, rch) >> ObjId(self)(self.N, self.n, self.v),\n #-----------------------------------------------------------------------\n new := (self, N, n, v) >> SPL(WithBases(self,\n rec(n := n, N := N, v := v))).setDims(),\n #-----------------------------------------------------------------------\n dims := self >> [self.v * self.N, self.v * self.n],\n #-----------------------------------------------------------------------\n transpose := self >> VGath_zero(self.N, self.n, self.v),\n #-----------------------------------------------------------------------\n print := (self,i,is) >> Print(self.__name__, \"(\", self.N, \", \",\n self.n, \", \", self.v,\")\", self.printA()),\n ));\n\n# ==========================================================================\n# VScat_sv(<func>, <v>, <sv>) - vector scatter (write) matrix on subvectors\n# ==========================================================================\nClass(VScat_sv, BaseSVScat, rec(\n #-----------------------------------------------------------------------\n rChildren := self >> [self.func], # self >> [self.func, self.v, self.sv],\n rSetChild := rSetChildFields(\"func\"), # rSetChildFields(\"func\", \"v\", \"sv\"),\n from_rChildren := (self, rch) >> ObjId(self)(rch[1], self.v, self.sv, self.rem),\n #-----------------------------------------------------------------------\n dims := self >> [self.sv * self.func.range(),\n _roundup(self.sv * self.func.domain(), self.v)],\n #-----------------------------------------------------------------------\n transpose := self >> VGath_sv(self.func, self.v, self.sv, self.rem),\n));\n\n# ==========================================================================\n# RCVScat_sv(<func>, <v>, <sv>) - vector scatter (write) matrix on subvectors\n# ==========================================================================\nClass(RCVScat_sv, BaseSVScat, rec(\n #-----------------------------------------------------------------------\n rChildren := self >> [self.func], # self >> [self.func, self.v, self.sv],\n rSetChild := rSetChildFields(\"func\"), # rSetChildFields(\"func\", \"v\", \"sv\"),\n from_rChildren := (self, rch) >> ObjId(self)(rch[1], self.v, self.sv, self.rem),\n #-----------------------------------------------------------------------\n dims := self >> let(\n\tn := self.func.domain() * self.sv, nv := _roundup(n, self.v), \n\tN := self.func.range() * self.sv, \n\t[2N, 2nv]),\n #-----------------------------------------------------------------------\n transpose := self >> RCVGath_sv(self.func, self.v, self.sv, self.rem),\n));\n\n# ==========================================================================\n# VStretchScat(<func>, part, <v>) - vector scatter (write) matrix on subvectors\n# ==========================================================================\nClass(VStretchScat, BaseSVScat, rec(\n #-----------------------------------------------------------------------\n rChildren := self >> [self.func],\n rSetChild := rSetChildFields(\"func\"),\n from_rChildren := (self, rch) >> ObjId(self)(rch[1], self.part, self.v),\n #-----------------------------------------------------------------------\n dims := self >> let(\n\tn := self.func.domain(), N := self.func.range(), \n\tnv := self.part * _roundup(n / self.part, self.v),\n [N, nv]),\n #-----------------------------------------------------------------------\n abbrevs := [],\n new := (self, func, part, v) >> SPL(WithBases(self, \n\trec(func := func, part := part, v := v))).setDims(),\n #-----------------------------------------------------------------------\n transpose := self >> VStretchGath(self.func, self.part, self.v),\n #-----------------------------------------------------------------------\n print := (self,i,is) >> Print(self.__name__, \"(\", self.func, \", \",\n self.part, \", \", self.v, \")\", self.printA()),\n));\n\n\n# ==========================================================================\n# vRCStretchScat(<func>, part, <v>) - vector scatter (write) matrix on subvectors\n# ==========================================================================\nClass(vRCStretchScat, BaseSVScat, rec(\n #-----------------------------------------------------------------------\n rChildren := self >> [self.func],\n rSetChild := rSetChildFields(\"func\"),\n from_rChildren := (self, rch) >> ObjId(self)(rch[1], self.part, self.v),\n #-----------------------------------------------------------------------\n dims := self >> let(\n\tn := self.func.domain(), N := self.func.range(), \n\tnv := self.part * _roundup(n / self.part, self.v/2),\n 2[N, nv]),\n #-----------------------------------------------------------------------\n abbrevs := [],\n new := (self, func, part, v) >> SPL(WithBases(self, \n rec(func := func, part := part, v := v))).setDims(),\n #-----------------------------------------------------------------------\n transpose := self >> vRCStretchGath(self.func, self.part, self.v),\n #-----------------------------------------------------------------------\n print := (self,i,is) >> Print(self.__name__, \"(\", self.func, \", \",\n self.part, \", \", self.v, \")\", self.printA()),\n));\n\n# ==========================================================================\n# RCVStretchScat(<func>, part, <v>) - vector scatter (write) matrix on subvectors\n# ==========================================================================\nClass(RCVStretchScat, BaseSVScat, rec(\n #-----------------------------------------------------------------------\n rChildren := self >> [self.func],\n rSetChild := rSetChildFields(\"func\"),\n from_rChildren := (self, rch) >> ObjId(self)(rch[1], self.part, self.v),\n #-----------------------------------------------------------------------\n dims := self >> let(\n\tn := self.func.domain(), N := self.func.range(), \n\tnv := self.part _roundup(n / self.part, self.v),\n 2[N, nv]),\n #-----------------------------------------------------------------------\n abbrevs := [],\n new := (self, func, part, v) >> SPL(WithBases(self, rec(\n func := func, part := part, v := v))).setDims(),\n #-----------------------------------------------------------------------\n transpose := self >> RCVStretchGath(self.func, self.part, self.v),\n #-----------------------------------------------------------------------\n print := (self,i,is) >> Print(self.__name__, \"(\", self.func, \", \",\n self.part, \", \", self.v, \")\", self.printA()),\n ));\n\n# ==========================================================================\n# VScat_pc(N, n, ofs, v) - vector scatter (write) matrix writing unaligned\n# partial contiguous vectors\n# ==========================================================================\nClass(VScat_pc, BaseSVScat, rec(\n #-----------------------------------------------------------------------\n rChildren := self >> [self.N, self.n, self.ofs, self.v],\n rSetChild := rSetChildFields(\"N\", \"n\", \"ofs\", \"v\"),\n #-----------------------------------------------------------------------\n dims := self >> let(nv := _roundup(self.n, self.v), [self.N, nv]),\n #-----------------------------------------------------------------------\n abbrevs := [],\n new := (self, N, n, ofs, v) >> SPL(WithBases(self, rec(\n N := N, n:= n, ofs := ofs, v := v))).setDims(),\n #-----------------------------------------------------------------------\n transpose := self >> VGath_pc(self.N, self.n, self.ofs, self.v),\n #-----------------------------------------------------------------------\n print := (self,i,is) >> Print(self.__name__, \"(\", self.N, \", \", self.n, \", \",\n self.ofs, \", \", self.v,\")\", self.printA()),\n));\n\n# ==========================================================================\n# IxVScat_pc(k, N, n, ofs, v) - vector gather (read)\n# matrix reading unaligned\n# partial REAL contiguous vectors\n# ==========================================================================\nClass(IxVScat_pc, BaseSVScat, rec(\n #-----------------------------------------------------------------------\n rChildren := self >> [self.k, self.N, self.n, self.ofs, self.v],\n rSetChild := rSetChildFields(\"k\", \"N\", \"n\", \"ofs\", \"v\"),\n\n from_rChildren := (self, rch) >> ObjId(self)(self.k, self.N, self.n, self.ofs, self.v),\n #-----------------------------------------------------------------------\n dims := self >> let(nv := _roundup(self.n, self.v), [self.kself.N, self.knv]),\n #-----------------------------------------------------------------------\n abbrevs := [],\n new := (self, k, N, n, ofs, v) >> SPL(WithBases(self, rec(\n k := k, N := N, n:= n, ofs := ofs, v := v))).setDims(),\n #-----------------------------------------------------------------------\n transpose := self >> IxVGath_pc(self.k, self.N, self.n, self.ofs, self.v),\n #-----------------------------------------------------------------------\n toloop := (self, bksize) >> self.transpose().toloop(bksize).transpose(),\n #-----------------------------------------------------------------------\n print := (self,i,is) >> Print(self.__name__, \"(\", self.k, \", \", self.N, \", \",\n self.n, \", \", self.ofs, \", \", self.v,\")\", self.printA()),\n));\n\n# ==========================================================================\n# IxRCVScat_pc(k, N, n, ofs, v) - vector gather (read)\n# matrix reading unaligned\n# partial REAL contiguous vectors\n# ==========================================================================\nClass(IxRCVScat_pc, BaseSVScat, rec(\n #-----------------------------------------------------------------------\n rChildren := self >> [], # self >> [self.ofs], # SEEMS NOT TO WORK?!\n rSetChild := rSetChildFields(), # rSetChildFields(\"ofs\"),\n from_rChildren := (self, rch) >> ObjId(self)(self.k, self.N, self.n, self.ofs, self.v),\n #-----------------------------------------------------------------------\n dims := self >> let(nv := _roundup(self.n, self.v), 2 [self.kself.N, self.knv]),\n #-----------------------------------------------------------------------\n abbrevs := [],\n new := (self, k, N, n, ofs, v) >> SPL(WithBases(self, rec(\n k := k, N := N, n := n, ofs := ofs, v := v))).setDims(),\n #-----------------------------------------------------------------------\n transpose := self >> IxRCVGath_pc(self.k, self.N, self.n, self.ofs, self.v),\n #-----------------------------------------------------------------------\n print := (self,i,is) >> Print(self.__name__, \"(\", self.k, \", \", self.N, \", \",\n self.n, \", \", self.ofs, \", \", self.v,\")\", self.printA()),\n));\n\n\n# ==========================================================================\n# Accumulative scatter versions\n# NOTE: to be replaced by a Sigma-SPL lowering step, CodeSumsAcc, and \n# a specialized CodegenAcc\n#\n# NOTE(!!!): .transpose().transpose() on below classes will lead to non-accumulative\n# versions, and thus invalid code!\nClass(VScatAcc, VScat, rec());\nClass(VScatAcc_u, VScat_u, rec());\nClass(VScat_svAcc, VScat_sv, rec());\nClass(VScat_pcAcc, VScat_pc, rec());\n\n\n# ==========================================================================\n# Methods for vectorization of ScatGath constructs\n# NOTE: This is a hack\n\n# BB needed, as basic block size is not known due to varying function domain\nScatGath.toloopRCVec := (self, _bksize, v) >> let(\n bksize := When(_bksize = 1, v, _bksize),\n dom := RulesMergedStrengthReduce(_divideFunc(self.gfunc.domain(), bksize)), \n i := Ind(dom), #ok := Error(\"caught\"),\n sfunc := RulesFuncSimp(self.sfunc),\n ISum(i, dom,\n BB(\n Compose(When(ObjId(sfunc)=fId, [], [RCVScat_sv(sfunc, v, 1)]) ::\n\t\t [VScat(fTensor(fBase(i), fId(2bksize/v)), v)]) \n RCVGath_sv(fCompose(self.gfunc, fTensor(fBase(i), fId(bksize))).setDomain(bksize), v, 1)\n )\n )\n);\n\nScatGath.toloopVec := (self, _bksize, v) >> let(\n bksize := When(_bksize = 1, v, _bksize),\n dom := RulesMergedStrengthReduce(_divideFunc(self.gfunc.domain(), bksize)), \n i := Ind(dom),\n sfunc := RulesFuncSimp(self.sfunc),\n ISum(i, dom,\n BB(\n Compose(When(ObjId(sfunc)=fId, [], [VScat_sv(sfunc, v, 1)]) :: \n\t\t [ VScat(fTensor(fBase(i), fId(bksize/v)), v)]) *\n VGath_sv(fCompose(self.gfunc, fTensor(fBase(i), fId(bksize))).setDomain(bksize), v, 1)\n )\n )\n);\n", "meta": {"hexsha": "729579d50f2a29c5d0dbf5e6a614725bcd7b7199", "size": 15944, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/vector/sigmaspl/scatter.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/scatter.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/scatter.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": 50.9392971246, "max_line_length": 100, "alphanum_fraction": 0.3724912193, "num_tokens": 3484, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7310585669110202, "lm_q2_score": 0.5926665999540698, "lm_q1q2_score": 0.43327399521844917}}
	{"text": "\nlocal reps,tori,labels,I,II,ords,mizuno,blocks;\n\nmizuno:=[[ 1, 2, 3, 4, 5, 6, fail,\n 7, 8, 9, 10,\n 11, 6, 12, 13,\n 15, 14, 16, 11,\n 17, 18, 19, 21,\n 20, 16, 22, 23,\n 24, 25, 21, 20,\n 26, 27, 23, 28,\n 25, 29, 30, 27,\n 31, 28, 32, 33,\n 30, 31, 34, 32,\n 33, fail, 35, 34,\n fail, 36, 35, fail,\n 36, fail, fail, fail,\n fail, fail, fail, fail ],\n []];\n\nreps:=[[[1,1],[2,1],[3,1],[4,1],[5,1],[6,1]], # E_6\n [[2,1],[4,1],[5,1],[6,1],[8,1],[16,1]], # E_6(a_1)\n [[1,1],[2,1],[10,1],[11,1],[12,1]], # D_5\n [[8,1],[9,1],[12,1],[10,1],[11,1],[16,1]], # A_5+A_1\n [[8,1],[9,1],[16,1],[12,1],[18,1]], # D_5(a_1)\n [[1,1],[15,1],[16,1],[17,1],[6,1]], # A_5\n [[14,1],[15,1],[16,1],[17,1],[12,1]], # A_4+A_1\n [[2,1],[14,1],[16,1],[18,1]], # D_4\n [[14,1],[15,1],[17,1],[12,1]], # A_4\n [[14,1],[16,1],[22,1],[24,1]], # D_4(a_1)\n [[14,1],[22,1],[23,1],[24,1]], # A_3+A_1\n [[20,1],[21,1],[28,1],[23,1],[24,1]], # 2A_2+A_1\n [[14,1],[22,1],[24,1]], # A_3\n [[26,1],[27,1],[28,1],[29,1]], # A_2+2A_1\n [[20,1],[21,1],[23,1],[24,1]], # 2A_2\n [[26,1],[27,1],[35,1]], # A_2+A_1\n [[26,1],[35,1]], # A_2\n [[37,1],[38,1],[40,1]], # 3A_1\n [[42,1],[43,1]], # 2A_1\n [[53,1]] # A_1\n ];\n\nlabels:=[\"E_6\",\n \"E_6(a_1)\",\n \"D_5\",\n \"A_5+A_1\",\n \"D_5(a_1)\",\n \"A_5\",\n \"A_4+A_1\",\n \"D_4\",\n \"A_4\",\n \"D_4(a_1)\",\n \"A_3+A_1\",\n \"2A_2+A_1\",\n \"A_3\",\n \"A_2+2A_1\",\n \"2A_2\",\n \"A_2+A_1\",\n \"A_2\",\n \"3A_1\",\n \"2A_1\",\n \"A_1\",\n ];\n\nI:=[ [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ] ];\n\nII:=[ [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ] ];\n\ntori:=[ [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ] ];\n\n#blocks:=[];\nblocks:=[[[16, 4], [8, 1], [6, 1]], [[16, 2], [11, 2], [8, 2], [4, 2]], [[8, 9], [6, 1]], [[8, 8], [4, 2], [3, 2]], [[8, 5], [6, 1], [4, 8]], [[8, 8], [2, 6], [1, 2]], [[8, 4], [6, 2], [5, 2], [4, 4], [2, 4]], [[8, 1], [6, 9], [2, 8]], [[8, 2], [7, 4], [5, 2], [4, 2], [3, 4], [1, 4]], [[4, 18], [3, 2]], [[4, 16], [2, 6], [1, 2]], [[4, 16], [2, 6], [1, 2]], [[4, 16], [2, 4], [1, 6]], [[4, 10], [3, 2], [2, 16]], [[4, 16], [1, 14]], [[4, 8], [3, 6], [2, 10], [1, 8]], [[4, 2], [3, 18], [1, 16]], [[2, 38], [1, 2]], [[2, 32], [1, 14]], [[2, 22], [1, 34]]];\n\n#ords:=[];\nords:=[ 16, 16, 8, 8, 8, 8, 8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2 ];\n\nreturn [reps,tori,labels,I,II,ords,blocks,mizuno];\n", "meta": {"hexsha": "0f3ef03ce49c351abd66d723ec48d4b317f2b95e", "size": 3243, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "lib/data/dataE6char2Mizuno.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/data/dataE6char2Mizuno.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/data/dataE6char2Mizuno.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": 41.5769230769, "max_line_length": 556, "alphanum_fraction": 0.2553191489, "num_tokens": 1555, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7341195152660688, "lm_q2_score": 0.588889130767832, "lm_q1q2_score": 0.4323150032247374}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n#F PolyDTT( <dtt-nonterminal> )\n#F Parameters: <nonterminal for a (optionally skew) DCT or DST of type 1--8>\n#F Definition: Let <t> be an (otionally skew) DCT or DST of type 1--8. Then\n#F Transform( \"PolyDTT\", <t> ) represents the (n x n)-matrix\n#F obtained from dividing every row in <t> by its first\n#F entry.\n#F This transform is called the polynomial version of\n#F the DCT or DST.\n#F Note: The transpose of PolyDTT(<t>) is\n#F TPolyDTT(<t>^T).\n#F Example: PolyDTT(DCT2(8)).\n#F\nClass(PolyDTT, NonTerminal, rec(\n _short_print := true,\n abbrevs := [ nt -> Checked(IsNonTerminal(nt), \n\t ObjId(nt) in \n\t [ DCT1, DCT3, DCT5, DCT7, # PolyDTT(T)=T for these\n\t DCT2, DCT4, DCT6, DCT8, \n\t DST1, DST2, DST3, DST4,\n\t DST5, DST6, DST7, DST8,\n\t SkewDTT],\n\t [ Copy(nt) ]\n\t)],\n dims := self >> self.params[1].dimensions,\n terminate := self >> Mat(PolynomialDTT(MatSPL(TerminateSPL(self.params[1])))),\n isReal := True\n));\n\nClass(fr, Exp, rec(\n ev := self >> let(\n\tm := self.args[1].ev(),\n\ti := self.args[2].ev(),\n\tr := self.args[3].ev(),\n\tCond(i mod 2 = 0, (r + 2 * Int(i/2)) / m,\n\t i mod 2 = 1, (2 - r + 2 * Int(i/2)) / m))));\n\n#F Rules\n#F -----\nRulesFor(PolyDTT, rec(\n PolyDTT_ToNormal := rec(\n\tisApplicable := P -> ObjId(P[1]) in [DCT1, DCT3, DCT5, DCT7],\n\tallChildren := P -> [P[1]],\n\trule := P -> P[1]\n ),\n\n #F PolyDTT_Base2: (base case for non-skew DTTs of size 2)\n #F\n #F pDCT2_2 = F_2\n #F pDCT4_2 = F_2 * [[1, -1], [0, sqrt(2)]]\n #F pDCT6_2 = [ [ 1, 1 ], [ 1, -2 ] ]\n #F pDCT8_2 = [ [ 1, cos(2pi/5) ], [ 1, cos(4pi/5) ] ]\n #F pDST4_2 = F_2 * [[1, 1], [0, sqrt(2)]]\n #F\n #F Pueschel/Moura: Discrete Cosine and Sine Transforms, in preparation\n #F\n PolyDTT_Base2 := rec (\n\tinfo := \"pDTT_2 -> F_2\",\n\tisApplicable := P -> Rows(P[1]) = 2 and ObjId(P[1]) <> SkewDTT,\n\tallChildren := P -> [[ ]],\n\trule := (P, C) -> let(nt := ObjId(P[1]), Cond(\n\t\tnt = DCT2, F(2),\n\t\tnt = DCT4, F(2) * Mat([[1, -1], [0,sqrt(2)]]),\n\t\tnt = DCT6, Mat([[1,1], [1,-2]]),\n\t\tnt = DCT8, Mat([[1,2CosPi(2/5)], [1,2CosPi(4/5)]]),\n\t\tnt = DST2, F(2),\n\t\tnt = DST3, F(2) * Diag([1, sqrt(2)]),\n\t\tnt = DST4, F(2) * Mat([[1, 1], [0, sqrt(2)]]),\n\t\tnt = DST5, Mat([[1,2CosPi(2/5)], [1,2CosPi(4/5)]]),\n\t\tnt = DST6, Mat([[1,2CosPi(1/5)], [1,2CosPi(3/5)]]),\n\t\tnt = DST7, Mat([[1,2CosPi(1/5)], [1,2CosPi(3/5)]]),\n\t\tnt = DST8, Mat([[1,2], [1,-1]]), \n\t\tError(\"unrecognized <L.symbol>\"))\n\t)\n ),\n\n PolyDTT_SkewBase2 := rec (\n\tinfo := \"pDTT_2 -> F_2\",\n\tisApplicable := P -> Rows(P[1]) = 2 and ObjId(P[1]) = SkewDTT and\n\t ObjId(P[1].params[1]) = DST3, \n\tallChildren := P -> [[ ]],\n\trule := (P, C) -> let(skewnt := ObjId(P[1].params[1]), r := P[1].params[2], \n\t Cond(\n\t\tskewnt = DST3, F(2) * Diag(1, 2CosPi(r/2)),\n\t\tError(\"unrecognized <L.symbol>\"))\n\t)\n ),\n\n PolyDTT_SkewDST3_CT := rec(\n isApplicable := P -> ObjId(P[1]) = SkewDTT and\n ObjId(P[1].params[1]) = DST3 and\n Rows(P[1]) > 2 and not IsPrime(Rows(P[1])),\n\n allChildren := P -> let(\n\t N := Rows(P[1].params[1]), r := P[1].params[2],\n\t List(DivisorPairs(N), d->\n\t let(i := Ind(d[2]),\n\t\t ri := fr(d[2], i, r),\n\t\t [ PolyDTT(SkewDTT(DST3(d[1]), ri)), \n\t\t PolyDTT(SkewDTT(DST3(d[2]), r)) ]))), \n\t\t\n rule := (P,C) -> let(\n\t MN := Rows(P[1]), N := Rows(C[1]), M := Rows(C[2]), \n\t r := P[1].params[2],\n\t i := C[1].root.params.params[2].args[2],\n\n\t K(MN, N) \n\t IterDirectSum(i, i.range, C[1]) \n\t Tensor(C[2], I(N)) \n\t B_DST3_U(MN, M)\n )\n )\n));\n", "meta": {"hexsha": "abe956f4b77ad55bde64beefd42b519dd57e23f6", "size": 3853, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/dtt/polydtt.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/dtt/polydtt.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/dtt/polydtt.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": 32.6525423729, "max_line_length": 82, "alphanum_fraction": 0.4949390086, "num_tokens": 1552, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7634837743174788, "lm_q2_score": 0.5660185351961015, "lm_q1q2_score": 0.43214596758517027}}
	{"text": "#############################################################################\n##\n#W matgrp4.gi Karel Dekimpe\n#W Bettina Eick\n##\n## This file contains the 4-dimensional almost crystallographic groups\n## as integral matrix groups. There are 95 types of groups.\n##\nACDim4Nr001 := function ( k1, k2, k3)\nlocal a, b, c, d;\na :=[[1, 0, -k1/2, -k2/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, -k3/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nc :=[[1, k2/2, k3/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d] , IdentityMat(5) );\nend;\n \nACDim4Nr002 := function ( k1, k2, k3, k4, k5, k6, k7)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, -k2/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, -k3/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nc :=[[1, k2/2, k3/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k4, k5, k6, k7/2], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr003 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, 0, k3, k4/2], [0, -1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr004 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, 0, - k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, 0, k3, k4/2], [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr004b := function ( k1, k2, k3)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, -k2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, k2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, -k1/2, 2k3, k2/2, 0], [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr005 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k2, k3, k4/2], [0, 0, -1, 0, 0], [0, -1, 0, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr006 := function ( k1, k2, k3)\nlocal a, b, c, d, alfa;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, 0, k2, 0, k3/2], [0, 1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr007 := function ( k1, k2, k3)\nlocal a, b, c, d, alfa;\na :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k1/2, k2, 0, k3/2], [0, 1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr007b := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, -k2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, k2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, -k3, -k2/2, 2k4, 0], [0, 1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr008 := function ( k1, k2, k3)\nlocal a, b, c, d, alfa;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k2, 0, k3/2], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr009 := function ( k1, k2, k3)\nlocal a, b, c, d, alfa;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -k1/4 + k2, (3k1)/4 - k2, 0, k3/2], [0, 0, 1, 0, 0], \n [0, 1, 0, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr009b := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, -k2/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, k2/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nc :=[[1, k2/2, -k2/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, k2/4 - k3, (3k2)/4 - k3, 2k4, 0], [0, 0, 1, 0, 0], \n [0, 1, 0, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr010 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, 0, k3, k4/2], [0, -1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[1, k2, k5, k3, k6/2], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr011 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, 0, k3, k4/2], [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[1, k2, -2k6, k3, k5/2], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr012 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k2, k3, k4/2], [0, 0, -1, 0, 0], [0, -1, 0, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[1, k5, 2k2 - k5, k3, k6/2], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr013 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k1/2 + k2, 0, -2k6, k3/2 + k6/2], [0, -1, 0, 0, 0], \n [0, 0, 1, 0, 0], [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, k1 + k2, k4, -2k6, k5/2], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr014 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na:=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb:=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc:=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd:=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:=[[1, k1/2+ k2, 0, k3, -k3/4 + k4/2], [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\nbeta:=[[1, k1 + k2, -k3 - 2k6, k3, k5/2], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr014b := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, -k2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, k2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, -k1/2, -k2/2 + 2k3, k2/2, 0], [0, -1, 0, 0, 0], \n [0, 0, 1, 0, 1/2], [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, k4, k2 - 2k3, k2 + 2k3 - 2k5 + 2k6, k5/2], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr015 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k1/4 + k2, k1/4 + k2, -2k6, k3/2 + k6/2], [0, 0, -1, 0, 0], \n [0, -1, 0, 0, 0], [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, k4, k1 + 2k2 - k4, -2k6, k5/2], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr018 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -k1 + 2k2 - 2k3 + 2k4, k1/2 - 2k3, 0, \n k2/2 - (-k1 + 2k2 - 2k3 + 2k4)/4], [0, -1, 0, 0, 1/2], \n [0, 0, -1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1/2, 2k3, 0, 0], [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr019 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, -k1/2, 0, k1/2 + 2k2, 0], [0, -1, 0, 0, 1/2], \n [0, 0, -1, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, 3k1 + 2k2 - 2k3 + 2k4, 0, -k1 - 2k2, k3/2], \n [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr019b := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -k1 + 2k2 - 2k3 + 2k4, k1/2 - 2k3, 0, \n k2/2 - (-k1 + 2k2 - 2k3 + 2k4)/4], [0, -1, 0, 0, 1/2], \n [0, 0, -1, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1/2, 2k3, 0, 0], [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr019c := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, k1, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, 0, -k1/2, 2k2, -(- (3k1)/2 - k4)/2], [0, -1, 0, 0, 1/2], \n [0, 0, -1, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[-1, 0, 2k3, k1/2, 0], [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr026 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, -k1/2, 0, 2k2, 0], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, 0, k3, 0, k4/2], [0, 1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr027 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k3, 0, k4/2], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k2, 0, 2k5, 0], [0, 1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr029 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, -k1/2, 0, 2k2, 0], [0, -1, 0, 0, 0], [0, 0, -1, 0, 1/2], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, k1/2, 2k2 - 2k3 + 2k4, 0, k3/2], [0, 1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr029b := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k1/2 + k2, 2k3 - 2k4 + 2k5, 0, k3/2 - (2k3 - 2k4 + 2k5)/4], \n [0, -1, 0, 0, 0], [0, 0, -1, 0, 1/2], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1 - k2, 0, 2k4, 0], [0, 1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr029c := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, -2k1, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 2k1, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, 0, -k1, -k1 + 2(k1 + k2), -k1], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 1/2], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k3, -k1, 2(k1 + k2), -k4/2], [0, 1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr030 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k1/2 + k2, 2k3 + 2k5, 0, k3/2 - (2k3 + 2k5)/4], \n [0, -1, 0, 0, 0], [0, 0, -1, 0, 1/2], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1 - k2, 0, 2k4, 0], [0, 1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr031 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, -k1/2, 0, 2k2, 0], [0, -1, 0, 0, 0], [0, 0, -1, 0, 1/2], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, 0, -2k3 + 2k4, 0, k3/2], [0, 1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr032 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -k1/2 - 2k4, -3k1 + 2k2 - 2k4 + 2k5, 0, \n k2/2 - (-3k1 + 2k2 - 2k4 + 2k5)/4], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 1/2], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, 2k4, k1/2, -k3, 0], [0, 1, 0, 0, 1/2], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr033 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, -k1/2, 0, 2k2, 0], [0, -1, 0, 0, 0], [0, 0, -1, 0, 1/2], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, 0, -k1 - 2k3 + 2k4, -k1/2, k3/2], [0, 1, 0, 0, 1/2], \n [0, 0, -1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr033b := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -k1/2 - 2k4, -3k1 + 2k2 + k3 - 2k4 + 2k5, 0, \n k2/2 - (-3k1 + 2k2 + k3 - 2k4 + 2k5)/4], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 1/2], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[-1, 2k4, k1/2, -k3, 0], [0, 1, 0, 0, 1/2], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr033c := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, k1, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, 0, -k1/2, k1/2 + 2k2, k2/2], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 1/2], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[-1, 2k3, 0, k1 + 2k2, -k4/2], [0, 1, 0, 0, 1/2], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr034 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k1/2 + k2, -2k1 + k2 + 2k3 + 2k5, 0, \n k3/2 - (-2k1 + k2 + 2k3 + 2k5)/4], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 1/2], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1 - k2, k1/2, k1 + k2 + 2k4, 0], [0, 1, 0, 0, 1/2], \n [0, 0, -1, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr036 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1, k1, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, -k1/2, -k1/2, 2k2, 0], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, k3, -k3, 0, k4/2], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr037 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k2 + 2k4, 0, k3/2], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k4, -k4, 2k5, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr041 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1, k1, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k2, k1 - 2k5, -k2/2 + k3/2], [0, 0, -1, 0, 1/2], \n [0, -1, 0, 0, 1/2], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, k1/2 - k4, (-3k1)/2 + k4, 2k5, 0], [0, 0, -1, 0, 0], \n [0, -1, 0, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr043 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1/2, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, -k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -k1/4 + k2 + 2k3 + 2k5, k1/4 + k2, 2k2 + 2k3 + 2k5, \n k3/2 - (2k2 + 2k3 + 2k5)/4], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], \n [0, -1, -1, -1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1/4 + k2 + 2k4, 2k4, -k1/4 - k2, 0], [0, 0, 0, -1, 0], \n [0, 1, 1, 1, 1/2], [0, -1, 0, 0, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr045 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na:=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb:=[[1, 0, 0, k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc:=[[1, k1/2, -k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd:=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:=[[1,k2, -k2, k2 - 2k4 - 2k5, k3/2], [0, 0, 1, -1, 0], [0, 1, 0, -1, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nbeta:=[[-1, -k4, k4 + 2k5, k4, 0], [0, 0, 1, -1, 1/2], [0, 0, 1, 0, 1/2], \n [0, -1, 1, 0, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr055 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta, gamma;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -k1 - 2k2 + 2k3 - 2k4, -k1 - 2k3, 0, k2/2], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1/2, k1/2 + 2k3, 0, 0], [0, -1, 0, 0, 1/2], \n [0, 0, 1, 0, 1/2], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\ngamma :=[[1, -k1 - 2k2 + 2k3 - 2k4, -k1 - 2k3, k5, \n (2k1 + k2 + k4 + k6)/2], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta, gamma] , IdentityMat(5) );\nend;\n \nACDim4Nr056 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta, gamma;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -k1/2 + 2k2 - 2k3 + 2(k1 - k2 + 2k3 - k4), k1/2 - 2k3, 0, \n k2/2 - (k1 - 2k3)/4 - (-k1 + 2k2 - 2k3 + 2(k1 - k2 + 2k3 - k4))/4], \n [0, -1, 0, 0, 1/2], [0, 0, -1, 0, 1/2], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1/2, 2k3, 0, 0], [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\ngamma :=[[1, 2k2 - 2k3 + 2(k1 - k2 + 2k3 - k4), -2k3, \n 2k3 + 2k5 - 2k6, k6/2], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta, gamma] , IdentityMat(5) );\nend;\n \nACDim4Nr058 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta, gamma;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -k1 - 2k2 + 2k3 - 2k4, -k1 - 2k3, 0, k2/2], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1/2, k1/2 + 2k3, 0, 0], [0, -1, 0, 0, 1/2], \n [0, 0, 1, 0, 1/2], [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\ngamma :=[[1, -k1 - 2k2 + 2k3 - 2k4, -k1 - 2k3, \n 4k1 + 2k2 + 2k4 + 2k5 - 2k6, k6/2], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta, gamma] , IdentityMat(5) );\nend;\n \nACDim4Nr060 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta, gamma;\na :=[[1, 0, -2k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 2k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -2(k1 - k2 + k3 - k4), k1 - 2k3, 0, \n k2/2 + (k1 - k2 + k3 - k4)/2], [0, -1, 0, 0, 1/2], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1, 2k3, 0, 0], [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\ngamma :=[[1, -2(k1 - k2 + k3 - k4), -2k3, 2k3 + 2k5 - 2k6, k6/2], \n [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta, gamma] , IdentityMat(5) );\nend;\n \nACDim4Nr061 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta, gamma;\na :=[[1, 0, 0, -2k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 2k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, -k1, 0, k1 + 2k2, 0], [0, -1, 0, 0, 1/2], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, 7k1 + 2k2 - 2k3 + 2k4, 0, -2k1 - 2k2, \n -(-2k1 - 2k2)/4 + k3/2], [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\ngamma :=[[1, 8k1 + 2k2 - 2k3 + 2k4, 2k1 + 2k2 - 2k6, -2k1 - 2k2, \n (-k1 + k3 - k4 + k5)/2], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta, gamma] , IdentityMat(5) );\nend;\n \nACDim4Nr061b := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta, gamma;\na :=[[1, 0, -2k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 2k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -2k3 - 2k5 - 2k6 + 2(-k1 + k2 + k4 + k5 + k6), k1 - 2k3, 0, \n k2/2 - (-2k3 - 2k5 - 2k6 + 2(-k1 + k2 + k4 + k5 + k6))/4], \n [0, -1, 0, 0, 1/2], [0, 0, -1, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1, 2k3, 0, 0], [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\ngamma :=[[1, -2k3 - 2k5 - 2k6 + 2(-k1 + k2 + k4 + k5 + k6), -2k3, \n 2k3 + 2k6 - 2(-k1 + k2 + k4 + k5 + k6), (-k1 + k2 + k4 + k5 + k6)/2], \n [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta, gamma] , IdentityMat(5) );\nend;\n \nACDim4Nr061c := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta, gamma;\na :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, -2k1, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 2k1, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, 0, -k1, 2k2, 2k1 - k2/2], [0, -1, 0, 0, 1/2], \n [0, 0, -1, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[-1, 0, -3k1 - 2k2 - 2k6 + 2(k1 + k2 + k3 + k6), k1, -k4/2], \n [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\ngamma :=[[1, 2k2 + 2k5 - 2(k1 + k2 + k3 + k6), \n 4k1 + 2k2 + 2k6 - 2(k1 + k2 + k3 + k6), -2k2, (k1 + k2 + k3 + k6)/2], \n [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta, gamma] , IdentityMat(5) );\nend;\n \nACDim4Nr062 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta, gamma;\na :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, -k1/2, 0, k1/2 + 2k2, 0], [0, -1, 0, 0, 1/2], \n [0, 0, -1, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, 3k1 + 2k2 - 2k3 + 2k4, 0, -k1 - 2k2, k3/2], \n [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\ngamma :=[[1, 3k1 + 2k2 - 2k3 + 2k4, -2k6, -k1 - 2k2, (k3 - k4 + k5)/2], \n [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta, gamma] , IdentityMat(5) );\nend;\n \nACDim4Nr075 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k3, 0, k4/4], [0, 0, -1, 0, 0], [0, 1, 0, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr076 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k3, 0, k4/4], [0, 0, -1, 0, 0], [0, 1, 0, 0, 0], \n [0, 0, 0, 1, 1/4], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr077 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k3, 0, k4/4], [0, 0, -1, 0, 0], [0, 1, 0, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr079 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, -k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k2, k3, k4/4], [0, 0, 1, 0, 0], [0, 0, 1, -1, 0], \n [0, -1, 1, 0, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr080 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, -k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -k1/4 + k2, k1/4 - k2, k3, k1/16 - k2/4 + k3/4 + k4/4], \n [0, 0, 1, 0, 1/2], [0, 0, 1, -1, 0], [0, -1, 1, 0, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr081 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k3, k4, k5/4], [0, 0, 1, 0, 0], [0, -1, 0, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr082 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, -k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k3, k4, k5/4], [0, 0, -1, 0, 0], [0, 0, -1, 1, 0], \n [0, 1, -1, 0, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr083 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k3, 0, k4/4], [0, 0, -1, 0, 0], [0, 1, 0, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[1, k2 + k3, -k2 + k3, k5, k6/2], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr084 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k3, 0, k4/4], [0, 0, -1, 0, 0], [0, 1, 0, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, k2 + k3, -k2 + k3, -2k6, k5/2], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr085 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k1/2 + k2 - 2k6, 0, \n -k1/8 + k2/4 + k3/4 - (-k1 + k2 - 2k6)/4], [0, 0, -1, 0, 0], \n [0, 1, 0, 0, 1/2], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[1, 2k2 - 2k6, -2k6, k4, k5/2], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr086 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k1/2 + k3, 0, -k1/8 + k2/4 - k3/4 + k4/4], [0, 0, -1, 0, 0], \n [0, 1, 0, 0, 1/2], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, k1 + k2 + k3, k1 - k2 + k3, -k1 + k2 - k3 - 2k6, k5/2], \n [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr087 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, -k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k2, k3, k4/4], [0, 0, 1, 0, 0], [0, 0, 1, -1, 0], \n [0, -1, 1, 0, 0], [0, 0, 0, 0, 1]];\nbeta :=[[1, k5, -2k2 + 2k3 + k5, 2k2 - k5, k6/2], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr088 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, -k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k2, -k1/4 + k3, -(-k1/4 + k2 + k3 - k4)/4], [0, 0, 1, 0, 0], \n [0, 0, 1, -1, 0], [0, -1, 1, 0, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, 2k2 + 2k6, -k1 + 2k3 + 2k6, -2k6, k5/2], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr103 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k3, 0, k4/4], [0, 0, -1, 0, 0], [0, 1, 0, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k2 - k3, 0, 2k5, 0], [0, 1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr104 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k1/2 + k2, -k1 + k2 + 2k3 + 2k5, 0, \n -k1/8 - k2/4 + k3/4 - (-k1 + k2 + 2k3 + 2k5)/4], [0, 0, -1, 0, 1/2], \n [0, 1, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -2k2 - 2k3 - 2k5, k1/2, 2k2 + 2k3 + 2k4 + 2k5, 0], \n [0, 1, 0, 0, 1/2], [0, 0, -1, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr106 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k1/2 + k2, -k1 - k2 - 2k5, 0, \n -k1/8 - k2/4 + k3/4 - (-k1 - k2 - 2k5)/4], [0, 0, -1, 0, 1/2], \n [0, 1, 0, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[-1, 2k5, k1/2, -2k4, 0], [0, 1, 0, 0, 1/2], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr110 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, k1, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1, -k1, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, 4k1 - 4k2 + 2k3 - 3k4 + 2k5, \n -4k1 + 4k2 - 2k3 + 3k4 - 2k5, -k1/2 + k2, \n -(-k1/2 + k2 - k3 - (3(-4k1 + 4k2 - 2k3 + 3k4 - 2k5))/2 - \n (4k1 - 4k2 + 2k3 - 3k4 + 2k5)/2)/4], [0, 0, 1, 0, 0], \n [0, 0, 1, -1, 0], [0, -1, 1, 0, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k4, 2(k1 - k2 - k4) + k4, k4, 0], [0, 0, 1, -1, 1/2], \n [0, 0, 1, 0, 1/2], [0, -1, 1, 0, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr114 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -k1/2 + k2, k1 - k2 - 2k4, 2k1 - 2k2 + 2k3 - 2k4 + 2k5, \n -(k1/2 + k3 + 2k5)/4], [0, 0, 1, 0, 1/2], [0, -1, 0, 0, 0], \n [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1/2, 2k4, 0, 0], [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr143 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na:= [[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb:= [[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc:= [[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[1, k2, -k1/2 + k3, 0, k4/3], [0, 0, -1, 0, 0], [0, 1, -1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr144 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k1/2 + k3, 0, k4/3], [0, 0, -1, 0, 0], [0, 1, -1, 0, 0], \n [0, 0, 0, 1, 1/3], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr146 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, -k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nc :=[[1, -k1/2, k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k3, -k2 - k3, k4/3], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0], \n [0, 0, 1, 0, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr147 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k1/2 + k3, k4, k5/6], [0, 0, 1, 0, 0], [0, -1, 1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr148 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, -k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nc :=[[1, -k1/2, k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k3, k4, k5/6], [0, 0, 0, -1, 0], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr158 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k1/2 + k3, 0, k4/3], [0, 0, -1, 0, 0], [0, 1, -1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k2, k2, 2k5, 0], [0, 0, -1, 0, 0], [0, -1, 0, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr159 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k1 - 2k2 + 3k4, -k1/2 + k2, 0, k3/3], [0, 0, -1, 0, 0], \n [0, 1, -1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k4, -k4, 2k5, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr161 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1/2, k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, -k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nc :=[[1, -k1/2, k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k1/4 + k2, k3, -k1/4 - k2 - k3, \n -((5k1)/8 + k2 + (-k2 - k3)/2 + (3k3)/2 - k4)/3], [0, 0, 0, 1, 1/2], \n [0, 1, 0, 0, 1/2], [0, 0, 1, 0, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1/4 - k2 - 2k3 + 2k5, (-3k1)/4 - k2 - 2k3 + 2k5, 2k5, \n 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr168 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k1/2 + k3, 0, k4/6], [0, 0, 1, 0, 0], [0, -1, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr169 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k1/2 + k3, 0, k4/6], [0, 0, 1, 0, 0], [0, -1, 1, 0, 0], \n [0, 0, 0, 1, 5/6], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr172 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k1/2 + k3, 0, k4/6], [0, 0, 1, 0, 0], [0, -1, 1, 0, 0], \n [0, 0, 0, 1, 1/3], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr173 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k1/2 + k3, 0, k4/6], [0, 0, 1, 0, 0], [0, -1, 1, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr174 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k1/2 + k3, k4, k5/6], [0, 0, -1, 0, 0], [0, 1, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr175 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k1/2 + k3, 0, k4/6], [0, 0, 1, 0, 0], [0, -1, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[1, k1 - 2k3, -k1 + 2k2 + 2k3, k5, k6/2], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr176 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k1/2 + k3, 0, k4/6], [0, 0, 1, 0, 0], [0, -1, 1, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, k1 - 2k3, -k1 + 2k2 + 2k3, 2k6, k5/2], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr184 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k1/2 + k3, 0, k4/6], [0, 0, 1, 0, 0], [0, -1, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1 + k2 + 2k3, k1 - k2 - 2k3, 2k5, 0], [0, 0, -1, 0, 0], \n [0, -1, 0, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4NrB1 := function ( k, k1, k2, k3)\nlocal a, b, c, d;\na:= [[1, (-2k2)/3, 0, -k1/2 - (2kk3)/3 + (2k(k2 + k3))/3, 0], \n [0, 1, 0, -k/2, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb:= [[1, (-2k3)/3, k1/2 - (2kk3)/3, 0, 0], [0, 1, k/2, 0, 0], \n [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, k2/3, k3/3, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d] , IdentityMat(5) );\nend;\n \nACDim4NrB2 := function ( k, k1, k2, k3)\nlocal a, b, c, d, alfa;\na:= [[1, (-4k1)/3, 0, (2kk1)/3 + (2kk2)/3 - 2kk3 + \n (-4kk1 - (16kk2)/3 - 2kk3 + 2(2kk1 + 2kk2 + 2kk3))/2, 0], \n [0, 1, 0, -k, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb:= [[1, (-4k2)/3, (-4kk1 - (16kk2)/3 - 2kk3 + \n 2(2kk1 + 2kk2 + 2kk3))/2, 0, 0], [0, 1, k, 0, 0], \n [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, (2k1)/3, (2k2)/3, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[-1, 2k3, -k1/3, -k2/3, 0], [0, 1, 0, 0, 1/2], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4NrB3c := function (l, k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na:= [[1, 0, 0, (k1l)/3 + k3l + ((-8k1l)/3 + k3l + 2(k1l - k3l))/2, \n 0], [0, 1, 0, -l, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb:= [[1, (-2k1)/3, ((-8k1l)/3 + k3l + 2(k1l - k3l))/2, -k2, 0], \n [0, 1, l, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, 0, k1/3, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[1, k3, 0, 0, k4/2], [0, -1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4NrB3b := function (l, k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na:= [[1, 0, 0, k1 + (2k1l)/3 - 2k2l + ((2k1)/3 - (16k1l)/3 - 2k2l + \n 2(-k1 + 2k1l + 2k2l))/2, 0], [0, 1, 0, -l, 0], [0, 0, 1, 0, 1], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb:= [[1, (-4k1)/3, ((2k1)/3 - (16k1l)/3 - 2k2l + \n 2(-k1 + 2k1l + 2k2l))/2, -k3, 0], [0, 1, l, 0, 0], \n [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, 0, (2k1)/3, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[1, -2k2, -k2, 0, k4/2], [0, -1, -1, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4NrB3 := function (l, k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na:= [[1, 0, 0, (2k1)/3 + (k1l)/3 + (-k1 - (2k1l)/3)/2, 0], \n [0, 1, 0, (-1 - 2l)/2, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb:= [[1, (-2k1)/3, (-k1 - (2k1l)/3)/2, -k3, 0], [0, 1, (1 + 2l)/2, 0, 0], \n [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, 0, k1/3, -k2], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[1, 0, 0, 0, k4/2], [0, -1, -1, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4NrB4 := function (k, k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na:= [[1, 0, 0, (kk1)/3 + kk3 + ((-2kk1)/3 - kk3)/2, -k4], \n [0, 1, 0, -k, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb:= [[1, (-2k1)/3, ((-2kk1)/3 - kk3)/2, -(kk1)/2 - k2 + (3kk3)/4, 0], \n [0, 1, k, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, 0, k1/3, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[1, k3, 0, 0, 0], [0, -1, 0, k/2, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4NrB4b := function (k, k1, k2, k3)\nlocal a, b, c, d, alfa;\na:= [[1, (4k1)/3, 0, (-5kk1)/3 + 2k2 - 2((-2kk1)/3 + k2), -k3], \n [0, 1, 0, -k, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb:= [[1, 0, -2((-2kk1)/3 + k2), 0, 0], [0, 1, k, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, (-2k1)/3, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[-1, (-2k1)/3, 0, 0, 0], [0, -1, 0, k/2, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4NrB5 := function (l, k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na:= [[1, (-2k1)/3, 0, k3l, k2], [0, 1, 0, -l, 0], [0, 0, 1, 0, 1], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb:= [[1, (2k1)/3, 0, 0, 0], [0, 1, l, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, k1/3, -k1/3, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[1, k3, 0, 0, k4/2], [0, -1, 0, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 1, 0, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4NrB5b := function (l, k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na:= [[1, (-2k1)/3, 0, k3(1 + 2l), k2], [0, 1, 0, (-1 - 2l)/2, 0], \n [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb:= [[1, (2k1)/3, 0, 0, 0], [0, 1, (1 + 2l)/2, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, k1/3, -k1/3, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[1, 2k3, 0, 0, k4/2], [0, -1, 0, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 1, 0, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4NrB7 := function (l, k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na:= [[1, 0, 0, (4k1l)/3 - 4k2l + ((-8k1l)/3 + 4k2l)/2, 0], \n [0, 1, 0, -2l, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb:= [[1, (-4k1)/3, ((-8k1l)/3 + 4k2l)/2, 0, (5k1)/6 - 2k2 + \n ((-2k1)/3 + 2k2)/2 - k4], [0, 1, 2l, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, 0, (2k1)/3, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[-1, 2k2, 0, -k1/3, 0], [0, 1, 0, 0, 1/2], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nbeta:= [[1, (2k1)/3 - 2k2, -(((2k1)/3 - 2k2)l)/2, 2k3, 0], \n [0, -1, l, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4NrB7b := function (l, k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na:= [[1, 0, 0, (4k1(1 + 2l))/3 - 2k2(1 + 2l) + \n ((-8k1(1 + 2l))/3 + 2k2(1 + 2l))/2, 0], [0, 1, 0, -1 - 2l, 0], \n [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb:= [[1, (-8k1)/3, ((-8k1(1 + 2l))/3 + 2k2(1 + 2l))/2, 0, \n (5k1)/3 - 2k2 + ((-4k1)/3 + 2k2)/2 - k4], [0, 1, 1 + 2l, 0, 0], \n [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, 0, (4k1)/3, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[-1, 2k2, 0, (-2k1)/3, 0], [0, 1, 0, 0, 1/2], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nbeta:= [[1, (4k1)/3 - 2k2, -(((4k1)/3 - 2k2)(1 + 2l))/4, 2k3, 0], \n [0, -1, (1 + 2l)/2, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, -1, 1/2], \n [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4NrB8 := function (k, k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na:= [[1, 0, 0, -2k(k1 - 2k2) - 8kk2 + (8k(2(k1 - 2k2) + 4k2))/3 + \n (-4kk2 - (14k(2(k1 - 2k2) + 4k2))/3 + \n 2(2k(k1 - 2k2) + 8kk2))/2, \n (k(k1 + (-2(k1 - 2k2) - 4k2)/6 - 2k2))/4 - k3 + \n (k1 + (17k(k1 - 2k2))/3 - 3k2 + (34kk2)/3 + (-k1 + 2k2)/2 + \n (-2k(k1 - 2k2) - 8kk2)/2 + (k1 - 2k(k1 - 2k2) - 6kk2)/2 + \n 2k3 - 2k4)/2], [0, 1, 0, -2k, 0], [0, 0, 1, 0, 1], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb:= [[1, (-2(2(k1 - 2k2) + 4k2))/3, \n (-4kk2 - (14k(2(k1 - 2k2) + 4k2))/3 + \n 2(2k(k1 - 2k2) + 8kk2))/2, k1 + (-2(k1 - 2k2) - 4k2)/3 - \n 2k(k1 - 2k2) - 2kk2 + (4k(2(k1 - 2k2) + 4k2))/3 + \n ((-2(k1 - 2k2) - 4k2)/3 - 4kk2)/2, 0], [0, 1, 2k, 0, 0], \n [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, 0, (2(k1 - 2k2) + 4k2)/3, 0], [0, 1, 0, 0, 1], \n [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[-1, 2k2, 2kk2, ((-2(k1 - 2k2) - 4k2)/3 - 4kk2)/2, 0], \n [0, 1, 2k, -2k, 1/2], [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], \n [0, 0, 0, 0, 1]];\nbeta:= [[1, k1 + (-2(k1 - 2k2) - 4k2)/6 - 2k2, \n (k(k1 + (-2(k1 - 2k2) - 4k2)/6 - 2k2))/2, \n k1 + (17k(k1 - 2k2))/3 - 3k2 + (34kk2)/3 + (-k1 + 2k2)/2 + \n (-2k(k1 - 2k2) - 8kk2)/2 + (k1 - 2k(k1 - 2k2) - 6kk2)/2 + \n 2k3 - 2k4, 0], [0, -1, -k, k, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4NrB8b := function (k, k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na:= [[1, (4k1)/3, (-2k1)/3 + (4kk1)/3 + \n ((-16kk1)/3 + 8kk2 - 2(-2kk1 + 4kk2))/2 + \n 2(k1/3 - (2kk1)/3 + ((16kk1)/3 - 8kk2 + \n 2(-2kk1 + 4kk2))/ 2), (-10kk1)/3 + ((16kk1)/3 - 8kk2 + \n 2(-2kk1 + 4kk2))/2, \n ((8kk1)/3 - 2kk2 + (-2kk1 + 4kk2)/2 + \n ((-16kk1)/3 + 8kk2 - 2(-2kk1 + 4kk2))/2)/2 - k3], \n [0, 1, 0, -2k, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb:= [[1, 0, ((16kk1)/3 - 8kk2 + 2(-2kk1 + 4kk2))/2, 0, \n (-2k1)/3 - (2kk1)/3 + k2 + 4kk2 + (2kk1 - 4kk2)/2 + \n ((-16kk1)/3 + 8kk2 - 2(-2kk1 + 4kk2))/4 + \n (k1/3 - (2kk1)/3 + ((16kk1)/3 - 8kk2 + 2(-2kk1 + 4kk2))/2)/ 2 \n + ((-8kk1)/3 + 2kk2 + (2kk1 - 4kk2)/2 + \n ((16kk1)/3 - 8kk2 + 2(-2kk1 + 4kk2))/2)/2 + k3 + k4], \n [0, 1, 2k, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, (-2k1)/3, 0, -k2], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[-1, 0, k1/3 - (2kk1)/3 + ((16kk1)/3 - 8kk2 + \n 2(-2kk1 + 4kk2))/2, 0, 0], [0, 1, 2k, -2k, 1/2], \n [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nbeta:= [[-1, (-2k1)/3, 0, (8kk1)/3 - 2kk2 + (-2kk1 + 4kk2)/2 + \n ((-16kk1)/3 + 8kk2 - 2(-2kk1 + 4kk2))/2, 0], \n [0, -1, -k, k, 0], [0, 0, 1, 0, 1/2], [0, 0, 0, -1, 1/2], \n [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n\n#############################################################################\n##\n#V ACDim4Funcs\n#V ACDim4Param\n#V ACDim4Types\n##\n\n#############################################################################\n##\n## some small helpers\n##\nACDim4Funcs := [ ACDim4Nr001, ACDim4Nr002, ACDim4Nr003, ACDim4Nr004,\nACDim4Nr004b, ACDim4Nr005, ACDim4Nr006, ACDim4Nr007, ACDim4Nr007b,\nACDim4Nr008, ACDim4Nr009, ACDim4Nr009b, ACDim4Nr010, ACDim4Nr011,\nACDim4Nr012, ACDim4Nr013, ACDim4Nr014,\nACDim4Nr014b, ACDim4Nr015, ACDim4Nr018, ACDim4Nr019, ACDim4Nr019b,\nACDim4Nr019c, ACDim4Nr026, ACDim4Nr027, ACDim4Nr029, ACDim4Nr029b,\nACDim4Nr029c, ACDim4Nr030, ACDim4Nr031, ACDim4Nr032, ACDim4Nr033,\nACDim4Nr033b, ACDim4Nr033c, ACDim4Nr034, ACDim4Nr036, ACDim4Nr037,\nACDim4Nr041, ACDim4Nr043, ACDim4Nr045, ACDim4Nr055, ACDim4Nr056,\nACDim4Nr058, ACDim4Nr060, ACDim4Nr061, ACDim4Nr061b, ACDim4Nr061c,\nACDim4Nr062, ACDim4Nr075, ACDim4Nr076, ACDim4Nr077, ACDim4Nr079,\nACDim4Nr080, ACDim4Nr081, ACDim4Nr082, ACDim4Nr083, ACDim4Nr084, ACDim4Nr085,\nACDim4Nr086, ACDim4Nr087, ACDim4Nr088, ACDim4Nr103, ACDim4Nr104, ACDim4Nr106,\nACDim4Nr110, ACDim4Nr114, ACDim4Nr143, ACDim4Nr144, ACDim4Nr146, ACDim4Nr147,\nACDim4Nr148, ACDim4Nr158, ACDim4Nr159, ACDim4Nr161, ACDim4Nr168, ACDim4Nr169,\nACDim4Nr172, ACDim4Nr173, ACDim4Nr174, ACDim4Nr175, ACDim4Nr176, ACDim4Nr184,\nACDim4NrB1, ACDim4NrB2, ACDim4NrB3c, ACDim4NrB3b, ACDim4NrB3, ACDim4NrB4,\nACDim4NrB4b, ACDim4NrB5, ACDim4NrB5b, ACDim4NrB7, ACDim4NrB7b, ACDim4NrB8,\nACDim4NrB8b ];\nMakeReadOnlyGlobal( \"ACDim4Funcs\" );\n\n#############################################################################\nACDim4Types := [\n\"001\", \"002\", \"003\", \"004\", \"004b\", \"005\", \"006\", \"007\", \"007b\", \"008\",\n\"009\", \"009b\", \"010\", \"011\", \"012\", \"013\", \"014\", \"014b\", \"015\", \"018\",\n\"019\", \"019b\", \"019c\", \"026\", \"027\", \"029\", \"029b\", \"029c\", \"030\", \"031\",\n\"032\", \"033\", \"033b\", \"033c\", \"034\", \"036\", \"037\", \"041\", \"043\", \"045\",\n\"055\", \"056\", \"058\", \"060\", \"061\", \"061b\", \"061c\", \"062\", \"075\", \"076\",\n\"077\", \"079\", \"080\", \"081\", \"082\", \"083\", \"084\", \"085\", \"086\", \"087\", \"088\",\n\"103\", \"104\", \"106\", \"110\", \"114\", \"143\", \"144\", \"146\", \"147\", \"148\", \"158\",\n\"159\", \"161\", \"168\", \"169\", \"172\", \"173\", \"174\", \"175\", \"176\", \"184\", \"B1\",\n\"B2\", \"B3c\", \"B3b\", \"B3\", \"B4\", \"B4b\", \"B5\", \"B5b\", \"B7\", \"B7b\", \"B8\", \"B8b\"\n];\nMakeReadOnlyGlobal( \"ACDim4Types\" );\n\n#############################################################################\nACDim4Param :=\n[ 3, 7, 4, 4, 3, 4, 3, 3, 4, 3, 3, 4, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 5,\n 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4,\n 4, 4, 4, 5, 5, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 4, 4, 4, 5, 5, 5, 5, 5, 4,\n 4, 4, 4, 5, 6, 6, 5, 4, 4, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5 ];\nMakeReadOnlyGlobal( \"ACDim4Param\" );\n\n", "meta": {"hexsha": "eec6d2c6269174c6f6f8baa92d895223e01b0591", "size": 76488, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "gap/matgrp4.gi", "max_stars_repo_name": "alex-konovalov/aclib", 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	{"text": "# Copyright (c) 2018-2020, Carnegie Mellon University\n# See LICENSE for details\n#\n# Contains the rewrite rulesets for SPL-expression simplification\n# After the Breakdown Stage\n# Current Demo version focuses on CNOTs, and so we do not cancel single-qubit gates\n# Eventually we will convert all gates to generic rotations in Quantum_Format\n# Combine rotations in Quantum_Simplify, and convert back into non-generic rotations in Quantum_Terminate\n#\n# Additionally, Junction steps should be factored out in this stage versus in the unparser to enable a \n# few more optimizations. A SWE effort is underway.\n#\n\n##\n#F CheckIdentitySplit( <a>, <b> )\n##\n## return true if we can split an Identity transform into smaller matrices\nCheckIdentitySplit := function(a, b)\n if(ObjId(a) = I) then \n if a.params[1] > 2 then\n return true;\n fi;\n fi;\n if(ObjId(b) = I) then \n if b.params[1] > 2 then\n return true;\n fi;\n fi;\n return false;\nend;\n\n##\n#F CheckIdentity( <a>, <b> )\n##\n## are both objects identity\nCheckIdentity := function(a, b)\n if(ObjId(a) = I) then \n if(ObjId(b) = I) then \n return true;\n fi;\n fi;\n return false;\nend;\n\n##\n#F PullInTensor( <ch1>, <ch2> )\n##\n## compress two tensor expressions by pulling in symbols wherever sizes align\nPullInTensor := function(ch1, ch2)\n local pos1, pos2, e1, e2, up1, up2, siz1, siz2;\n pos1 := 1;\n pos2 := 1;\n siz1 := 0;\n siz2 := 0;\n while pos1 <= Length(ch1) and pos2 <= Length(ch2) do\n e1 := ch1[pos1];\n e2 := ch2[pos2];\n if ( (e1.dims()[1] = e2.dims()[1]) and (pos1 = pos2) ) then \n ch1[pos1] := ch1[pos1] * ch2[pos2];\n ch2[pos2] := I(e2.dims()[1]);\n fi;\n up1 := siz1 + log(e1.dims()[1], 2).v;\n up2 := siz2 + log(e2.dims()[1], 2).v;\n if (up1 <= up2) then \n pos1 := pos1 + 1;\n siz1 := siz1 + log(e1.dims()[1], 2).v;\n fi;\n if (up1 > up2) then \n pos2 := pos2 + 1;\n siz2 := siz2 + log(e2.dims()[1], 2).v;\n fi;\n od;\n return [ch1, ch2];\nend;\n\n##\n#F CanPullIn( <ch1>, <ch2> )\n##\n## Similar to PullInTensor, but just checks to see if there is any simplification possible\nCanPullIn := function(ch1, ch2)\n local pos1, pos2, e1, e2, up1, up2, siz1, siz2;\n pos1 := 1;\n pos2 := 1;\n siz1 := 0;\n siz2 := 0;\n while pos1 <= Length(ch1) and pos2 <= Length(ch2) do\n e1 := ch1[pos1];\n e2 := ch2[pos2];\n if ( (e1.dims()[1] = e2.dims()[1]) and (pos1 = pos2) and ObjId(e2) <> I) then \n return true;\n fi;\n up1 := siz1 + log(e1.dims()[1], 2).v;\n up2 := siz2 + log(e2.dims()[1], 2).v;\n if (up1 <= up2) then \n pos1 := pos1 + 1;\n siz1 := siz1 + log(e1.dims()[1], 2).v;\n fi;\n if (up1 > up2) then \n pos2 := pos2 + 1;\n siz2 := siz2 + log(e2.dims()[1], 2).v;\n fi;\n od;\n return false;\nend;\n\n##\n#F ValidTensSimplifyMatch( <e1>, <e2> )\n##\n## SWrapper function to deterrmine if the tensor rewrite rule can be applied\nValidTensSimplifyMatch := function(e1, e2)\n if ObjId(e1)=Tensor and ObjId(e2)=Tensor then \n if CanPullIn(e1._children, e2._children) then \n return true;\n fi;\n fi;\n return false;\nend;\n\n##\n#F CombineReord( <ord1>, <dir1>, <ord2>, <dir2>, <arch> )\n##\n## Combine Reorder steps\nCombineReord := function(ord1, dir1, ord2, dir2, arch)\n local idx, adj1, adj2, adj3, start, n, t1, t2, a, b, new_list, o1, o2;\n adj1 := [];\n adj2 := [];\n if dir1 = -1 then\n idx := 0;\n for o1 in ord1 do \n Add(adj1, [idx, o1]);\n idx := idx + 1;\n od;\n fi;\n if dir1 = 1 then\n idx := 0;\n for o1 in ord1 do \n Add(adj1, [o1, idx]);\n idx := idx + 1;\n od;\n fi;\n if dir2 = -1 then\n idx := 0;\n for o2 in ord2 do \n Add(adj2, [idx, o2]);\n idx := idx + 1;\n od;\n fi;\n if dir2 = 1 then\n idx := 0;\n for o2 in ord2 do \n Add(adj2, [o2, idx]);\n idx := idx + 1;\n od;\n fi;\n # now have adj1 and adj2\n adj3 := [];\n for a in adj1 do \n start := a[1];\n t1 := a[2];\n t2 := -1;\n for b in adj2 do\n if b[1] = t1 then \n t2 := b[2];\n fi;\n od;\n Add(adj3, [start, t2]);\n od;\n # full combine, and then check validity. If it isnt valid, then just dont simplify\n # TODO do a partial recombine if the entire reorder cannot be combined and be still implementable\n # not much harder, just a lot of code\n new_list := [0..Length(ord1)-1];\n idx := 1;\n for n in new_list do \n for a in adj3 do\n if n = a[1] then \n new_list[idx] := a[2];\n fi;\n od;\n idx := idx + 1;\n od;\n if VerifyPath(new_list, [0..Length(ord1)-1], arch) = true then \n return Reord(new_list, arch, 1);\n fi;\n return (Reord(ord1, arch, dir1) * Reord(ord2, arch, dir2));\nend;\n\n##\n#F Quantum_Format ruleset\n## \nClass(Quantum_Format, RuleSet);\nRewriteRules(Quantum_Format, rec(\n # Remove Grp structure \n remove_grp := ARule( Grp, [@(1)], x-> [(@(1).val)] ),\n\n # Flatten Tensors\n flatten_tensor_asoc := ARule(Tensor, [@(1), @(2).cond(e-> ObjId(@(1).val)=Tensor or ObjId(e)=Tensor)],\n\t e -> let(\n\t ch1 := Cond(ObjId(@(1).val)=Tensor, @(1).val._children, [@(1).val]),\n\t ch2 := Cond(ObjId(@(2).val)=Tensor, @(2).val._children, [@(2).val]),\n\t ch1::ch2\n\t )),\n\n #Split identities into I(2)\n split_identity := ARule(Tensor, [@(1), @(2).cond(e-> (CheckIdentitySplit(@(1).val, e)) )],\n\t e -> let(\n\t ch1 := Cond(ObjId(@(1).val)=I and @(1).val.params[1] > 2, Tensor(I(2), I(@(1).val.params[1]/2)), [@(1).val]),\n\t ch2 := Cond(ObjId(@(2).val)=I and @(2).val.params[1] > 2, Tensor(I(2), I(@(2).val.params[1]/2)), [@(2).val]),\n [ch1]::[ch2]\n\t )),\n));\n\n##\n#F Quantum_Simplify ruleset\n## \nClass(Quantum_Simplify, RuleSet);\nRewriteRules(Quantum_Simplify, rec(\n\n # Pull-In Tensors \n pull_in_tensor := ARule(Compose, [@(1), @(2).cond(e-> ValidTensSimplifyMatch(@(1).val, e))],\n\t e -> let(\n # both 1 ans 2 are tensors, can access a list of arguments via _children\n ch := PullInTensor(@(1).val._children, @(2).val._children),\n\t [Tensor(ch[1])]::[Tensor(ch[2])]\n\t )),\n\n # Remove Identity Multiplications\n remove_identity_right := ARule( Compose, [@(1), @(2).cond(e -> ObjId(e)=I)], x-> [(@(1).val)]),\n remove_identity_left := ARule( Compose, [@(1).cond(e -> ObjId(e)=I), @(2)], x-> [(@(2).val)]),\n\n # Cancel Composition of CNOTS\n cancel_cnot := ARule(Compose, [[CNOT, @(1), @(2)], [CNOT, @(3).cond(x -> (x = @(1).val)), @(4).cond(x -> (x = @(2).val))]], x->[I(2^(@(1).val + 1))] ),\n\n # Combine Reorder Compositions\n cancel_reorder := ARule(Compose, [[Reord, @(1), @(2), @(3)], [Reord, @(4), @(5), @(6)]], x-> [CombineReord(@(1).val, @(3).val, @(4).val, @(6).val, @(5).val)]),\n));\n\n\n##\n#F Quantum_Terminate ruleset\n## \nClass(Quantum_Terminate, RuleSet);\nRewriteRules(Quantum_Terminate, rec(\n # Recombine Identities - Good\n recomb_identity := ARule(Tensor, [@(1), @(2).cond(e-> (CheckIdentity(@(1).val, e) ))],\n\t e -> [I(@(1).val.params[1] * @(2).val.params[1])]),\n\n # Remove Identity Multiplications - Good\n remove_identity_right := ARule( Compose, [@(1), @(2).cond(e -> ObjId(e)=I)], x-> [(@(1).val)]),\n remove_identity_left := ARule( Compose, [@(1).cond(e -> ObjId(e)=I), @(2)], x-> [(@(2).val)]),\n\n));\n\n\n##\n#F QuantumRewriteInternal( <s>, <opts> )\n##\n## Rewrites a quantum SPL expression, for internal use\nQuantumRewriteInternal := function (s, opts)\n s := ApplyStrategy(s, [Quantum_Format], BUA, opts); \n s := ApplyStrategy(s, [Quantum_Simplify], BUA, opts);\n s := ApplyStrategy(s, [Quantum_Terminate], BUA, opts);\n return s;\nend;\n\n##\n#F BestCircuitInternal( <t>, <opts> )\n##\n## Finds the best circuit implementing transform t, for internal use\nBestCircuitInternal := function (t, opts)\n local dpopts, best, s;\n dpopts := rec(verbosity := 0, hashTable := HashTableDP()); \n dpopts.measureFunction := (rt, opts) ->\n let(c := SPLRuleTree(rt), # generate SPL Ruletree and then run a collect on CNOTs \n c2 := QuantumRewriteInternal(c, opts),\n Length(Collect(c2, @(1,CNOT)))\n ); \n best := DP(t, dpopts, opts);\n s := QuantumRewriteInternal(SPLRuleTree(best[1].ruletree), opts);\n return s;\nend;\n\n##\n#F TerminateReord( <l>, <arch>, <dir> )\n##\n## Convert a reorder object to CNOTs\nTerminateReord := function (l, arch, dir)\n local mats, mat, dir, spl;\n mats := ShiftMat(l, [0..Length(arch)-1], arch, Length(arch));\n if dir = -1 then \n mat := mats[2];\n fi;\n if dir = 1 then\n mat := mats[1];\n fi;\n # now mat in an unreduced Non-terminal expression\n # we need the SPL expression\n spl := BestCircuitInternal(mat, SpiralDefaults);\n return spl;\nend;\n\n##\n#F Quantum_Reorder ruleset\n## \nClass(Quantum_Reorder, RuleSet);\nRewriteRules(Quantum_Reorder, rec(\n\n # Combine Reorder Compositions\n reorder_convert := Rule([Reord, @(1), @(2), @(3)], x-> TerminateReord(@(1).val, @(2).val, @(3).val)),\n));\n\n\n# ------------------------- For External Use ----------------------------------------\n\n##\n#F QuantumRewrite( <s>, <opts> )\n##\n## Simplifies an SPL expression representing a quantum circuit (s)\nQuantumRewrite := function (s, opts)\n s := ApplyStrategy(s, [Quantum_Format], BUA, opts); \n s := ApplyStrategy(s, [Quantum_Simplify], BUA, opts);\n s := ApplyStrategy(s, [Quantum_Reorder], BUA, opts);\n s := RulesSums(s);\n s := ApplyStrategy(s, [Quantum_Format], BUA, opts); \n s := ApplyStrategy(s, [Quantum_Simplify], BUA, opts);\n s := ApplyStrategy(s, [Quantum_Terminate], BUA, opts);\n return s;\nend;\n\n##\n#F BestCircuit( <t>, <opts> )\n##\n## Finds the best circuit implementing transform t\n## Hardcoded to count number CNOT gates as the cost function\nBestCircuit := function (t, opts)\n local dpopts, best, s, cnot_list;\n dpopts := rec(verbosity := 1, hashTable := HashTableDP()); \n dpopts.measureFunction := (rt, opts) ->\n let(c := SPLRuleTree(rt), # generate SPL Ruletree and then run a collect on CNOTs \n c2 := QuantumRewrite(c, opts),\n Length(Collect(c2, @(1,CNOT)))\n ); \n best := DP(t, dpopts, opts);\n Print(\"\\n SPL \\n\");\n Print(SPLRuleTree(best[1].ruletree));\n Print(\"\\n\");\n s := QuantumRewrite(SPLRuleTree(best[1].ruletree), opts);\n Print(\"\\ncost :\");\n Print(Length(Collect(s, @(1,CNOT))));\n Print(\"\\n\");\n Print(\"---------------- BestCircuit: \\n\");\n return s;\nend;\n\n\n\n\n", "meta": {"hexsha": "a0a7e78606106d0c2dd9f5399597de1ad69942e3", "size": 10880, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "qrewrite.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": "qrewrite.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": "qrewrite.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": 30.4761904762, "max_line_length": 163, "alphanum_fraction": 0.5509191176, "num_tokens": 3439, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. 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	{"text": "\n\nNewRulesFor(PrunedMDPRDFT, rec(\n PrunedMDPRDFT_Base := rec(\n applicable := nt -> Length(nt.params[1]) = 1,\n\n children := nt -> [[ PrunedPRDFT(nt.params[1][1], nt.params[2]).withTags(nt.getTags()) ]],\n\n apply := (nt, C, Nonterms) -> C[1]\n ),\n\n PrunedMDPRDFT_RowCol1 := rec(\n applicable := nt -> Length(nt.params[1]) > 1 and not nt.hasTags(),\n\n children := nt -> [[ PrunedMDDFT(DropLast(nt.params[1], 1), nt.params[3], 1, DropLast(nt.params[2], 1)),\n PrunedPRDFT(Last(nt.params[1]), nt.params[3], 1, Last(nt.params[2])) ]],\n\n apply := (nt, C, cnt) -> RC(Tensor(C[1], I(C[2].dims()[1]/2))) * Tensor(I(Product(List(cnt[1].params[4], i->Length(i)))), C[2])\n )\n));\n\n\nNewRulesFor(PrunedIMDPRDFT, rec(\n PrunedIMDPRDFT_Base := rec(\n applicable := nt -> Length(nt.params[1]) = 1,\n\n children := nt -> [[ PrunedIPRDFT(nt.params[1][1], nt.params[2]).withTags(nt.getTags()) ]],\n\n apply := (nt, C, Nonterms) -> C[1]\n ),\n\n PrunedIMDPRDFT_RowCol1 := rec(\n applicable := nt -> Length(nt.params[1]) > 1 and not nt.hasTags(),\n\n children := nt -> [[ PrunedIPRDFT(Last(nt.params[1]), nt.params[3], 1, Last(nt.params[2])),\n PrunedIMDDFT(DropLast(nt.params[1], 1), nt.params[3], 1, DropLast(nt.params[2], 1)) ]],\n\n apply := (nt, C, cnt) -> Tensor(I(Product(List(cnt[2].params[4], i->Length(i)))), C[1]) * RC(Tensor(C[2], I(C[1].dims()[2]/2)))\n )\n));\n\n\n\n", "meta": {"hexsha": "28cb1fb3701aae461f9dd15e62e5f680d19b5373", "size": 1538, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "breakdown/prune.gi", "max_stars_repo_name": "mikefranusich/spiral-package-fftx", "max_stars_repo_head_hexsha": "a1a355f3764aade9665145aa63c2318201421543", "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": "breakdown/prune.gi", "max_issues_repo_name": "mikefranusich/spiral-package-fftx", "max_issues_repo_head_hexsha": "a1a355f3764aade9665145aa63c2318201421543", "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": "breakdown/prune.gi", "max_forks_repo_name": "mikefranusich/spiral-package-fftx", "max_forks_repo_head_hexsha": "a1a355f3764aade9665145aa63c2318201421543", "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": 34.9545454545, "max_line_length": 136, "alphanum_fraction": 0.5253576073, "num_tokens": 502, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6959583124210896, "lm_q2_score": 0.6150878555160665, "lm_q1q2_score": 0.4280755059156686}}
	{"text": "\n#\n# ---------- Constructors ----------\n#\n\nInstallMethod(Unipotent,\n \"Unipotent element in simple adjoint type\",\n [IsChevalleyAdj,IsList,IsList,IsInt],\n function(sys,coeffs,ordering,order)\n local object;\n \n if Filtered(coeffs,i->not i[2] in Integers)=[] then coeffs:=List(coeffs,i->[i[1],One(ring(sys))i[2]]);\n elif Filtered(coeffs,i->not i[2] in ring(sys))<>[] then Error(\"The coefficients ar not in indicated ring.\"); fi;\n\n object:=Objectify(NewType(NewFamily(\"UnipotentFamily\"),\n IsAttributeStoringRep and\n IsUnipotent and\n IsMultiplicativeElementWithInverse and\n IsMultiplicativeElementWithOne),\n rec());\n\n SetchevalleyAdj(object,sys);\n SetOrdering(object,ordering);\n \n Setcoefficients(object,Canonic(sys,coeffs,ordering));\n# SetInverse(object,InverseOp(object)); This is set at the first call Inverse(obj);\n\n if order = -1 and Characteristic(sys)>0 then\n SetOrder(object,OrderOp(object));\n elif order > -1 then\n SetOrder(object,order);\n fi;\n \n SetName(object,Concatenation(\"<unipotent element for \",type(sys),String(rank(sys)),\n \" in characteristic \",String(Characteristic(sys)),\">\"));\n return object;\nend);\n\nInstallMethod(Unipotent,\n \"Unipotent element in simple adjoint type\",\n [IsChevalleyAdj,IsList,IsList],\n function(sys,coeffs,ordering)\n\n return Unipotent(sys,coeffs,ordering,-2);\nend);\n\nInstallMethod(Unipotent,\n \"Unipotent element in simple adjoint type\",\n [IsChevalleyAdj,IsList,IsInt],\n function(sys,coeffs,order)\n local ordering,tmp,i,slot;\n \n tmp:=ShallowCopy(coeffs);\n Sort(tmp,function(a,b) return a[1]<b[1]; end);\n\n ordering:=[1..Length(positiveRoots(sys))];\n tmp:=List(tmp,i->ordering[i[1]]);\n\n for i in [1..Length(coeffs)] do\n ordering[coeffs[i][1]]:=tmp[i];\n od; \n\n return Unipotent(sys,Filtered(coeffs,i->i[2]<>Zero(ring(sys))),ordering,order);\nend);\n\nInstallMethod(Unipotent,\n \"Unipotent element in simple adjoint type\",\n [IsChevalleyAdj,IsList],\n function(sys,coeffs)\n\n return Unipotent(sys,coeffs,-2);#-1);\nend);\n\nInstallMethod(Unipotent,\n \"Unipotent element in simple adjoint type\",\n [IsNilpotentChv],\n function(e)\n\n return Unipotent(chevalleyAdj(e),coefficients(e));\nend);\n\n\n#\n# ---------- Canonic form of element ----------\n#\n\nInstallMethod(Canonic,\n \"Canonic form of coefficients of unipotent element in given ordering\",\n [IsChevalleyAdj,IsList,IsList],\n function(sys,coeffs,ordering)\n local lista,\n pr,Cijrs,\n flag,i,temp,suma,param,cc,k;\n \n lista:=List(coeffs,i->ShallowCopy(i));\n pr:=positiveRoots(sys);\n\n Cijrs:=C(sys);\n flag:=true;\n while flag do\n flag:=false;\n i:=Length(lista);\n while 0 < i do\n if lista[i][2] = Zero(ring(sys)) then \n Remove(lista,i);\n flag:=true;\n elif 1 < i and lista[i][1] = lista[i-1][1] then\n lista[i-1][2]:=lista[i-1][2]+lista[i][2];\n Remove(lista,i);\n flag:=true;\n elif 1 < i and ordering[lista[i][1]] < ordering[lista[i-1][1]] then\n temp:=lista[i]; lista[i]:=lista[i-1]; lista[i-1]:=temp;\n \n #aici r si s sunt pe pozitia i-1 si repsectiv i\n k:=1;\n for cc in Cijrs[lista[i-1][1]][lista[i][1]] do\n suma:=cc[1]pr[lista[i-1][1]]+cc[2]pr[lista[i][1]];\n param:=cc[3]((-1)^cc[1])(lista[i-1][2]^cc[1])(lista[i][2]^cc[2]);\n Add(lista,[Position(pr,suma),param],i+k);\n k:=k+1;\n od;\n flag:=true;\n fi;\n i:=i-1;\n od;\n od;\n\n return Immutable(lista);\nend);\n\n#\n# ---------- Arithmetic Operations ----------\n#\n\nInstallMethod(InverseMutable,\n \"Inverse of unipotent element\",\n [IsUnipotent],\n function(u)\n local i,lista,len,reverse_order;\n \n lista:=List(coefficients(u),i->StructuralCopy(i));\n len:=Length(lista);\n for i in [1..len] do\n Add(lista,[lista[len-i+1][1],-lista[len-i+1][2]]);\n Remove(lista,len-i+1);\n od;\n\n reverse_order:=function(o)\n local maxim;\n maxim:=Maximum(o);\n return List(o,i->maxim-i+1);\n end;\n \n return Unipotent(chevalleyAdj(u),lista,reverse_order(Ordering(u)),-2);#0);\nend);\n\nInstallMethod(OneMutable,\n \"Inverse of unipotent element\",\n [IsUnipotent],\n function(u)\n\n return One(chevalleyAdj(u),[],0);\nend);\n\nInstallMethod(\\,\n \"Multiplication for unipotent elements ab with the ordering of b\",\n [IsUnipotent,IsUnipotent],\n function(u1,u2)\n local sys1,sys2,\n generic,result,coeffs1,coeffs2,\n APR,avars,pr_len,\n i;\n\n sys1:=chevalleyAdj(u1);\n sys2:=chevalleyAdj(u2);\n if type(sys1)<>type(sys2) or\n rank(sys1)<>rank(sys2) or\n ring(sys1)<>ring(sys2) then Error(\"Not in the same family.\"); fi;\n \n return Unipotent(sys2,Concatenation(coefficients(u1),coefficients(u2)),Ordering(u2));\nend);\n\nInstallMethod(\\,\n \"Action of unipotent element u on nilpotent e: ue\",\n [IsUnipotent,IsNilpotentChv],\n function(u,e)\n local result,\n sys1,sys2,Mrsi,pr,\n uas,r,s,i,pos;\n \n sys1:=chevalleyAdj(u);\n sys2:=chevalleyAdj(e);\n if type(sys1)<>type(sys2) or\n rank(sys1)<>rank(sys2) or\n ring(sys1)<>ring(sys2) then Error(\"Not in the same family.\");\n fi;\n \n pr:=positiveRoots(sys1);\n Mrsi:=M(sys1);\n\n uas:=Reversed(coefficients(u));\n result:=List(coefficients(e),i->ShallowCopy(i));\n\n # for this see Carter pg.64\n for r in uas do\n for s in result do\n for i in [1..Length(Mrsi[r[1]][s[1]])] do\n pos:=Position(pr,ipr[r[1]]+pr[s[1]]);\n result:=Concatenation(result,[[pos,Mrsi[r[1]][s[1]][i]r[2]^is[2]]]);\n od;\n od;\n od;\n\n return NilpotentChv(sys2,result);\nend);\n\nInstallMethod(OrderOp,\n \"Order of unipotent element\",\n [IsUnipotent],\n function(u)\n local result,\n p,u_to_p,putere,i;\n\n if coefficients(u)=[] then return 1; fi;\n\n p:=Characteristic(chevalleyAdj(u));\n\n u_to_p:=u;\n for i in [1..p-1] do u_to_p:=u_to_pu; od;\n\n result:=1;\n putere:=u_to_p;\n while coefficients(putere)<>[] do\n putere:=putereu_to_p;\n result:=result+1;\n od;\n \n return presult;\nend);\n\nInstallMethod(Comm,\n \"Commutator for unipotent elements a^-1b^-1ab with the ordering of b\",\n [IsUnipotent,IsUnipotent],\n function(u1,u2)\n local sys1,sys2;\n\n sys1:=chevalleyAdj(u1);\n sys2:=chevalleyAdj(u2);\n if type(sys1)<>type(sys2) or\n rank(sys1)<>rank(sys2) or\n ring(sys1)<>ring(sys2) then Error(\"Not in the same family.\"); fi;\n return Unipotent(sys2,\n Concatenation(coefficients(u1^-1),coefficients(u2^-1),\n coefficients(u1),coefficients(u2)),\n Ordering(u2));\nend);\n\nInstallMethod(Conj,\n \"Conjugation for unipotent elements b^-1ab with the ordering of b\",\n [IsUnipotent,IsUnipotent],\n function(u1,u2)\n local sys1,sys2;\n\n sys1:=chevalleyAdj(u1);\n sys2:=chevalleyAdj(u2);\n if type(sys1)<>type(sys2) or\n rank(sys1)<>rank(sys2) or\n ring(sys1)<>ring(sys2) then Error(\"Not in the same family.\"); fi;\n return Unipotent(sys2,\n Concatenation(coefficients(u2^-1),coefficients(u1),coefficients(u2)),\n Ordering(u2));\nend);\n\nInstallMethod(Subword,\n \"Subword of a unipotent element by list of roots\",\n [IsUnipotent,IsList],\n function(u,l)\n local coeffs;\n coeffs:=Filtered(coefficients(u),i->i[1] in l);\n \n return Unipotent(chevalleyAdj(u),coeffs,Ordering(u));\nend);\n\nInstallMethod(InsertWord,\n \"Shuffles a word into a unipotent element u according to the ordering of u\",\n [IsUnipotent,IsList],\n function(u,word)\n local coeffs,\n sys,check,ord;\n\n sys:=chevalleyAdj(u);\n check:=ForAll(word,i-> i[2] in ring(sys));\n if not check then\n Error(\"The word cannot be shuffled into u: not over the same ring!\\n\");\n fi;\n\n coeffs:=coefficients(u);\n coeffs:=Concatenation(coeffs,word);\n ord:=Ordering(u);\n Sort(coeffs,function(a,b) return ord[a[1]]<ord[b[1]]; end);\n coeffs:=Canonic(sys,coeffs,ord);\n\n# Setcoefficients(u,coeffs); Doesn't work this way\n\n return Unipotent(sys,coeffs,Ordering(u));\nend);\n\n\n#\n# ---------- Lie Algebra Action ----------\n#\n\nInstallMethod(AduAlphat,\n \"Adu_{alpha}(t) on the whole Lie algebra\",\n [IsChevalleyAdj,IsPosInt,IsRingElement],\n function(sys,root,param)\n local result,\n pr,pr_len,roots,\n A_rs,M_rsi,\n L,CB,Rank,B,cochars,h,\n tmp,zero,unu,s,i,poz;\n\n pr:=positiveRoots(sys);\n pr_len:=Length(pr);\n roots:=Concatenation(pr,-pr);\n \n L:=lieAlgebra(sys);\n CB:=ChevalleyBasis(L);\n Rank:=rank(sys);\n B:=Basis(L);\n cochars:=Cocharacters(L);\n cochars:=List(cochars,i->Coefficients(B,i));\n \n zero:=Zero(ring(sys));\n unu:=One(ring(sys));\n\n A_rs:=A(sys);\n M_rsi:=M(sys);\n\n result:=[];\n # s in positive roots\n for s in [1..pr_len] do\n tmp:=List([1..Dimension(L)],i->zero);\n \n if s = root then\n tmp[s]:=unu;\n else\n tmp[s]:=unu;\n for i in [1..Length(M_rsi[root][s])] do\n poz:=Position(roots,iroots[root]+roots[s]);\n tmp[poz]:=M_rsi[root][s][i]param^i;\n od;\n fi;\n Add(result,tmp);\n od;\n\n # s in negative roots\n for s in [1..pr_len]+pr_len do\n tmp:=List([1..Dimension(L)],i->zero);\n \n if s = root+pr_len then\n # e_{-r}\n tmp[s]:=unu;\n # -t^2e_{r}\n tmp[root]:=-param^2;\n # th_{r}\n tmp:=tmp+paramcochars[root];\n else\n tmp[s]:=unu;\n for i in [1..Length(M_rsi[root][s])] do\n poz:=Position(roots,iroots[root]+roots[s]);\n tmp[poz]:=M_rsi[root][s][i]param^i;\n od;\n fi;\n Add(result,tmp);\n od;\n\n # h_s\n for s in [1..Rank] do\n tmp:=List([1..Dimension(L)],i->zero);\n # h_s\n tmp:=tmp+cochars[s];\n # -A_{sr}te_r\n tmp[root]:=-A_rs[s][root]param;\n Add(result,tmp);\n od;\n\n return result;#TransposedMat(result);\nend);\n\nInstallMethod(Adu,\n \"Adu on the whole Lie algebra\",\n [IsUnipotent],\n function(u)\n return Product(coefficients(u),i->AduAlphat(chevalleyAdj(u),i[1],i[2]));\nend);\n\nInstallMethod(AduJordanBlocksOp,\n \"Computes Jordan Blocks of Adu using SageMath\",\n [IsUnipotent],\n function(u)\n local sage_script,current_dir,tmp_file,result,\n ad,dim,i,j;\n\n sage_script:=Concatenation(\"~/sage/sage-4.7.2-linux-32bit-ubuntu_10.04_lts-i686-Linux/sage \",\n \"~/workspace/ChevalleyAdj/sage/tmp/jordan.sage\");\n current_dir:=Directory(\"~/workspace/ChevalleyAdj/sage/tmp/\");\n tmp_file:=Filename(current_dir,\"matrix.sage\");\n result:=Filename(current_dir,\"blocks.gap\");\n\n #while IsPolynomialRing(ring(chevalleyAdj(u))) do u:=Descend(u,CoefficientsRing(ring(chevalleyAdj(u)))); od;\n if IsAlgebraicU(chevalleyAdj(u)) then u:=Descend(u,chevalleyAdj(chevalleyAdj(u))); fi;\n ad:=Adu(u);\n ad:=List(ad,i->List(i,j->Int(j)));\n PrintTo(tmp_file,\"p=\",String(Characteristic(chevalleyAdj(u))),\"\\nmat=\");\n AppendTo(tmp_file,\"[\");\n dim:=Length(ad);\n for i in [1..dim] do\n AppendTo(tmp_file,\"[\");\n for j in [1..dim] do\n AppendTo(tmp_file,String(ad[i][j]));\n if j<>dim then AppendTo(tmp_file,\",\"); fi;\n od;\n AppendTo(tmp_file,\"]\");\n if i<>dim then AppendTo(tmp_file,\",\\n\"); fi;\n od;\n AppendTo(tmp_file,\"]\");\n\n Exec(sage_script);\n\n result:=ReadAsFunction(result);\n result:=result();\n\n return result;\nend);\n\nInstallMethod(PositiveAdu,\n \"Ad(u) restricted to Lie(U) where U is spanned by positive root groups\",\n [IsUnipotent],\n function(u)\n local result,\n sys,\n baza,b,pr,pr_len;\n\n sys:=chevalleyAdj(u);\n pr:=positiveRoots(sys);\n pr_len:=Length(pr);\n baza:=List([1..pr_len],i->NilpotentChv(sys,[[i,1]]));\n\n result:=[];\n for b in baza do\n result:=Concatenation(result,[ub]);\n od;\n\n return List(result,i->LieAlgebraCoeffs(i){[1..pr_len]});\nend);\n\nInstallMethod(RestrictedAdu,\n \"Ad(u) restricted to a subspace of Lie(U) spanned given (positive) roots\",\n [IsUnipotent,IsList],\n function(u,roots)\n local sys,adu,pr,\n croots,check;\n\n if not IsInt(roots[1]) then TryNextMethod(); fi;\n\n sys:=chevalleyAdj(u);\n adu:=PositiveAdu(u);\n pr:=positiveRoots(sys);\n croots:=Filtered([1..Length(pr)],i->not i in roots);\n\n check:=Filtered(Concatenation(List(croots,i->adu[i]{roots})),j->j<>Zero(ring(sys)));\n if check<>[] then Error(\"Ade cannot be restricted like this.\"); fi;\n check:=Filtered(Concatenation(List(roots,i->adu[i]{croots})),j->j<>Zero(ring(sys)));\n if check<>[] then Error(\"Ade cannot be restricted like this.\"); fi;\n \n return List(roots,i->adu[i]{roots});\nend);\n\nInstallMethod(RestrictedAdu,\n \"Ad(u) restricted to a subspace of Lie(U) spanned given (positive) roots\",\n [IsUnipotent,IsList],\n 1,\n function(u,vectors)\n local result,vectors_len,\n adu,img,\n CPR,cvar_names,cvars,cvectors,sysCPR,uu,\n tmp,generic,relations,relations_len,sol,i;\n\n vectors_len:=Length(vectors);\n\n cvar_names:=List([1..vectors_len],i->Concatenation(\"c_\",String(i)));\n CPR:=PolynomialRing(ring(chevalleyAdj(u)),cvar_names);\n cvars:=IndeterminatesOfPolynomialRing(CPR);\n sysCPR:=ChevalleyAdj(chevalleyAdj(u),CPR);\n\n cvectors:=List(vectors,i->Ascend(i,sysCPR));\n uu:=Ascend(u,sysCPR);\n img:=List(cvectors,i->uui);\n\n result:=[];\n for i in [1..vectors_len] do\n tmp:=ShallowCopy(cvars);\n generic:=Sum(List([1..vectors_len],i->tmp[i]cvectors[i]));\n relations:=List(coefficients(img[i]-generic),i->i[2]);\n relations:=Filtered(relations,i->i<>Zero(CPR));\n #Error(\"!\");\n tmp:=SolveRelations(relations,cvars,tmp,CPR);\n if tmp[2]<>[] then\n #Error(\"!\");\n Print(\"RestrictedAdu: did not solve all relations! \",relations,\"\\n\");\n fi;\n tmp:=List(tmp[1],i->Value(i,cvars,cvars));\n #tmp:=Sum(List([1..vectors_len],i->tmp[i]vectors[i])); # I want the matrix\n Add(result,tmp);\n od;\n\n return result; \nend);\n\nInstallMethod(PositiveFixedspace,\n \"Ker of PositiveAdu\",\n [IsUnipotent],\n function(u)\n local result,\n adu,sys,unu,pr,pr_len,ns;\n\n sys:=chevalleyAdj(u);\n pr:=positiveRoots(sys);\n pr_len:=Length(pr);\n\n adu:=PositiveAdu(u);\n unu:=DiagonalMat(List([1..pr_len],i->One(ring(sys))));\n ns:=NullspaceMat(adu-unu);\n\n result:=List(ns,v->List([1..pr_len],j->[j,v[j]]));\n result:=List(result,i->NilpotentChv(sys,i));\n \n return result;\nend);\n\nInstallMethod(RestrictedFixedspace,\n \"Ker of RestrictedAdu\",\n [IsUnipotent,IsList],\n function(u,roots)\n local result,\n radu,sys,unu,roots_len,ns;\n\n sys:=chevalleyAdj(u);\n roots_len:=Length(roots);\n\n radu:=RestrictedAdu(u,roots);\n unu:=DiagonalMat(List([1..roots_len],i->One(ring(sys))));\n ns:=NullspaceMat(radu-unu);\n\n result:=List(ns,v->List([1..roots_len],j->[roots[j],v[j]]));\n result:=List(result,i->NilpotentChv(sys,i));\n \n return result;\nend);\n\n\n", "meta": {"hexsha": "a1d3fc619e8b254502d90afd9af6b356c5182013", "size": 19936, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "lib/unichv.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/unichv.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/unichv.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": 35.4103019538, "max_line_length": 126, "alphanum_fraction": 0.4629313804, "num_tokens": 4607, "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(JoinDirectSums, RuleSet);\nRewriteRules(JoinDirectSums, rec(\n combine := ARule(Compose, [@(1, DelayedDirectSum), @(2, DelayedDirectSum,\n e -> let(c1:=@(1).val.children(), c2:=e.children(), Length(c1) = Length(c2) and ForAll([1..Length(c1)], i->c1[i].dims()[2] = c2[i].dims()[1]))) ],\n e -> let(c1:=@(1).val.children(), c2:=@(2).val.children(), [ DelayedDirectSum(List([1..Length(c1)], i -> c1[i] * c2[i])) ])\n )\n));\n\nClass(TerminateDirectSums, RuleSet);\nRewriteRules(TerminateDirectSums, rec(\n terminate := Rule(@(1, DelayedDirectSum), e-> DirectSum(@(1).val.children()).sums())\n));\n", "meta": {"hexsha": "964158d586ae0f472c596ce652b5faf1735eff5b", "size": 694, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/sigma/directsum.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/sigma/directsum.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/sigma/directsum.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": 38.5555555556, "max_line_length": 154, "alphanum_fraction": 0.6325648415, "num_tokens": 226, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7090191337850932, "lm_q2_score": 0.600188359260205, "lm_q1q2_score": 0.42554503059056686}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n# ==========================================================================\n# Sparse\n# ==========================================================================\nClass(Sparse, BaseMat, rec(\n new := meth(self, L)\n Constraint(IsList(L));\n\tif not ForAll(L, t -> IsList(t) and Length(t)=3 and \n\t\t IsInt(t[1]) and IsInt(t[2])) then\n\t Error(\"<L> must be a list of triples [i, j, a_(i,j)]\");\n\tfi;\t\n return SPL(WithBases( self, rec( element := L,\n\t\t\t\t dimensions := [ Maximum(List(L, t->t[1])),\n\t\t\t\t Maximum(List(L, t->t[2])) ]\n )));\n end,\n #-----------------------------------------------------------------------\n dims := self >> [ Maximum(List(self.element, t->t[1])), \n\t Maximum(List(self.element, t->t[2])) ],\n #-----------------------------------------------------------------------\n isPermutation := False, \n #-----------------------------------------------------------------------\n isReal := self >> ForAll(self.element, t -> IsRealNumber(t[3])),\n #-----------------------------------------------------------------------\n toAMat := self >> AMatMat(List(MatSparseSPL(self), r -> List(r, EvalScalar))),\n #-----------------------------------------------------------------------\n transpose := meth(self) # we use CopyFields to copy all fields of self\n local L, t;\n\tL := [ ];\n\tfor t in self.element do\n\t Add(L, [t[2], t[1], t[3]]);\n\tod;\n\treturn CopyFields(self, rec(element := L, \n\t\t dimensions := Reversed(self.dims())));\n end,\n conjTranspose := meth(self) # we use CopyFields to copy all fields of self\n local L, t;\n\tL := [ ];\n\tfor t in self.element do\n\t Add(L, [t[2], t[1], Global.Conjugate(t[3])]);\n\tod;\n\treturn CopyFields(self, rec(element := L, \n\t\t dimensions := Reversed(self.dims())));\n end,\n #-----------------------------------------------------------------------\n arithmeticCost := meth(self, costMul, costAddMul)\n local cost, row, elms;\n\tcost := costMul(0) - costMul(0); # will work even when costMul(0) <> 0\n\tfor row in [1..self.dimensions[1]] do\n\t elms := Filtered(self.element, e -> e[1]=row);\n\t if Length(elms) > 0 then\n\t\tcost := cost + costMul(elms[1][3]) \n\t\t + Sum(elms{[2..Length(elms)]}, e -> costAddMul(e[3]));\n\t fi;\n\tod;\n\treturn cost;\n end\n));\n\n", "meta": {"hexsha": "98600b50d9d7c68e417c1239c5f00dd26879f3ca", "size": 2474, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/spl/Sparse.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/Sparse.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/Sparse.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": 38.65625, "max_line_length": 82, "alphanum_fraction": 0.4114793856, "num_tokens": 583, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7090191214879992, "lm_q2_score": 0.600188359260205, "lm_q1q2_score": 0.42554502320999416}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n\n#F RuleTreeOps.\\=( <ruletree1>, <ruletree2> )\n#F returns true if <ruletree1> and <ruletree2> are equal, i.e., they\n#F represent the same breakdown strategy. Otherwise, false is returned.\n#F\n\nRuleTreeOps := CantCopy(OperationsRecord(\"RuleTreeOps\"));\n\n\nIsRuleTree := T -> IsRec(T) and IsBound(T.isRuleTree) and T.isRuleTree;\n\n\n#F Ruletrees\n#F =========\n#F\n#F A ruletree is a record with the following mandatory fields:\n#F\n#F isRuleTree = \"true\" # identifies ruletrees\n#F operations = RuleTreeOps # operations record\n#F node = <spl> # the spl expanded\n#F transposed = false/true # indicates whether <rule> or\n#F transpose - <rule> - transpose\n#F rule = <rule> # the rule chosen\n#F children = <list> # the children, a list of\n#F ruletrees/non-terminal spls\n#F\n#F Note that children can be a list of ruletrees as well as non-terminal spls.\n#F The field children is empty iff the ruletree is a leaf.\n#F In general, the .node is a non-terminal spl that is expanded by .rule.\n#F\n#F The following fields are optional:\n#F splOptions = [ <option1>, <option2>, .. ]\n#F valid <options> : \"unrolled\", \"pcl\"\n#F\n\nClass(RuleTreeClass, rec(\n spl := self >> SPLRuleTree(self),\n measure := self >> SPLRuleTree(self).measure(),\n shortPrint := false,\n dims := self >> self.node.dims(),\n dmn := self >> self.node.dmn(),\n rng := self >> self.node.rng(),\n\n print := meth(self, i, is)\n local ch;\n\n if Length(self.children) = 0 then\n # print leaves in one line\n Print(self.rule, \"( \");\n When (self.transposed, Print(\"\\\"T\\\",\"));\n self.node.print(i+is, is);\n When (IsBound(self.splOptions),\n Print(\", \", self.splOptions, \" )\"),\n Print(\" )\"));\n else\n # print children on separate lines\n Print(self.rule, \"( \",\n When(self.transposed, \"\\\"T\\\", \", \"\"),\n When(not self.shortPrint, self.node.print(i+is, is), \"\"), \",\\n\", Blanks(i+is)\n );\n self.children[1].print(i+is, is);\n for ch in Drop(self.children, 1) do\n Print(\",\\n\", Blanks(i+is));\n ch.print(i+is, is);\n od;\n\n When (IsBound(self.splOptions),\n Print(\"\\n\", Blanks(i), \", \", self.splOptions, \" )\"),\n Print(\" )\"));\n fi;\n end,\n\n # new with tSPL and opts.baseHash:\n # we cannot blindly transpose everything, as vector\n # permutations that are automatically generated\n # may not support transposition\n transpose := self >>\n When((not self.node.transposeSymmetric()) and self.node.isSymmetric(),\n self,\n RuleTree(\n self.rule,\n When(self.transposed, \"\", \"T\"),\n self.node.transpose(),\n List(self.children, x->x.transpose())\n )\n ),\n # RuleTreeRewriting enabled by default\n # one can disable it with \"EnableRuleTreeRewriting(false)\"\n rChildren := (self) >> [ self.node, self.children ],\n rSetChild := rSetChildFields(\"node\", \"children\"),\n from_rChildren := (self, rch) >>\n RuleTree(self.rule, When(self.transposed, \"T\", \"\"), rch[1], rch[2])\n));\n\nRuleTreeOps.\\= := function( T1, T2 )\n return\n IsRuleTree(T1) and IsRuleTree(T2) and\n T1.rule = T2.rule and\n T1.transposed = T2.transposed and\n IsIdenticalSPL(T1.node, T2.node) and\n T1.children = T2.children and\n ( ( IsBound(T1.splOptions) and \n\t\t IsBound(T2.splOptions) and\n T1.splOptions = T2.splOptions\n\t\t\t) or\n ( not IsBound(T1.splOptions) and \n\t\t\t not IsBound(T2.splOptions)\n\t\t\t)\n );\nend;\n\n#F RuleTreeNC( <rule>, <non-terminal spl>, <children> )\n#F returns the corresponding ruletree without any checking.\n\nRuleTreeNC := function ( R, S, C )\n return WithBases(RuleTreeClass,\n rec(\n isRuleTree := true,\n operations := RuleTreeOps,\n node := S,\n transposed := false,\n rule := R,\n children := C\n\t\t)\n );\nend;\n\n\n#F RuleTree(\n#F <rule>,\n#F [ \"T\" ,]\n#F <non-terminal spl>\n#F [, <children> ]\n#F [, <list-of-sploptions> ]\n#F )\n#F\n#F Creates a ruletree for <non-terminal spl>\n#F using <rule> with <children>. The <children> can be non-terminal spls\n#F or ruletrees. It is checked whether <children> can be derived\n#F from <non-terminal spl> using <rule>.\n#F If the string \"T\" is supplied, then instead of <rule>, the\n#F sequence transpose - <rule> - transpose is denoted. In this case\n#F <non-terminal spl> and <children> are also transposed. This construction\n#F avoids unnecessary recoding of rules that are just transposes of\n#F other rules. In this case, <rule> must have the field\n#F .forTransposition set to true.\n#F\n#F The argument <list-of-sploptions> provides options used for spl compilation.\n#F See top of this file for valid options; examples are \"unrolled\" and \"pcl\".\n#F <children> might be empty (default) in which case the ruletree\n#F returned is a leaf.\n#F\nRuleTree := function ( arg )\n local a, R, t, S, C, u, S1, C1, RT;\n S := false;\n t := false;\n u := [ ];\n C := [ ];\n R := false;\n\n for a in arg do\n if IsString(a) and a = \"T\" then \n\t t := true;\n elif IsList(a) and ForAll(a, IsString) then \n\t u := a;\n elif IsSPL(a) then\n\t\t\tif S=false then \n\t\t\t\tS := a;\n\t\t\telse \n\t\t\t\tAdd(C, a); \n\t\t\tfi;\n\t\telif IsRuleTree(a) then \n\t\t\tAdd(C, a);\n\t\telif IsList(a) then \n\t\t\tAppend(C, a);\n\t\telif IsRule(a) and R=false then \n\t\t\tR := a;\n\t\telse Error(\n\t\t\t\"usage: \\n\",\n\t\t\t\" RuleTree( \\n\",\n\t\t\t\" <rule>, [ \\\"T\\\" ,] <non-terminal spl> \\n\",\n\t\t\t\" [, <children> ] [, <list-of-sploptions> ] )\");\n\n\t\tfi;\n od;\n\n Constraint(IsRule(R));\n Constraint(IsSPL(S));\n\n if not IsList(u) and ForAll(u, IsString) then\n Error(\"<u> must be a list of spl options\");\n elif not (IsList(C) and ForAll(C, c -> IsSPL(c) or IsRuleTree(c))) then\n Error(\"<C> must be a list of ruletrees or non-terminal spls\");\n fi;\n\n RT := RuleTreeNC(R, S, C);\n if u <> [ ]\n\t then RT.splOptions := u;\n\tfi;\n return RT;\nend;\n\n\n#F ExtractChildrenSPL ( <spl> )\n#F returns the list of non-terminal spls contained in <spl>.\n#F The order is left first - depth first (non-terminals are\n#F always leaves.\n#F\nExtractChildrenSPL := S -> Collect(S, @.cond(IsNonTerminal));\n\n\n#F CopyRuleTree( <ruletree> )\n#F returns a copy of <ruletree>. All fields apart from .children\n#F are copied by reference.\n#F\nCopyRuleTree := function( orig )\n local new;\n new := ShallowCopy(orig);\n if IsRuleTree(new) then \n\t new.children := List(orig.children, CopyRuleTree);\n\tfi;\n return new;\nend;\n\n_matchChildren := (C1, C2) ->\n Length(C1)=Length(C2) and\n ForAll([1..Length(C1)],\n j -> IsHashIdenticalSPL(HashAsSPL(C1[j]), HashAsSPL(C2[j])) or\n (ObjId(C1[j])=InfoNt and ObjId(C2[j])=InfoNt));\n\n#F ApplyRuleTreeSPL( <ruletree>, <spl>, <opts> )\n#F creates a ruletree for <spl> using rules from the <ruletree>\n#F (if possible)\n#F Uses: opts.breakdownRules (for backwards compatibility of R.switch only)\nApplyRuleTreeSPL := function ( rtree, spl, opts )\n local i, R, C, C1, CC, children, L;\n Constraint(IsRuleTree(rtree));\n Constraint(IsSPL(spl));\n\n if rtree.transposed then\n return ApplyRuleTreeSPL(rtree.transpose(), spl.transpose(), opts).transpose();\n fi;\n\n R := rtree.rule;\n children:=[];\n\n # if <spl> was not compatible with <ruletree>.node to start with\n # then at some point there will be a split in <ruletree> that is not\n # applicable to the generated ruletree.\n if not IsApplicableRule( R, spl, opts.breakdownRules ) then\n Error(\"<rtree> can not be expanded from <spl>\");\n fi;\n\n # determine the right set of children from allChildren to be used\n # in expansion\n C1 := _allChildren(R, rtree.node, opts);\n C := List([1..Length(rtree.children)], c -> rtree.children[c].node);\n i := PositionProperty([1..Length(C1)], j -> _matchChildren(C1[j], C));\n\n # DEBUG HACK: AppendTo(\"applytree\", R, \"\\n\", C, \"\\n\", C1, \"\\n---------\\n\");\n if i = false then\n Error(\"<ruletree> can not be expanded from <spl>, could not find matching children\"); \n\tfi;\n\n # determine all children for <spl> and pick the right set\n L := _allChildren(R, spl, opts);\n if i > Length(L) then\n Error(\"<ruletree> can not be expanded from <spl>\");\n else\n C1 := L[i];\n fi;\n\n # recurse and return\n children := List([1..Length(rtree.children)], i -> ApplyRuleTreeSPL(rtree.children[i], C1[i], opts));\n\n return RuleTreeNC(R, spl, children);\nend;\n\n\n#F Printing RuleTrees\n#F ------------------\n#F\n\n#F RuleTreeOps.Print( <ruletree> [, <indent> , <indentStep> ] )\n#F prints <ruletree> with <indent>. Further indenting is done\n#F in steps of size <indentStep>. The default is\n#F indent = 0, indentStep = 2.\n#F\nRuleTreeOps.Print := function ( arg )\n local T, indent, indentStep; \n\tif Length(arg) = 1 then\n T := arg[1];\n indent := 0;\n indentStep := 2;\n elif Length(arg) = 3 then\n T := arg[1];\n indent := arg[2];\n indentStep := arg[3];\n else\n Error(\"usage: RuleTreeOps.Print( <ruletree> [, <indent> , <indentStep> ] )\");\n fi;\n Constraint(IsRuleTree(T));\n Constraint(IsPosInt0(indent));\n Constraint(IsPosInt0(indentStep));\n T.print(indent, indentStep);\nend;\n\nPrintRuleTreeCustom := function (T, i, is, spl_print, ruletree_print)\n local ch;\n Constraint(IsRuleTree(T) or IsSPL(T));\n Constraint(IsPosInt0(i));\n Constraint(IsPosInt0(is));\n\n if IsSPL(T) then \n spl_print(T);\n else # T is a ruletree\n Print(Blanks(i), ruletree_print(T), \"\\n\");\n for ch in T.children do\n PrintRuleTreeCustom(ch, i+is, is, spl_print, ruletree_print);\n od;\n fi;\nend;\n\n#F PrintNodesRuleTree(\n#F <ruletree/non-terminal spl> [, <indent> , <indentStep> ]\n#F )\n#F pretty prints <ruletree> by displaying only the nodes (non-terminals)\n#F and its parameters. The tree structure is expressed by indentation.\n#F Non-terminals are being marked by (nt).\n#F\n\nPrintNodesRuleTree := function ( arg )\n local T, i, is;\n if Length(arg) = 1 then\n T := arg[1]; \n\t\ti := 0; \n\t\tis := 2;\n elif Length(arg) = 3 then\n T := arg[1];\n\t\ti := arg[2];\n\t\tis := arg[3];\n else\n Error(\"usage: PrintNodesRuleTree( <ruletree> [, <indent> , <indentStep> ] )\");\n fi;\n PrintRuleTreeCustom(T, i, is,\n T -> Print(T, \" (nt)\"),\n T -> Print(T.node));\nend;\n\n\n#F PrintRulesRuleTree(\n#F <ruletree/non-terminal spl> [, <indent> , <indentStep> ]\n#F )\n#F pretty prints <ruletree> by displaying only the rules and\n#F the node sizes in parentheses. Transposed rules are marked\n#F by ^T. The tree structure is expressed by indentation.\n#F Non-terminals are denoted by nt.\n#F\nPrintRulesRuleTree := function(arg)\n local T, i, is;\n if Length(arg) = 1 then\n T := arg[1]; i := 0; is := 2;\n elif Length(arg) = 3 then\n T := arg[1]; i := arg[2]; is := arg[3];\n else\n Error(\"usage: PrintRulesRuleTree( <ruletree> [, <indent> , <indentStep> ] )\");\n fi;\n PrintRuleTreeCustom(T, i, is,\n T -> Print(\"nt (\", T.dimensions[1], \")\"),\n T -> Print(T.rule, When(T.transposed,\" ^ T\",\"\"), \"(\", T.node.dimensions[1], \")\"));\nend;\n\n\n\n#F PrettyPrintRuleTree(\n#F <ruletree/non-terminal spl> [, <whiteIndent> [, <linedIndent> ] ]\n#F )\n#F pretty prints <ruletree> by displaying only the nodes (non-terminals),\n#F their parameters, and the rules. The tree structure is expressed by\n#F indentation. Non-terminals are being marked by (nt).\n#F\n\nPrettyPrintRuleTree := function ( arg )\n local T, chIndent, whiteIndent, linedIndent, oldLinedIndent, newline, params, i;\n\n # new line plus indents\n newline := function ( )\n local i;\n\n Print(\"\\n\");\n for i in [1..whiteIndent] do\n Print(\" \");\n od;\n if not linedIndent = \"\" then\n Print( linedIndent, \"--\" );\n fi;\n end;\n\n # decode arg\n if Length(arg) = 1 then\n T := arg[1];\n whiteIndent := 0;\n linedIndent := \"\";\n elif Length(arg) = 2 then\n T := arg[1];\n whiteIndent := arg[2];\n linedIndent := \"\";\n elif Length(arg) = 3 then\n T := arg[1];\n whiteIndent := arg[2];\n linedIndent := arg[3];\n else\n Error(\"usage: PrintNodesRuleTree( <ruletree> [, <indent> , <indentStep> ] )\");\n fi;\n\n # check arguments\n if not ( IsRuleTree(T) or IsSPL(T) and T.type = \"nonTerminal\" ) then\n Error(\"<T> must be a ruletree or a non-terminal spl\");\n fi;\n if not IsInt(whiteIndent) and whiteIndent >= 0 then\n Error(\"<whiteIndent> must be pos-int\");\n fi;\n if not IsString(linedIndent) then\n Error(\"<linedIndent> must be a string\");\n fi;\n\n chIndent := whiteIndent+Length(linedIndent)+4;\n # spl case\n if IsSPL(T) then\n T.print(chIndent, 2); Print(\" (nt)\");\n return;\n fi;\n \n T.node.print(chIndent, 2);\n Print(\" {\" );\n Print(T.rule);\n if T.transposed then\n Print(\" ^ T\");\n fi;\n if IsBound(T.splOptions) then\n Print(\", \", T.splOptions);\n fi;\n Print( \"}\" );\n\n if Length(T.children) > 0 then\n if linedIndent = \"\" then\n oldLinedIndent := linedIndent;\n else\n oldLinedIndent := Concatenation( linedIndent, \" \" );\n fi;\n linedIndent := Concatenation( oldLinedIndent, \" \|\" );\n for i in [1..Length(T.children)-1] do\n newline();\n PrettyPrintRuleTree(T.children[i], whiteIndent, linedIndent);\n od;\n linedIndent := Concatenation( oldLinedIndent, \" \\`\" );\n newline();\n linedIndent := Concatenation( oldLinedIndent, \" \" );\n PrettyPrintRuleTree(T.children[Length(T.children)],\n whiteIndent, linedIndent);\n linedIndent := oldLinedIndent;\n fi;\n if whiteIndent = 0 and linedIndent = \"\" then\n newline();\n fi;\nend;\n\n\n#F Converting RuleTrees\n#F --------------------\n#F\n\n#F AMatRuleTree( <ruletree> ) - returns an amat corresponding to ruletree.\n#F\nAMatRuleTree := T -> AMatSPL(SPLRuleTree(T));\n\n#F MatRuleTree( <ruletree> ) - returns the matrix corresponding to ruletree.\n#F\nMatRuleTree := T -> MatSPL(SPLRuleTree(T));\n\n\n#F Creating Random RuleTrees\n#F -------------------------\n#F\n\nDeclare(SemiRandomRuleTree, _SemiRandomRuleTree);\n\n#F RandomRuleTree( <spl> , <opts>)\n#F returns a random rule tree for <spl>\n#F or 'false' if no breakdown rule combination leads to a\n#F fully expanded ruletree.\n#F\n#F Uses: opts.baseHashes\n#F opts.breakdownRules\n#F Optional: (see Doc(_allChildren) ) for usage\n#F opts.restrictSplit\n#F opts.restrictSplitSize\n#F\nRandomRuleTree := (spl, opts) -> _SemiRandomRuleTree(spl, false, s->false, opts);\n\nRandomRuleTreeCutoff := (spl, cutoff_func, opts) -> _SemiRandomRuleTree(spl, false, cutoff_func, opts);\n\nRandomRuleTreeDP := (t, opts) -> let(res := spiral.search.DP(t, rec(measureFunction := (R,O)->Random([1..10000]), verbosity := 0), opts), When(res = [], false, res[1].ruletree));\n\n#F SemiRandomRuleTree( <spl>, <top_rule>, opts )\n#F returns a random rule tree for <spl> with fixed top-level rule\n#F or 'false' if no breakdown rule combination leads to a\n#F fully expanded ruletree.\n#F\n#F Uses: opts.baseHashes\n#F opts.breakdownRules\n#F Optional: (see Doc(_allChildren) ) for usage\n#F opts.restrictSplit\n#F opts.restrictSplitSize\n#F\nSemiRandomRuleTree := (spl, top_rule, opts) -> _SemiRandomRuleTree(spl, top_rule, s->false, opts);\n\n\n_SemiRandomRuleTree := function(spl, top_rule, cutoff_func, opts)\n local ch, i, R, rules, rule, rand, candidates, ch, children, ch_candidates;\n\n if not (IsSPL(spl)) then\n Error(\"usage: SemiRandomRuleTree( <spl>, <top_rule>, <cutoff>, <opts> )\");\n elif cutoff_func(spl) then\n\t return spl;\n elif MultiHashLookup(opts.baseHashes, spl) <> false then\n return MultiHashLookup(opts.baseHashes, spl)[1].ruletree;\n else\n if top_rule <> false then\n rules := [top_rule];\n else\n rules := AllApplicableRulesDirect(spl, opts.breakdownRules);\n if rules = [ ] then\n return false;\n fi;\n fi;\n\n candidates := Set([1..(Length(rules))]);\n while candidates <> [] do\n rand := RandomList(candidates);\n RemoveSet(candidates, rand);\n\n if rand <= Length(rules) then\n rule := rules[rand];\n ch_candidates := _allChildren(rule, spl,opts);\n ch_candidates := Permuted(ch_candidates, Random(SymmetricGroup(Length(ch_candidates))));\n for children in ch_candidates do\n children := List( children, s -> _SemiRandomRuleTree(s, false, cutoff_func, opts) );\n if not ForAny(children, c -> IsBool(c) and c=false) then\n return RuleTreeNC( rule, spl, children );\n fi;\n od;\n fi;\n od;\n return false;\n fi;\nend;\n\n\n#F Creating all RuleTrees\n#F ----------------------\n#F\n#ExpandSPLRules := function( S, ruleset )\nExpandSPLRules := function( arg )\n local i, L, R, S, ruleset, opts;\n S := arg[1];\n ruleset := arg[2];\n Constraint(IsSPL(S));\n\n if IsBound(arg[3]) then\n\t opts := arg[3];\n else \n\t opts := rec();\n\tfi;\n\n L := [ ];\n for R in AllApplicableRulesDirect(S, ruleset) do\n Append(L, List(_allChildren(R,S,opts), c -> RuleTreeNC(R, S, c)));\n od;\n\n return L;\nend;\n\n#F ExpandSPL( <spl>, <opts> )\n#F performs one expansion of <spl> in all possible ways,\n#F and returns the list of the derived ruletrees.\n#F If there are no breakdown rules for <spl> (i.e., not a non-terminal)\n#F then the default base cases rule @_Base is used, which means that\n#F the recursion will continue on its children\n#F\n#F Uses: opts.baseHashes\n#F opts.breakdownRules\n#F\nExpandSPL := (S, opts) -> ExpandSPLRules(S, opts.breakdownRules, opts);\n\n\n_AllRuleTrees := function ( S, cutoff, memohash, opts )\n local L, L1, T, Lc, i, cs, T1, lkup;\n\n # check cutoff, baseHashes, and our memoization hash\n if cutoff(S) then\n\t\treturn [S];\n\tfi;\n lkup := MultiHashLookup(opts.baseHashes, S);\n if lkup <> false then\n\t\treturn [lkup[1].ruletree];\n\tfi;\n\n lkup := HashLookup(memohash, S);\n if lkup <> false\n\t\tthen return lkup;\n\tfi;\n\n L := ExpandSPL(S, opts);\n if ForAll(L, r -> r.children = [ ]) then\n\t\tHashAdd(memohash, S, L);\n\t\treturn L;\n fi;\n\n L1 := [ ];\n for T in L do\n Lc := [ ];\n\t\tfor i in [1..Length(T.children)] do\n Lc[i] := _AllRuleTrees(T.children[i], cutoff, memohash, opts);\n\t\tod;\n\t\tfor cs in Cartesian(Lc) do\n T1 := ShallowCopy(T);\n\t\t\tT1.children := cs;\n\t\t\tAdd(L1, T1);\n\t\tod;\n od;\n\n HashAdd(memohash, S, L1);\n return L1;\nend;\n\n#F AllRuleTrees( <spl>, <opts> )\n#F expands <spl> in all possible ways and returns the obtained list\n#F of fully expanded ruletrees (ruletrees containing no non-terminals).\n#F Note that subtrees are \"by reference\", i.e., modifying one subtree\n#F alters the same subtree in some other expansions.\n#F\n#F Uses: opts.baseHashes\n#F opts.breakdownRules\n#F Optional: (see Doc(_allChildren) ) for usage\n#F opts.restrictSplit\n#F opts.restrictSplitSize\n#F\nAllRuleTrees := (S, opts) -> _AllRuleTrees(S, x->false, HashTableSPL(), opts);\n\n#F AllRuleTreesCutoff( <spl>, <cutoff_func>, <opts> )\n#F expands <spl> in all possible ways and returns the obtained list\n#F of fully expanded ruletrees (ruletrees containing no non-terminals).\n#F Note that subtrees are \"by reference\", i.e., modifying one subtree\n#F alters the same subtree in some other expansions.\n#F <cutoff_func> is of the form e -> e = <cutoff>\n#F\n#F Uses: opts.baseHashes\n#F opts.breakdownRules\n#F\nAllRuleTreesCutoff := (S, cutoff_func, opts) -> _AllRuleTrees(S, cutoff_func, HashTableSPL(), opts);\n\n\n\n_NofRuleTrees := function ( S, cutoff, memohash, opts, level, trace )\n local p, Cs, n, lkup, indentstr, i;\n Constraint(IsSPL(S));\n Constraint(IsRec(opts));\n\n if trace then\n indentstr := \"\";\n for i in [2..level] do\n indentstr := Concat(indentstr, \". \");\n od;\n indentstr := Concat(indentstr, String(level), \" \");\n Print(indentstr, \">> _NofRuleTrees(\", S, \")\\n\");\n fi;\n\n # check cutoff, baseHashes, and our memoization hash\n if cutoff(S) then\n if trace then\n Print(indentstr, \"<< (cutoff) 1\\n\");\n fi;\n return 1; \n fi;\n if MultiHashLookup(opts.baseHashes, S) <> false then\n if trace then\n Print(indentstr, \"<< (MultiHashLookup) 1\\n\");\n fi;\n return 1; \n fi;\n lkup := HashLookup(memohash, S);\n if lkup <> false then\n if trace then\n Print(indentstr, \"<< hashed: \", lkup, \"\\n\");\n fi;\n return lkup; \n fi;\n\n # first apply rules as they are\n Cs := List(AllApplicableRulesDirect(S, opts.breakdownRules), r -> _allChildren(r,S, opts));\n\tif trace then\n Print(indentstr, \" Cs: \", Cs, \"\\n\");\n fi;\n\n if Cs = [ [ ] ] then\n n := 1;\n else\n n := Sum(Cs, c -> Sum(c, l -> Product(l, x -> _NofRuleTrees(x, cutoff, memohash, opts, level+1, trace))));\n fi;\n\n HashAdd(memohash, S, n);\n \n if trace then\n Print(indentstr, \"<< (\", S, \") \", n, \"\\n\");\n fi;\n \n return n;\nend;\n\n#F NofRuleTrees ( <spl>, <opts> )\n#F returns the number of ruletrees for <spl>.\n#F\n#F Uses: opts.baseHashes\n#F opts.breakdownRules\n#F Optional: (see Doc(_allChildren) ) for usage\n#F opts.restrictSplit\n#F opts.restrictSplitSize\n#F\n#F if opts.verbosity > 3 prints trace info\n\nNofRuleTrees := (spl, opts) -> _NofRuleTrees(spl, x->false, HashTableSPL(), opts, 1, IsBound(opts.verbosity) and (opts.verbosity > 3));\n\nNofRuleTreesCutoff := (spl, cutoff_func, opts) -> _NofRuleTrees(spl, cutoff_func, HashTableSPL(), opts, 1, IsBound(opts.verbosity) and (opts.verbosity > 3));\n\n\n#F RulesInRuleTree( <ruletree> )\n#F return the set of rules contained in <ruletree>.\n#F\nRulesInRuleTree := function ( T )\n local C;\n Constraint(IsRuleTree(T));\n\n # base case\n if T.children = [ ] then\n\t return Set([T.rule]);\n\tfi;\n\n # recurse with ruletree children\n C := Filtered(T.children, IsRuleTree);\n C := Set(Concatenation(List(C, RulesInRuleTree)));\n AddSet(C, T.rule);\n return C;\nend;\n\n\n#F RulesInRuleTreeAll( <ruletree> )\n#F return the histogram of all rules contained in <ruletree> as set\n#F of pairs [rule, number].\n#F\nRulesInRuleTreeAll := function ( T )\n local C, C1, c, i;\n Constraint(IsRuleTree(T));\n\n # base case\n if T.children = [ ] then\n\t return Set([ [T.rule, 1] ]);\n\tfi;\n\n # recurse with ruletree children\n C := Filtered(T.children, IsRuleTree);\n C := Concatenation(List(C, RulesInRuleTreeAll));\n\n # merge\n C1 := [ ];\n for c in C do\n i := PositionProperty(C1, p -> c[1] = p[1]);\n if i = false then\n AddSet(C1, c);\n else\n C1[i][2] := C1[i][2] + c[2];\n fi;\n od;\n\n i := PositionProperty(C1, p -> p[1] = T.rule);\n if i = false then\n AddSet(C1, [T.rule, 1]);\n else\n C1[i][2] := C1[i][2] + 1;\n fi;\n return C1;\nend;\n\n\nApplyRuleTreeStep := function ( rt, recurse )\n local nt, C, Nonterms, S, c;\n if IsNonTerminal(rt) or IsSPL(rt) then \n\t return rt;\n\tfi;\n\n Constraint(IsRuleTree(rt));\n\n C := List(rt.children, recurse);\n nt := rt.node;\n Nonterms := List(rt.children, c -> When(IsRuleTree(c), c.node, c));\n\n if rt.transposed then\n nt := TransposedSPL(nt);\n C := List(C, TransposedSPL);\n Nonterms := List(Nonterms, TransposedSPL);\n fi;\n\n S := _apply(rt.rule, nt, C, Nonterms);\n if rt.transposed then \n\t S := TransposedSPL(S); \n\tfi;\n\n trace_log.addTreeExpansion(rt.rule,nt,S,rt.children,CopyFields(rt.node, rec(params := C)), var);\n\n S.root := rt.node;\n return S;\nend;\n\nSPLRuleTreeStep := rt -> ApplyRuleTreeStep(rt, c -> RecursStep(\n When(IsRuleTree(c), RTWrap(c), c)));\n\n_SPLRuleTree := rt -> ApplyRuleTreeStep(rt, _SPLRuleTree);\n\nSPLRuleTree := function(rt)\n local spl, t, tag;\n trace_log.beginStage(\"tSPL\",\"SPL\", rt.node); \n spl := ApplyRuleTreeStep(rt, _SPLRuleTree);\n\n # tags may inject container objects\n t := rt.node;\n if IsBound(t.getTags) then\n for tag in Reversed(t.getTags()) do\n if IsBound(tag.container)\n\t\t\t then spl := tag.container(spl);\n\t\t\tfi;\n od;\n fi;\n trace_log.endStage(\"tSPL\",\"SPL\", spl); \n return spl;\nend;\n\n# forward declaration for function that does all the work.\nDeclare(_ruleTreeN);\n\n#F RandomRuleTrees( <spl>, <num>, <opts>)\n#F returns <num> random rule trees for <spl>\n#F uniformly distributed amongst the potential trees\n#F or 'false' if no breakdown rule combination leads to a\n#F fully expanded ruletree.\n#F\n#F Uses: opts.baseHashes\n#F opts.breakdownRules\n#F Optional: (see Doc(_allChildren) ) for usage\n#F\nRandomRuleTrees := function(spl, num, opts)\n local n, rand, memohash;\n\n memohash := HashTableSPL();\n\n n := _NofRuleTrees(spl, s -> false, memohash, opts, 1, false);\n\n if num >= n then\n rand := [1..n];\n else\n rand := [];\n while Length(rand) <> num do\n rand := Set(Concat(rand, [RandomList([1..n])]));\n od;\n fi;\n\n return List(rand, e -> _ruleTreeN(spl, e-1, memohash, opts));\nend;\n\n# helper functions/arrays for _ruleTreeN and _ruleTree1\n\n_getNumTrees := (s, memohash, opts) -> let(\n n := HashLookup(memohash, s), \n When(n = false,\n _NofRuleTrees(s, e -> false, memohash, opts, 1, false),\n n\n )\n);\n#F RuleTreeN(<spl>, <num>, <opts>)\n#F returns ruletree of index <num>\n#F\n#F Uses: opts.basHashes, opts.breakdownRules.\n#F\nRuleTreeN := function(spl, num, opts)\n local memohash, n, r;\n\n memohash := HashTableSPL();\n n := _NofRuleTrees(spl, s -> false, memohash, opts, 1, false);\n\n if num in [1..n] then\n r := _ruleTreeN(spl, num-1, memohash, opts);\n\n else\n r := false;\n fi;\n\n return r;\nend;\n\n\n# fold list inside out, favoring the right hand side\n\n_foldedMidFirst := function(origlist)\n\tlocal len, midpt, front, back, newlist;\n\t\n\tlen := Length(origlist);\n\tif len < 2 then\n\t\treturn origlist;\n\tfi;\n\tmidpt := Int(len/2);\n\tfront := Reversed(Sublist(origlist, [1..midpt]));\n\tback := Sublist(origlist, [midpt+1..len]);\n\t\n\tnewlist := [];\n\t\n\tif IsOddInt(len) then\n\t\tAppend(newlist, [back[1]]);\n\t\tback := Drop(back,1);\n\tfi;\n\t\n\twhile (front <> []) or (back <> []) do\n\t\tif back <> [] then\n\t\t\tAppend(newlist, [back[1]]);\n\t\t\tback := Drop(back,1);\n\t\tfi;\n\t\tif front <> [] then\n\t\t\tAppend(newlist, [front[1]]);\n\t\t\tfront := Drop(front, 1);\n\t\tfi;\t\n\tod;\n\t\n\treturn newlist;\nend;\n\n\nDeclare(_ruleTreeMid);\n\n#F RuleTreeMid(spl, opts)\n#F\n#F Similar to RuleTree1, but tries to grab the middle of each range of choices\n#F \n\nRuleTreeMid := (spl, opts) -> _ruleTreeMid(spl, HashTableSPL(), opts);\n\n_ruleTreeMid := function(spl, memohash, opts)\n local h, R, r, C, c, ch, npc, idx, idxlist, ridx, ridxlist;\n\n h := MultiHashLookup(opts.baseHashes, spl);\n\n if h <> false then\n return h[1].ruletree;\n fi;\n\n R := AllApplicableRulesDirect(spl, opts.breakdownRules);\n\tridxlist := [1..Length(R)];\n\tif Length(ridxlist) > 1 then\n\t\tif Length(_allChildren(R[1], spl, opts)) < 2 then\n\t\t\tridxlist := _foldedMidFirst(ridxlist);\n\t\tfi;\n\tfi;\n for ridx in ridxlist do\n\t\tr := R[ridx];\n\t\tC := _allChildren(r, spl, opts);\n\t\tidxlist := _foldedMidFirst([1..Length(C)]);\n\t\tfor idx in idxlist do \n\t\t\tc := C[idx];\n\t\t\tnpc := Product(c, e -> _getNumTrees(e, memohash, opts));\n\t\t\tif npc > 0 then\n\t\t\t\tch := List(c, e -> _ruleTreeMid(e, memohash, opts));\n\t\t\t\tif not ForAny(ch, e -> IsBool(e) and e=false) then\n\t\t\t\t\treturn RuleTreeNC(r, spl, ch);\n\t\t\t\tfi;\n\t\t\tfi;\n\n od;\n od;\n\t# no tree, return original spl\n return spl;\nend;\n\n\nDeclare(_ruleTree1);\n\n#F RuleTree1(spl, opts)\n#F\n#F returns the first ruletree. this is often useful for\n#F testing whether a particular rule is firing, and you\n#F want to avoid the randomness of RandomRuleTree\n#F\n#F NOTE: this function does not check if a tree can\n#F actually just be created, it just tries to return\n#F the first one. RuleTreeN(spl, 1, opts) does the\n#F same thing but first checks.\n#F \n\nRuleTree1 := (spl, opts) -> _ruleTree1(spl, HashTableSPL(), opts);\n\n_ruleTree1 := function(spl, memohash, opts)\n local h, R, r, i, c, ch, npc;\n\n h := MultiHashLookup(opts.baseHashes, spl);\n\n if h <> false then\n return h[1].ruletree;\n fi;\n\n R := AllApplicableRulesDirect(spl, opts.breakdownRules);\n for r in R do\n\t\tfor c in _allChildren(r, spl, opts) do \n\t\t\tnpc := Product(c, e -> _getNumTrees(e, memohash, opts));\n\t\t\tif npc > 0 then\n\t\t\t\tch := List(c, e -> _ruleTree1(e, memohash, opts));\n\t\t\t\tif not ForAny(ch, e -> IsBool(e) and e=false) then\n\t\t\t\t\treturn RuleTreeNC(r, spl, ch);\n\t\t\t\tfi;\n\t\t\tfi;\n od;\n od;\n\t# no tree, return original spl\n return spl;\nend;\n \n\n#F _ruleTreeN(<spl>, <num>, <memohash>, <opts>)\n#F internal function which returns a ruletree for \n#F <spl> with index given by <num>. This is a recursive\n#F routine. Note that <num> is 0-based, unlike everything\n#F else in SPIRAL, which is 1-based.\n#F \n_ruleTreeN := function(spl, num, memohash, opts)\n local R, rtNC, h, r, c, npc, off, ch, i, n, p, offset;\n\n # lookup stuff like SSE base cases.\n h := MultiHashLookup(opts.baseHashes, spl);\n\n if h <> false then\n return h[1].ruletree;\n fi;\n\n # get list of normal rules\n R := AllApplicableRulesDirect(spl, opts.breakdownRules);\n offset := 0;\n\n for r in R do\n for c in _allChildren(r, spl, opts) do \n # figure out which group of children we should be looking at.\n npc := Product(c, e -> _getNumTrees(e, memohash, opts));\n\n # is this the correct group?\n if num < offset + npc then\n off := npc;\n ch := [];\n\n # step through the kids, and push down the ruletree number\n for i in [1..Length(c)] do\n n := _getNumTrees(c[i], memohash, opts);\n\n off := When(n > 0, off / n, off);\n\n p := When(n <= 0 or num <= offset, \n 0, \n RemInt(QuoInt(num - offset, off), n)\n );\n\n # all the kids get evaluated\n Add(ch, _ruleTreeN(c[i], p, memohash, opts));\n od;\n\n # no kids should be false, but just in case.\n if not ForAny(ch, e -> IsBool(e) and e=false) then\n return RuleTreeNC(r, spl, ch);\n fi;\n fi;\n\n # fixup offset\n offset := offset + npc;\n od;\n od;\n\n\t# no tree, return original spl\n return spl;\nend;\n\nDeclare(_ruleTreeGetN);\n\n#F RuleTreeGetN(<ruletree>, <opts>)\n#F given a ruletree, determine the index\n#F\n#F uses:\n#F opts.breakdownRules\n#F opts.baseHashes\n#F\n\nRuleTreeGetN := function(ruletree, opts)\n local memohash, r;\n \n memohash := HashTableSPL();\n\n # prime the memohash.\n _NofRuleTrees(ruletree.node, s -> false, memohash, opts, 1, false);\n\n r := _ruleTreeGetN(ruletree, memohash, opts, 0);\n\n # ruleTreeGetN may return false if we couldn't match the tree in the passed\n # in breakdownRules/baseHashes.\n return When(IsInt(r), r + 1, false);\nend;\n\n_ruleTreeGetN := function(rt, memohash, opts, offset)\n local h, R, r, c, ch, off, n;\n\n # is the ruletree something from the baseHashes?\n h := MultiHashLookup(opts.baseHashes, rt.node);\n if IsList(h) and rt = h[1].ruletree then\n return offset;\n fi;\n\n R := AllApplicableRulesDirect(rt.node, opts.breakdownRules);\n\n for r in R do\n # does rule match?\n if r = rt.rule then\n for c in _allChildren(r, rt.node, opts) do\n # does child match?\n if c = List(rt.children, e -> e.node) then\n off := Product(rt.children, e -> _getNumTrees(e.node, memohash, opts));\n for ch in rt.children do\n n := _getNumTrees(ch.node, memohash, opts);\n off := When(n > 0, off / n, off);\n offset := offset + (off * _ruleTreeGetN(ch, memohash, opts, 0));\n od;\n return offset;\n # child doesn't match, increase offset\n else\n offset := offset + Product(c, e -> _getNumTrees(e, memohash, opts));\n fi; \n od;\n # rule doesn't match, so increase offset by all possible expansions we didn't use\n else\n offset := offset \n + Sum(_allChildren(r, rt.node, opts), C -> \n Product(C, c -> _getNumTrees(c, memohash, opts))\n );\n fi;\n od;\n\n return offset;\nend;\n", "meta": {"hexsha": "1d0009a09272fd41a4782af754b83ad098ad272d", "size": 33659, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/formgen/ruletree.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/formgen/ruletree.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/formgen/ruletree.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": 28.9415305245, "max_line_length": 178, "alphanum_fraction": 0.5857868624, "num_tokens": 9761, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6513548646660543, "lm_q2_score": 0.6513548646660542, "lm_q1q2_score": 0.42426315972413386}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n# ================================================================\n# Simplification of Intervals\n# ================================================================\n\nfull_II := (int, size) -> \n [int.target(II), size, 0, @.cond(e->e=size.val)];\n\nempty_II := (int, size) -> \n [int.target(II).cond(e->e.params[2]=e.params[3]), size, @, @];\n\nleft_II := (int, size, endd) -> \n [int.target(II), size, 0, endd];\n\nright_II := (int, size,start) -> \n [int.target(II), size, start, @.cond(e->e=size.val)];\n\nClass(RulesII, RuleSet);\n\nRewriteRules(RulesII, rec(\n # full II o index mapping func @(3) = II with domain of @(3)\n # II(n, 0, n) o f = II(domain(f), 0, domain(f))\n FullII_f := ARule(fCompose, [ full_II(@, @(1)), @(2) ], e -> [ II(@(2).val.domain()) ]),\n EmptyII_f := ARule(fCompose, [ empty_II(@, @(1)), @(2) ], e -> [ II(@(2).val.domain(),0,0) ]),\n\n # partial II o dirsum of perms\n # II(n, 0, k) o fDirsum(perm_k, perm_?) -> II(n,0,k)\n LeftII_fDirsum := ARule(fCompose, \n [ left_II(@(0), @(1), @(2)), [fDirsum, @(3).cond(e -> is_perm(e) and e.range()=@(2).val), ...]],\n e -> [ @(0).val ]),\n\n # partial II o dirsum of perms\n # II(n, n-k, n) o fDirsum(perm_?, perm_k) -> II(n,n-k,n)\n RightII_fDirsum := ARule( fCompose, \n [ right_II(@(0), @(1), @(2)), [fDirsum, ..., @(4).cond(e -> is_perm(e) and e.range() = @(1).val-@(2).val)]],\n e -> [ @(0).val ]),\n\n # fTensor(IIn, IIk) -> II(nk)\n fullII_tensor_fullII := ARule(diagTensor, [full_II(@(0), @(1)), full_II(@(0), @(2))], \n e -> [ II(@(1).val @(2).val) ]),\n\n # fDirsum(IIn, IIk) -> II(n+k)\n fullII_dirsum_fullII := ARule(diagDirsum, [full_II(@(0), @(1)), full_II(@(0), @(2))], \n e -> [ II(@(1).val + @(2).val) ]),\n\n diagTensor_emptyII := Rule([diagTensor, ..., empty_II(@(1), @(2)), ...], e -> II(e.domain(),0,0)),\n diagTensor_fullII_Id1 := ARule(diagTensor, [@(0), full_II(@(1), @(2).cond(e->e=1))], e -> [ @(0).val ]),\n diagTensor_fullII_Id2 := ARule(diagTensor, [full_II(@(1), @(2).cond(e->e=1)), @(0)], e -> [ @(0).val ]),\n\n\n II_dirsum_emptyII := ARule(diagDirsum, [[II, @(1), @(2), @(3)], empty_II(@(4), @(5))], \n e -> [ II(@(1).val + @(5).val), @(2).val, @(3).val ]),\n\n emptyII_dirsum_II := ARule(diagDirsum, [empty_II(@(4), @(5)), [II, @(1), @(2), @(3)]], \n e -> [ II(@(1).val + @(5).val), @(5).val + @(2).val, @(5).val + @(3).val ]),\n\n # II Shifting, we support shift left (shift <= start), and right (shift >= end)\n # II o Z = shifted II# \n II_Z := ARule(fCompose, [[II, @(1), @(2), @(3)], [Z, @(4), @(5).cond(e -> (e<=@(2).val) or (e >= @(3).val))]],\n e -> [II(@(1).val, (@(2).val-@(5).val) mod @(1).val, \n # this makes 0->size, because size mod size = 0\n let(last:=(@(3).val-@(5).val) mod @(1).val, \n When(last=0, @(1).val, last))) ]),\n\n DiagFullII_toId := Rule([Diag, full_II(@(1), @(2))], e -> I(@(2).val)),\n Diag_fConst_toId := Rule([Diag, [fConst, @(2), @(1), 1]], e -> I(@(1).val)),\n Diag_fConstV_toId := Rule([Diag, [fConst, @(2), @(1), _1]], e -> I(@(1).val)),\n\n COND_fullII := Rule([COND, full_II(@(1), @(2)), @(3), @(4)], e -> @(3).val),\n COND_emptyII := Rule([COND, full_II(@(1), @(2)), @(3), @(4)], e -> @(4).val)\n));\n", "meta": {"hexsha": "1ffde4fb9b8a73ad175686815d1f2bb4d2458ed4", "size": 3376, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/sigma/ii_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/sigma/ii_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/sigma/ii_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": 45.0133333333, "max_line_length": 116, "alphanum_fraction": 0.4721563981, "num_tokens": 1235, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6992544210587585, "lm_q2_score": 0.600188359260205, "lm_q1q2_score": 0.4196843636807008}}
	{"text": "#############################################################################\n##\n## ExternalPolymakePolytope.gi JConvex package\n## Martin Bies\n##\n## Copyright 2021 University of Pennsylvania\n##\n## A Gap package to do convex geometry by Polymake, Cdd and Normaliz\n##\n## Chapter Polytopes in Polymake\n##\n#############################################################################\n\n\n##############################################################################################\n##\n## Section GAP category of PolymakePolytopes\n##\n##############################################################################################\n\nDeclareRepresentation( \"IsPolymakePolytopeRep\", IsPolymakePolytope and IsAttributeStoringRep, [ ] );\n\nBindGlobal( \"TheFamilyOfPolymakePolytopes\", NewFamily( \"TheFamilyOfPolymakePolytopes\" ) );\n\nBindGlobal( \"TheTypeOfPolymakePolytope\", NewType( TheFamilyOfPolymakePolytopes, IsPolymakePolytopeRep ) );\n\nBindGlobal( \"MakePolymakePolytopeVRep\", function( vertices, lineality )\n local poly, kwargs, new_vertices, new_lin, v;\n poly := Objectify( TheTypeOfPolymakePolytope,\n rec( vertices := Immutable( vertices ),\n lineality := Immutable( lineality ),\n number_type := \"rational\",\n rep_type := \"V-rep\" ) );\n\n # add 1s at the beginning, since Polymake always considers polytopes as intersections with the hyperplane x0 = 1\n new_vertices := [];\n for v in vertices do\n v := ShallowCopy( v );\n Add( v, 1, 1 );\n Add( new_vertices, v );\n od;\n new_lin := [];\n for v in lineality do\n v := ShallowCopy( v );\n Add( v, 1, 1 );\n Add( new_lin, v );\n od;\n\n kwargs := rec();\n\n # TODO: verify that kwargs is set correctly, also if one or both lists are empty\n\n # check for degenerate case\n if Length( new_vertices ) > 0 then\n kwargs.POINTS := JuliaMatrixInt( new_vertices );\n\n # if we also have lineality, add them\n if Length( new_lin ) > 0 then\n kwargs.INPUT_LINEALITY := JuliaMatrixInt( new_lin );\n fi;\n elif Length( new_lin ) > 0 then\n kwargs.POINTS := JuliaMatrixInt( new_lin );\n kwargs.INPUT_LINEALITY := kwargs.POINTS;\n fi;\n\n poly!.pmobj := CallJuliaFunctionWithKeywordArguments( _Polymake_jl.polytope.Polytope, [], kwargs );\n return poly;\nend);\n\nBindGlobal( \"MakePolymakePolytopeHRep\", function( inequalities, equalities )\n local poly, kwargs;\n poly := Objectify( TheTypeOfPolymakePolytope,\n rec( inequalities := Immutable( inequalities ),\n equalities := Immutable( equalities ),\n number_type := \"rational\",\n rep_type := \"H-rep\" ) );\n\n kwargs := rec();\n\n # TODO: verify that kwargs is set correctly, also if one or both lists are empty\n\n # check for degenerate case\n if Length( inequalities ) > 0 then\n kwargs.INEQUALITIES := JuliaMatrixInt( inequalities );\n\n # check if we also need equalities\n if Length( equalities ) > 0 then\n kwargs.EQUATIONS := JuliaMatrixInt( equalities );\n fi;\n elif Length( equalities ) > 0 then\n kwargs.INEQUALITIES := JuliaMatrixInt( equalities );\n kwargs.EQUATIONS := kwargs.INEQUALITIES;\n fi;\n\n poly!.pmobj := CallJuliaFunctionWithKeywordArguments( _Polymake_jl.polytope.Polytope, [], kwargs );\n return poly;\nend);\n\n\n##############################################################################################\n##\n## Constructors for PolymakePolytopes\n##\n##############################################################################################\n\n\nInstallGlobalFunction( Polymake_PolytopeByGenerators,\n function( arg )\n local poly, i, matrix, temp, dim;\n \n if Length( arg )= 0 or ForAll( arg, IsEmpty ) then\n \n Error( \"Wrong input: Please provide some input!\" );\n \n elif Length( arg ) = 1 and IsList( arg[1] ) then\n \n return Polymake_PolytopeByGenerators( arg[ 1 ], [ ] );\n \n elif Length( arg ) = 2 and IsList( arg[ 1 ] ) and IsList( arg[ 2 ] ) then\n \n if ( not IsEmpty( arg[ 1 ] ) ) and not ( IsMatrix( arg[ 1 ] ) ) then\n Error( \"Wrong input: The first argument should be a Gap matrix!\" );\n fi;\n \n if ( not IsEmpty( arg[ 2 ] ) ) and not ( IsMatrix( arg[ 2 ] ) ) then\n Error( \"Wrong input: The second argument should be a Gap matrix!\" );\n fi;\n \n poly := MakePolymakePolytopeVRep( arg[ 1 ], arg[ 2 ] );\n return Polymake_CanonicalPolytopeByGenerators( poly );\n \n fi;\n \nend );\n\n\nInstallGlobalFunction( Polymake_PolytopeFromInequalities,\n function( arg )\n local poly, i, temp, matrix, dim;\n \n if Length( arg ) = 0 or ForAll( arg, IsEmpty ) then\n \n Error( \"Wrong input: Please provide some input!\" );\n \n elif Length( arg ) = 1 and IsList( arg[ 1 ] ) then\n \n return Polymake_PolytopeFromInequalities( arg[ 1 ], [ ] );\n \n elif Length( arg ) = 2 and IsList( arg[ 1 ] ) and IsList( arg[ 2 ] ) then\n \n if ( not IsEmpty( arg[ 1 ] ) ) and not ( IsMatrix( arg[ 1 ] ) ) then\n Error( \"Wrong input: The first argument should be a Gap matrix!\" );\n fi;\n \n if ( not IsEmpty( arg[ 2 ] ) ) and not ( IsMatrix( arg[ 2 ] ) ) then\n Error( \"Wrong input: The second argument should be a Gap matrix!\" );\n fi;\n \n poly := MakePolymakePolytopeHRep( arg[ 1 ], arg[ 2 ] );\n return Polymake_CanonicalPolytopeFromInequalities( poly );\n \n fi;\n \nend );\n\n\n##############################################################################################\n##\n## Canonicalize polytopes\n##\n##############################################################################################\n\nInstallMethod( Polymake_CanonicalPolytopeByGenerators,\n [ IsPolymakePolytope ],\n function( poly )\n local vertices, v_copy, scaled_vertices, i, scale, lineality, scaled_lineality;\n \n if poly!.rep_type = \"H-rep\" then\n \n return fail;\n \n else\n \n # compute vertices\n vertices := PolymakeMatrixToGAP( poly!.pmobj.VERTICES );\n \n # sometimes, Polymake returns rational vertices - we turn them into integral vectors\n # also, Polymake requires x0 = 1 in affine coordinates - we remove this 1\n scaled_vertices := [];\n for i in [ 1 .. Length( vertices ) ] do\n v_copy := ShallowCopy( vertices[ i ] );\n Remove( v_copy, 1 );\n Add( scaled_vertices, v_copy );\n od;\n \n # extract lineality\n lineality := PolymakeMatrixToGAP( poly!.pmobj.LINEALITY_SPACE );\n \n # sometimes, Polymake returns rational lineality - we turn them into integral vectors\n scaled_lineality := [];\n for i in [ 1 .. Length( lineality ) ] do\n v_copy := ShallowCopy( lineality[ i ] );\n Remove( v_copy, 1 );\n Add( scaled_lineality, v_copy );\n od;\n \n # construct the new poly\n return MakePolymakePolytopeVRep( scaled_vertices, scaled_lineality );\n \n fi;\n \nend );\n\nInstallMethod( Polymake_CanonicalPolytopeFromInequalities,\n [ IsPolymakePolytope ],\n function( poly )\n local ineqs, eqs;\n \n if poly!.rep_type = \"V-rep\" then\n \n return fail;\n \n else\n \n # compute facets\n ineqs := PolymakeMatrixToGAP( poly!.pmobj.FACETS );\n \n # compute affine hull\n eqs := PolymakeMatrixToGAP( poly!.pmobj.AFFINE_HULL );\n \n # construct the new poly\n return MakePolymakePolytopeHRep( ineqs, eqs );\n \n fi;\n \nend );\n\n\n##############################################################################################\n##\n## Conversion of polytopes\n##\n##############################################################################################\n\nInstallMethod( Polymake_V_Rep,\n [ IsPolymakePolytope ],\n function( poly )\n local vertices, v_copy, scaled_vertices, i, lineality, scaled_lineality;\n \n if poly!.rep_type = \"V-rep\" then\n \n return poly;\n \n else\n \n # compute vertices\n vertices := PolymakeMatrixToGAP( poly!.pmobj.VERTICES );\n \n # sometimes, Polymake returns rational vertices - we turn them into integral vectors\n scaled_vertices := [];\n for i in [ 1 .. Length( vertices ) ] do\n v_copy := ShallowCopy( vertices[ i ] );\n Remove( v_copy, 1 );\n Add( scaled_vertices, v_copy );\n od;\n \n # compute lineality\n lineality := PolymakeMatrixToGAP( poly!.pmobj.LINEALITY_SPACE );\n \n # sometimes, Polymake returns rational lineality - we turn them into integral vectors\n scaled_lineality := [];\n for i in [ 1 .. Length( lineality ) ] do\n v_copy := ShallowCopy( lineality[ i ] );\n Remove( v_copy, 1 );\n Add( scaled_lineality, v_copy );\n od;\n \n # construct the new poly\n return MakePolymakePolytopeVRep( scaled_vertices, scaled_lineality );\n \n fi;\n \nend );\n\n\nInstallMethod( Polymake_H_Rep,\n [ IsPolymakePolytope ],\n function( poly )\n local ineqs, eqs;\n \n if poly!.rep_type = \"H-rep\" then\n \n return poly;\n \n else\n \n if poly!.rep_type = \"V-rep\" and poly!.vertices = [] then\n return Polymake_PolytopeFromInequalities( [ [ 0, 1 ], [ -1, -1 ] ] );\n fi;\n \n # compute inequalities\n ineqs := PolymakeMatrixToGAP( poly!.pmobj.FACETS );\n \n # compute equalities\n eqs := PolymakeMatrixToGAP( poly!.pmobj.AFFINE_HULL );\n \n # construct the new poly\n return MakePolymakePolytopeHRep( ineqs, eqs );\n \n fi;\n \nend );\n\n\n##############################################################################################\n##\n## Attributes of PolymakeCones\n##\n##############################################################################################\n\nInstallMethod( Polymake_AmbientSpaceDimension,\n \"finding the dimension of the ambient space of the poly\",\n [ IsPolymakePolytope ],\n function( poly )\n \n return Length( Polymake_V_Rep( poly )!.vertices[0] );\n \nend );\n\n\nInstallMethod( Polymake_Dimension,\n \" returns the dimension of the poly\",\n [ IsPolymakePolytope ],\n function( poly )\n \n if Polymake_IsEmpty( poly ) then\n return -1;\n fi;\n \n return poly!.pmobj.CONE_DIM - 1;\n \nend );\n\n\nInstallMethod( Polymake_Vertices,\n \" return the list of generating vertices\",\n [ IsPolymakePolytope ],\n function( poly )\n \n return Set( Polymake_V_Rep( poly )!.vertices );\n \nend );\n\n\nInstallMethod( Polymake_Linealities,\n \" return the list of linealities\",\n [ IsPolymakePolytope ],\n function( poly )\n \n return Set( Polymake_V_Rep( poly )!.linealities );\n \nend );\n\n\nInstallMethod( Polymake_Equalities,\n \" return the list of equalities of a poly\",\n [ IsPolymakePolytope ],\n function( poly )\n \n return Set( ( Polymake_H_Rep( poly ) )!.equalities );\n \nend );\n\n\nInstallMethod( Polymake_Inequalities,\n \" return the list of inequalities of a poly\",\n [ IsPolymakePolytope ],\n function( poly )\n \n return Set( ( Polymake_H_Rep( poly ) )!.inequalities );\n \nend );\n\n\nInstallMethod( Polymake_LatticePoints,\n \" return the list of the lattice points of poly\",\n [ IsPolymakePolytope ],\n function( poly )\n local point_list, lattice_points, i, copy;\n \n point_list := JuliaToGAP( IsList, JuliaMatrixInt( poly!.pmobj.LATTICE_POINTS_GENERATORS[1] ), true );\n\n # the point list is in affine coordinate, that is we have a 1 at position one, which should be removed\n lattice_points := [];\n for i in [ 1 .. Length( point_list ) ] do\n copy := ShallowCopy( point_list[ i ] );\n Remove( copy, 1 );\n Add( lattice_points, copy );\n od;\n \n # return result\n return lattice_points;\n \nend );\n\n\nInstallMethod( Polymake_Intersection,\n [ IsPolymakePolytope, IsPolymakePolytope ],\n function( poly1, poly2 )\n local poly1_h, poly2_h, new_ineqs, new_equ;\n \n # compute H-reps\n poly1_h := Polymake_H_Rep( poly1 );\n poly2_h := Polymake_H_Rep( poly2 );\n \n # add the inequalities and equalities\n new_ineqs := Concatenation( poly1_h!.inequalities, poly2_h!.inequalities );\n new_equ := Concatenation( poly1_h!.equalities, poly2_h!.equalities );\n \n # return result\n return Polymake_PolytopeFromInequalities( new_ineqs, new_equ );\n \nend );\n\n\n##############################################################################################\n##\n## Properties of PolymakeCones\n##\n##############################################################################################\n\nInstallMethod( Polymake_IsEmpty,\n \"finding if the poly empty is or not\",\n [ IsPolymakePolytope ],\n function( poly )\n \n return Length( Polymake_V_Rep( poly )!.vertices ) = 0;\n \nend );\n\n\nInstallMethod( Polymake_IsPointed,\n \"finding if the poly is pointed or not\",\n [ IsPolymakePolytope ],\n function( poly )\n return poly!.pmobj.POINTED;\n \nend );\n\n\nInstallMethod( Polymake_IsBounded,\n \" returns if the polytope is bounded or not\",\n [ IsPolymakePolytope ],\n function( poly )\n return poly!.pmobj.BOUNDED;\n \nend );\n", "meta": {"hexsha": "c969f54a2ca86be189c7a4ab0d0f99f4f58edd28", "size": 13778, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "pkg/JConvex/gap/ExternalPolymakePolytope.gi", "max_stars_repo_name": "HereAround/JToric.jl", "max_stars_repo_head_hexsha": "e8907f1ccd10a637254808916f859e354e479296", "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": "pkg/JConvex/gap/ExternalPolymakePolytope.gi", "max_issues_repo_name": "HereAround/JToric.jl", "max_issues_repo_head_hexsha": "e8907f1ccd10a637254808916f859e354e479296", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 44, "max_issues_repo_issues_event_min_datetime": "2021-09-17T01:15:32.000Z", "max_issues_repo_issues_event_max_datetime": "2021-11-25T00:15:13.000Z", "max_forks_repo_path": "pkg/JConvex/gap/ExternalPolymakePolytope.gi", "max_forks_repo_name": "HereAround/JToric.jl", "max_forks_repo_head_hexsha": "e8907f1ccd10a637254808916f859e354e479296", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2021-08-20T12:56:11.000Z", "max_forks_repo_forks_event_max_datetime": "2021-08-20T12:56:11.000Z", "avg_line_length": 30.0829694323, "max_line_length": 116, "alphanum_fraction": 0.5379590652, "num_tokens": 3364, "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\nClass(WarpXOpts, FFTXConvOpts, rec(\n tags := [],\n operations := rec(Print := s -> Print(\"<FFTX WarpX options record>\")) \n));\n\nwarpxOpts := function(arg) # specific to WarpX size 100...\n local opts, rfs;\n \n rfs := Copy(RulesFuncSimp);\n Unbind(rfs.rules.TensorIdId);\n \n opts := Copy(WarpXOpts);\n opts.breakdownRules.Circulant := [Circulant_PRDFT_FDataNT];\n opts.breakdownRules.PRDFT := List([PRDFT1_Base1, PRDFT1_Base2, CopyFields(PRDFT1_CT, \n rec(allChildren := P ->Filtered(PRDFT1_CT.allChildren(P), i->When(P[1] = 100, Cols(i[1]) = 4, true)))), \n PRDFT_PD], _noT);\n opts.breakdownRules.IPRDFT := List([ IPRDFT1_Base1, IPRDFT1_Base2, IPRDFT1_CT, IPRDFT_PD ], _noT);\n opts.breakdownRules.PRDFT3 := List([ PRDFT3_Base1, PRDFT3_Base2, PRDFT3_CT ], _noT);\n opts.breakdownRules.IPRDFT2 := List([ IPRDFT2_Base1, IPRDFT2_Base2, IPRDFT2_CT ], _noT);\n opts.breakdownRules.DFT := [ DFT_Base, \n CopyFields(DFT_CT, rec(children := nt ->Filtered(DFT_CT.children(nt), i->When(nt.params[1] = 100, Cols(i[1]) = 4, true)))), \n DFT_PD ];\n opts.breakdownRules.TTensorInd := [dsA_base, L_dsA_L_base, dsA_L_base, L_dsA_base]; \n opts.breakdownRules.MDDFT := [ MDDFT_Base, MDDFT_RowCol ];\n opts.breakdownRules.TL := [L_base];\n opts.breakdownRules.TSparseMat := [ TSparseMat_base ];\n \n opts.globalUnrolling := 23;\n opts.codegen := CopyFields( MultiPtrCodegenMixin, spiral.libgen.VecRecCodegen);\n opts.sumsgen.IterHStack := MultiPtrSumsgenMixin.IterHStack;\n opts.preProcess := t -> ApplyStrategy(t, \n [ RulesFFTXPromoteWarpX1, \n MergedRuleSet(rfs, RulesSums, RulesFFTXPromoteWarpX2), \n RulesFFTXPromoteNT, \n MergedRuleSet(rfs, RulesSums, RulesFFTXPromoteWarpX3) ],\n BUA, opts);\n opts.useDeref := false;\n # for debugging...\n opts.generateInitFunc := false;\n# opts.codegen := DefaultCodegen;\n opts.arrayBufModifier := \"\";\n opts.arrayDataModifier := \"static\";\n \n return opts;\nend;\n\n\nwarpxConf := rec(\n defaultName := \"defaultWarpXConf\",\n defaultOpts := (arg) >> rec(useWarpX := true),\n confHandler := warpxOpts \n);\n\nfftx.FFTXGlobals.registerConf(warpxConf);\n\n\n\n", "meta": {"hexsha": "0568b507b3b64208089c740a99feb5c2e144ddda", "size": 2348, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "knowledgebase/warpx.gi", "max_stars_repo_name": "franzfranchetti/spiral-package-fftx", "max_stars_repo_head_hexsha": "3149606d3d60a9b50c225ec1e8450628d543698b", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-06-15T12:40:19.000Z", "max_stars_repo_stars_event_max_datetime": "2021-06-15T12:40:19.000Z", "max_issues_repo_path": "knowledgebase/warpx.gi", "max_issues_repo_name": "franzfranchetti/spiral-package-fftx", "max_issues_repo_head_hexsha": "3149606d3d60a9b50c225ec1e8450628d543698b", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2021-01-05T20:58:29.000Z", "max_issues_repo_issues_event_max_datetime": "2021-08-18T20:10:45.000Z", "max_forks_repo_path": "knowledgebase/warpx.gi", "max_forks_repo_name": "franzfranchetti/spiral-package-fftx", "max_forks_repo_head_hexsha": "3149606d3d60a9b50c225ec1e8450628d543698b", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 5, "max_forks_repo_forks_event_min_datetime": "2020-12-14T18:24:29.000Z", "max_forks_repo_forks_event_max_datetime": "2021-06-15T12:40:20.000Z", "avg_line_length": 37.8709677419, "max_line_length": 132, "alphanum_fraction": 0.6528960818, "num_tokens": 732, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7956580903722561, "lm_q2_score": 0.523420348936324, "lm_q1q2_score": 0.41646363529665553}}
	{"text": "#############################################################################\n##\n#W autom.gi automgrp package Yevgen Muntyan\n#W Dmytro Savchuk\n##\n#Y Copyright (C) 2003 - 2018 Yevgen Muntyan, Dmytro Savchuk\n##\n\n\n###############################################################################\n##\n#R IsAutomRep\n##\n## This is how IsAutom object is stored in GAP:\n## IsAutom object is a thing of kind \"w = (w_1, w_2, ..., w_d)\\pi\", where\n## deg = d - arity of tree;\n## perm = \\pi - permutation on first level;\n## w, w_1, ..., w_d - elements of free group representing elements of\n## automata group;\n## word = w;\n## states = [w_1, ..., w_d].\n##\nDeclareRepresentation(\"IsAutomRep\",\n IsComponentObjectRep and IsAttributeStoringRep,\n [\"word\", \"states\", \"perm\", \"deg\"]);\n\n\nInstallGlobalFunction(__AG_CreateAutom,\nfunction(family, word, states, perm, invertible)\n local a, cat;\n\n if invertible then\n cat := IsInvertibleAutom and IsAutomRep;\n\n if perm^-1=fail then\n Error(perm, \" is not invertible\");\n else\n perm := AG_PermFromTransformation(perm);\n fi;\n else\n cat := IsAutom and IsAutomRep;\n fi;\n\n a := Objectify(NewType(family, cat),\n rec(word := word,\n states := states,\n perm := perm,\n deg := family!.deg));\n\n SetIsActingOnBinaryTree(a, a!.deg = 2);\n\n return a;\nend);\n\n###############################################################################\n##\n#M Autom(<word>, <fam>)\n##\nInstallMethod(Autom, \"for [IsAssocWord, IsAutomFamily]\",\n [IsAssocWord, IsAutomFamily],\nfunction(w, fam)\n local exp, wstates, curstate, newstate, curletter, newletter,\n nperm, i, j, perm, a, wtmp, reduced, invertible;\n\n if fam!.use_rws then\n w := AG_ReducedForm(fam!.rws, w);\n fi;\n\n if Length(w) = 0 then\n return One(fam);\n elif Length(w) = 1 then\n if ExponentSyllable(w, 1) = 1 then\n return fam!.automgens[GeneratorSyllable(w, 1)];\n else\n return fam!.automgens[GeneratorSyllable(w, 1) + fam!.numstates];\n fi;\n fi;\n\n # TODO\n exp := LetterRepAssocWord(w);\n for i in [1..Length(exp)] do\n if exp[i] < 0 then exp[i] := -exp[i] + fam!.numstates; fi;\n od;\n wstates := [];\n nperm := ();\n for i in [1..Length(exp)] do\n nperm := nperm * fam!.automatonlist[exp[i]][fam!.deg+1];\n od;\n\n for i in [1..fam!.deg] do\n wstates[i] := [];\n perm := ();\n\n for j in [1..Length(exp)] do\n newstate := fam!.automatonlist[exp[j]][i^perm];\n if newstate <> fam!.trivstate then\n if newstate > fam!.numstates then\n newstate := -(newstate - fam!.numstates);\n fi;\n if Length(wstates[i]) > 0 and wstates[i][Length(wstates[i])] = -newstate then\n Remove(wstates[i], Length(wstates[i]));\n else\n Add(wstates[i], newstate);\n fi;\n fi;\n perm := perm * fam!.automatonlist[exp[j]][fam!.deg+1];\n od;\n if Length(wstates[i]) > 0 then\n wstates[i] := AssocWordByLetterRep(FamilyObj(w), wstates[i]);\n else\n wstates[i] := One(fam!.freegroup);\n fi;\n if fam!.use_rws and not IsOne(wstates[i]) then\n wstates[i] := AG_ReducedForm(fam!.rws, wstates[i]);\n fi;\n od;\n\n invertible := true;\n if not fam!.isgroup then\n for i in exp do\n if i <= fam!.numstates and not IsInvertibleAutom(fam!.automgens[i]) then\n invertible := false;\n break;\n fi;\n od;\n fi;\n\n return __AG_CreateAutom(fam, w, wstates, nperm, invertible);\nend);\n\n\n###############################################################################\n##\n#M Autom(<word>, <a>)\n##\nInstallMethod(Autom, \"for [IsAssocWord, IsAutom]\", [IsAssocWord, IsAutom],\nfunction(w, a)\n return Autom(w, FamilyObj(a));\nend);\n\n\nInstallMethod(MappedWord, [IsAssocWord,\n IsList and IsAssocWordCollection,\n IsList and IsAutomCollection],\nfunction(w, fgens, agens)\n local img;\n img := MappedWord(w, fgens, List(agens, a -> a!.word));\n return Autom(img, FamilyObj(agens[1]));\nend);\n\n\n###############################################################################\n##\n#M Autom(<word>, <list>)\n##\nInstallMethod(Autom, \"for [IsAssocWord, IsList]\",\n [IsAssocWord, IsList],\nfunction(w, list)\n local fam;\n fam := AutomFamily(list);\n if fam = fail then\n return fail;\n fi;\n return Autom(w, fam);\nend);\n\n\n###############################################################################\n##\n#M PrintObj(<a>)\n##\nInstallMethod(PrintObj, \"for [IsAutom]\",\n [IsAutom],\nfunction (a)\n local deg, printword, i;\n\n printword := function(w)\n if IsOne(w) then Print(AG_Globals.identity_symbol);\n else Print(w); fi;\n end;\n\n if true then\n View(a);\n return;\n fi;\n\n deg := a!.deg;\n printword(a!.word);\n Print(\" = (\");\n for i in [1..deg] do\n printword(a!.states[i]);\n if i <> deg then Print(\", \"); fi;\n od;\n Print(\")\");\n if not IsOne(a!.perm) then AG_PrintTransformation(a!.perm); fi;\nend);\n\n\n###############################################################################\n##\n#M ViewObj(<a>)\n##\nInstallMethod(ViewObj, \"for [IsAutom]\",\n [IsAutom],\nfunction (a)\n if IsOne(a!.word) then Print(AG_Globals.identity_symbol);\n else Print(a!.word); fi;\nend);\n\n\n###############################################################################\n##\n#M String(<a>)\n##\nInstallMethod(String, \"for [IsAutom]\",\n [IsAutom],\nfunction (a)\n if IsOne(a!.word) then return AG_Globals.identity_symbol;\n else return String(a!.word); fi;\nend);\n\n\n###############################################################################\n##\n#M Perm(<a>)\n##\nInstallMethod(Perm, \"for [IsAutom]\", [IsAutom],\nfunction(a)\n return a!.perm;\nend);\n\n\n###############################################################################\n##\n#M Word(<a>)\n##\nInstallMethod(Word, \"for [IsAutom]\", [IsAutom],\nfunction(a)\n return a!.word;\nend);\n\n\n###############################################################################\n##\n#M <a1> * <a2>\n##\nInstallMethod(\\, \"for [IsAutom, IsAutom]\", [IsAutom, IsAutom],\nfunction(a1, a2)\n local a, i, fam, word, states;\n\n fam := FamilyObj(a1);\n word := a1!.word a2!.word;\n\n if fam!.use_rws then\n word := AG_ReducedForm(fam!.rws, word);\n fi;\n\n if IsOne(word) then\n return One(a1);\n fi;\n\n states := List([1..a1!.deg], i -> a1!.states[i] * a2!.states[i^(a1!.perm)]);\n\n if fam!.use_rws then\n for i in [1..a1!.deg] do\n states[i] := AG_ReducedForm(fam!.rws, states[i]);\n od;\n fi;\n\n return __AG_CreateAutom(FamilyObj(a1), word, states, a1!.perm * a2!.perm,\n IsInvertibleAutom(a1) and IsInvertibleAutom(a2));\nend);\n\n\nAG_IsOne_Autom := function(a)\n local deg, w, aw, checked, to_check;\n\n if IsOne(a!.word) then\n return true;\n fi;\n\n if not IsOne(a!.perm) then\n return false;\n fi;\n\n deg := a!.deg;\n checked := [];\n to_check := Filtered(a!.states, w -> not IsOne(w) and w <> a!.word);\n\n while not IsEmpty(to_check) do\n w := Remove(to_check, Length(to_check));\n # TODO Use AddSet() here?\n Add(checked, w);\n aw := Autom(w, a);\n if not IsOne(aw!.perm) then\n return false;\n fi;\n for w in aw!.states do\n if not IsOne(w) and not w in checked and not w in to_check then\n # TODO Use AddSet() here?\n Add(to_check, w);\n fi;\n od;\n od;\n\n return true;\nend;\n\n###############################################################################\n##\n#M IsOne(a)\n##\nInstallMethod(IsOne, \"for [IsAutom]\", [IsAutom],\nfunction(a)\n local i, w, nw, d, to_check, checked, deb_i, perm, autlist, pos, istrivstate, exp, G, trivstate;\n\n if IsOne(a!.word) then return true; fi;\n\n G := GroupOfAutomFamily(FamilyObj(a));\n if G <>fail and HasIsContracting(G) and IsContracting(G) and FamilyObj(a)!.use_contraction = true then\n return IsOneContr(a);\n fi;\n\n # this seems working well enough\n return AG_IsOne_Autom(a);\n\n d := a!.deg;\n autlist := FamilyObj(a)!.automatonlist;\n trivstate := FamilyObj(a)!.trivstate;\n checked := [];\n\n istrivstate := function(v)\n local i, j, perm;\n\n if IsEmpty(v) then\n return true;\n fi;\n\n if v in checked then\n return true;\n else\n perm := ();\n for i in [1..Length(v)] do perm := perm * autlist[v[i]][d+1]; od;\n if perm <> () then return false; fi;\n Add(checked, v);\n for j in [1..d] do\n if not istrivstate(AG_WordStateInList(v, j, autlist, true, trivstate)) then\n return false;\n fi;\n od;\n return true;\n fi;\n end;\n\n exp := LetterRepAssocWord(a!.word);\n for i in [1..Length(exp)] do\n if exp[i] < 0 then\n exp[i] := -exp[i] + FamilyObj(a)!.numstates;\n fi;\n od;\n\n return istrivstate(exp);\nend);\n\n\n###############################################################################\n##\n#M a1 = a2\n##\nInstallMethod(\\=, \"for [IsAutom, IsAutom]\", IsIdenticalObj, [IsAutom, IsAutom],\nfunction(a1, a2)\n local areequalstates, exp, i, d, checked, autlist, G, trivstate;\n\n G := GroupOfAutomFamily(FamilyObj(a1));\n if G <> fail and HasIsContracting(G) and IsContracting(G) and UseContraction(G) then\n return IsOneContr(a1a2^-1);\n fi;\n\n # TODO can there be a problem if we do this?\n if G <> fail then\n return AG_IsOne_Autom(a1a2^-1);\n fi;\n\n d := a1!.deg;\n checked := [];\n autlist := FamilyObj(a1)!.automatonlist;\n trivstate := FamilyObj(a1)!.trivstate;\n\n areequalstates := function(p)\n local i, j, perm1, perm2;\n\n if p[1] = p[2] then\n return true;\n fi;\n\n if p in checked then\n return true;\n else\n perm1 := ();\n perm2 := ();\n\n for i in [1..Length(p[1])] do\n perm1 := perm1 * autlist[p[1][i]][d+1];\n od;\n for i in [1..Length(p[2])] do\n perm2 := perm2 * autlist[p[2][i]][d+1];\n od;\n\n if perm1 <> perm2 then\n return false;\n fi;\n\n AddSet(checked, p);\n for j in [1..d] do\n if not areequalstates([AG_WordStateInList(p[1], j, autlist, true, trivstate),\n AG_WordStateInList(p[2], j, autlist, true, trivstate)])\n then\n return false;\n fi;\n od;\n return true;\n fi;\n end;\n\n exp := [LetterRepAssocWord(a1!.word), LetterRepAssocWord(a2!.word)];\n for i in [1..Length(exp[1])] do\n if exp[1][i] < 0 then exp[1][i] := -exp[1][i] + FamilyObj(a1)!.numstates; fi;\n od;\n for i in [1..Length(exp[2])] do\n if exp[2][i] < 0 then exp[2][i] := -exp[2][i] + FamilyObj(a2)!.numstates; fi;\n od;\n return areequalstates(exp);\nend);\n\n\n###############################################################################\n##\n#M a1 < a2\n##\nInstallMethod(\\<, \"for [IsAutom, IsAutom]\", IsIdenticalObj, [IsAutom, IsAutom],\nfunction(a1, a2)\n local d, checked, pos, aw1, aw2, p, np, i, exp, perm1, perm2, autlist, cmp;\n\n d := a1!.deg;\n autlist := FamilyObj(a1)!.automatonlist;\n exp := [LetterRepAssocWord(a1!.word), LetterRepAssocWord(a2!.word)];\n for i in [1..Length(exp[1])] do\n if exp[1][i] < 0 then exp[1][i] := -exp[1][i] + FamilyObj(a1)!.numstates; fi;\n od;\n for i in [1..Length(exp[2])] do\n if exp[2][i] < 0 then exp[2][i] := -exp[2][i] + FamilyObj(a2)!.numstates; fi;\n od;\n checked := [exp];\n pos := 0;\n\n while Length(checked) <> pos do\n pos := pos + 1;\n p := checked[pos];\n perm1 := ();\n perm2 := ();\n for i in [1..Length(p[1])] do perm1 := perm1 * autlist[p[1][i]][d+1]; od;\n for i in [1..Length(p[2])] do perm2 := perm2 * autlist[p[2][i]][d+1]; od;\n cmp := AG_TrCmp(perm1, perm2, d);\n if cmp < 0 then\n return true;\n elif cmp > 0 then\n return false;\n fi;\n for i in [1..d] do\n np := [AG_WordStateInList(p[1], i, autlist, false, 0),\n AG_WordStateInList(p[2], i, autlist, false, 0)];\n if not np in checked then\n Add(checked, np);\n fi;\n od;\n od;\n\n return false;\nend);\n\n\n###############################################################################\n##\n#M InverseOp(<a>)\n##\nInstallMethod(InverseOp, \"for [IsInvertibleAutom]\", [IsInvertibleAutom],\nfunction(a)\n local i, inv, fam, word, states;\n\n fam := FamilyObj(a);\n word := a!.word ^ -1;\n if fam!.use_rws then\n word := AG_ReducedForm(fam!.rws, word);\n if IsOne(word) then\n return One(a);\n fi;\n fi;\n\n states := List([1..a!.deg], i -> a!.states[i^(a!.perm^-1)]^-1);\n\n if fam!.use_rws then\n for i in [1..a!.deg] do\n states[i] := AG_ReducedForm(fam!.rws, states[i]);\n od;\n fi;\n\n return __AG_CreateAutom(FamilyObj(a), word, states, a!.perm^-1, true);\nend);\n\n\n###############################################################################\n##\n#M OneOp(<a>)\n##\nInstallMethod(OneOp, \"for [IsAutom]\", [IsAutom],\nfunction(a)\n return One(FamilyObj(a));\nend);\n\n\n###############################################################################\n##\n#M StatesWords(<a>)\n##\nInstallMethod(StatesWords, \"for [IsAutom]\", [IsAutom],\nfunction(a)\n return a!.states;\nend);\n\n\n###############################################################################\n##\n#M Sections(a)\n##\nInstallMethod(Sections, \"for [IsAutom]\", [IsAutom],\nfunction(a)\n return List(a!.states, s -> Autom(s, a));\nend);\n\n\n###############################################################################\n##\n#M Section(a, k)\n##\nInstallMethod(Section, \"for [IsAutom, IsPosInt]\", [IsAutom, IsPosInt],\nfunction(a, k)\n if k > a!.deg then\n Error(\"in Section(IsAutom, IsPosInt): invalid vertex \", k);\n fi;\n return Autom(a!.states[k], a);\nend);\n\n\n###############################################################################\n##\n#M Section(a, seq)\n##\n## TODO\nInstallMethod(Section, \"for [IsAutom, IsList]\", [IsAutom, IsList],\nfunction(a, v)\n if Length(v) = 0 then\n return a;\n fi;\n\n if Length(v) = 1 then\n return Section(a, v[1]);\n fi;\n\n return Section(Section(a, v[1]), v{[2..Length(v)]});\nend);\n\n\n###############################################################################\n##\n#M k ^ a\n##\nInstallMethod(\\^, \"for [IsPosInt, IsAutom]\", [IsPosInt, IsAutom],\nfunction(k, a)\n return k ^ Perm(a);\nend);\n\n\n###############################################################################\n##\n#M seq ^ a\n##\nInstallMethod(\\^, \"for [IsList, IsAutom]\", [IsList, IsAutom],\nfunction(seq, a)\n local i, deg, img, cur;\n\n deg := DegreeOfTree(a);\n for i in seq do\n if not IsInt(i) or i < 1 or i > deg then\n Error(\"\\^(IsList, IsAutom): \",\n i, \" is out of range 1..\", deg, \" and is not a letter of the alphabet\\n\");\n# Print(\"\\^(IsList, IsAutom): \",\n# i, \" is out of range 1..\", deg, \" and is not a letter of the alphabet\\n\");\n# return seq;\n fi;\n od;\n\n if Length(seq) = 0 then return []; fi;\n if Length(seq) = 1 then return [seq[1]^Perm(a)]; fi;\n\n cur := LetterRepAssocWord(Word(a));\n for i in [1..Length(cur)] do\n if cur[i] < 0 then cur[i] := -cur[i]+FamilyObj(a)!.numstates; fi;\n od;\n cur := [cur, Perm(a)];\n\n img := [];\n for i in [1..Length(seq)] do\n img[i] := seq[i]^cur[2];\n cur := AG_WordStateAndPermInList(cur[1], seq[i],\n FamilyObj(a)!.automatonlist);\n od;\n\n return img;\nend);\n\n\n###############################################################################\n##\n#M PermOnLevelOp(a, k)\n##\n## TODO\nInstallMethod(PermOnLevelOp, \"for [IsIsInvertibleAutom, IsPosInt]\",\n [IsInvertibleAutom, IsPosInt],\nfunction(a, k)\n local dom, perm;\n\n if k = 1 then\n return a!.perm;\n fi;\n\n dom := AsList(Tuples([1.. a!.deg], k));\n perm := List(dom, s -> s ^ a);\n perm := PermListList(dom, perm);\n\n return perm;\nend);\n\nInstallMethod(TransformationOnFirstLevel, [IsAutom],\nfunction(a)\n return AsTransformation(a!.perm);\nend);\n\n\n###############################################################################\n##\n#M IsActingOnBinaryTree(<a>)\n##\nInstallMethod(IsActingOnBinaryTree, \"for [IsAutom]\",\n [IsAutom],\nfunction(a)\n return a!.deg = 2;\nend);\n\n\nInstallMethod(SphericalIndex, \"for [IsAutom]\", [IsAutom],\nfunction(a)\n # XXX check uses of SphericalIndex everywhere\n return rec(start := [], period := [a!.deg]);\nend);\n\n# XXX check uses of this everywhere\nInstallMethod(DegreeOfTree, \"for [IsAutom]\", [IsAutom],\nfunction(a)\n return a!.deg;\nend);\n\n# XXX check uses of this everywhere\nInstallMethod(TopDegreeOfTree, \"for [IsAutom]\", [IsAutom],\nfunction(a)\n return a!.deg;\nend);\n\n\n###############################################################################\n##\n#M CanEasilyTestSphericalTransitivity(<a>)\n##\nInstallTrueMethod(CanEasilyTestSphericalTransitivity,\n IsActingOnBinaryTree and IsAutom);\n\n\n###############################################################################\n##\n#M IsSphericallyTransitive(<a>)\n##\nInstallMethod(IsSphericallyTransitive, \"for [IsAutom]\",\n [IsInvertibleAutom],\nfunction(a)\n local w, i, ab, abs;\n\n if IsOne(Word(a)) then\n Info(InfoAutomGrp, 3, \"IsSphericallyTransitive(a): false\");\n Info(InfoAutomGrp, 3, \" IsOne(Word(a)): a = \", a);\n return false;\n fi;\n\n TryNextMethod();\nend);\n\n\n#########################################################################\n##\n#M Order(<a>)\n##\nInstallMethod(Order, \"for [IsInvertibleAutom]\", true,\n [IsInvertibleAutom],\nfunction(a)\n local ord_loc;\n if IsGeneratedByBoundedAutomaton(GroupOfAutomFamily(FamilyObj(a))) then\n return OrderUsingSections(a, infinity);\n fi;\n if IsActingOnBinaryTree(a) and IsSphericallyTransitive(a) then\n return infinity;\n fi;\n ord_loc := OrderUsingSections(a, 10);\n if ord_loc <> fail then\n return ord_loc;\n fi;\n return OrderUsingSections(a, infinity);\nend);\n\n\n#########################################################################\n##\n#M IsTransitiveOnLevel( <a>, <lev> )\n##\nInstallMethod(IsTransitiveOnLevel, \"for [IsInvertibleAutom, IsPosInt]\",\n [IsInvertibleAutom, IsPosInt],\nfunction(a, lev)\n return Length(OrbitPerms([PermOnLevel(a, lev)], 1)) = a!.deg^lev;\nend);\n\n\n\n#########################################################################\n##\n#M AllSections( <a> )\n##\nInstallMethod(AllSections, \"for [IsAutom]\",\n [IsAutom],\nfunction(a)\n local states, find_all_sections;\n\n find_all_sections := function(s)\n local i;\n if not s in states then\n Add(states, s);\n for i in [1..s!.deg] do find_all_sections(Section(s, i)); od;\n fi;\n end;\n\n states := [];\n find_all_sections(a);\n return states;\nend);\n\n\n#E\n", "meta": {"hexsha": "1a258a4efd57dc34d94a2cc904edf914da996765", "size": 18607, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "gap/autom.gi", "max_stars_repo_name": "gap-packages/automgrp", "max_stars_repo_head_hexsha": "1beb0cbc96c9748cf912433c27c661e1f87ef5dc", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-10-02T15:00:11.000Z", "max_stars_repo_stars_event_max_datetime": "2021-10-02T15:00:11.000Z", "max_issues_repo_path": "gap/autom.gi", "max_issues_repo_name": "gap-packages/automgrp", "max_issues_repo_head_hexsha": "1beb0cbc96c9748cf912433c27c661e1f87ef5dc", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 9, "max_issues_repo_issues_event_min_datetime": "2019-09-21T22:10:40.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-26T23:51:41.000Z", "max_forks_repo_path": "gap/autom.gi", "max_forks_repo_name": "gap-packages/automgrp", "max_forks_repo_head_hexsha": "1beb0cbc96c9748cf912433c27c661e1f87ef5dc", "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": 24.3547120419, "max_line_length": 105, "alphanum_fraction": 0.5134626753, "num_tokens": 5207, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6959583376458152, "lm_q2_score": 0.5964331462646254, "lm_q1q2_score": 0.41509262099119204}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n# ==========================================================================\n# IDirSum(<var>, <range>, <spl>) - Iterative direct sum.\n# Dimensions of <spl> are assumed to not depend on <var>.\n# ==========================================================================\nClass(IDirSum, BaseIterative, rec(\n directOper := DirectSum,\n #-----------------------------------------------------------------------\n dims := self >> let(d:=self._children[1].dimensions,\n [d[1]* self.domain, d[2]self.domain]),\n# dims := self >> _evInt(self.unroll().dims()),\n #-----------------------------------------------------------------------\n unroll := self >> DirectSum(self.unrolledChildren()),\n #-----------------------------------------------------------------------\n transpose := self >> CopyFields(self, rec(\n _children := [self._children[1].transpose()],\n dimensions := Reversed(self.dimensions))),\n #-----------------------------------------------------------------------\n conjTranspose := self >> CopyFields(self, rec(\n _children := [self._children[1].conjTranspose()],\n dimensions := Reversed(self.dimensions))),\n #-----------------------------------------------------------------------\n inverse := self >> CopyFields(self, rec(\n _children := [self._children[1].inverse()],\n dimensions := Reversed(self.dimensions)))\n));\n\nDeclare(IColDirSum, IRowDirSum);\n\n# ==========================================================================\n# IRowDirSum(<var>, <range>, <overlap>, <spl>) - Iterative direct sum.\n# Dimensions of <spl> are assumed to not depend on <var>.\n# ==========================================================================\nClass(IRowDirSum, BaseIterative, rec(\n directOper := RowDirectSum,\n transposeOper := self >> IColDirSum,\n abbrevs := [ (v, expr) -> [v, v.range, 0, expr] ],\n\n rChildren := self >> Concat([self.var, self.overlap, self._children], When(IsBound(self._setDims), [self._setDims],[])),\n rSetChild := rSetChildFields(\"var\", \"overlap\", \"_children\", \"_setDims\"),\n\n new := meth(self, var, domain, overlap, expr)\n local res;\n Constraint(IsSPL(expr));\n Constraint(not IsInt(domain) or domain > 0);\n var.isLoopIndex := true;\n res := SPL(WithBases(self, rec(_children := [expr], var := var, domain := domain, overlap := overlap)));\n res.dimensions := res.dims();\n return res;\n end,\n #-----------------------------------------------------------------------\n print := meth(self, indent, indentStep)\n Print(self.name, \"(\", self.var, \", \", self.domain, \", \", self.overlap, \",\");\n self._newline(indent + indentStep);\n SPLOps.Print(self._children[1], indent+indentStep, indentStep); #, \", \", self.nt_maps);\n self._newline(indent);\n Print(\")\");\n if IsBound(self._setDims) then\n Print(\".overrideDims(\", self._setDims, \")\");\n fi;\n end,\n #-----------------------------------------------------------------------\n _dims := self >> self.unroll().dims(),\n dims := self >> When(IsBound(self._setDims), self._setDims, let(d := Try(self._dims()), When(d[1], d[2], [errExp(), errExp()]))),\n #-----------------------------------------------------------------------\n unroll := self >> ApplyFunc(self.directOper, [self.overlap, self.unrolledChildren()]),\n #-----------------------------------------------------------------------\n transpose := self >> ApplyFunc(self.transposeOper(), [self.var, self.domain, self.overlap, self.child(1).transpose()]),\n #-----------------------------------------------------------------------\n conjTranspose := self >> ApplyFunc(self.transposeOper(), [self.var, self.domain, self.overlap, self.child(1).conjTranspose()])\n));\n\n\n# ==========================================================================\n# IColDirSum(<var>, <range>, <overlap>, <spl>) - Iterative direct sum.\n# Dimensions of <spl> are assumed to not depend on <var>.\n# ==========================================================================\nClass(IColDirSum, IRowDirSum, rec(\n directOper := ColDirectSum,\n transposeOper := self >> IRowDirSum\n));\n\n\n# ==========================================================================\n# IterCompose(<var>, <domain>, <spl>) - iterative compose\n# <spl> must be square\n# ==========================================================================\nClass(IterCompose, BaseIterative, rec(\n directOper := Compose,\n #-----------------------------------------------------------------------\n dims := self >> self._children[1].dimensions,\n #-----------------------------------------------------------------------\n unroll := self >> Compose(self.unrolledChildren()),\n #-----------------------------------------------------------------------\n # NOTE: this is incorrect, one has to reverse the order\n transpose := self >> CopyFields(self, rec(\n _children := [self._children[1].transpose()],\n domain := self.domain,\n dimensions := self.dimensions))\n # NOTE: conjTranspose() is missing\n));\n\nDeclare(IterVStack);\n\n# ==========================================================================\n# IterHStack(<var>, <domain>, <spl>)\n# Dimensions of <spl> are assumed to not depend on <var>.\n# ==========================================================================\nClass(IterHStack, BaseIterative, rec(\n directOper := HStack,\n #-----------------------------------------------------------------------\n unroll := self >> HStack(self.unrolledChildren()),\n #-----------------------------------------------------------------------\n dims := self >> [ self.child(1).dimensions[1],\n self.child(1).dimensions[2] self.domain ],\n #-----------------------------------------------------------------------\n transpose := self >> IterVStack(self.var, self.domain, self.child(1).transpose()),\n conjTranspose := self >> IterVStack(self.var, self.domain, self.child(1).conjTranspose())\n));\n\n# this is a HStack that is guaranteed not to perform any ops, and doesnt need ScatAcc in SumsGen\nClass(IterHStack1, IterHStack);\n# ==========================================================================\n# IterVStack(<var>, <domain>, <spl>)\n# Dimensions of <spl> are assumed to not depend on <var>.\n# ==========================================================================\nClass(IterVStack, BaseIterative, rec(\n directOper := VStack,\n #-----------------------------------------------------------------------\n unroll := self >> VStack(self.unrolledChildren()),\n #-----------------------------------------------------------------------\n dims := self >> [ self.child(1).dimensions[1] * self.domain,\n self.child(1).dimensions[2] ],\n #-----------------------------------------------------------------------\n transpose := self >> IterHStack(self.var, self.domain, self.child(1).transpose()),\n conjTranspose := self >> IterHStack(self.var, self.domain, self.child(1).conjTranspose())\n));\n\n#IterDirectSum := IDirSum;\n# ==========================================================================\n# IterDirectSum(<var>, <domain>, <spl>)\n# Dimensions of <spl> are assumed to not depend on <var>.\n# ==========================================================================\nClass(IterDirectSum, BaseIterative, rec(\n directOper := DirectSum, \n #-----------------------------------------------------------------------\n unroll := self >> DirectSum(self.unrolledChildren()),\n #-----------------------------------------------------------------------\n dims := self >> [self.child(1).dimensions[1] * self.domain, self.child(1).dimensions[2]*self.domain],\n #-----------------------------------------------------------------------\n transpose := self >> IterHStack(self.var, self.domain, self.child(1).transpose()),\n conjTranspose := self >> IterHStack(self.var, self.domain, self.child(1).conjTranspose())\n));\n", "meta": {"hexsha": "1603ccc9edf04657c1e08a4645385925d5a4bd46", "size": 8097, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/spl/Iter.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/Iter.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/Iter.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": 51.246835443, "max_line_length": 133, "alphanum_fraction": 0.4213906385, "num_tokens": 1527, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6297746213017459, "lm_q2_score": 0.6584175072643413, "lm_q1q2_score": 0.4146546362958401}}
	{"text": "################################################################################\n##\n#W TY_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 near_group_data functions of the GroupTheoretical Package\n##\n#Y Copyright (C) 2016, Battelle Memorial Institute\n##\n################################################################################\n\n\n################################################################################\n##\n#F near_group_data(<group>,<int>). . . . . . compute the data\n## . . . . . . . . . . . . . . . . . . . . . for a neargroup category k=0 is TY.\n##\nInstallGlobalFunction(near_group_data, function(G,k)\n local Simples,m,N,rank,x,FPdimC,FPdim,S,T,g_idx,h_idx,g,h;\n\n if k < 0 or not(IsInt(k)) then\n Error(\"k must be a non-negative integer\\n\");\n fi;\n\n if k > 0 then\n\n Error(\"k > 0 is not currently supported. We need to unravel Siehler's paper 'Near-group categories\\n\");\n\n if Order(G) > k+1 then\n Error(\"near group categories only admit monoidal structure for \|G\| <= k+1\");\n fi;\n\n if Order(G) = k+1 and not(IsCyclic(G) and Size(Set(FactorsInt(Order(G)+1))) = 1) then\n Error(\"for \|G\| = k+1, the near group category only admits monoidal structure if G is the multiplicative group of a finite field.\");\n fi;\n\n if Order(G) = 1 and ( (k mod 4) = 2 or (k mod 4) = 3) then\n Error(\"For \|G\| = 1, the near group category does not admit monoidal structure if k = 2 or 3 mod 4.\");\n fi;\n fi;\n\n Simples := ShallowCopy(AsSet(G));\n m:=\"m\";\n Add(Simples,m);\n rank:=Size(Simples);\n N:=List([1..rank],x->NullMat(rank,rank));\n # compute the fusion rules\n for g_idx in [1..rank] do\n g:=Simples[g_idx];\n for h_idx in [1..rank] do\n h:=Simples[h_idx];\n if g_idx = rank then\n if h_idx = rank then\n # m\\otimes m = Sum_{k\\in G}k+km\n N[g_idx][h_idx]:=List([1..rank],x->1);\n N[g_idx][h_idx][rank] := k;\n else\n N[g_idx][h_idx][rank] := 1; # m\\otimes h = m\n fi;\n else\n if h_idx = rank then\n N[g_idx][h_idx][rank] := 1; # g\\otimes m = m\n else \n # g\\otimes h = gh\n N[g_idx][h_idx][Position(Simples,gh)] := 1;\n fi;\n fi;\n od;\n od;\n\n FPdimC := 2Order(G);\n FPdim := List([1..rank],x->1);\n FPdim[rank] := Sqrt(Order(G));\n return [Simples, N, FPdim, FPdimC];\nend);\n\n################################################################################\n##\n#F TY_data(<group>,<bicharacter>,<num>,<list>,<sign>). . . . compute the data for TY(G,chi,tau,delta,Tsign)\n##\nInstallGlobalFunction(TY_data, function(G,chi,tau,delta,Tsign)\n local Simples,m,N,rank,x,FPdimC,FPdim,S,T,sigma1,sigma3_1,sigma3,sigma3_squared,sigma3_squared_trace,g_idx,h_idx,g,h;\n\n if not(IsInt(Tsign)) or Tsign^2 <> 1 then\n Error(\"Tsign must be +/-1\");\n fi;\n\n if Size(delta)<>Order(G)+1 or false in List(delta,x->(IsInt(x) and x^2=1)) then\n Error(\"delta must be a list of length \|G\|+1 and consist entirely of +/- 1\");\n fi;\n\n if (1/tau)^2 <> Order(G) then\n Error(\"tau must be a choice of squareroot of 1/\|G\|\");\n fi;\n\n Simples := ShallowCopy(AsSet(G));\n m:=\"m\";\n Add(Simples,m);\n rank:=Size(Simples);\n N:=List([1..rank],x->NullMat(rank,rank));\n # compute the fusion rules\n for g_idx in [1..rank] do\n g:=Simples[g_idx];\n for h_idx in [1..rank] do\n h:=Simples[h_idx];\n if g_idx = rank then\n if h_idx = rank then\n # m\\otimes m = Sum_{k\\in G}k+km\n N[g_idx][h_idx]:=List([1..rank],x->1);\n N[g_idx][h_idx][rank] := 0;\n else\n N[g_idx][h_idx][rank] := 1; # m\\otimes h = m\n fi;\n else\n if h_idx = rank then\n N[g_idx][h_idx][rank] := 1; # g\\otimes m = m\n else \n # g\\otimes h = gh\n N[g_idx][h_idx][Position(Simples,gh)] := 1;\n fi;\n fi;\n od;\n od;\n\n FPdimC := 2Order(G);\n FPdim := List([1..rank],x->1);\n FPdim[rank] := Sqrt(Order(G));\n\n if not(IsAbelian(G) and Exponent(G)=2) then\n # not braided. Return the fusion rules and simples (arxiv:math/0011037v1)\n Display(\"G is not an elementary abelian 2-group and so the associated category does not admit a braiding.\");\n return [Simples, N, FPdim, FPdimC];\n else\n # the category admits a braiding.\n # \n # need to compute the S-matrix and T-matrix\n #\n # First we compute T\n sigma1:=List([1..rank-1],x->delta[x]Sqrt(chi[x][x]));\n sigma3_1:=delta[1]Sqrt(tauSum(sigma1));\n T:=List([1..rank],x->0);\n for x in [1..rank-1] do\n T[x] := chi[x][x];\n od;\n T[rank]:=Tsign/sigma3_1;\n S:=NullMat(rank,rank);\n # sigma1 = sigma2 (Seihler section 2.3)\n # since delta[x] = pm1 we have sigma1[g]sigma2[g] = chi[g][g]\n sigma3:=List([1..rank-1],x->sigma3_1sigma1[x]chi[x][x]);\n sigma3_squared:=List(sigma3,x->x^2);\n sigma3_squared_trace:=Sum(sigma3);\n for g in [1..rank-1] do\n for h in [1..rank-1] do\n # group elements are invertible\n #S[g][h] := chi[g][h]chi[h][g]FPdim[g]FPdim[h];\n S[g][h] := chi[g][h]chi[h][g];\n od;\n #S[g][m] := sigma1[g]sigma2[g]FPdim[g]FPdim[rank];\n # group elements are invertible\n S[g][rank] := chi[g][g]FPdim[rank];\n S[rank][g] := S[g][rank];\n od;\n S[rank][rank] := sigma3_squared_traceFPdim[rank]FPdim[rank];\n Display(\"VERIFY S and T\\n\");\n return [Simples,S,T,N,FPdim,FPdimC];\n fi;\nend);\n#E near_group_data.gi . . . . . . . . . . . . . . . . . . . . . . . . ends here\n", "meta": {"hexsha": "19e6999dc875f63c493675658423d5f92c2f7ca8", "size": 5573, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "lib/near_group_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/near_group_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/near_group_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": 32.5906432749, "max_line_length": 138, "alphanum_fraction": 0.5420778755, "num_tokens": 1842, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7154240079185319, "lm_q2_score": 0.5774953651858118, "lm_q1q2_score": 0.4131540487156097}}
	{"text": "#############################################################################\n##\n#W mindeg.gi GAP 4 package SingerAlg Thomas Breuer\n##\n## This file contains the implementation for GAP functions related to\n## the numbers <M>m(q,e)</M>.\n##\n\n\n#############################################################################\n##\n#M SingerAlgE( <A> )\n#M SingerAlgE( <q>[, <n>], <z> )\n##\nInstallMethod( SingerAlgE,\n [ \"IsSingerAlgebra\" ],\n A -> CallFuncList( SingerAlgE, ParametersOfSingerAlgebra( A ) ) );\n\nInstallMethod( SingerAlgE,\n [ \"IsPosInt\", \"IsPosInt\", \"IsPosInt\" ],\n { q, n, z } -> (q^n-1) / z );\n\nInstallMethod( SingerAlgE,\n [ \"IsPosInt\", \"IsPosInt\" ],\n { q, z } -> (q^OrderMod( q, z )-1) / z );\n\n\n#############################################################################\n##\n#M MinimalDegreeOfSingerAlgebraGAP( <A> )\n#M MinimalDegreeOfSingerAlgebraGAP( <q>, <e> )\n#M MinimalDegreeOfSingerAlgebraGAP( <q>, <n>, <e> )\n##\n## If the <Ref Attr=\"LoewyStructureInfo\" Label=\"for a Singer algebra\"/>\n## value of the Singer algebra <A>A</A> is known then use it.\n## If the cheap criteria suffice then take their result.\n## Otherwise call the hard method for <A>q</A> and <A>e</A>;\n## if the dimension of the algebra is small then use the algebra\n## also if just the parameters <A>q</A> and <A>e</A> are given.\n##\nInstallMethod( MinimalDegreeOfSingerAlgebraGAP,\n [ \"IsSingerAlgebra and HasLoewyStructureInfoGAP\" ],\n A -> LoewyStructureInfoGAP( A ).m );\n\nInstallMethod( MinimalDegreeOfSingerAlgebraGAP,\n [ \"IsSingerAlgebra\" ],\n function( A )\n local paras, q, n, e;\n\n # Note that we cannot assume that the parameter 'n' is equal to\n # the multiplicative order of 'q' modulo 'e'.\n paras:= ParametersOfSingerAlgebra( A );\n q:= paras[1];\n n:= paras[2];\n e:= SingerAlgE( A );\n return MinimalDegreeOfSingerAlgebraGAP( q, OrderModExt( q, e, n ), e );\n end );\n\nInstallMethod( MinimalDegreeOfSingerAlgebraGAP,\n [ \"IsPosInt\", \"IsPosInt\" ],\n { q, e } -> MinimalDegreeOfSingerAlgebraGAP( q, OrderMod( q, e ), e ) );\n\nInstallMethod( MinimalDegreeOfSingerAlgebraGAP,\n [ \"IsPosInt\", \"IsPosInt\", \"IsPosInt\" ],\n function( q, n, e )\n local e_str, cache_e, m;\n\n q:= q mod e;\n e_str:= String( e ); # large integers cannot be record component names\n\n if not IsBound( MinimalDegreeOfSingerAlgebraCache.( e_str ) ) then\n cache_e:= rec();\n MinimalDegreeOfSingerAlgebraCache.( e_str ):= cache_e;\n else\n cache_e:= MinimalDegreeOfSingerAlgebraCache.( e_str );\n if IsBound( cache_e.( q ) ) then\n return cache_e.( q );\n fi;\n fi;\n\n m:= MinimalDegreeCheapGAP( q, n, e );\n if m = 0 then\n m:= MinimalDegreeHardGAP( q, n, e );\n fi;\n\n # Extend the cache.\n cache_e.( q ):= m;\n\n return m;\n end );\n\n\n#############################################################################\n##\n#F MinimalDegreeCheapGAP( <q>, <n>, <e> )\n##\n## Return either <C>0</C> or the number <M>m( <A>q</A>, <A>e</A> )</M>,\n## which is the smallest number of powers of <A>q</A>\n## such that <A>e</A> divides the sum of these powers.\n## <P/>\n## The return value <C>0</C> means that the cheap criteria from\n## the two papers <Cite Key=\"BHHK1\"/> and <Cite Key=\"BHHK2\"/>\n## do not suffice to determine <M>m( <A>q</A>, <A>e</A> )</M>.\n## <P/>\n## We assume that\n## <A>q</A> is smaller than <A>e</A>,\n## the argument <A>n</A> is\n## <C>OrderMod( </C><A>q</A><C>, </C><A>e</A><C> )</C>.\n## The function does not use cached values of <M>m( <A>q</A>, <A>e</A> )</M>\n## or values known via the database of low dimensional Singer algebras.\n##\nInstallGlobalFunction( MinimalDegreeCheapGAP, function( q, n, e )\n local e1, e2, m;\n\n if e = 1 then\n return 1;\n fi;\n\n Assert( 2, PowerMod( q, n, e ) = 1 and OrderModExt( q, e, n ) = n );\n\n if q = 1 then\n # Example I.6.1.\n return e;\n elif IsEvenInt( n ) and PowerModInt( q, n/2, e ) = e-1 then\n # Decide the case m = 2, see Lemma I.6.3.\n return 2;\n elif n = 2 then\n # Prop. II.2.7.\n e1:= Gcd( e, q-1 );\n e2:= Gcd( e, q+1 );\n if e2 <= e1 or ( IsEvenInt( e ) and IsEvenInt( (q^2-1)/e ) ) then\n return e1;\n else\n return 2 * e1;\n fi;\n fi;\n\n # Deal with those cases where e is a prime power,\n # and where we know the value of m(q,e).\n if IsPrimePowerInt( e ) then\n # Let e = p^k for a prime p.\n if e mod 2 = 0 then\n # see Prop. II.2.9, note that here we have e > 4 and q mod e <> q-1.\n if q mod 4 = 1 then\n return Gcd( e, q-1 );\n else\n Assert( 1, ( q+1 ) mod e <> 0 );\n return 4;\n fi;\n else\n # see Prop. II.2.10, note that q \\equiv 1 \\pmod{p}\n # if and only if \\gcd( e, q-1 ) \\not= 1 holds.\n m:= Gcd( e, q-1 );\n if m <> 1 then\n return m;\n elif n mod 3 = 0 then\n # Here we know that m(q,e) > 2 and thus p \\not= 3.\n # Hence \\gcd( e, q^{n/3}-1 ) = 1 holds,\n # because otherwise q^{n/3} would be a p-element in (Z/eZ)^.\n # Thus Lemma I.6.4 yields m(q,e) \\leq 3.\n # (This is a generalization of Cor. II.2.11.)\n return 3;\n elif 2 n = Phi( e ) then\n # Cor. II.2.14.\n return 3;\n elif e mod 11 = 0 then\n # Prop. II.2.16.\n return 5;\n fi;\n fi;\n fi;\n\n # Deal with those cases where e is twice an odd prime power,\n # and where we know the value of m(q,e).\n if IsEvenInt( e ) and IsPrimePowerInt( e/2 ) then\n # see Prop. II.2.17, note that the order of q mod e is a power of p\n # if and only if \\gcd( e/2, q-1 ) \\not= 1 holds.\n m:= Gcd( e, q-1 );\n if m > 2 then\n return m;\n fi;\n fi;\n\n # We give up.\n return 0;\n end );\n\n\n#############################################################################\n##\n#F VectorIterator( m, n, s )\n##\n## iterator for all vectors of length n\n## with entries in { 0, 1, 2, ... m }\n## and coefficient sum s, such that ...\n##\n## fill the first n positions in v with smallest partition of s into\n## numbers at most m\n## (we assume that s <= mn)\n##\nBindGlobal( \"VectorIterator_ResetPrefix\", function( v, m, n, s )\n local rest, i, j;\n\n rest:= s;\n i:= 1;\n while m < rest do\n v[i]:= m;\n rest:= rest - m;\n i:= i + 1;\n od;\n v[i]:= rest;\n for j in [ i+1 .. n ] do\n v[j]:= 0;\n od;\n\n return v;\n end );\n\nBindGlobal( \"VectorIterator\", function( m, n, s )\n local next;\n\n if s > mn then\n # The iterator is empty.\n next:= false;\n else\n # Initialize the coefficient vector.\n next:= VectorIterator_ResetPrefix( [], m, n, s );\n fi;\n\n return IteratorByFunctions( rec(\n NextIterator:= function( iter )\n local result, pos, succ;\n\n result:= iter!.next;\n # Find the first position with a nonzero value\n # such that the value on the right is smaller than m.\n pos:= First( [ 1 .. iter!.n - 1 ],\n i -> result[i] <> 0 and result[ i+1 ] < iter!.m );\n if pos = fail then\n succ:= false;\n else\n succ:= ShallowCopy( result );\n succ[ pos ]:= result[ pos ] - 1;\n succ[ pos + 1 ]:= result[ pos + 1 ] + 1;\n VectorIterator_ResetPrefix( succ, iter!.m, pos,\n Sum( succ{ [ 1 .. pos ] } ) );\n fi;\n iter!.next:= succ;\n return result;\n end,\n\n IsDoneIterator:= iter -> ( iter!.next = false ),\n\n ShallowCopy:= function( iter )\n end,\n\n m:= m,\n n:= n,\n s:= s,\n\n next:= next,\n ) );\n end );\n\n\n#############################################################################\n##\n#F MinimalDegreeHardGAP( <q>, <n>, <e> )\n##\n## - assume that the cheap criteria do not yield the result\n## (e.g., m = 2 cannot occur here)\n## - assume q < e\n## - assume that n equals OrderMod( q, e )\n## - do not use the cache\n## - do not create the monomials by computing all q-adic expansions at once,\n## but create these coefficient vectors one by one, using an iterator\n## - for increasing values of m, run over those coefficient vectors\n## of length n and with entries in \\{ 0, 1, \\ldots, m \\}\n## such that the coefficient sum is s\n## and such that a largest entry is in the first position.\n##\nInstallGlobalFunction( MinimalDegreeHardGAP, function( q, n, e )\n local z, e1, m, powers, a, v;\n\n Assert( 2, PowerMod( q, n, e ) = 1 and OrderModExt( q, e, n ) = n );\n\n # If A[q,n,z] has small dimension and e is not very small\n # then enumerate its basis.\n # (For small e, we known that the m values are small,\n # so it is cheaper not to enumerate.)\n if e > 100 then\n z:= ( q^n - 1 ) / e;\n if z <= 10^5 then\n return LoewyStructureInfoGAP( q, n, z ).m;\n fi;\n fi;\n\n # m(q,e) is divisible by \\gcd( e, q-1 ), and m(q,e) \\geq 3.\n e1:= Gcd( e, q-1 );\n if e1 = 1 then\n m:= 3;\n elif e1 = 2 then\n m:= 4;\n else\n m:= e1;\n fi;\n\n powers:= List( [ 1 .. n-1 ], i -> PowerModInt( q, i, e ) );\n\n while true do\n for a in [ 1 .. m ] do\n for v in VectorIterator( a, n-1, m-a ) do\n if ( a + v * powers ) mod e = 0 then\n return m;\n fi;\n od;\n od;\n m:= m + e1;\n od;\n end );\n\n\n#############################################################################\n##\n#M MinimalDegreeOfSingerAlgebraJulia( <A> )\n#M MinimalDegreeOfSingerAlgebraJulia( <q>, <e> )\n#M MinimalDegreeOfSingerAlgebraJulia( <q>, <n>, <e> )\n##\n## Use the same criteria as for the &GAP; variant.\n## These methods are available only if &Julia; is available.\n##\nif IsPackageMarkedForLoading( \"JuliaInterface\", \"\" ) then\n\nInstallMethod( MinimalDegreeOfSingerAlgebraJulia,\n [ \"IsSingerAlgebra and HasLoewyStructureInfoJulia\" ],\n A -> JuliaToGAP( IsInt,\n Julia.Base.get( LoewyStructureInfoJulia( A ),\n JuliaSymbol( \"m\" ), 0 ) ));\n\nInstallMethod( MinimalDegreeOfSingerAlgebraJulia,\n [ \"IsSingerAlgebra\" ],\n function( A )\n local paras, q, n, e;\n\n # Note that we cannot assume that the parameter 'n' is equal to\n # the multiplicative order of 'q' modulo 'e'.\n paras:= ParametersOfSingerAlgebra( A );\n q:= paras[1];\n n:= paras[2];\n e:= SingerAlgE( A );\n\n # Supply 'A' as an argument in order to set the GAP attribute.\n return JuliaToGAP( IsInt,\n Julia.SingerAlg.MinimalDegree( q, OrderModExt( q, e, n ), e,\n A ) );\n end );\n\nInstallMethod( MinimalDegreeOfSingerAlgebraJulia,\n [ \"IsPosInt\", \"IsPosInt\" ],\n { q, e } -> JuliaToGAP( IsInt,\n Julia.SingerAlg.MinimalDegree( q, GAPToJulia( e ) ) ) );\n\nInstallMethod( MinimalDegreeOfSingerAlgebraJulia,\n [ \"IsPosInt\", \"IsPosInt\", \"IsPosInt\" ],\n { q, n, e } -> JuliaToGAP( IsInt,\n Julia.SingerAlg.MinimalDegree( q, n, GAPToJulia( e ) ) ) );\n\nfi;\n\n\n#############################################################################\n##\n#E\n\n", "meta": {"hexsha": "c2162ad72bc30d4587b9d2cc1a5abfbb585ac241", "size": 11349, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "gap/mindeg.gi", "max_stars_repo_name": "oscar-system/SingerAlg", "max_stars_repo_head_hexsha": "7d303756163638d97fa3bc93dd3546b400a4122f", "max_stars_repo_licenses": ["Naumen", "Condor-1.1", "MS-PL"], "max_stars_count": 3, "max_stars_repo_stars_event_min_datetime": "2020-09-11T10:12:03.000Z", "max_stars_repo_stars_event_max_datetime": "2021-10-02T13:37:49.000Z", "max_issues_repo_path": "gap/mindeg.gi", "max_issues_repo_name": "oscar-system/SingerAlg", "max_issues_repo_head_hexsha": "7d303756163638d97fa3bc93dd3546b400a4122f", "max_issues_repo_licenses": ["Naumen", "Condor-1.1", "MS-PL"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2021-05-04T21:41:17.000Z", "max_issues_repo_issues_event_max_datetime": "2021-05-04T21:41:17.000Z", "max_forks_repo_path": "gap/mindeg.gi", "max_forks_repo_name": "oscar-system/SingerAlg", "max_forks_repo_head_hexsha": "7d303756163638d97fa3bc93dd3546b400a4122f", "max_forks_repo_licenses": ["Naumen", "Condor-1.1", "MS-PL"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 30.264, "max_line_length": 78, "alphanum_fraction": 0.5167856199, "num_tokens": 3457, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. 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	{"text": "#\n# walrus: Computational Methods for Finitely Generated Monoids and Groups\n#\n\nInstallGlobalFunction(NewPregroupWord,\nfunction(pg, word)\n local maxk, rel;\n maxk := MaxPowerK(word);\n return Objectify(IsPregroupRelatorType,\n rec( pregroup := pg\n , base := maxk[1]\n , exponent := maxk[2]\n , baselen := Length(maxk[1]) ) );\nend);\n\nInstallGlobalFunction(NewPregroupRelator,\nfunction(pres, word, id)\n local maxk, rel;\n maxk := MaxPowerK(word);\n rel := Objectify(IsPregroupRelatorType,\n rec( pres := pres\n , base := maxk[1]\n , exponent := maxk[2]\n , baselen := Length(maxk[1])\n , __ID := id)\n );\n return rel;\nend);\n\nInstallMethod(Base, \"for a pregroup relator\",\n [IsPregroupRelator and IsPregroupRelatorRep ],\n r -> r!.base);\n\nInstallMethod(Exponent, \"for a pregroup relator\",\n [IsPregroupRelator and IsPregroupRelatorRep ],\n r -> r!.exponent);\n\nInstallMethod(Inverse, \"for a pregroup relator\",\n [ IsPregroupRelator and IsPregroupRelatorRep ],\n r -> Objectify(IsPregroupRelatorType,\n rec( pres := r!.pres\n , base := List(Reversed(r!.base), PregroupInverse)\n , exponent := r!.exponent\n , baselen := r!.baselen\n , __ID := -r!.__ID)\n ));\nInstallMethod(PregroupPresentationOf,\n \"for pregroup relators\",\n [IsPregroupRelator],\n r -> r!.pres);\n\nInstallMethod(Locations, \"for a pregroup relator\",\n [IsPregroupRelator],\nfunction(r)\n return List([1..r!.baselen], i -> NewLocation(r, i));\nend);\n\nInstallMethod(\\[\\], \"for a pregroup relator\",\n [IsPregroupRelator and IsPregroupRelatorRep, IsInt],\nfunction(r, p)\n local i, l;\n i := RemInt(p - 1, r!.baselen);\n if i < 0 then\n i := i + r!.baselen;\n fi;\n return r!.base[i + 1];\nend);\n\nInstallMethod(Length, \"for a pregroup relator\",\n [ IsPregroupRelator and IsPregroupRelatorRep ],\nfunction(r)\n return r!.baselen * r!.exponent;\nend);\n\n# we could possibly store this on creation\n# But this is run at most once anyway\nInstallMethod(Places, \"for a pregroup relator\",\n [ IsPregroupRelator and IsPregroupRelatorRep ],\nfunction(r)\n local P, res;\n\n res := [];\n\n for P in Places(PregroupPresentationOf(r)) do\n if Relator(P) = r then\n Add(res, P);\n fi;\n od;\n return res;\nend);\n\nInstallMethod(ViewString, \"for a pregroup relator\",\n [IsPregroupRelator],\nfunction(r)\n if Exponent(r) > 1 then\n return STRINGIFY(\"<pregroup relator (\"\n , List(r!.base, ViewString)\n , \")^\", r!.exponent, \">\");\n else\n return STRINGIFY(\"<pregroup relator \"\n , List(r!.base, ViewString)\n , \">\");\n fi;\nend);\n\nInstallMethod(IsBound\\[\\], \"for a pregroup relator, and an position\",\n [IsPregroupRelator, IsInt], ReturnTrue );\n\n\nInstallMethod(\\=, \"for a pregroup relator, and a pregroup relator\",\n [IsPregroupRelator, IsPregroupRelator],\nfunction(l,r)\n # id is uniqe wrt pregroup presentation. We should probably\n # make a family of relators for each presentation etc\n return l!.__ID = r!.__ID;\n return (l!.exponent = r!.exponent)\n and (l!.base = r!.base);\nend);\n\nInstallMethod(\\in, \"for a generator and a pregroup relator\",\n [ IsElementOfPregroup, IsPregroupRelator and IsPregroupRelatorRep],\nfunction(e,r)\n return e in r!.base;\nend);\n\n#T redo and move to pregroup files\nInstallGlobalFunction(ReduceUPregroupWord,\nfunction(word)\n local rw, rw2, i, j, one;\n\n if Length(word) = 0 then\n return [];\n fi;\n\n one := PregroupOf(word[1])[1];\n rw := ShallowCopy(word);\n\n for i in [2..Length(rw)] do\n if rw[i-1] * rw[i] <> fail then\n rw[i] := rw[i-1] * rw[i];\n rw[i-1] := one;\n fi;\n od;\n\n i := 1; j := 1;\n rw2 := [];\n while i <= Length(rw) do\n if rw[i] <> one then\n rw2[j] := rw[i];\n j := j + 1;\n fi;\n i := i + 1;\n od;\n\n return rw2;\nend);\n\n\n", "meta": {"hexsha": "6c6c84d3a5ffc56e47950eb2fe19144738114982", "size": 4467, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "gap/relator.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/relator.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/relator.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": 28.0943396226, "max_line_length": 82, "alphanum_fraction": 0.5374972017, "num_tokens": 1195, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. 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	{"text": "MEMO_Base64Digits :=\n \"0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz-_\";\n\nInstallGlobalFunction(MEMO_Digits,\nfunction(n, base, args...)\n local minlen, len, digits, str;\n # Adapted from the DigitsNumber function in GAPDoc-1.6.1\n if Length(args) = 0 then\n minlen := 0;\n elif Length(args) = 1 then\n minlen := args[1];\n else\n return fail;\n fi;\n digits := MEMO_Base64Digits;\n str := \"\";\n while n <> 0 do\n Add(str, digits[(n mod base) + 1]);\n n := QuoInt(n, base);\n od;\n if Length(str) < minlen then\n # Pad with zeroes\n Append(str, ListWithIdenticalEntries(minlen - Length(str), digits[1]));\n fi;\n return Reversed(str);\nend);\n\nInstallGlobalFunction(MEMO_Hash,\nfunction(key)\n local str, ints, sum, i;\n IO_ClearPickleCache(); # In case IO_Pickle was recently interrupted\n str := IO_Pickle(key); # Pickle the key to a string\n ints := SHA256String(str); # Get the SHA-256 checksum in 32-bit chunks\n sum := 0; # Bring all 256 bits together into a single integer\n for i in [1..Length(ints)] do\n sum := sum + ints[i] * 2 ^ (32 * (i-1));\n od;\n str := MEMO_Digits(sum, 64, 43); # Make into a padded base-64 string\n return str;\nend);\n", "meta": {"hexsha": "6486b6644034bb56e30018e056958a561f2bc4f8", "size": 1187, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "gap/hashing.gi", "max_stars_repo_name": "gap-packages/Memoisation", "max_stars_repo_head_hexsha": "0b1c1c172d52d57376876fd345aaa7db81792df1", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 3, "max_stars_repo_stars_event_min_datetime": "2019-08-20T21:02:33.000Z", "max_stars_repo_stars_event_max_datetime": "2019-12-19T09:25:15.000Z", "max_issues_repo_path": "gap/hashing.gi", "max_issues_repo_name": "gap-packages/Memoisation", "max_issues_repo_head_hexsha": "0b1c1c172d52d57376876fd345aaa7db81792df1", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 7, "max_issues_repo_issues_event_min_datetime": "2018-08-06T11:56:51.000Z", "max_issues_repo_issues_event_max_datetime": "2020-02-04T15:04:36.000Z", "max_forks_repo_path": "gap/hashing.gi", "max_forks_repo_name": "gap-packages/Memoisation", "max_forks_repo_head_hexsha": "0b1c1c172d52d57376876fd345aaa7db81792df1", "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": 28.9512195122, "max_line_length": 75, "alphanum_fraction": 0.6663858467, "num_tokens": 369, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7025300573952054, "lm_q2_score": 0.5813030906443133, "lm_q1q2_score": 0.4083828936343597}}
	{"text": "\n# Copyright 2018-2019, Carnegie Mellon University\n# See LICENSE for details\n\nDeclare(OLCompose);\n\nClass(OLCompose, Compose, rec(\n printSeparationChar := \" o \",\n toOperator := self >> (vec -> Checked(Length(vec)=self.dims()[2], OLCompose(DropLast(self._children, 1)).toOperator()(Last(self._children).toOperator()(vec))))\n));\n\nClass(LinearSystem, BaseMat, rec(\n abbrevs := [ (A, b) -> [A, b] ],\n new := (self, A, b) >> SPL(WithBases(self, rec(\n mat := A, rhs := b, dimensions := [Rows(A), Cols(A)]))),\n print := (self, i, is) >> Print(\"LinearSystem(\", self.mat, \", \", self.rhs, \")\"),\n dims := self >> self.dimensions,\n rChildren := self >> [self.mat, self.rhs],\n rSetChild := rSetChildFields(\"mat\", \"rhs\"),\n isReal := True\n));\n\nClass(Reduction, BaseMat, rec(\n abbrevs := [ (N, op, idval, isSaturated) -> [N, op, idval, isSaturated] ],\n new := (self, N, op, idval, isSaturated) >> SPL(WithBases(self, rec(\n N := N, op := op, idval := idval, isSaturated := isSaturated, dimensions := [1, N]))),\n print := (self, i, is) >> Print(\"Reduction(\", self.N, \", \", self.op, \", \", self.idval, \", \", self.isSaturated, \")\"),\n dims := self >> self.dimensions,\n rChildren := self >> [self.N, self.op, self.idval, self.isSaturated],\n rSetChild := rSetChildFields(\"N\", \"op\", \"idval\", \"isSaturated\"),\n transpose := self >> self,\n isReal := True,\n toOperator := self >> (vec -> Checked(Length(vec)=self.dims()[2], [RulesStrengthReduce(FoldL(vec, self.op, self.idval)).v]))\n));\n\nClass(Induction, BaseMat, rec(\n abbrevs := [ (N, op, initval) -> [N, op, initval] ],\n new := (self, N, op, initval) >> SPL(WithBases(self, rec(\n N := N, op := op, initval := initval, dimensions := [N, 1]))),\n print := (self, i, is) >> Print(\"Induction(\", self.N, \", \", self.op, \", \", self.initval, \")\"),\n dims := self >> self.dimensions,\n rChildren := self >> [self.N, self.op, self.initval],\n rSetChild := rSetChildFields(\"N\", \"op\", \"initval\"),\n isReal := True,\n recurrence := self >> ((j,v)->When(j=0, self.initval, self.op.at(self.recurrence()(j-1,v),v))),\n toOperator := self >> (vec -> Checked(Length(vec)=self.dims()[2], List([0..self.N-1], i->_unwrap(RulesStrengthReduce(self.recurrence()(i,vec[1]))))))\n));\n\nClass(PointWise, BaseMat, rec(\n abbrevs := [ (N, op) -> [N, op] ],\n new := (self, N, op) >> SPL(WithBases(self, rec(\n N := N, op := op, dimensions := [N, N]))),\n print := (self, i, is) >> Print(\"PointWise(\", self.N, \", \", self.op, \")\"),\n dims := self >> self.dimensions,\n rChildren := self >> [self.N, self.op],\n rSetChild := rSetChildFields(\"N\", \"op\"),\n transpose := self >> self,\n isReal := True,\n toOperator := self >> (vec -> Checked(Length(vec)=self.dims()[2], List([0..Length(vec)-1], j->RulesStrengthReduce(self.op.at(vec[j+1], j)).v)))\n));\n\nClass(BinOp, BaseMat, rec(\n abbrevs := [ (N, op) -> [N, op] ],\n new := (self, N, op) >> SPL(WithBases(self, rec(\n N := N, op := op, dimensions := [N, 2N]))),\n print := (self, i, is) >> Print(\"BinOp(\", self.N, \", \", self.op, \")\"),\n dims := self >> self.dimensions,\n rChildren := self >> [self.N, self.op],\n rSetChild := rSetChildFields(\"N\", \"op\"),\n isReal := True,\n toOperator := self >> (vec -> Checked(Length(vec)=self.dims()[2], List([1..Length(vec)/2], j->RulesStrengthReduce(self.op.at(vec[j], vec[j+self.N])).v)))\n));\n\nClass(ScalarProd, BaseMat, rec(\n abbrevs := [ (N, scalars) -> [N, scalars] ],\n new := (self, N, scalars) >> SPL(WithBases(self, rec(\n N := N, scalars := scalars, dimensions := [1, N]))),\n print := (self, i, is) >> Print(\"ScalarProd(\", self.N, \", \", self.scalars, \")\"),\n dims := self >> self.dimensions,\n rChildren := self >> [self.N, self.scalars],\n rSetChild := rSetChildFields(\"N\", \"scalars\"),\n isReal := True,\n toOperator := self >>(vec -> Checked(Length(vec)=self.dims()[2], [_unwrapVec(self.scalars) vec]))\n));\n\nClass(Constant, BaseMat, rec(\n abbrevs := [ x -> [x]],\n new := (self, x) >> SPL(WithBases(self, rec(\n value := x, dimensions := [1,0]))),\n print := (self, i ,is) >> Print(\"Constant(\",self.value,\")\"),\n dims := self >> self.dimensions,\n rChildren := self >> [self.value],\n rSetChild := rSetChildFields(\"value\"),\n isReal := True\n));\t\t\n\nspiral.spl.IterVStack.toOperator := \n self >> (vec -> Checked(Length(vec)=self.dims()[2], \n Flat(List([0..self.var.range-1], \n j->RulesStrengthReduce(\n SubstVars(Copy(self._children[1]), \n rec((self.var.id):=V(j))\n )\n ).toOperator()(vec) )\n )\n )\n );\n\nspiral.spl.HStack.toOperator := \n self >> (vec -> Checked(Length(vec)=self.dims()[1]Length(self.children()), \n \t \t Sum(List([1..Length(self.children())], \n\t i->self.children()[i].toOperator()(vec{[(i-1)self.dims()[1] + 1..i*self.dims()[1]]})\n\t\t ))\n\t \t )\n );\n\nspiral.spl.DirectSum.toOperator := self >> (vec -> Checked(Length(vec)=Sum(List(self.children(), i->i.dims()[2])), \n ApplyFunc(Concat, List([1..Length(self.children())], \n i->self.children()[i].toOperator()(vec{\n [Sum(List(self.children(){[1..i-1]}, j->j.dims()[2]))+1..Sum(List(self.children(){[1..i]}, j->j.dims()[2]))]\n })))));\n\n\n\nspiral.spl.I.N := self >> self.params[1];\n", "meta": {"hexsha": "415716060653413e3b29aa137cee928de1a506cc", "size": 5515, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "spl.gi", "max_stars_repo_name": "spiral-software/spiral-package-hcol", "max_stars_repo_head_hexsha": "b4a0118382e3bba91ecd82a6c667f2cdb6389ceb", "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": "spl.gi", "max_issues_repo_name": "spiral-software/spiral-package-hcol", "max_issues_repo_head_hexsha": "b4a0118382e3bba91ecd82a6c667f2cdb6389ceb", "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": "spl.gi", "max_forks_repo_name": "spiral-software/spiral-package-hcol", "max_forks_repo_head_hexsha": "b4a0118382e3bba91ecd82a6c667f2cdb6389ceb", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2019-11-26T05:21:02.000Z", "max_forks_repo_forks_event_max_datetime": "2019-11-26T05:21:02.000Z", "avg_line_length": 43.7698412698, "max_line_length": 163, "alphanum_fraction": 0.5410698096, "num_tokens": 1673, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7025300573952054, "lm_q2_score": 0.5774953651858118, "lm_q1q2_score": 0.4057078520494534}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nImportAll(paradigms.smp); # for AParSMP\nImportAll(paradigms.vector); # for VRCLR\nImport(approx); # for CeilingRat.\n\n_swrap := (nt) -> let(t:=nt.firstTag(), ScratchWrap(t.size,t.nsgmts,t.linesize));\n\n_nodeFitsTensorDoesnt := (nt) -> let (\n k := nt.getTag(1).size,\n m := nt.params[1].dims()[2],\n n := nt.params[2],\n\n 2m <= k and mn >= k\n);\n\n_isALStoreTag := (nt) -> nt.isTag(1,ALStore) or nt.isTag(1,ALStoreCx);\n\nNewRulesFor(TTensorI, rec(\n# (In x Am)_{LS(<=k)} -> In x (Am)_{LS(<=k)} for m > k\n IxA_scratch_push := rec(\n forTransposition := false,\n applicable := nt -> nt.hasTags() \n and _isALStoreTag(nt)\n and IsParPar(nt.params) \n and nt.params[1].dims()[2] > nt.getTag(1).size,\n\n children := nt -> [[ nt.params[1].withTags(nt.getTags()) ]],\n apply := (nt, c, cnt) -> Tensor(I(nt.params[2]), c[1])\n ),\n \n AxI_scratch_push := rec(\n forTransposition := false,\n applicable := nt -> nt.hasTags()\n and _isALStoreTag(nt)\n and IsVecVec(nt.params)\n and nt.params[1].dims()[2] > nt.getTag(1).size,\n children := nt -> [[nt.params[1].withTags(nt.getTags())]],\n apply := (nt, c, cnt) -> Tensor(c[1], I(nt.params[2]))\n ),\n\n# ==========================================================\n# synchronous rules\n\n# (In x Am)_{LS(<=k)} -> Imn/k x (Ik/m x Am) for m\|k and k\|mn\n IxA_scratch := rec(\n forTransposition := false,\n applicable := nt -> nt.hasTags() \n and _isALStoreTag(nt)\n\t and IsParPar(nt.params)\n and IsPosInt(nt.getTag(1).size / nt.params[1].dims()[2])\n and IsPosInt(nt.params[1].dims()[2] * nt.params[2] / nt.getTag(1).size),\n\n children := nt -> [[ \n TTensorI(\n nt.params[1],\n nt.getTag(1).size / nt.params[1].dims()[2], \n APar, APar\n ).withTags(Drop(nt.getTags(),1)).setWrap(\n _swrap(nt)\n )\n ]],\n apply := (nt, c, cnt) -> let(k := nt.getTag(1).size, m := nt.params[1].dims()[2], n:= nt.params[2],\n DMAFence(Tensor(\n I(mn/k),\n LSKernel(c[1], nt.params[1].normalizedArithCost() k/m)\n )))\n ),\n\n# (Am x In)_{LS(<=k)} -> (L^m^2n/k_m x Ik/m) (Imn/k x (Am x Ik/m)) (L^m^2n/k_mn/k x Ik/m) for m\|k and k\|mn\n AxI_scratch := rec(\n forTransposition := false,\n applicable := nt -> nt.hasTags() \n and _isALStoreTag(nt)\n\t and IsVecVec(nt.params) \n and IsPosInt(nt.getTag(1).size / nt.params[1].dims()[2])\n and IsPosInt(nt.params[1].dims()[2]nt.params[2] / nt.getTag(1).size),\n\n children := nt -> [[ let(t := nt.firstTag(),\n TTensorI(\n nt.params[1], \n t.size / nt.params[1].dims()[2], \n AVec, AVec\n ).withTags(Drop(nt.getTags(),1)).setWrap(_swrap(nt))\n ) ]],\n\n apply := (nt, c, cnt) -> let(\n k := nt.getTag(1).size, \n m := nt.params[1].dims()[2], \n n:= nt.params[2],\n\n DMAFence(Prm(fTensor(L(m^2n/k, m), fId(k/m))) \n Tensor(\n I(mn/k),\n LSKernel(c[1], nt.params[1].normalizedArithCost() * k/m)\n ) \n Prm(fTensor(L(m^2n/k, mn/k), fId(k/m))))\n )\n ),\n\n IxAL_scratch := rec(\n forTransposition := false,\n applicable := nt -> nt.hasTags()\n and _isALStoreTag(nt)\n and IsParVec(nt.params)\n and IsPosInt(nt.getTag(1).size/ nt.params[1].dims()[2])\n and IsPosInt(nt.params[1].dims()[2]nt.params[2]/nt.getTag(1).size),\n children := nt -> let(\n k := nt.firstTag().size,\n m := nt.params[1].dims()[2],\n\n [[ TTensorI(\n nt.params[1], \n k/m, \n APar,AVec\n ).withTags(Drop(nt.getTags(),1)).setWrap(_swrap(nt)) \n ]]),\n\n apply := (self, nt, c, cnt) >> let(\n k := nt.getTag(1).size, \n m := nt.params[1].dims()[2], \n n := nt.params[2],\n\n DMAFence(\n Tensor(\n I(mn/k),\n LSKernel(c[1],nt.normalizedArithCost() k/m)\n ) \n Prm(fTensor(L(m^2n/k,mn/k),fId(k/m)))\n )\n ),\n ),\n\n L_IxA_scratch := rec(\n forTransposition := false,\n applicable := nt -> nt.hasTags() \n and _isALStoreTag(nt) \n\t and IsVecPar(nt.params),\n\n children := nt -> [[ \n TTensorI(\n nt.params[1], \n nt.getTag(1).size / nt.params[1].dims()[2], \n AVec, APar\n ).withTags(Drop(nt.getTags(),1)).setWrap(\n _swrap(nt)\n )\n ]],\n\n apply := (self, nt, c, cnt) >> let(\n k := nt.getTag(1).size,\n m := nt.params[1].dims()[2], \n n:= nt.params[2],\n\n DMAFence( \n Prm(fTensor(L(m^2n/k, mn/k), fId(k/m))\n ) Tensor(LSKernel(\n c[1], nt.normalizedArithCost() * k/m\n ), I(mn/k))\n )\n )\n ),\n#====================================================================\n# SWP Rules - double buffering is applied\n IxA_scratch_swp := rec(\n forTransposition := false,\n applicable := nt -> nt.hasTags() \n and _isALStoreTag(nt)\n\t and IsParPar(nt.params)\n and IsPosInt(nt.getTag(1).size / (2 nt.params[1].dims()[2]))\n and IsPosInt(2 * nt.params[1].dims()[2] * nt.params[2] / nt.getTag(1).size),\n\n children := nt -> [[ \n TTensorI(\n nt.params[1],\n nt.getTag(1).size / (2 * nt.params[1].dims()[2]), \n APar, APar\n ).withTags(Drop(nt.getTags(),1)).setWrap(\n _swrap(nt)\n )\n ]],\n apply := (nt, c, cnt) -> let(k := nt.getTag(1).size, m := nt.params[1].dims()[2], n:= nt.params[2],\n DMAFence(Tensor(\n I(2mn/k),\n LSKernel(c[1], nt.params[1].normalizedArithCost() * k/(2m))\n )))\n ),\n\n AxI_scratch_swp := rec(\n forTransposition := false,\n applicable := nt -> nt.hasTags() \n and _isALStoreTag(nt)\n\t and IsVecVec(nt.params) \n and IsPosInt(nt.getTag(1).size / (2nt.params[1].dims()[2]))\n and IsPosInt(2nt.params[1].dims()[2]nt.params[2] / nt.getTag(1).size),\n\n children := nt -> [[ let(t := nt.firstTag(),\n TTensorI(\n nt.params[1], \n t.size / (2nt.params[1].dims()[2]), \n AVec, AVec\n ).withTags(Drop(nt.getTags(),1)).setWrap(_swrap(nt))\n ) ]],\n\n apply := (nt, c, cnt) -> let(\n k := nt.getTag(1).size, \n m := nt.params[1].dims()[2], \n n:= nt.params[2],\n\n DMAFence(Prm(fTensor(L(2m^2n/k, 2m), fId(k/(2m)))) \n Tensor(\n I(2mn/k),\n LSKernel(c[1], nt.params[1].normalizedArithCost() * k/(2m))\n ) \n Prm(fTensor(L(2m^2n/k, 2mn/k), fId(k/(2m)))))\n )\n ),\n\n IxAL_scratch_swp := rec(\n forTransposition := false,\n applicable := nt -> nt.hasTags()\n and _isALStoreTag(nt)\n and IsParVec(nt.params)\n and IsPosInt(nt.getTag(1).size/ (2nt.params[1].dims()[2]))\n and IsPosInt(2nt.params[1].dims()[2]nt.params[2]/nt.getTag(1).size),\n children := nt -> let(\n k := nt.firstTag().size,\n m := nt.params[1].dims()[2],\n\n [[ TTensorI(\n nt.params[1], \n k/(2m), \n APar,AVec\n ).withTags(Drop(nt.getTags(),1)).setWrap(_swrap(nt)) \n ]]),\n\n apply := (self, nt, c, cnt) >> let(\n k := nt.getTag(1).size, \n m := nt.params[1].dims()[2], \n n := nt.params[2],\n\n DMAFence(\n Tensor(\n I(2mn/k),\n LSKernel(c[1],nt.normalizedArithCost() k/(2m))\n ) \n Prm(fTensor(L(2m^2n/k,2mn/k),fId(k/(2m))))\n )\n ),\n ),\n\n L_IxA_scratch_swp := rec(\n forTransposition := false,\n applicable := nt -> nt.hasTags() \n and _isALStoreTag(nt) \n\t and IsVecPar(nt.params)\n and IsPosInt(nt.getTag(1).size/ (2nt.params[1].dims()[2]))\n and IsPosInt(2nt.params[1].dims()[2]nt.params[2]/nt.getTag(1).size),\n\n children := nt -> [[ \n TTensorI(\n nt.params[1], \n nt.getTag(1).size / (2nt.params[1].dims()[2]), \n AVec, APar\n ).withTags(Drop(nt.getTags(),1)).setWrap(\n _swrap(nt)\n )\n ]],\n\n apply := (self, nt, c, cnt) >> let(\n k := nt.getTag(1).size,\n m := nt.params[1].dims()[2], \n n:= nt.params[2],\n\n DMAFence( \n Prm(fTensor(L(2m^2n/k, 2mn/k), fId(k/(2m)))\n ) * Tensor(LSKernel(\n c[1], nt.normalizedArithCost() * k/(2m)\n ), I(2m*n/k))\n )\n )\n )\n));\n", "meta": {"hexsha": "30680d70d4a8a18801d2f33da0edacb57129f681", "size": 9722, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/scratchpad/breakdown.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/scratchpad/breakdown.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/scratchpad/breakdown.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": 33.8745644599, "max_line_length": 108, "alphanum_fraction": 0.4279983542, "num_tokens": 2720, "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\nNewRulesFor(TRaderMid, rec(\n Pad_vec := rec(\n applicable := (self, t) >> t.isTag(1, AVecReg) or t.isTag(1, AVecRegCx),\n forTransposition := false,\n apply := (t, C, Nonterms) -> let(\n v := t.firstTag().v,\n ds := Rows(t)-1,\n When(IsInt(ds/v),\n DelayedDirectSum(VScat_sv(fId(1), v , 1), I(ds))\n * VecRaderMid(t.params[1], t.params[2], t.params[3], v)\n * DelayedDirectSum(VGath_sv(fId(1), v , 1), I(ds)),\n DelayedDirectSum(VScat_sv(fId(1), v , 1), VScat_sv(fId(ds), v, 1))\n * VecRaderMid(t.params[1], t.params[2], t.params[3], v)\n * DelayedDirectSum(VGath_sv(fId(1), v , 1), VGath_sv(fId(ds), v, 1))\n )\n )\n )\n));\n", "meta": {"hexsha": "fc452e6cddff6bf6917c5eb061d675215195ec82", "size": 860, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/vector/breakdown/tradermid.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/tradermid.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/breakdown/tradermid.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": 35.8333333333, "max_line_length": 84, "alphanum_fraction": 0.511627907, "num_tokens": 276, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7490872131147275, "lm_q2_score": 0.5389832206876841, "lm_q1q2_score": 0.4037454387005374}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nClass(UTwid, DiagFunc, rec(\n def := (N, n, k, a, b, i) -> rec(size:=n),\n lambda := self >> let(N:=self.params[1], n:=self.size, k:=self.params[3],\n\ta := self.params[4], b := self.params[5], i := self.params[6],\n\tna := Numerator(a), nb := Numerator(b),\n\tda := Denominator(a), db := Denominator(b),\n\tw := E(Ndadb)^k, j := Ind(n),\n\tLambda(j, cond(eq(j,n/2), omega(dadb,k), omega(Ndadb, k(ida+na)(jdb+nb)))))\n));\nClass(UTwid1, DiagFunc, rec(\n def := (N, n, k, a, b, i) -> rec(size:=n),\n lambda := self >> let(N:=self.params[1], n:=self.size, k:=self.params[3],\n\ta := self.params[4], b := self.params[5], i := self.params[6],\n\tna := Numerator(a), nb := Numerator(b),\n\tda := Denominator(a), db := Denominator(b),\n\tw := E(Ndadb)^k, j := Ind(n),\n\tLambda(j, cond(eq(j,n/2), 1, omega(Ndadb, k(ida+na)(jdb+nb)))))\n));\n\nClass(UDFT_NonTerm, DFT_NonTerm, rec(\n isReal := False,\n));\n\nClass(UDFT, UDFT_NonTerm, rec(\n abbrevs := [ \n (n) -> Checked(IsPosIntSym(n), AnySyms(n) or (n mod 2=0), [n, 1]),\n (n,k) -> Checked(IsPosIntSym(n), AnySyms(n) or (n mod 2=0), \n\t IsIntSym(k), AnySyms(n,k) or Gcd(n,k)=1, \n\t\t [n, When(AnySyms(n,k), k, k mod n)]) ],\n omega4pow := (r,c)->4rc,\n terminate := self >> let(\n\tn:=self.params[1], k:=self.params[2], m:=MatSPL(DFT(2))^-1,\n\tDirectSum(Mat(m), I(n-2))^L(n,n/2) \n\tDFT(n,k).terminate()),\n\n conjTranspose := self >> ObjId(self)(self.params[1], -self.params[2]).transpose()\n));\nUDFT1 := UDFT;\n\nClass(UDFT2, UDFT_NonTerm, rec(\n abbrevs := [ \n (n) -> Checked(IsPosIntSym(n), AnySyms(n) or (n mod 2=0), [n, 1]),\n (n,k) -> Checked(IsPosIntSym(n), AnySyms(n) or (n mod 2=0), \n\t IsIntSym(k), AnySyms(n,k) or Gcd(n,k)=1, \n\t\t [n, When(AnySyms(n,k), k, k mod (2n))]) ],\n omega4pow := (r,c)->2r(2c+1),\n terminate := self >> let(\n\tn:=self.params[1], k:=self.params[2], m:=MatSPL(DFT2(2,k))^-1,\n\tDirectSum(Mat(m), I(n-2))^L(n,n/2) \n\tDFT2(n,k).terminate()),\n));\n\nClass(UUDFT, UDFT_NonTerm, rec(\n abbrevs := [ \n (n) -> Checked(IsPosIntSym(n), AnySyms(n) or (n mod 4=0), [n, 1]),\n (n,k) -> Checked(IsPosIntSym(n), AnySyms(n) or (n mod 4=0), \n\t IsIntSym(k), AnySyms(n,k) or Gcd(n,k)=1, \n\t\t [n, When(AnySyms(n,k), k, k mod n)]) ],\n omega4pow := (r,c)->4rc,\n terminate := self >> let(\n\tn:=self.params[1], k:=self.params[2], m:=MatSPL(DFT(2))^-1,\n\tDirectSum(Mat(m), I((n-4)/2), Mat(m), I((n-4)/2))^L(n,n/2) \n\tDFT(n,k).terminate()),\n));\nUUDFT1 := UUDFT;\n\nClass(UUDFT2, UDFT_NonTerm, rec(\n abbrevs := [ \n (n) -> Checked(IsPosIntSym(n), AnySyms(n) or (n mod 4=0), [n, 1]),\n (n,k) -> Checked(IsPosIntSym(n), AnySyms(n) or (n mod 4=0), \n\t IsIntSym(k), AnySyms(n,k) or Gcd(n,k)=1, \n\t\t [n, When(AnySyms(n,k), k, k mod (2n))]) ],\n omega4pow := (r,c)->2r(2c+1),\n terminate := self >> let(\n\tn:=self.params[1], k:=self.params[2], m:=MatSPL(DFT2(2,k))^-1,\n\tDirectSum(Mat(m), I((n-2)/2), Mat(m), I((n-2)/2))^L(n,n/2) *\n\tDFT2(n,k).terminate()),\n));\n", "meta": {"hexsha": "0f61c691bb7e9a2e56a15a697cbd3f0d38d9256b", "size": 3168, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/dft/udft.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/udft.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/udft.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": 37.7142857143, "max_line_length": 84, "alphanum_fraction": 0.5299873737, "num_tokens": 1233, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.757794360334681, "lm_q2_score": 0.5312093733737563, "lm_q1q2_score": 0.4025474672995523}}
	{"text": "#!/usr/bin/gap\n\n# time gap -o 8g clifford.gap\n\n# Build clifford groups, up to 3 qubits, and\n# search for T operators defined by field extensions......\n\n\nPrint(\"running clifford.gap\\n\");;\n\n# See:\n# https://www.mathstat.dal.ca/~selinger/papers/clifford.pdf\n\nr2 := Sqrt(2);;\nir2 := 1/r2;;\n\ni := [[1, 0], [0, 1]];;\nw := [[E(4), 0], [0, E(4)]];;\nx := [[0, 1], [1, 0]];;\nz := [[1, 0], [0, -1]];;\ns := [[1, 0], [0, E(4)]];;\nh := [[ir2, ir2], [ir2, -ir2]];;\n\nCliff1 := Group(w, s, h);; # Order 192\nPauli1 := Group(w, x, z);; # Order 32\n\nfor U in Cliff1 do\n found := false;;\n #Udag := Inverse(U);\n #Print(\"found? \");\n for g in Pauli1 do\n if (UgInverse(U)Inverse(g) in Pauli1) then found:=true; break; fi;\n od;\n if not found then Print(\"Not found\\n\"); fi;\nod;\n\nxi := KroneckerProduct(x, i);;\nix := KroneckerProduct(i, x);;\nzi := KroneckerProduct(z, i);;\niz := KroneckerProduct(i, z);;\nsi := KroneckerProduct(s, i);;\nis := KroneckerProduct(i, s);;\nhi := KroneckerProduct(h, i);;\nih := KroneckerProduct(i, h);;\nwi := KroneckerProduct(w, i);;\n\n\ncz := [\n [1, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, -1]];;\n\nCliff2 := Group(si, is, hi, ih, wi, cz);; # Order 92160\n#for g in Cliff2 do Print(g, \"\\n\"); od;\nPauli2 := Group(wi, xi, ix, zi, iz);;\n\n# Works:\nfor U in Cliff2 do\n found := false;;\n #Udag := Inverse(U);\n #Print(\"found? \");\n for g in Pauli2 do\n if (UgInverse(U)Inverse(g) in Pauli2) then found:=true; break; fi;\n od;\n if not found then Print(\"Not found\\n\"); fi;\nod;\n\na := [\n [0, 1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n [-1, 0, 0, 0]];; # a in G2 = true\n\n#Print(aa, \"\\n\");\n#Print(aaa, \"\\n\");\n#Print(aaaa, \"\\n\");\n\n# Print(Order(G2));\n\n\nxii := KroneckerProduct(xi, i);;\nixi := KroneckerProduct(i, xi);;\niix := KroneckerProduct(i, ix);;\n\nzii := KroneckerProduct(zi, i);;\nizi := KroneckerProduct(i, zi);;\niiz := KroneckerProduct(i, iz);;\n\nsii := KroneckerProduct(si, i);;\nisi := KroneckerProduct(i, si);;\niis := KroneckerProduct(i, is);;\n\nhii := KroneckerProduct(hi, i);;\nihi := KroneckerProduct(i, hi);;\niih := KroneckerProduct(i, ih);;\n\nwii := KroneckerProduct(wi, i);;\n\nicz := KroneckerProduct(i, cz);;\nczi := KroneckerProduct(cz, i);;\n\nca := [\n [1, 0, 0, 0, 0, 0, 0, 0],\n [0, 1, 0, 0, 0, 0, 0, 0],\n [0, 0, 1, 0, 0, 0, 0, 0],\n [0, 0, 0, 1, 0, 0, 0, 0],\n [0, 0, 0, 0, 0, 1, 0, 0],\n [0, 0, 0, 0, 0, 0, 1, 0],\n [0, 0, 0, 0, 0, 0, 0, 1],\n [0, 0, 0, 0, -1, 0, 0, 0]];;\n\ncb := [\n [1, 0, 0, 0, 0, 0, 0, 0],\n [0, 1, 0, 0, 0, 0, 0, 0],\n [0, 0, 1, 0, 0, 0, 0, 0],\n [0, 0, 0, 1, 0, 0, 0, 0],\n [0, 0, 0, 0, 0, 0, 1, 0],\n [0, 0, 0, 0, 0, 0, 0, 1],\n [0, 0, 0, 0, -1, 0, 0, 0],\n [0, 0, 0, 0, 0, -1, 0, 0]];;\n\ncc := [\n [1, 0, 0, 0, 0, 0, 0, 0],\n [0, 1, 0, 0, 0, 0, 0, 0],\n [0, 0, 1, 0, 0, 0, 0, 0],\n [0, 0, 0, 1, 0, 0, 0, 0],\n [0, 0, 0, 0, 0, 0, 0, 1],\n [0, 0, 0, 0, -1, 0, 0, 0],\n [0, 0, 0, 0, 0, -1, 0, 0],\n [0, 0, 0, 0, 0, 0, -1, 0]];;\n\n\nTofolli := [\n [1, 0, 0, 0, 0, 0, 0, 0],\n [0, 1, 0, 0, 0, 0, 0, 0],\n [0, 0, 1, 0, 0, 0, 0, 0],\n [0, 0, 0, 1, 0, 0, 0, 0],\n [0, 0, 0, 0, 1, 0, 0, 0],\n [0, 0, 0, 0, 0, 1, 0, 0],\n [0, 0, 0, 0, 0, 0, 0, 1],\n [0, 0, 0, 0, 0, 0, 1, 0]];;\n\n\nCliff3 := Group(sii, isi, iis, hii, ihi, iih, wii, icz, czi);; # Order 743178240\nPauli3 := Group(wii, xii, ixi, iix, zii, izi, iiz);; # Order 256\n\n# Print(Order(Pauli3), \"\\n\");;\n\n# ca in Cliff3 = false\n# ca in third level of clifford hierarchy = true\n\n\nCliff3_12 := Group(sii, isi, hii, ihi, wii, czi);;\nCliff3_13 := Group(sii, iis, hii, iih, wii);; # cz on 1&3 ??\nCliff3_23 := Group(isi, iis, ihi, iih, wii, icz);;\n\n#SmCliff3 := Group(sii, isi, iis, hii, ihi, iih, icz, czi);; # Order 743178240\n\nPrint(\"warming up...\\n\");\nOrder(Cliff3);; # need this line otherwise membership test eats all memory...!\nPrint(\"Ok\\n\");\n\nin_third_level := function(U)\n # Is U in the third level of the clifford hierarchy ?\n local A;\n for g in Pauli3 do\n A := UgInverse(U)Inverse(g);\n if A in Cliff3_12 then continue; fi;\n if A in Cliff3_13 then continue; fi;\n if A in Cliff3_23 then continue; fi;\n if A in Cliff3 then continue; fi;\n return false; # no\n od;\n return true; # yes\nend;;\n\n\nPrint(\"in_third_level(ca):\", in_third_level(ca), \"\\n\"); # true\nPrint(\"in_third_level(cb):\", in_third_level(cb), \"\\n\"); # true\nPrint(\"in_third_level(cc):\", in_third_level(cc), \"\\n\"); # true\nPrint(\"in_third_level(Tofolli):\", in_third_level(Tofolli), \"\\n\"); # true\nPrint(\"in_third_level(Tofollica):\", in_third_level(Tofolli*ca), \"\\n\"); # false\n\nU3 := [ \n [1, 0, 0, 0, 0, 0, 0, 0],\n [0, 1, 0, 0, 0, 0, 0, 0],\n [0, 0, 1, 0, 0, 0, 0, 0],\n [0, 0, 0, 1, 0, 0, 0, 0],\n [0, 0, 0, 0, 1, 0, 0, 0],\n [0, 0, 0, 0, 0, 1, 0, 0],\n [0, 0, 0, 0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0, 0, 0, 0]];\n\nPrint(\"# Where do control control 1-qubit Pauli gates live ?\\n\");\nfor g in Pauli1 do \n #Print(g, \"\\n\");\n U3{[7,8]}{[7,8]} := g;\n if U3 in Pauli3 then Print(\"1\\c\"); continue; fi;\n if U3 in Cliff3 then Print(\"2\\c\"); continue; fi;\n if in_third_level(U3) then Print(\"3\\c\"); else Print(\".\\c\"); fi;\nod;\nPrint(\"\\n\");\n\nPrint(\"# Where do control control 1-qubit clifford gates live ?\\n\");\nfor g in Cliff1 do \n #Print(g, \"\\n\");\n U3{[7,8]}{[7,8]} := g;\n if U3 in Pauli3 then Print(\"1\\c\"); continue; fi;\n if U3 in Cliff3 then Print(\"2\\c\"); continue; fi;\n if in_third_level(U3) then Print(\"3\\c\"); else Print(\".\\c\"); fi;\nod;\nPrint(\"\\n\");\n\nPrint(\"# Where do control 2-qubit Pauli gates live ?\\n\");\nfor g in Pauli2 do \n #Print(g, \"\\n\");\n U3{[5,6,7,8]}{[5,6,7,8]} := g;\n if U3 in Pauli3 then Print(\"1\\c\"); continue; fi;\n if U3 in Cliff3 then Print(\"2\\c\"); continue; fi;\n if in_third_level(U3) then Print(\"3\\c\"); else Print(\".\\c\"); fi;\nod;\nPrint(\"\\n\");\n\nPrint(\"# Where do control 2-qubit clifford gates live ?\\n\");\nfor g in Cliff2 do \n #Print(g, \"\\n\");\n U3{[5,6,7,8]}{[5,6,7,8]} := g;\n if U3 in Pauli3 then Print(\"1\\c\"); continue; fi;\n if U3 in Cliff3 then Print(\"2\\c\"); continue; fi;\n if in_third_level(U3) then Print(\"3\\c\"); else Print(\".\\c\"); fi;\nod;\n\nPrint(\"\\n\");\n\nPrint(\"Done.\\n\");\n\n\n", "meta": {"hexsha": "99b868878e0cf5e0ad4958cda6de0234c36a9d5d", "size": 6194, "ext": "gap", "lang": "GAP", "max_stars_repo_path": "bruhat/dev/clifford.gap", "max_stars_repo_name": "punkdit/bruhat", "max_stars_repo_head_hexsha": "3231eacc49fd3464542f7eb72684751371d9876c", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 3, "max_stars_repo_stars_event_min_datetime": "2020-04-07T13:21:30.000Z", "max_stars_repo_stars_event_max_datetime": "2020-07-15T02:07:20.000Z", "max_issues_repo_path": "bruhat/dev/clifford.gap", "max_issues_repo_name": "punkdit/bruhat", "max_issues_repo_head_hexsha": "3231eacc49fd3464542f7eb72684751371d9876c", "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": "bruhat/dev/clifford.gap", "max_forks_repo_name": "punkdit/bruhat", "max_forks_repo_head_hexsha": "3231eacc49fd3464542f7eb72684751371d9876c", "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": 25.9163179916, "max_line_length": 80, "alphanum_fraction": 0.5182434614, "num_tokens": 2859, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. NO", "lm_q1_score": 0.8221891392358015, "lm_q2_score": 0.48828339529583464, "lm_q1q2_score": 0.40146130448141687}}
	{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nDeclare(GT);\nDeclare(ListProduct);\n\nListProduct := function(l)\n local prod, i;\n if Length(l) <=0 then return 0; fi;\n prod := 1;\n for i in l do\n prod := prod * i;\n od;\n return(prod);\nend;\n\nGTVec := XChain([0,1]);\nGTPar := XChain([1,0]);\n\nTTensorI_GT := function(gt)\n local spl, g, s, v, tags;\n [spl,g,s,v] := gt.params;\n tags := gt.getTags();\n Constraint(IsList(v) and Length(v)=1 and IsPosInt(v[1]));\n g := When(g=XChain([0,1]), AVec, APar);\n s := When(s=XChain([0,1]), AVec, APar);\n return TTensorI(spl, v[1], s, g).withTags(tags);\nend;\n\nGT_TTensorI := function(tt)\n local spl, g, s, v, tags;\n [spl,v,s,g] := tt.params;\n tags := tt.getTags();\n g := When(g=AVec, GTVec, GTPar);\n s := When(s=AVec, GTVec, GTPar);\n return GT(spl, g, s, [v]).withTags(tags);\nend;\n\nIsGT := x -> IsRec(x) and IsBound(x.isGT) and x.isGT;\n\nClass(GTBase, rec(\n isGT := true,\n\n freeTags := self >> Filtered(self.tags, x -> not x.isSticky),\n stickyTags := self >> Filtered(self.tags, x -> x.isSticky),\n\n stickyRank := self >> Length(self.stickyTags()),\n freeRank := self >> self.rank() - self.stickyRank(),\n freeLoops := self >> [self.stickyRank()+1 .. self.rank()],\n\n transposedTags := self >> List(self.tags, x->x.transpose()),\n\n getSpl := self >> self.params[1],\n setSpl := (self, spl) >> ApplyFunc(ObjId(self), Concatenation([spl], Drop(self.params, 1)))\n .withTags(self.tags),\n\n # need setIts(its) and getIts()\n _fmanip := meth(self, func_manip, gt_manip, newits) \n local cpy, z;\n\t cpy := Copy(self);\n \t z := SubstTopDownNR_named(cpy, @.cond(x -> (not Same(x, cpy) and IsGT(x)) or IsFunction(x) or IsFuncExp(x) or ObjId(x)=ind), \n\t e -> When(IsGT(e), gt_manip(e), func_manip(e)), \"__GT._fmanip\");\n return z.setIts(newits);\n end,\n\n bodyRank := self >> Maximum( [0] ::\n\tList(Collect(self.getSpl(), @.cond(e->IsFunction(e) or IsFuncExp(e))), _rank)),\n\n downRankFull := (self, inds) >> let(thisrank := self.rank(), \n\tself._fmanip(f -> f.downRankFull(inds), \n\t e -> Cond(e.bodyRank()=0, e, Error(\".downRankFull does not work with nested GTs\")),\n\t\t [])),\n\n\n downRank := (self, loopid, ind) >>\n self._fmanip(f -> f.downRank(loopid, ind), \n\t e -> e.downRankOuter(loopid + e.rank(), ind), \n\t ListWithout(self.getIts(), loopid)),\n # downRankOuter: notification that downRank performed on some outer GT, \n # so that this GT can update its functions and notify children.\n downRankOuter := (self, loopid, ind) >>\n self._fmanip(f -> f.downRank(loopid + self.rank(), ind), \n\t e -> e.downRankOuter(loopid + e.rank(), ind), \n\t self.getIts()),\n\n rotate := (self, n) >> When(n=1, self, let(\n\tits := self.getIts(), \n\ttags := self.getTags(),\tstags := self.stickyTags(), ftags := self.freeTags(),\n res := self._fmanip(\n\t f -> f.rotate(n), \n\t e -> Cond(e.bodyRank() <= e.rank(), e, \n\t\t Error(\".rotate() doesn't support nested GTs where inner GTs depend on outer indices\")),\n\t [its[n]] :: its{[1..n-1]} :: its{[n+1..Length(its)]}),\n\tCond(self.stickyRank() = 0, \n\t res,\n\t n <= self.stickyRank(),\n\t res.setTags( ftags :: [stags[n]] :: stags{[1..n-1]} :: stags{[n+1..Length(stags)]}),\n\t # else, n > self.stickyRank(),\n \t Error(\"Can't make non-sticky rank <n> an inner loop, because sticky tags exist\")\n # it could look like this instead: res.setTags( [ANoTag] :: tags )\n\t))),\n\n rotateIntoSticky := (self, n, newtag) >> let(\n\tits := self.getIts(), \n\ttags := self.getTags(),\tstags := self.stickyTags(), ftags := self.freeTags(),\n res := self._fmanip(\n\t f -> f.rotate(n),\n\t e -> Cond(e.bodyRank() <= e.rank(), e, \n\t\t Error(\".rotate() doesn't support nested GTs where inner GTs depend on outer indices\")),\n\t [its[n]] :: its{[1..n-1]} :: its{[n+1..Length(its)]}),\n\tCond(self.stickyRank() = 0, \n\t res.setTags(tags :: [newtag]),\n\t n <= self.stickyRank(),\n\t res.setTags( ftags :: [newtag] :: stags{[1..n-1]} :: stags{[n+1..Length(stags)]}),\n\t # else, n > self.stickyRank(),\n res.setTags( ftags :: [newtag] :: stags )\n\t)),\n\n # NOTE: upRank() leaves GT in inconsistent state, because sticky tags still need to be shifted\n upRank := self >> self._fmanip(\n\tf -> f.upRank(), \n\te -> Cond(e.bodyRank() <= e.rank(), e, \n\t Error(\".upRank() doesn't support nested GTs where inner GTs depend on outer indices\")),\n\tConcatenation([0], self.getIts())),\n\n # NOTE: upRank() leaves GT in inconsistent state, because sticky tags still need to be shifted\n upRankBy := (self, n) >> self._fmanip(\n\tf -> f.upRankBy(n), \n\te -> Cond(e.bodyRank() <= e.rank(), e, \n\t Error(\".upRankBy() doesn't support nested GTs where inner GTs depend on outer indices\")),\n\tConcatenation(Replicate(n, 0), self.getIts())),\n\n split := (self, loopid, inner_its, outer_its) >> let(its := self.getIts(),\n self._fmanip(\n\t f -> f.split(loopid, inner_its, outer_its),\n\t e -> e.splitOuter(loopid + e.rank(), inner_its, outer_its), \n Concatenation(its{[1..loopid-1]}, [inner_its, outer_its], its{[loopid+1..Length(its)]}))),\n # splitOuter: notification that some outer GT is splitting loop, \n # so that this GT can update its functions and notify children.\n splitOuter := (self, loopid, inner_its, outer_its) >> let(its := self.getIts(),\n self._fmanip(\n\t f -> f.split(loopid + self.rank(), inner_its, outer_its),\n\t e -> e.splitOuter(loopid + e.rank(), inner_its, outer_its), \n its)),\n\n getGath := self >> Error(\"Must be implemented in a subclass\"),\n\n getScat := self >> Error(\"Must be implemented in a subclass\"),\n\n isReal := self >> self.params[1].isReal(),\n toAMat := self >> self.toSpl().toAMat(),\n # when self.getIts() returns empty list it actually means single iteration,\n # that's why [1] appended to the list\n normalizedArithCost := self >> self.getSpl().normalizedArithCost() * ListProduct(self.getIts() :: [1]),\n\n children := self >> [self.params[1]],\n child := (self, n) >> Checked( n = 1, self.params[1] ),\n\n # overrideing withTags() to make sure non-sticky/sticky tags order is preserved\n # returns a copy of the object with 'tags' added on to any existing tags.\n withTags := (self, tags) >> self.setTags(Flat(TransposedMat(\n List([self.tags, tags], t -> SplitBy(t, e -> not e.isSticky))))),\n));\n\n# GT(<spl>, <gath>, <scat>, <v>) - generalized problem spec\n#\n# NOTE: assumes tightly packed data, i.e. Dims(GT(spl)) = Dims(spl) * Product(v)\n# (if gath/scat functions have domain&range == 0)\nClass(GT, GTBase, Tagged_tSPL, rec(\n abbrevs := [\n (spl, gath, scat, v) -> Checked(\n IsSPL(spl), IsIndexMapping(gath), IsIndexMapping(scat), IsList(v),\n ForAll(v, IsPosInt0Sym),\n [spl, gath, scat, v]\n ) ],\n\n dims := self >> let(p := self.params, r := range(p[3]), c := range(p[2]), d := p[1].dims(),\n When(r<>0 and c<>0,\n [r, c],\n let(prod := Product(p[4]), [d[1]prod, d[2]prod]))), # NOTE: assumes XChain.\n\n advdims := self >> let(p := self.params, [p[3].advrange(), p[2].advrange()]),\n\n getIts := self >> self.params[4],\n setIts := (self,its) >> ObjId(self)(self.params[1], self.params[2], self.params[3], its).withTags(self.tags),\n getGath := self >> self.params[2],\n getScat := self >> self.params[3],\n\n rank := self >> Length(self.params[4]),\n\n _scat := Scat,\n _gath := Gath,\n\n # NOTE: toSpl doesn't work with nested GTs. It should use downRank method for function manipulations\n toSpl := self >> self.toSplCx([]),\n toSplCx := (self, outer_inds) >> let(\n p := self.params, spl := Copy(p[1]), g := Copy(p[2]), s := Copy(p[3]), dims := p[4],\n inds := List(dims, Ind), allinds := Concatenation(inds, outer_inds),\n kernel := self._scat(s.toSpl(allinds, Rows(spl))) * spl * self._gath(g.toSpl(allinds, Cols(spl))),\n kerneld := Cond(inds=[], kernel, # downRank only if not rank-0\n SubstTopDownNR(kernel, @.cond(e->IsFunction(e) or IsFuncExp(e)), e->e.downRankFull(allinds))),\n FoldL(inds, (ker, idx) -> ISum(idx.setAttr(\"GT\"), ker), kerneld)\n ),\n\n toISums := self >> let(\n inds := List(self.getIts(), Ind),\n kernel := self._scat(self.getScat()) * self.params[1] * self._gath(self.getGath()),\n FoldL(inds, (ker, idx) -> ISum(idx.setAttr(\"GT\"), ker), kernel)\n ),\n\n transpose := self >> let(p:=self.params,\n GT(p[1].transpose(), p[3], p[2], p[4]).withTags(self.transposedTags())),\n\n conjTranspose := self >> let(p:=self.params,\n GT(p[1].conjTranspose(), p[3], p[2], p[4]).withTags(self.transposedTags())),\n\n hashAs := self >> let(p:=self.params,\n ObjId(self)(HashAsSPL(p[1]), p[2], p[3], p[4]).withTags(self.tags)),\n));\n\nDeclare(GTAccT, GTAcc0T);\n\n# GTAcc(<spl>, <gath>, <scat>, <v>) - generalized problem spec with accumulation on output side\n#\nClass(GTAcc, GT, rec(\n transpose := self >> let(p:=self.params,\n GTAccT(p[1].transpose(), p[3], p[2], p[4]).withTags(self.transposedTags())),\n _scat := ScatAcc\n));\n\nClass(GTAcc0, GT, rec(\n transpose := self >> let(p:=self.params,\n GTAcc0T(p[1].transpose(), p[3], p[2], p[4]).withTags(self.transposedTags())),\n _scat := ScatAcc,\n\n toSplCx := (self, outer_inds) >> Checked(self.rank()=1, let( # NOTE: works only for rank-1\n dims := self.getIts(),\n inds0 := Concatenation(List(DropLast(dims,1), Ind), [0]),\n inds := Concatenation(List(DropLast(dims,1), Ind), [Ind(Last(dims)-1)]),\n inds_shft := Concatenation(DropLast(inds,1), [Last(inds)+1]),\n\n dr0 := self.downRankFull(Concatenation(inds0, outer_inds)),\n dr := self.downRankFull(Concatenation(inds_shft, outer_inds)),\n kernel0 := Scat(dr0.getScat()) * dr0.params[1] * self._gath(dr0.getGath()),\n kernel := ScatAcc(dr.getScat()) * dr .params[1] * self._gath(dr .getGath()),\n When(Last(dims)=1,\n kernel0,\n SUM(kernel0, FoldL(inds, (ker, idx) -> ISum(idx.setAttr(\"GT\"), ker), kernel))))\n ),\n));\n\n# GTAccT == GTAcc.transpose(), even though semantically GTAccT == GT, we need a separate object, so that\n# GTAccT.transpose() is back to GTAcc itself.\nClass(GTAccT, GT, rec(\n transpose := self >> let(p:=self.params,\n GTAcc(p[1].transpose(), p[3], p[2], p[4]).withTags(self.transposedTags())),\n));\n\nClass(GTAcc0T, GT, rec(\n transpose := self >> let(p:=self.params,\n GTAcc0(p[1].transpose(), p[3], p[2], p[4]).withTags(self.transposedTags())),\n));\n\nDeclare(GTInplace);\n\nClass(GTInplace, GTBase, Tagged_tSPL, rec(\n abbrevs := [ (spl, gathscat, v) -> Checked(\n IsSPL(spl), IsIndexMapping(gathscat), IsList(v), ForAll(v, IsPosInt0Sym),\n [spl, gathscat, v]) ],\n\n dims := self >> let(p := self.params, rc := range(p[2]), d := p[1].dims(),\n When(rc<>0,\n [rc, rc],\n let(prod:=Product(p[3]), [d[1]prod, d[2]prod]))), # NOTE: assumes XChain.\n\n getIts := self >> self.params[3],\n setIts := (self,its) >> GTInplace(self.params[1], self.params[2], its).withTags(self.tags),\n\n getGath := self >> self.params[2],\n getScat := self >> self.params[2],\n\n rank := self >> Length(self.params[3]),\n toGT := self >> let(p:=self.params, GT(p[1], p[2], p[2], p[3]).withTags(self.tags)),\n toNonInplace := self >> self.toGT(),\n toSpl := self >> Inplace(self.toGT().toSpl()),\n isInplace := self >> true,\n\n conjTranspose := self >> let(p:=self.params,\n GTInplace(p[1].conjTranspose(), p[2], p[3]).withTags(self.transposedTags())),\n\n transpose := self >> let(p:=self.params,\n GTInplace(p[1].transpose(), p[2], p[3]).withTags(self.transposedTags())),\n\n hashAs := self >> let(p:=self.params,\n ObjId(self)(HashAsSPL(p[1]), p[2], p[3]).withTags(self.tags))\n));\n\n\n#\n# NOTE: what if there is no SUM scatters or gathers\n#\n\nClass(GTPS, GTBase, Tagged_tSPL, rec(\n abbrevs := [\n (spl, fb_cnt, gath, scat, v) -> Checked(\n IsSPL(spl), IsPosInt(fb_cnt), IsIndexMapping(gath), IsIndexMapping(scat), IsList(v),\n ForAll(v, IsPosInt0Sym),\n [spl, fb_cnt, gath, scat, v]\n ) ],\n\n dims := self >> let( p := self.params, r := range(p[4]), c := range(p[3]), \n d := p[1].dims(), \n [ StripList(Flat([d[1]]){[1..p[2]]} :: Flat([r])), \n StripList(Flat([d[2]]){[1..p[2]]} :: Flat([c])) ]),\n\n advdims := self >> let(p := self.params, r := p[4].advrange(), c := p[3].advrange(), \n d := p[1].advdims(), \n [ StripList(Flat([d[1]]){[1..p[2]]} :: Flat([r])), \n StripList(Flat([d[2]]){[1..p[2]]} :: Flat([c])) ]),\n\n getIts := self >> self.params[5],\n setIts := (self,its) >> ObjId(self)(self.params[1], self.params[2], self.params[3], self.params[4], its).withTags(self.tags),\n getGath := self >> fCross(List(Flat([self.params[1].advdims()[1]]){[1..self.params[2]]}, e -> fId(e)) :: [self.params[3]]),\n getScat := self >> fCross(List(Flat([self.params[1].advdims()[2]]){[1..self.params[2]]}, e -> fId(e)) :: [self.params[4]]),\n\n rank := self >> Length(self.params[5]),\n\n toSpl := self >> let(\n inds := List(self.params[5], Ind),\n kernel := FoldR([1..self.rank()], (ker, i) -> ker.downRank(i, inds[i]), Copy(self)),\n spl := Scat(kernel.getScat()) * kernel.child(1) * Gath(kernel.getGath()),\n FoldL(inds, (ker, idx) -> IParSeq(idx.setAttr(\"GT\"), kernel.params[2], ker), spl)),\n\n hashAs := self >> let(p:=self.params,\n ObjId(self)(HashAsSPL(p[1]), p[2], p[3], p[4], p[5]).withTags(self.tags)),\n \n));\n\n# Useful identities:\n#\n# Tr(m,n) = GT(I(m), XChain([0,1]), XChain([1,0]), [n]) =\n# GT(I(n), XChain([1,0]), XChain([0,1]), [m]) = L(mn, n)\nGT_Tr1 := (m,n) -> GT(I(m), XChain([0,1]), XChain([1,0]), [n]);\nGT_Tr2 := (m,n) -> GT(I(n), XChain([1,0]), XChain([0,1]), [m]);\n\nGT_Tr1u := (m,n,u) -> let(uu:=When(m mod u = 0, u, 1),\n GT(BB(I(uu)), XChain([1,0,2]), XChain([2,1,0]), [m/uu, n]));\n\nGT_Tr2u := (m,n,u) -> let(uu:=When(n mod u = 0, u, 1),\n GT(BB(I(uu)), XChain([2,1,0]), XChain([1,0,2]), [n/uu, m]));\n\n\nNewRulesFor(GT, rec(\n GT_Base := rec(\n\tswitch := false,\n\ta := rec(maxSize := false),\n # requiredFirstTag := ANoTag,\n\tapplicable := (self, t) >> let(rank := Length(t.params[4]), spl := t.params[1],\n rank = 0 and (self.a.maxSize=false\n\t\tor Rows(spl) <= self.a.maxSize or Cols(spl) <= self.a.maxSize)),\n freedoms := (self, t) >> [],\n\tchild := (t, fr) -> [ t.params[1].withTags(t.getTags()) ],\n\tapply := (t, C, Nonterms) -> let(\n g := t.params[2], s := t.params[3],\n Scat(s.toSpl([], Rows(C[1]))) C[1] * Gath(g.toSpl([], Cols(C[1])))\n )\n ),\n\n GT_NthLoop := rec(\n\t requiredFirstTag := [ANoTag, ALimitNthLoop],\n\t applicable := t -> let(rank := Length(t.params[4]), rank > 0), \n\n # restrict to innermost first (i.e. loop interchange)\n\t # to search over loop orders use [1..nloops]\n\n # Limit tag reduces the number of loop interchanges.\n # it is useful when you don't want the number of potential\n # ruletrees to explode, and you are not overtly concerned\n # with having access to all the potential ones.\n freedoms := t -> let(\n fr := [1..Length(t.params[4])], \n When(t.hasTag(ALimitNthLoop),\n [[1]],\n [fr]\n )\n ),\n\n\t child := (t, fr) -> let(\n\t spl := t.params[1], \n g := t.params[2], \n s := t.params[3], \n loopid := fr[1],\n\t [ \n GT(spl, g.without(loopid), \n s.without(loopid), ListWithout(t.params[4], loopid)), \n InfoNt(loopid) \n ]\n ),\n\n\t apply := (t, C, Nonterms) -> let(\n\t loopid := Nonterms[2].params[1], \n dft := Nonterms[1].params[1], \n\t g := t.params[2], \n s := t.params[3],\n\t loop_dims := t.params[4],\n\t i := Ind(loop_dims[loopid]),\n\n\t ISum(i, Scat(s.part(loopid, i, Rows(dft), loop_dims)) \n * C[1] \n * Gath(g.part(loopid, i, Cols(dft), loop_dims)))\n )\n ),\n\n GT_BufReshape := rec(\n bufIters := [2, 4, 8, 16, 32],\n requiredFirstTag := ANoTag,\n\n applicable := (self, t) >> Length(t.params[4])=1 and let(\n N := Minimum(t.params[1].dimensions), its := t.params[4][1],\n PatternMatch(t, [GT, @, @(2,XChain), @(3,XChain), ...], empty_cx()) and\n (@(2).val.params[1] = [0,1] or @(3).val.params[1] = [0,1]) and\n ForAny(self.bufIters, bi -> bi < its and IsInt(its/bi))),\n\n u := [2,4,8,16],\n\n children := (self, t) >> let(\n spl := t.params[1], its := t.params[4][1],\n bufiters := Filtered(self.bufIters, bi -> (bi < its) and IsInt(its/bi)),\n Map2(Cartesian(bufiters, self.u), (bi, u) ->\n [ GT(spl, XChain([1,0]), XChain([1,0]), [bi]),\n InfoNt(u) ])),\n\n apply := (self, t, C, Nonterms) >> let(\n g := t.params[2].params[1], s := t.params[3].params[1],\n gg := When(g=[0,1], XChain([0,1,2]), XChain([1,2,0])),\n ss := When(s=[0,1], XChain([0,1,2]), XChain([1,2,0])),\n spl := t.params[1], its := t.params[4][1], inner := Nonterms[1].params[4][1],\n i := Ind(its / inner),\n u := When(IsBound(Nonterms[2]), Nonterms[2].params[1], 4),\n\n ISum(i, Scat(ss.part(1, i, Rows(spl), [i.range, inner])) \n When(s=[0,1], GT_Tr2u(inner, Rows(spl), u).toSpl(), I(Rows(spl)inner)) \n C[1] \n When(g=[0,1], GT_Tr1u(Cols(spl), inner, u).toSpl(), I(Cols(spl)inner)) \n Gath(gg.part(1, i, Cols(spl), [i.range, inner]))\n )\n )\n )\n));\n", "meta": {"hexsha": "96647f9fa2ada3b111abfb5b8f18a7e91e0d4333", "size": 17897, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/common/gt.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/common/gt.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/common/gt.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": 39.5951327434, "max_line_length": 129, "alphanum_fraction": 0.5567413533, "num_tokens": 5721, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. 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	{"text": "IsSymInf := x -> IsSymbolic(x) and IsBound(x.isSymInf) and x.isSymInf;\n\nClass(SymInf, Symbolic, rec(\n __call__ := (self, t) >> WithBases(self, rec(\n t := Checked(IsType(t), t),\n operations := rec(Print := x-> When(IsBound(x.print), x.print(), Print(x.__name__)))\n )),\n print := self >> Print(self.__name__, \"(\", self.t, \")\"),\n isSymInf := true,\n isValue := true,\n ev := self >> self,\n computeType := self >> self.t\n));\n\n# ==========================================================================\n# Semiring\n# ==========================================================================\n\nIsSemiring := x -> IsType(x) and IsBound(x.isSemiring) and x.isSemiring;\n\nIsSemiring_Arithmetic := x -> IsSemiring(x) and IsBound(x.isSemiring_Arithmetic) and x.isSemiring_Arithmetic;\n\nIsSemiring_MinPlus := x -> IsSemiring(x) and IsBound(x.isSemiring_MinPlus) and x.isSemiring_MinPlus;\n\nIsSemiring_MinTimes := x -> IsSemiring(x) and IsBound(x.IsSemiring_MinTimes) and x.isSemiring_MinTimes;\n\nisSemiring_Boolean := x -> IsSemiring(x) and IsBound(x.isSemiring_Boolean) and x.isSemiring_Boolean;\n\nClass(TSemiring, CompositeTyp, rec(\n __call__ := (self, t) >> WithBases(self, rec(\n t := Checked(IsType(t), t),\n operations := TypOps\n )),\n base_t := self >> self.t,\n isSemiring := true,\n\n print := self >> Print(self.__name__, \"(\", self.t, \")\"),\n\n check := (self, v) >> Cond(\n UnifyTypes([self.t, InferType(v)]) = self.t,\n v,\n Error(\"type mismatch: semiring is type \", self.t)\n ),\n\n rChildren := self >> [self.t],\n rSetChild := rSetChildFields(\"t\"),\n from_rChildren := (self, rch) >> self,\n\n zero := self >> Error(\"method on undefined semiring\"),\n one := self >> Error(\"method on undefined semiring\"),\n\n sum := self >> Error(\"method on undefined semiring\"),\n product := self >> Error(\"method on undefined semiring\")\n));\n\nClass(TSemiring_Arithmetic, TSemiring, rec(\n zero := self >> self.t.zero(),\n one := self >> self.t.one(),\n\n sum := (self, v1, v2) >> Cond(\n UnifyTypes([self.t, InferType(v1), InferType(v2)]) = self.t,\n self.t.sum(v1, v2),\n Error(\"type mismatch: semiring is type \", self.t)\n ),\n product := (self, v1, v2) >> Cond(\n UnifyTypes([self.t, InferType(v1), InferType(v2)]) = self.t,\n self.t.product(v1, v2),\n Error(\"type mismatch: semiring is type \", self.t)\n ),\n\n OpenMP_sum := \"+\",\n OpenMP_product := \"\",\n\n isSemiring_Arithmetic := true\n));\n\nClass(TSemiring_MinPlus, TSemiring, rec(\n zero := self >> SymInf(self.t),\n one := self >> self.t.zero(),\n\n sum := (self, v1, v2) >> Cond(\n IsSymInf(v1) and IsSymInf(v2),\n SymInf(self.t),\n IsSymInf(v1) and UnifyTypes([self.t, v2.t]) = self.t,\n v2,\n IsSymInf(v2) and UnifyTypes([self.t, v1.t]) = self.t,\n v1,\n UnifyTypes([self.t, InferType(v1), InferType(v2)]) = self.t,\n min(v1, v2),\n Error(\"type mismatch: semiring is type \", self.t)\n ),\n product := (self, v1, v2) >> Cond(\n IsSymInf(v1) or IsSymInf(v2),\n SymInf(self.t),\n UnifyTypes([self.t, InferType(v1), InferType(v2)]) = self.t,\n self.t.sum(v1, v2),\n Error(\"type mismatch: semiring is type \", self.t)\n ),\n\n OpenMP_sum := \"min\",\n OpenMP_product := \"+\",\n\n isSemiring_MinPlus := true\n));\n\n\nClass(TSemiring_MinTimes, TSemiring, rec(\n zero := self >> SymInf(self.t),\n one := self >> self.t.zero(),\n\n sum := (self, v1, v2) >> Cond(\n IsSymInf(v1) and IsSymInf(v2),\n SymInf(self.t),\n IsSymInf(v1) and UnifyTypes([self.t, v2.t]) = self.t,\n v2,\n IsSymInf(v2) and UnifyTypes([self.t, v1.t]) = self.t,\n v1,\n UnifyTypes([self.t, InferType(v1), InferType(v2)]) = self.t,\n min(v1, v2),\n Error(\"type mismatch: semiring is type \", self.t)\n ),\n product := (self, v1, v2) >> Cond(\n UnifyTypes([self.t, InferType(v1), InferType(v2)]) = self.t,\n self.t.product(v1, v2),\n Error(\"type mismatch: semiring is type \", self.t)\n ),\n\n OpenMP_sum := \"min\",\n OpenMP_product := \"\",\n\n isSemiring_MinTimes := true\n));\n\n\nClass(TSemiring_Boolean, TSemiring, rec(\n zero := self >> self.t.zero(),\n one := self >> self.t.one(),\n\n sum := (self, v1, v2) >> Cond(let(\n l := UnifyTypes([self.t, InferType(v1), InferType(v2)]), Cond(IsArrayT(l), l.t = self.t, l = self.t)),\n logic_or(v1, v2),\n Error(\"type mismatch: semiring is type \", self.t)\n ),\n product := (self, v1, v2) >> Cond(let(\n l := UnifyTypes([self.t, InferType(v1), InferType(v2)]), Cond(IsArrayT(l), l.t = self.t, l = self.t)),\n logic_and(v1,v2),\n Error(\"type mismatch: semiring is type \", self.t)\n ),\n\n OpenMP_sum := \"\|\|\",\n OpenMP_product := \"&&\",\n\n isSemiring_Boolean := true\n));", "meta": {"hexsha": "3c71b4c37e44edc5087c34108be0e49e1848c05e", "size": 4619, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/packages/graph/semiring.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": 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"lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7341195269001831, "lm_q2_score": 0.5467381519846138, "lm_q1q2_score": 0.4013711534732251}}