File size: 14,261 Bytes
5697766 | 1 2 3 | {"text": "(*\n * 保存不变量分类状态的对象\n * \n * 状态分为：\n * 1 线性偏微分方程组求解失败\n * 2 不变量方程组求解失败\n * 3 取特解失败\n * 4 变换方程求解失败\n * 5 变换方程求解成功，特解可能是代表元，是否是代表元留给人工判断\n*)\n$ifndef _INVSOL_\n$define _INVSOL_\n\nInvSol:=module()\n option object;\n export\n # 导出变量 \n stateCode::{1,2,3,4,5}, # 状态代码\n oieq:={}, # 导出新偏微分方程的不变量方程（如果存在的话）\n oisol, # 导出新偏微分方程的不变量方程的解（如果存在的话）\n oeq::set, # 导出不变量的偏微分方程\n Delta:=[], # 不变量\n orders:=[], # 不变量对应的阶数\n ieqCode, # 不变量方程的代码\n ieq::list, # 不变量方程\n isol, # 不变量方程的解（一个InvSol对象只含一个解）\n icon::set, # 不变量方程解的条件\n teq:=[[],[]], # 变换方程（有两个）\n tsol:=[[],[]], # 变换方程的解，每个方程都有可能有多个解\n tcon:=[[],[]], # 变换方程的解对于的条件\n rep, # 代表元的表达式形式\n rvec, # 代表元的系数矩阵形式\n vars, # 偏微分方程中的剩余自由变量，初始时为a[1]..a[nvars]\n nvars, # 生成元的个数\n As::static, # 每个生成元的伴随矩阵\n A::static, # 总的伴随变换矩阵\n # 导出函数\n ## 输出相关\n getDisplayIeq::static, # 简化显示的不变量方程，将不变量的实际表达式简写为Delta\n getDisplayDelta::static, # 输出不变量\n getDesc::static, # 获取对象的特征描述\n ModulePrint::static, # 打印和显示对象的值\n printSol::static, # 详细显示对象信息\n printTeq::static, # 显示变换方程的结果\n ## 设置相关\n setRep::static, # 重新取代表元\n setIsol::static, # 重新对不变量方程取解\n getRep::static; # 获取代表元，转化为global对象便于比较\n\n # 重新取代表元\n setRep:=proc(s::InvSol,rvec::list,{nocheck::boolean:=false})\n local v,r;\n if not nocheck then\n # 解的检验\n r:=eval(subs(seq(a[i]=rvec[i],i=1..numelems(rvec)),s:-ieq));\n if not andmap(evalb,r) then\n error \"不是不变量方程的解，代入结果为%1\",r;\n end if;\n end if;\n s:-stateCode:=4;\n s:-rvec:=Matrix(rvec);\n s:-rep:=add(rvec[i]*v[i],i=1..numelems(rvec));\n return;\n end proc:\n\n # 重新对不变量方程取解\n setIsol:=proc(s::InvSol,isol,{nocheck::boolean:=false})\n local r;\n if not nocheck then\n # 解的检验\n r:=RealDomain:-simplify(subs(isol[],s:-ieq));\n if not andmap(evalb,r) then\n error \"不是不变量方程的解，代入结果为%1\",r;\n end if;\n end if;\n s:-stateCode:=3;\n s:-isol:=isol;\n s:-icon:=findSolutionDomain(isol);\n return;\n end proc:\n\n # 获取代表元，转化为global对象便于比较\n getRep:=proc(s::InvSol)\n return convert(s:-rep,`global`);\n end proc:\n\n # 简化显示的不变量方程，将不变量的实际表达式简写为Delta\n getDisplayIeq:=proc(self::InvSol)\n local Delta;\n return {seq(Delta[i]=rhs(self:-ieq[i]),i=1..numelems(self:-Delta))};\n end proc:\n\n # 输出不变量\n getDisplayDelta:=proc(self::InvSol)\n local Delta;\n return [seq(Delta[i]=self:-Delta[i],i=1..numelems(self:-Delta))];\n end proc:\n\n # 获取对象的特征描述\n getDesc:=proc(s)\n if (s:-stateCode=1) then\n return s:-oeq;\n elif (s:-stateCode=2) then\n return getDisplayIeq(s);\n elif (s:-stateCode=3) then\n return s:-isol;\n elif (s:-stateCode=4) then\n return s:-rep;\n elif (s:-stateCode=5) then\n return s:-rep;\n end if;\n end proc:\n\n # 打印和显示对象的值\n ModulePrint:=proc(s)\n return getDesc(s);\n end proc:\n\n # 输出解\n printSol:=proc(s::InvSol)\n printf(\"---------------------------------------------------------\");\n if (s:-stateCode=1) then\n printf(\"新的不变量求解失败，状态代码1\");\n print(s:-oieq);\n printf(\"取解\");\n print(s:-oisol);\n printf(\"求解失败的偏微分方程为\");\n print(s:-oeq);\n elif (s:-stateCode=2) then\n printf(\"不变量方程求解失败，状态代码2\");\n print(getDisplayIeq(s));\n elif (s:-stateCode=3) then\n printf(\"取代表元失败，状态代码3\");\n print(getDisplayIeq(s));\n printf(\"取解\");\n print(s:-isol);\n elif (s:-stateCode=4) then\n printf(\"变换方程求解失败，状态代码4\");\n print(getDisplayIeq(s));\n printf(\"取解\");\n print(s:-isol);\n printf(\"具有约束\");\n print(s:-icon);\n printf(\"取代表元\");\n print(s:-rep);\n printf(\"求解失败的两个变换方程为\");\n print~(s:-teq);\n elif (s:-stateCode=5) then\n printf(\"变换方程求解成功，状态代码5\");\n print(getDisplayIeq(s));\n printf(\"取解\");\n print(s:-isol);\n printf(\"具有约束\");\n print(s:-icon);\n printf(\"取代表元\");\n print(s:-rep);\n printf(\"变换方程有解\");\n printTeq(s,1);\n printTeq(s,2);\n end if;\n printf(\"---------------------------------------------------------\");\n return;\n end proc:\n\n # 输出变换方程和解\n printTeq:=proc(sol,pos)\n if (sol:-tsol[pos]=[]) then\n printf(\"变换方程 %d 无解\",pos);\n printf(\"方程为\");\n print(sol:-teq[pos]);\n else\n printf(\"变换方程 %d 有解\",pos);\n printf(\"方程为\");\n print(sol:-teq[pos]);\n printf(\"有解\");\n print(sol:-tsol[pos]);\n printf(\"具有条件\");\n print(sol:-tcon[pos]);\n end if;\n end proc:\nend module:\n\n$endif", "meta": {"hexsha": "6201db3758556a31278aabbc3c8e74cb79b70770", "size": 5489, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "old/InvSol.mpl", "max_stars_repo_name": "yu961549745/InvariantClassify", "max_stars_repo_head_hexsha": "eeb14ca2b39679e5a2da0f23888681ec7e2edd84", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "old/InvSol.mpl", "max_issues_repo_name": "yu961549745/InvariantClassify", "max_issues_repo_head_hexsha": "eeb14ca2b39679e5a2da0f23888681ec7e2edd84", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "old/InvSol.mpl", "max_forks_repo_name": "yu961549745/InvariantClassify", "max_forks_repo_head_hexsha": "eeb14ca2b39679e5a2da0f23888681ec7e2edd84", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 29.9945355191, "max_line_length": 76, "alphanum_fraction": 0.4454363272, "num_tokens": 1894, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. 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{"text": "######################################################################\n#\n# General circle operad framework.\n\n`check_semi_circ_args` := proc(i,m,n,U,V,is_el_CC)\n global reason;\n\n if not (type(i,posint) and\n type(m,nonnegint) and\n\t type(n,nonnegint) and\n\t i <= m) then\n reason := [convert(procname,string),\n \"numbers (i,m,n) do not satisfy 0 < i <= m; 0 <= n\",i,m,n];\n return false;\n fi;\n\n if not is_el_CC(m)(U) then\n reason := [convert(procname,string),\"U is not in C(m)\",eval(U),m];\n return false;\n fi;\n\n if not is_el_CC(n)(U) then\n reason := [convert(procname,string),\"V is not in C(n)\",eval(V),n];\n return false;\n fi;\n\n return true;\nend;\n\n######################################################################\n\n`check_semi_circ_axiom_nested` :=\n proc(i,j,l,m,n,U,V,W,is_el_CC,is_equal_CC,circ_CC)\n local UV,VW,UVW0,UVW1;\n global reason;\n\n if not (type(i,posint) and\n type(j,posint) and\n\t type(l,nonnegint) and\n\t type(m,nonnegint) and\n\t type(n,nonnegint) and\n\t i <= l and\n\t j <= m) then \n reason := [convert(procname,string),\n \"numbers (i,j,l,m,n) do not satisfy 0 < i <= l; 0 < j <= m; 0 <= n\",\n i,j,l,m,n];\n return false;\n fi;\n\n if not is_el_CC(l)(U) then\n reason := [convert(procname,string),\"U is not in O(l)\",l,eval(U)];\n return false;\n fi;\n\n if not is_el_CC(m)(V) then\n reason := [convert(procname,string),\"V is not in O(m)\",m,eval(V)];\n return false;\n fi;\n\n if not is_el_CC(n)(W) then\n reason := [convert(procname,string),\"W is not in O(n)\",n,eval(W)];\n return false;\n fi;\n\n UV := circ_CC(i,l,m)(U,V);\n\n if not is_el_CC(l+m-1)(UV) then\n reason := [convert(procname,string),\"U o_i V is not in O(l+m-1)\",i,l,m,eval(U),eval(V),eval(UV)];\n return false;\n fi;\n\n VW := circ_CC(j,m,n)(V,W);\n\n if not is_el_CC(m+n-1)(VW) then\n reason := [convert(procname,string),\"V o_j W is not in O(m+n-1)\",j,m,n,eval(VW)];\n return false;\n fi;\n\n UVW0 := circ_CC(i,l,m+n-1)(U,VW);\n\n if not is_el_CC(l+m+n-2)(UVW0) then\n reason := [convert(procname,string),\"U o_i (V o_j W) is not in O(l+m+n-2)\",i,j,l,m,n,eval(UVW0)];\n return false;\n fi;\n\n UVW1 := circ_CC(i+j-1,l+m-1,n)(UV,W);\n\n if not is_el_CC(l+m+n-2)(UVW1) then\n reason := [convert(procname,string),\"(U o_i V) o_(i+j-1) W is not in O(l+m+n-2)\",i,j,l,m,n,eval(UVW1)];\n return false;\n fi;\n\n if not is_equal_CC(l+m+n-2)(UVW0,UVW1) then\n reason := [convert(procname,string),\"UVW0 != UVW1\",eval(UVW0),eval(UVW1)];\n return false;\n fi;\n\n return true;\nend;\n\n`check_semi_circ_axiom_disjoint` :=\n proc(i,k,l,m,n,U,V,W,is_el_CC,is_equal_CC,circ_CC)\n local UV,UW,UVW,UWV;\n global reason;\n\n if not (type(i,posint) and\n type(k,posint) and\n\t type(l,nonnegint) and\n\t type(m,nonnegint) and\n\t type(n,nonnegint) and\n\t i < k and\n\t k <= l) then \n reason := [convert(procname,string),\n \"numbers (i,k,l,m,n) do not satisfy 0 < i < k <= l; 0 < j <= m; 0 <= n\",\n i,k,l,m,n];\n return false;\n fi;\n\n if not is_el_CC(l)(U) then\n reason := [convert(procname,string),\"U is not in O(l)\",l,eval(U)];\n return false;\n fi;\n\n if not is_el_CC(m)(V) then\n reason := [convert(procname,string),\"V is not in O(m)\",m,eval(V)];\n return false;\n fi;\n\n if not is_el_CC(n)(W) then\n reason := [convert(procname,string),\"W is not in O(n)\",n,eval(W)];\n return false;\n fi;\n\n UV := circ_CC(i,l,m)(U,V);\n\n if not is_el_CC(l+m-1)(UV) then\n reason := [convert(procname,string),\"U o_i V is not in O(l+m-1)\",i,l,m,eval(U),eval(V),eval(UV)];\n return false;\n fi;\n\n UW := circ_CC(k,l,n)(U,W);\n\n if not is_el_CC(l+n-1)(UW) then\n reason := [convert(procname,string),\"U o_k W is not in O(l+n-1)\",k,l,n,eval(UW)];\n return false;\n fi;\n\n UVW := circ_CC(k+m-1,l+m-1,n)(UV,W);\n\n if not is_el_CC(l+m+n-2)(UVW) then\n reason := [convert(procname,string),\"(U o_i V) o_(k+m-1) W is not in O(l+m+n-2)\",i,k,l,m,n,eval(UVW)];\n return false;\n fi;\n\n UWV := circ_CC(i,l+n-1,m)(UW,V);\n\n if not is_el_CC(l+m+n-2)(UWV) then\n reason := [convert(procname,string),\"(U o_k W) o_i V is not in O(l+m+n-2)\",i,k,l,m,n,eval(UWV)];\n return false;\n fi;\n\n if not is_equal_CC(l+m+n-2)(UVW,UWV) then\n reason := [convert(procname,string),\"UVW != UWV\",eval(UVW),eval(UWV)];\n return false;\n fi;\n\n return true;\nend;\n\n\n", "meta": {"hexsha": "1c0de01ca1ac1e6aaa15b702a82a26521985f19e", "size": 4131, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/semioperads/circ.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/semioperads/circ.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/semioperads/circ.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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": 24.1578947368, "max_line_length": 105, "alphanum_fraction": 0.5964657468, "num_tokens": 1449, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. NO", "lm_q1_score": 0.5660185205547239, "lm_q2_score": 0.44939263446475963, "lm_q1q2_score": 0.25436455410793307}}
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