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Member "singular-4.2.1/doc/orbitsG25.gp" (9 Jun 2021, 2521 Bytes) of package /linux/misc/singular-4.2.1.tar.gz:


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    1 G := Group(
    2  (2, 3)(5, 6)(9, 10), (1, 5, 9, 10, 3)(2, 7, 8, 4, 6)
    3 );;
    4 Size(G);
    5 dimQ:=5;
    6 
    7 minidx:=SmallestMovedPoint(G);
    8 maxidx:=LargestMovedPoint(G);
    9 XZorbitsRepresentatives:=[];;
   10 for k in [dimQ..(maxidx-minidx+1)] do
   11   Print("Considering faces of cardinality ",k,"\n");
   12   XZ := Combinations([minidx..maxidx],k);;
   13   Bahnen := OrbitsDomain(G,XZ,OnSets);;
   14   for i in [1..Size(Bahnen)] do
   15     Append(XZorbitsRepresentatives,[Bahnen[i][1]]);
   16   od;
   17 od;
   18 
   19 PrintTo("simplexOrbitRepresentativesG25.sing","list simplexOrbitRepresentatives = ");
   20 for k in [1..Size(XZorbitsRepresentatives)-1] do
   21   s:=String(XZorbitsRepresentatives[k]);
   22   s:=s{[2..Size(s)-1]};
   23   AppendTo ("simplexOrbitRepresentativesG25.sing","intvec(",s,"),\n");
   24 od;
   25 s:=String(XZorbitsRepresentatives[Size(XZorbitsRepresentatives)]);
   26 s:=s{[2..Size(s)-1]};
   27 AppendTo ("simplexOrbitRepresentativesG25.sing","intvec(",s,");\n");
   28 
   29 
   30 PrintTo("simplexSymmetryGroupG25.sing","list simplexSymmetryGroup = ");
   31 elementsG:=Elements(G);
   32 for i in [1..Size(elementsG)-1] do
   33    sigma:=elementsG[i];
   34    l:=ListPerm(sigma,maxidx);
   35    l:=l{[minidx..maxidx]};
   36    s:=String(l);
   37    s:=s{[2..Size(s)-1]};
   38    AppendTo ("simplexSymmetryGroupG25.sing","permutationFromIntvec(intvec(",s,")),\n");
   39 od;
   40 sigma:=elementsG[Size(elementsG)];
   41 l:=ListPerm(sigma,maxidx);
   42 l:=l{[minidx..maxidx]};
   43 s:=String(l);
   44 s:=s{[2..Size(s)-1]};
   45 AppendTo ("simplexSymmetryGroupG25.sing","permutationFromIntvec(intvec(",s,"));\n");
   46 
   47 
   48 PrintTo("elementsInTermsOfGeneratorsG25.sing","list generatorsG = ");
   49 L:=GeneratorsOfGroup(G);
   50 for i in [1..Size(L)-1] do
   51    sigma:=L[i];
   52    l:=ListPerm(sigma,maxidx);
   53    l:=l{[minidx..maxidx]};
   54    s:=String(l);
   55    s:=s{[2..Size(s)-1]};
   56    AppendTo ("elementsInTermsOfGeneratorsG25.sing","permutationFromIntvec(intvec(",s,")),\n");
   57 od;
   58    sigma:=L[Size(L)];
   59    l:=ListPerm(sigma,maxidx);
   60    l:=l{[minidx..maxidx]};
   61    s:=String(l);
   62    s:=s{[2..Size(s)-1]};
   63    AppendTo ("elementsInTermsOfGeneratorsG25.sing","permutationFromIntvec(intvec(",s,"));\n");
   64 
   65 AppendTo("elementsInTermsOfGeneratorsG25.sing","list elementsInTermsOfGenerators = ");
   66 hom:=EpimorphismFromFreeGroup(G);
   67    AppendTo ("elementsInTermsOfGeneratorsG25.sing","\"\",\n");
   68 for i in [2..Size(elementsG)-1] do
   69    sigma:=elementsG[i];
   70    l:=PreImagesRepresentative(hom,sigma);
   71    s:=String(l);
   72    AppendTo ("elementsInTermsOfGeneratorsG25.sing","\"",s,"\",\n");
   73 od;
   74 sigma:=elementsG[Size(elementsG)];
   75 l:=PreImagesRepresentative(hom,sigma);
   76 s:=String(l);
   77 AppendTo ("elementsInTermsOfGeneratorsG25.sing","\"",s,"\";\n");
   78 
   79