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Add GAP .tst extension plus two sample files
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Max Horn
@@ -823,6 +823,7 @@ GAP:
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- .gap
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- .gd
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- .gi
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- .tst
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GAS:
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type: programming
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161
samples/GAP/bugfix.tst
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161
samples/GAP/bugfix.tst
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@@ -0,0 +1,161 @@
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gap> START_TEST("Test for various former bugs");
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gap> # The following used to trigger an error starting with:
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gap> # "SolutionMat: matrix and vector incompatible called from"
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gap> K:=AbelianPcpGroup([3,3,3]);;
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gap> A:=Subgroup(K,[K.1]);;
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gap> cr:=CRRecordBySubgroup(K,A);;
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gap> ExtensionsCR(cr);;
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# Comparing homomorphisms used to be broken
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gap> K:=AbelianPcpGroup(1,[3]);;
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gap> hom1:=GroupHomomorphismByImages(K,K,[K.1],[K.1]);;
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gap> hom2:=GroupHomomorphismByImages(K,K,[K.1^2],[K.1^2]);;
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gap> hom1=hom2;
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true
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gap> hom1=IdentityMapping(K);
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true
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gap> hom2=IdentityMapping(K);
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true
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gap> # The following incorrectly triggered an error at some point
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gap> IsTorsionFree(ExamplesOfSomePcpGroups(5));
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true
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gap> # Verify IsGeneratorsOfMagmaWithInverses warnings are silenced
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gap> IsGeneratorsOfMagmaWithInverses(GeneratorsOfGroup(ExamplesOfSomePcpGroups(5)));
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true
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gap> # Check for a bug reported 2012-01-19 by Robert Morse
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gap> g := PcGroupToPcpGroup(SmallGroup(48,1));
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Pcp-group with orders [ 2, 2, 2, 2, 3 ]
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gap> # The next two commands used to trigger errors
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gap> NonAbelianTensorSquare(Centre(g));
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Pcp-group with orders [ 8 ]
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gap> NonAbelianExteriorSquare(Centre(g));
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Pcp-group with orders [ ]
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gap> # Check for a bug reported 2012-01-19 by Robert Morse
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gap> F := FreeGroup("x","y");
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<free group on the generators [ x, y ]>
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gap> x := F.1;; y := F.2;;
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gap> G := F/[x^2/y^24, y^24, y^x/y^23];
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<fp group on the generators [ x, y ]>
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gap> iso := IsomorphismPcGroup(G);
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[ x, y ] -> [ f1, f2*f5 ]
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gap> iso1 := IsomorphismPcpGroup(Image(iso));
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[ f1, f2, f3, f4, f5 ] -> [ g1, g2, g3, g4, g5 ]
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gap> G := Image(iso*iso1);
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Pcp-group with orders [ 2, 2, 2, 2, 3 ]
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gap> # The next command used to trigger an error
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gap> NonAbelianTensorSquare(Image(iso*iso1));
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Pcp-group with orders [ 2, 2, 3, 2, 2, 2, 2 ]
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gap> # The problem with the previous example is/was that Igs(G)
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gap> # is set to a non-standard value:
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gap> Igs(G);
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[ g1, g2*g5, g3*g4*g5^2, g4*g5, g5 ]
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gap> # Unfortunately, it seems that a lot of code that
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gap> # really should be using Ngs or Cgs is using Igs incorrectly.
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gap> # For example, direct products could return *invalid* embeddings:
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gap> D := DirectProduct(G, G);
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Pcp-group with orders [ 2, 2, 2, 2, 3, 2, 2, 2, 2, 3 ]
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gap> hom:=Embedding(D,1);;
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gap> mapi:=MappingGeneratorsImages(hom);;
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gap> GroupHomomorphismByImages(Source(hom),Range(hom),mapi[1],mapi[2]) <> fail;
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true
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gap> hom:=Projection(D,1);;
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gap> mapi:=MappingGeneratorsImages(hom);;
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gap> GroupHomomorphismByImages(Source(hom),Range(hom),mapi[1],mapi[2]) <> fail;
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true
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gap> # Check for bug computing Schur extension of infinite cyclic groups,
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gap> # found by Max Horn 2012-05-25
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gap> G:=AbelianPcpGroup(1,[0]);
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Pcp-group with orders [ 0 ]
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gap> # The next command used to trigger an error
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gap> SchurExtension(G);
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Pcp-group with orders [ 0 ]
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gap> # Check for bug computing Schur extensions of subgroups, found by MH 2012-05-25.
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gap> G:=HeisenbergPcpGroup(2);
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Pcp-group with orders [ 0, 0, 0, 0, 0 ]
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gap> H:=Subgroup(G,[G.2^3*G.3^2, G.1^9]);
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Pcp-group with orders [ 0, 0, 0 ]
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gap> # The next command used to trigger an error
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gap> SchurExtension(H);
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Pcp-group with orders [ 0, 0, 0, 0, 0, 0 ]
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gap> # Check for bug computing Schur extensions of subgroups, found by MH 2012-05-25.
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gap> G:=HeisenbergPcpGroup(2);
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Pcp-group with orders [ 0, 0, 0, 0, 0 ]
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gap> H:=Subgroup(G,[G.1, G.2]);
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Pcp-group with orders [ 0, 0 ]
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gap> # The next command used to trigger an error
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gap> SchurExtension(H);
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Pcp-group with orders [ 0, 0, 0 ]
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gap> # Check for bug computing normalizer of two subgroups, found by MH 2012-05-30.
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gap> # The problem was caused by incorrect resp. overly restrictive use of Parent().
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gap> G:=HeisenbergPcpGroup(2);
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Pcp-group with orders [ 0, 0, 0, 0, 0 ]
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gap> A:=Subgroup(Subgroup(G,[G.2,G.3,G.4,G.5]), [G.3]);
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Pcp-group with orders [ 0 ]
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gap> B:=Subgroup(Subgroup(G,[G.1,G.4,G.5]), [G.4]);
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Pcp-group with orders [ 0 ]
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gap> Normalizer(A,B);
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Pcp-group with orders [ 0 ]
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gap> # The following used to trigger the error "arguments must have a common parent group"
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gap> Normalizer(B,A);
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Pcp-group with orders [ 0 ]
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gap> # In polycyclic 2.9 and 2.10, the code for 2-cohomology computations was broken.
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gap> G := UnitriangularPcpGroup(3,0);
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Pcp-group with orders [ 0, 0, 0 ]
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gap> mats := G!.mats;
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[ [ [ 1, 1, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ],
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[ [ 1, 0, 0 ], [ 0, 1, 1 ], [ 0, 0, 1 ] ],
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[ [ 1, 0, 1 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ] ]
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gap> C := CRRecordByMats(G,mats);;
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gap> cc := TwoCohomologyCR(C);;
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gap> cc.factor.rels;
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[ 2, 0, 0 ]
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gap> c := cc.factor.prei[2];
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[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 1 ]
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gap> cc.gcb;
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[ [ 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
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[ 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0 ],
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[ 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1 ],
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[ -1, 0, 1, 1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
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[ 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1 ] ]
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gap> cc.gcc;
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[ [ 1, 0, 0, 0, 0, -2, -1, 0, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0 ],
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[ 0, 1, 0, 0, -1, -1, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0 ],
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[ 0, 0, 1, 0, 0, -2, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0 ],
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[ 0, 0, 0, 1, 0, 0, -1, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
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[ 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
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[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 1 ],
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[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1 ] ]
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gap> # LowerCentralSeriesOfGroup for non-nilpotent pcp-groups used to trigger
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gap> # an infinite recursion
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gap> G := PcGroupToPcpGroup(SmallGroup(6,1));
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Pcp-group with orders [ 2, 3 ]
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gap> LowerCentralSeriesOfGroup(G);
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[ Pcp-group with orders [ 2, 3 ], Pcp-group with orders [ 3 ] ]
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gap> STOP_TEST( "bugfix.tst", 10000000);
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21
samples/GAP/factor.tst
Normal file
21
samples/GAP/factor.tst
Normal file
@@ -0,0 +1,21 @@
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gap> START_TEST("Test of factor groups and natural homomorphisms");
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gap> G:=HeisenbergPcpGroup(2);
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Pcp-group with orders [ 0, 0, 0, 0, 0 ]
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gap> H:=Subgroup(G,[G.2,G.3,G.4,G.5]);
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gap> K:=G/H;
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gap> NaturalHomomorphism(K);
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gap> A:=Subgroup(H, [G.3]);
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Pcp-group with orders [ 0 ]
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gap> B:=Subgroup(Subgroup(G,[G.1,G.4,G.5]), [G.4]);
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Pcp-group with orders [ 0 ]
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gap> Normalizer(A,B);
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Pcp-group with orders [ 0 ]
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gap> # The following used to trigger the error "arguments must have a common parent group"
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gap> Normalizer(B,A);
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Pcp-group with orders [ 0 ]
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gap> STOP_TEST( "factor.tst", 10000000);
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