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Verify SubdirectProduct works correctly
In particular, verify that bug gap-system#3431 is fixed
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gap> START_TEST("SubdirectProduct.tst"); | ||
gap> f:=FreeGroup("a", "b");; | ||
gap> g:=f/[ f.1^6, f.2^4, f.1^3*f.2^(-2), f.2^(-1)*f.1*f.2*f.1];; | ||
gap> Size(g); | ||
12 | ||
gap> g0:=Subgroup(g, [g.1^2]);; | ||
gap> g1:=g/g0;; | ||
gap> ff:=FreeGroup("c");; | ||
gap> h:=ff/[ff.1^12];; | ||
gap> Size(h); | ||
12 | ||
gap> h0:=Subgroup(h,[h.1^4]);; | ||
gap> h1:=h/h0;; | ||
gap> ng:=NaturalHomomorphismByNormalSubgroup(g,g0);; | ||
gap> nh:=NaturalHomomorphismByNormalSubgroup(h,h0);; | ||
gap> phi:=IsomorphismGroups(g1,h1);; | ||
gap> ghom:=CompositionMapping(phi, ng);; | ||
gap> hhom:=nh;; | ||
gap> nn:=SubdirectProduct(g,h,ghom,hhom);; | ||
gap> Size(nn); | ||
36 | ||
gap> Projection(nn,1); | ||
[ f1, f2, f3, f4 ] -> [ b, a^9, a^4, <identity ...> ] | ||
gap> Projection(nn,2); | ||
[ f1, f2, f3, f4 ] -> [ c^9, c^6, <identity ...>, c^4 ] | ||
gap> STOP_TEST("SubdirectProduct.tst", 10000); |