"Source: Text/Algebra/AlgBas.text";
"Line: 2912";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Algebra/AlgBas.text, line: 2912
// Example: H94E20 ()
print "Example: H94E20";
ei := GetEchoInput();
SetEchoInput(true);
ff := GF(8);
FA<e1,e2,a,b,c> := FreeAlgebra(ff,5);
rrr := [a*b*a*b*a, c*c*c*c, a*b*c - c*a*b];
B := BasicAlgebra(FA,rrr,2,[<1,2>,<2,1>,<1,1>]);
B;
DimensionsOfProjectiveModules(B);
DimensionsOfInjectiveModules(B);
P1 := ProjectiveModule(B,1);
Socle(P1);
time in1 := CompactInjectiveResolution(P1,10);
SimpleCohomologyDimensions(P1);
M := InjectiveSyzygyModule(P1,6);
M;
hh := AHom(M,M);
hh;
[Rank(hh.i): i in [1 .. Dimension(hh)]];
vv := Random(hh);
Rank(vv);
vv*vv eq vv;
assert not $1;
[Rank(vv*vv-u*vv):u in ff];
[u:u in ff];
Rank(vv*vv - vv);
U := vv*vv - vv;
Rank(U);
Rank(U*U);
Rank(U*U*U);
Rank(U*U*U*U);
Rank(U*U*U*U*U);
Rank(U*U*U*U*U*U);
T := U*U*U*U;
N1 := Kernel(T);
N2 := Image(T);
Dimension(N1);
Dimension(N2);
Dimension(N1+N2);
SetEchoInput(ei);
