"Source: Text/Algebra/AlgInv.text";
"Line: 846";
"Date: Tue Feb 25 10:14:52 2020";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Algebra/AlgInv.text, line: 846
// Example: H96E9 ()
print "Example: H96E9";
ei := GetEchoInput();
SetEchoInput(true);
P1 := ClassicalSylow(GL(3, 43^2), 43);
Forms1 := PGroupToForms(P1);
A1 := AdjointAlgebra(Forms1);
RecogniseStarAlgebra(A1);
assert $1;
SimpleParameters(A1);
R<x> := PolynomialRing(GF(43));
S, f := quo< R | x^2 >;
G := GL(3, S);
Ua := G![1,1,0,0,1,0,0,0,1];
Wa := G![1,0,0,0,1,1,0,0,1];
Ub := G![1,x@f,0,0,1,0,0,0,1];
Wb := G![1,0,0,0,1,x@f,0,0,1];
P2 := sub< G | [ Ua, Wa, Ub, Wb ] >;
Forms2 := PGroupToForms(P2);
A2 := AdjointAlgebra(Forms2);
RecogniseStarAlgebra(A2);
assert $1;
SimpleParameters(A2);
SetEchoInput(ei);
