"Source: Text/Algebra/AlgBas.text";
"Line: 3429";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Algebra/AlgBas.text, line: 3429
// Example: H94E22 ()
print "Example: H94E22";
ei := GetEchoInput();
SetEchoInput(true);
A := MatrixAlgebra(GF(5),10);
U := A!0;
ElementaryMatrix := function(i,j);
    W := U;
    W[i,j] := 1;
    return W;
end function;
S := &cat[[ElementaryMatrix(i,j): i in [j .. 10]]:j in [1 .. 10]];
B := sub<A|S>;
B;
C := BasicAlgebra(B);
C;
SumOfBettiNumbersOfSimpleModules(C,9);
assert $1 eq 19;
SumOfBettiNumbersOfSimpleModules(C,10);
assert $1 eq 19;
D:= ExtAlgebra(C,10);
E := BasicAlgebraOfExtAlgebra(D);
E;
SumOfBettiNumbersOfSimpleModules(E,8);
assert $1 eq 54;
SumOfBettiNumbersOfSimpleModules(E,9);
assert $1 eq 55;
SumOfBettiNumbersOfSimpleModules(E,10);
assert $1 eq 55;
F := BasicAlgebraOfExtAlgebra(E,10);
F;
G := BasicAlgebraOfExtAlgebra(F,10);
G;
SetEchoInput(ei);
