"Source: Text/Algebra/AlgAss.text";
"Line: 958";
"Date: Thu Sep 25 14:47:46 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Algebra/AlgAss.text, line: 958
// Example: H90E7 ()
print "Example: H90E7";
ei := GetEchoInput();
SetEchoInput(true);
a1 := Matrix( [
[-184174/80137, -325/80137, 71/2163699, 0, 0, 0, 0, 0, 0],
[17713719/80137, 92087/80137, -325/80137, 0, 0, 0, 0, 0, 0],
[-2189265975/80137, -16429806/80137, 92087/80137, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 64850/80137, 1472/240411, -25/2163699, 0, 0, 0],
[0, 0, 0, -6237225/80137, -32425/80137, 1472/240411, 0, 0, 0],
[0, 0, 0, 3305230272/80137, 45310743/80137, -32425/80137, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 119324/80137, -497/240411, -46/2163699],
[0, 0, 0, 0, 0, 0, -11476494/80137, -59662/80137, -497/240411],
[0, 0, 0, 0, 0, 0, -1115964297/80137, -28880937/80137, -59662/80137] ] );
a2:= Matrix( [
[0, 0, 0, 282469/240411, 956/2163699, -26/2163699, 0, 0, 0],
[0, 0, 0, -6486714/80137, -21029/240411, 956/2163699, 0, 0, 0],
[0, 0, 0, 238511484/80137, -2766918/80137, -21029/240411, 0, 0, 0],
[0, 0, 0, 0, 0, 0, -85879/240411, -4894/2163699, 64/6491097],
[0, 0, 0, 0, 0, 0, 5322432/80137, 163145/240411, -4894/2163699],
[0, 0, 0, 0, 0, 0, -1220999166/80137, -13720122/80137, 163145/240411],
[-1183167/80137, -11814/80137, -14/80137, 0, 0, 0, 0, 0, 0],
[-94306842/80137, -2653965/80137, -11814/80137, 0, 0, 0, 0, 0, 0],
[-79581502242/80137, -1335450240/80137, -2653965/80137, 0, 0, 0, 0, 0, 0] ] );
M := MatrixAlgebra( Rationals(), 9 );
A := sub< M | [ a1, a2 ] >;
Dimension(A);
assert $1 eq 9;
JacobsonRadical(A);
O := MaximalOrder(A);
Discriminant(O);
assert $1 eq -19683;
Determinant(Matrix(9, [Trace(a*b) : a, b in Basis(O)]));
assert $1 eq -19683;
T :=MultiplicationTable(O);
T[3][7];
SetEchoInput(ei);
