"Source: Text/Algebra/AlgQuat.text";
"Line: 1977";
"Date: Thu Sep 25 14:47:46 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Algebra/AlgQuat.text, line: 1977
// Example: H95E17 ()
print "Example: H95E17";
ei := GetEchoInput();
SetEchoInput(true);
QQ:= Rationals();
A<i,j> := QuaternionAlgebra< QQ | -1, -11 >;
S := MaximalOrder(A);
P<x> := PolynomialRing(QQ);
P ! MinimalPolynomial(i);
I := lideal< S | 2, 1+i >;
Norm(I);
assert $1 eq 2;
I in MaximalLeftIdeals(S, 2);
assert $1;
Basis(I);
[ Eltseq(x) : x in Basis(I) ];
BasisMatrix(I, A);
I;
BasisMatrix(I);
SetEchoInput(ei);
