"Source: Text/Algebra/AlgQuat.text";
"Line: 2862";
"Date: Thu Sep 25 14:47:46 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Algebra/AlgQuat.text, line: 2862
// Example: H95E26 ()
print "Example: H95E26";
ei := GetEchoInput();
SetEchoInput(true);
P<x> := PolynomialRing(Rationals());
F<b> := NumberField(x^3-3*x-1);
Z_F := MaximalOrder(F);
F := FieldOfFractions(Z_F);
A<alpha,beta,alphabeta> := QuaternionAlgebra<F | -3, b>;
O := Order([alpha,beta,alphabeta]);
O;
I := ideal<O | 2>;
I eq (I + ideal<O | 2>);
assert $1;
I eq (I + ideal<O | 3>);
assert not $1;
Foo := InfinitePlaces(F);
A := QuaternionAlgebra(ideal<Z_F | 2*3*5>, Foo);
IsDefinite(A);
assert $1;
O := MaximalOrder(A);
I := rideal<O | Norm(O.2), O.2>;
J := rideal<O | Norm(O.3), O.3>;
IsIsomorphic(I, J);
SetEchoInput(ei);
