"Source: Text/Ring/RngOrd.text";
"Line: 1394";
"Date: Fri Sep 26 14:51:59 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/RngOrd.text, line: 1394
// Example: H39E7 ()
print "Example: H39E7";
ei := GetEchoInput();
SetEchoInput(true);
R<x> := PolynomialRing(Integers());
K<y> := NumberField(x^2-2);
KL<w> := NumberField(x^4-10*x^2+1);
H := hom< K -> KL | (9*w-w^3)/2 >;
H(y);
H(y)^2;
assert $1 eq 2;
f := x^4 + 5*x^3 - 25*x^2 + 125*x + 625;
M := MaximalOrder(f);
F<a, b, c, d> := FieldOfFractions(M);
FF := FiniteField(5, 3);
F;
FF;
h := hom< F -> FF | Coercion(Rationals(), FF), 3*FF.1>;
h;
h(5*b); h(5*5*c); h(5*5*5*d);
FF := FiniteField(11, 5);
h := hom< F -> FF | Coercion(Rationals(), FF), 7*FF.1>;
h(a);
assert $1 eq 1;
h(b); h(c); h(d);
7*FF.1;
5*h(b);
PrimitiveElement(F);
SetEchoInput(ei);
