"Source: Text/Module/ModDed.text";
"Line: 873";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Module/ModDed.text, line: 873
// Example: H61E6 ()
print "Example: H61E6";
ei := GetEchoInput();
SetEchoInput(true);
P<x> := PolynomialRing(Rationals());
P<y> := PolynomialRing(P);
F<c> := FunctionField(x^2 - y);
M := MaximalOrderFinite(F);
V := RModule(M, 3);
S := [V|[0,1,0], [4,4,0]];
Mod := Module(S);
W := KModule(FieldOfFractions(M), 4);
S := [W|[3, 2, 1, 0]];
N := Module(S);
h := hom<Mod -> N | W![3, 2, 1, 0], W![3*(M!F.1 + 1), 2*(M!F.1 + 1), 
M!F.1 + 1, 0] >;
h(Mod!(4*V.1));
h(Mod!V![0, 1, 0]);
I := Image(h);
I;
K := Kernel(h);
K;
IsSubmodule(K, Mod);
H, m := Hom(Mod, N);
H; m;
m(H![5, 20]);
SetEchoInput(ei);
