"Source: Text/Module/ModDed.text";
"Line: 416";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Module/ModDed.text, line: 416
// Example: H61E3 ()
print "Example: H61E3";
ei := GetEchoInput();
SetEchoInput(true);
P<x> := PolynomialRing(Rationals());
P<y> := PolynomialRing(P);
F<c> := FunctionField(x^2 - y);
M := MaximalOrderFinite(F);
Vs := RModule(M, 2);
s := [Vs | [1, 3], [2, 3]];
Mods := Module(s);
CoefficientRing(Mods);
Mods.1;
Determinant(Mods);
Vs := RSpace(M, 2);
s := [Vs | [1, 3], [2, 3]];
Mods := Module(s);
sMods := sub<Mods | Mods!Vs![1, 3]>;
qMods := quo<Mods | sMods>;
Degree(Mods);
assert $1 eq 2;
Ngens(Mods);
assert $1 eq 2;
Ngens(sMods);
assert $1 eq 1;
Degree(sMods);
assert $1 eq 2;
Degree(qMods);
assert $1 eq 2;
Ngens(qMods);
assert $1 eq 2;
Determinant(Mods);
Determinant(qMods);
SetEchoInput(ei);
