"Source: Text/Module/ModDed.text";
"Line: 562";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Module/ModDed.text, line: 562
// Example: H61E4 ()
print "Example: H61E4";
ei := GetEchoInput();
SetEchoInput(true);
P<x> := PolynomialRing(Integers());
K :=  NumberField([x^5 + 3, x^2 + 2]);
M := MaximalOrder(K);
Vs := RModule(M, 2);
s := [Vs | [1, 3], [2, 3]];
Mods := Module(s);
sMods := sub<Mods | Mods!Vs![1, 3]>;
Mods eq sMods;
assert not $1;
[1, 0] in Mods;
assert $1;
[1, 0] in sMods;
assert not $1;
sMods subset Mods;
assert $1;
Vs := RSpace(M, 2);
s := [Vs | [Random(M, 3), 3], [2, Random(M, 2)]];
Mods := Module(s);
sMods := sub<Mods | Mods!s[1]>;
(7*M + 11*K.1*M)*sMods;
Mods + sMods;
4*sMods;
SetEchoInput(ei);
