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#@local checkStandardAssociate, A, x, R
gap> START_TEST("associate.tst");
# test StandardAssociate, StandardAssociateUnit, IsAssociated
gap> checkStandardAssociate :=
> function(R, coll...)
> local r, u, s;
> if Length(coll) > 0 then
> coll := coll[1];
> elif Size(R) <= 1000 then
> coll := R;
> else
> coll := List([1..1000],i->Random(R));
> fi;
> for r in coll do
> u := StandardAssociateUnit(R,r); Assert(0, u in R);
> if not IsUnit(R,u) then Error("StandardAssociateUnit not a unit for ", [R,r]); fi;
> s := StandardAssociate(R,r); Assert(0, s in R);
> if u * r <> s then Error("StandardAssociate doesn't match its unit for ", [R,r]); fi;
> if not IsAssociated(R,r,s) then Error("r, s not associated for ", [R,r]); fi;
> od;
> return true;
> end;;
# rings in characteristic 0
gap> checkStandardAssociate(Integers, [-10..10]);
true
gap> checkStandardAssociate(Rationals);
true
gap> checkStandardAssociate(GaussianIntegers);
true
gap> checkStandardAssociate(GaussianRationals);
true
# finite fields
gap> ForAll(Filtered([2..50], IsPrimePowerInt), q->checkStandardAssociate(GF(q)));
true
# ZmodnZ
gap> ForAll([1..100], m -> checkStandardAssociate(Integers mod m));
true
gap> checkStandardAssociate(Integers mod ((2*3*5)^2));
true
gap> checkStandardAssociate(Integers mod ((2*3*5)^3));
true
gap> checkStandardAssociate(Integers mod ((2*3*5*7)^2));
true
gap> checkStandardAssociate(Integers mod ((2*3*5*7)^3));
true
# polynomial rings
gap> for A in [ GF(5), Integers, Rationals ] do
> for x in [1,3] do
> R:=PolynomialRing(A, x);
> checkStandardAssociate(R, List([1..30],i->PseudoRandom(R)));
> od;
> od;
#
gap> STOP_TEST("associate.tst");
[ Dauer der Verarbeitung: 0.7 Sekunden
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