Predicates#

IsAmbientSpace(M): ModSS -> BoolElt#: Returns true if the supersingular module \(M\) is the full module of supersingular points and not a submodule.

M1 eq M2: ModSS, ModSS -> BoolElt#: Returns true if the supersingular module \(M_1\) equals \(M_2\).

P eq Q: ModSSElt, ModSSElt -> BoolElt#: Returns true if the module element \(P\) equals \(Q\).

M1 subset M2: ModSS, ModSS -> BoolElt#: Returns true if the supersingular module \(M_1\) is a subset of \(M_2\).

UsesBrandt(M): ModSS -> BoolElt#: Returns true if the underlying computations on the supersingular module \(M\) are done using Brandt modules.

UsesMestre(M): ModSS -> BoolElt#: Returns true if the underlying computations on the supersingular module \(M\) are done using the Mestre-Oesterle method of graphs.

Example: Predicates (ex-999e2e)#

In this example we illustrate each of the above predicates.

> M := SupersingularModule(11);
> S := CuspidalSubspace(M);
> IsAmbientSpace(S);
false
> IsAmbientSpace(M);
true
> S eq M;
false
> S eq S;
true
> S.1 eq S.1;
true
> S.1 eq M.1 - M.2;
true
> S.1 eq M.1;
false
> S subset M;
true
> UsesBrandt(S);
false
> UsesMestre(S);
true
> M := SupersingularModule(11 : Brandt := true);
> UsesBrandt(M);
true
> UsesMestre(M);
false

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