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 M1 equals M2.
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 M1 is a subset of M2.
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 ModSS_Predicates (H144E6)

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
V2.28, 13 July 2023