Introduction
Brandt Module Creation BrandtModule(D) : RngIntElt -> ModBrdt BrandtModule(A) : AlgQuatOrd -> ModBrdt BaseExtend(M,R) : ModBrdt, Rng -> ModBrdt Example ModBrdt_ModBrdt:Constructors (H114E1)
Creation of Elements M ! x : ModBrdt, . -> ModBrdtElt M . i : ModBrdt, RngIntElt -> ModBrdtElt
Operations on Elements a * x : RngElt, ModBrdtElt -> ModBrdtElt x * T : ModBrdtElt, AlgMatElt -> ModBrdtElt x + y : ModBrdtElt, ModBrdtElt -> ModBrdtElt x - y : ModBrdtElt, ModBrdtElt -> ModBrdtElt x eq y : ModBrdtElt, ModBrdtElt -> BoolElt Eltseq(x) : ModBrdtElt -> SeqEnum InnerProduct(x,y) : ModBrdtElt, ModBrdtElt -> RngElt Norm(x) : ModBrdtElt -> RngElt
Categories and Parent Parent(x) : ModBrdtElt -> ModBrdt x in M : ModBrdtElt, ModBrdt -> BoolElt
Elementary Invariants Level(M) : ModBrdt -> RngIntElt Discriminant(M) : ModBrdt -> RngIntElt Conductor(M) : ModBrdt -> RngIntElt BaseRing(M) : ModBrdt -> Rng Basis(M) : ModBrdt -> SeqEnum
Associated Structures AmbientModule(M) : ModBrdt -> ModBrdt IsAmbient(M) : ModBrdt -> BoolElt Dimension(M) : ModBrdt -> RngIntElt Degree(M) : ModBrdt -> RngIntElt GramMatrix(M) : ModBrdt -> AlgMatElt InnerProductMatrix(M) : ModBrdt -> AlgMatElt Example ModBrdt_ModBrdt:Module-Creation (H114E2)
Verbose Output Example ModBrdt_ModBrdt:Verbose-Output (H114E3)
Subspaces and Decomposition EisensteinSubspace(M) : ModBrdt -> ModBrdt CuspidalSubspace(M) : ModBrdt -> ModBrdt OrthogonalComplement(M) : ModBrdt -> ModBrdt M meet N : ModBrdt, ModBrdt -> ModBrdt Decomposition(M,B) : ModBrdt, RngIntElt -> [ModBrdt] SortDecomposition(D) : [ModBrdt] -> SeqEnum Example ModBrdt_ModBrdt:Decomposition (H114E4)
Boolean Tests on Subspaces IsEisenstein(M) : ModBrdt -> BoolElt IsCuspidal(M) : ModBrdt -> BoolElt IsIndecomposable(M,B) : ModBrdt, RngIntElt -> BoolElt M1 subset M2 : ModBrdt, ModBrdt -> BoolElt M1 lt M2 : ModBrdt, ModBrdt -> BoolElt M1 gt M2 : ModBrdt, ModBrdt -> BoolElt Example ModBrdt_ModBrdt:EisensteinSubspace (H114E5)
Hecke Operators HeckeOperator(M, n) : ModBrdt, RngIntElt -> AlgMatElt AtkinLehnerOperator(M, p) : ModBrdt, RngIntElt -> AlgMatElt
q-Expansions ThetaSeries(x, y, prec) : ModBrdtElt, ModBrdtElt, RngIntElt -> RngSerElt qExpansionBasis(M, prec) : ModBrdt, RngIntElt -> SeqEnum
Dimensions of Spaces BrandtModuleDimension(D,N) : RngIntElt, RngIntElt -> RngIntElt
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