BRANDT MODULES
Acknowledgements
Introduction
Brandt Module Creation
Creation of Elements
Operations on Elements
Categories and Parent
Elementary Invariants
Associated Structures
Verbose Output
Subspaces and Decomposition
Boolean Tests on Subspaces
Hecke Operators
q-Expansions
Dimensions of Spaces
Brandt Modules Over Fq[t]
Bibliography
Introduction
Brandt Module Creation
BrandtModule(D) : RngIntElt -> ModBrdt
BrandtModule(A) : AlgQuatOrd -> ModBrdt
BaseExtend(M, R) : ModBrdt, Rng -> ModBrdt
BrandtModule(M, N) : AlgQuatOrd, RngElt -> ModBrdt
Example ModBrdt_ModBrdt:Constructors (H146E1)
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 (H146E2)
Ideals(M) : ModBrdt -> []
Verbose Output
Example ModBrdt_ModBrdt:Verbose-Output (H146E3)
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 (H146E4)
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 (H146E5)
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
Example ModBrdt_ModBrdt:Dimension (H146E6)
Brandt Modules Over Fq[t]
BrandtModuleDimension(D, N) : RngElt, RngElt -> RngIntElt
HeckeEigenvectors(M) : ModBrdt -> [ ModBrdt ]
HeckeEigenvalue(f, p) : ModBrdtElt, RngElt -> RngElt
Bibliography
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