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Computer • algebra
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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 (H143E1)
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 (H143E2)
Ideals(M) : ModBrdt -> []
Verbose Output
Example
ModBrdt_ModBrdt:Verbose-Output (H143E3)
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 (H143E4)
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 (H143E5)
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 (H143E6)
Brandt Modules Over F
q
[t]
BrandtModuleDimension(D, N) : RngElt, RngElt -> RngIntElt
HeckeEigenvectors(M) : ModBrdt -> [ ModBrdt ]
HeckeEigenvalue(f, p) : ModBrdtElt, RngElt -> RngElt
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V2.28, 13 July 2023