diff --git a/docs/src/manual/algebras/basics.md b/docs/src/manual/algebras/basics.md new file mode 100644 index 0000000000..9fc7ff026f --- /dev/null +++ b/docs/src/manual/algebras/basics.md @@ -0,0 +1,45 @@ +# Basics + +```@meta +CurrentModule = Hecke +DocTestSetup = quote + using Hecke +end +``` + +## Creation of algebras + +See the corresponding sections in ????? +```@docs +zero_algebra(::Field) +``` + +## Basic properties + +```@docs +base_ring(::Hecke.AbstractAssociativeAlgebra) +basis(::Hecke.AbstractAssociativeAlgebra) +``` + +## Predicates + +```@docs +is_zero(::Hecke.AbstractAssociativeAlgebra) +is_commutative(::Hecke.AbstractAssociativeAlgebra) +is_central(::AbstractAssociativeAlgebra) +``` + +## Generators + +```@docs +gens(::AbstractAssociativeAlgebra) +gens_with_data(::AbstractAssociativeAlgebra) +``` + +## Center + +```@docs +center(::Hecke.AbstractAssociativeAlgebra) +dimension_of_center(::Hecke.AbstractAssociativeAlgebra) +dimension_over_center(::Hecke.AbstractAssociativeAlgebra) +``` diff --git a/docs/src/manual/algebras/intro.md b/docs/src/manual/algebras/intro.md new file mode 100644 index 0000000000..9e21b4ce88 --- /dev/null +++ b/docs/src/manual/algebras/intro.md @@ -0,0 +1,21 @@ +```@meta +CurrentModule = Hecke +``` + +# [Introduction](@id Algebras) + +!!! note + The functions described in this section are experimental. While the overall + functionality provided will stay the same, names of specific functions or + conventions for the return values might change in future versions. + +This section describes the functionality for finite-dimensional associative +algebras (or just *algebras* for short). Since different applications have different requirements, +the following types of algebras are implemented: +- structure constant algebras, +- matrix algebras, +- group algebras, +- quaternion algebras. + +These share a common interface encompassing a wide range of functions, which is +indicated by the use of the type `AbstractAssociativeAlgebra` in the signature. diff --git a/docs/src/manual/algebras/structureconstant.md b/docs/src/manual/algebras/structureconstant.md new file mode 100644 index 0000000000..3cc4f003a2 --- /dev/null +++ b/docs/src/manual/algebras/structureconstant.md @@ -0,0 +1,21 @@ +# Structure constant algebras + +```@meta +CurrentModule = Hecke +DocTestSetup = quote + using Hecke +end +``` + +## Creation + +```@docs +structure_constant_algebra(::Ring, ::Array{<:Any, 3}) +structure_constant_algebra(::SimpleNumField) +``` + +## Structure constant table + +```@docs +structure_constant_table(::StructureConstantAlgebra) +```