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# Basics | ||
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```@meta | ||
CurrentModule = Hecke | ||
DocTestSetup = quote | ||
using Hecke | ||
end | ||
``` | ||
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## Creation of algebras | ||
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See the corresponding sections in ????? | ||
```@docs | ||
zero_algebra(::Field) | ||
``` | ||
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## Basic properties | ||
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```@docs | ||
base_ring(::Hecke.AbstractAssociativeAlgebra) | ||
basis(::Hecke.AbstractAssociativeAlgebra) | ||
``` | ||
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## Predicates | ||
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```@docs | ||
is_zero(::Hecke.AbstractAssociativeAlgebra) | ||
is_commutative(::Hecke.AbstractAssociativeAlgebra) | ||
is_central(::AbstractAssociativeAlgebra) | ||
``` | ||
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## Generators | ||
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```@docs | ||
gens(::AbstractAssociativeAlgebra) | ||
gens_with_data(::AbstractAssociativeAlgebra) | ||
``` | ||
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## Center | ||
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```@docs | ||
center(::Hecke.AbstractAssociativeAlgebra) | ||
dimension_of_center(::Hecke.AbstractAssociativeAlgebra) | ||
dimension_over_center(::Hecke.AbstractAssociativeAlgebra) | ||
``` |
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```@meta | ||
CurrentModule = Hecke | ||
``` | ||
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# [Introduction](@id Algebras) | ||
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!!! 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. | ||
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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. | ||
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These share a common interface encompassing a wide range of functions, which is | ||
indicated by the use of the type `AbstractAssociativeAlgebra` in the signature. |
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# Structure constant algebras | ||
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```@meta | ||
CurrentModule = Hecke | ||
DocTestSetup = quote | ||
using Hecke | ||
end | ||
``` | ||
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## Creation | ||
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```@docs | ||
structure_constant_algebra(::Ring, ::Array{<:Any, 3}) | ||
structure_constant_algebra(::SimpleNumField) | ||
``` | ||
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## Structure constant table | ||
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```@docs | ||
structure_constant_table(::StructureConstantAlgebra) | ||
``` |