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Added the groebner_basis method for FreeAssAlgIdeals to the docs. #3949

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Jul 17, 2024
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Added the groebner_basis method for FreeAssAlgIdeals to the docs. #3949

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834895c
added groebner_basis_docs
Sequenzer Jul 17, 2024
bce1641
Merge branch 'oscar-system:master' into feature/simple-quantumAut
Sequenzer Jul 17, 2024
4b72595
Update free_associative_algebra.md
micjoswig Jul 17, 2024
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11 changes: 10 additions & 1 deletion docs/src/NoncommutativeAlgebra/free_associative_algebra.md
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Expand Up @@ -20,7 +20,16 @@ ideal(g::Vector{T}) where T <: FreeAssAlgElem

### Ideal Membership

Non-commutative polynomial rings are not Noetherian. Hence, in general, Groebner bases do not exist. Hence calling the functions below may not terminate. Picking suitable term orders is difficult in the noncommutative case. Therefore, we fix the term order to be degree reverse lexicographic.

Setting the parameter `deg_bound` to a positive value yields the truncation of the Groebner bases to a fixed degree. Such a truncation is always finite.

```@docs
ideal_membership(a::FreeAssAlgElem, I::FreeAssAlgIdeal, deg_bound::Int)
groebner_basis(I::FreeAssAlgIdeal, deg_bound::Int=-1; protocol::Bool=false)
```

If a finite Gröbner basis exists, it solves the ideal membership problem.

```@docs
ideal_membership(a::FreeAssAlgElem, I::FreeAssAlgIdeal, deg_bound::Int)
```
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