Added the groebner_basis method for FreeAssAlgIdeals to the docs. (#…

…3949)

* added groebner_basis_docs

* Update free_associative_algebra.md

Added some math facts.

---------

Co-authored-by: Michael Joswig <[email protected]>

docs/src/NoncommutativeAlgebra/free_associative_algebra.md

@@ -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)
+```