7.4.2 Groebner bases in G-algebras
We follow the notations, used in the Manual (e.g. in Standard bases).
Definition
Remark: In general non-commutative algorithms are working with global well-orderings
only (see PLURAL, Monomial orderings and Term orderings), unless we deal with
graded commutative algebras via Graded commutative algebras (SCA).
Left Normal Form
Remark:
As we have already mentioned in the definitions ideal and module (see
PLURAL), by NF (or reduce ) understands a left normal form.
Note, that rightNF from nctools_lib allows to compute a right normal form.
Left ideal membership (plural)
For computing a left Groebner basis G of I , use std (plural).
For computing a left normal form of f with respect to G , use reduce (plural).
Right ideal membership (plural)
The right ideal membership is analogous to the left one:
for computing a right Groebner basis G of I , use rightstd (letterplace) from nctools_lib,
for computing a right normal form of f with respect to G , use rightNF from nctools_lib.
Two-sided ideal membership (plural)
For computing a two-sided Groebner basis T of J , use twostd (plural),
for computing a normal form of f with respect to T , use reduce (plural).
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