Singular Manual: Groebner bases in G-algebras

| ### 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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