Category:ApCoCoA-1:Package gbmr

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Revision as of 11:03, 9 July 2009 by (talk)

Package gbmr is designed to compute Groebner bases in monoid rings.

For the field of rationals Q and a monoid M presented by a string rewriting system, let Q[M] denote the ring of all finite formal sums (called polynomials) a_{1}*w_{1}+ a_{2}*w_{2} +...+a_{n}*w_{n} with coefficients a_{i} in Q\{0} and terms w_{i} in M. This ring is called the monoid ring of M over Q.

Let p, f be two non-zero polynomials in Q[M]. We say f prefix reduces p to q at a monomial a*t of p in one step, denoted by p-->_{f}q if

 (1) LT(f)w = t for some w in M, i.e., LT(f) is a prefix of t, and
 (2) q = p-a*LT(f)^{-1}*f*w.

A set G is said to be a Groebner basis with respect to the reduction -->, if <-->_{G} = Equiv_{Ideal(G)} and -->_{G} is confluent.

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