Some complexity results for prefix Gröbner bases in free monoid rings

On Gröbner bases in monoid and group rings

Some Results on Differential Gröbner Bases

We establish some results in the theory of standard bases of differential ideals (also known as differential Gröbner bases) in differential polynomial rings. This work was stimulated by some articles of V. Weispfenning, devoted to the classification of term-orders and parametric Gröbner bases of ideals generated by monomials and binomials.

Gröbner-Shirshov bases for some braid groups

Presenting 2-generator Artin groups A(m) and braid groups B3 and B4 as towers of HNN extensions of free groups, we obtain Gröbner–Shirshov bases, normal forms and rewriting systems for these groups. c © 2005 Elsevier Ltd. All rights reserved.

Pivoting in Extended Rings for Computing Approximate Gröbner Bases

It is well known that in the computation of Gröbner bases arbitrarily small perturbations in the coefficients of polynomials may lead to a completely different staircase, even if the solutions of the polynomial system change continuously. This phenomenon is called artificial discontinuity in Kondratyev’s Ph.D. thesis. We show how such phenomenon may be detected and even “repaired” by using a ne...

GrÖbner-shirshov Bases for Free Inverse Semigroups

A new construction for free inverse semigroups was obtained by Poliakova and Schein in 2005. Based on their result, we find Gröbner-Shirshov bases for free inverse semigroups with respect to the deg-lex order of words. In particular, we give the (unique and shortest) normal forms in the classes of equivalent words of a free inverse semigroup together with the Gröbner-Shirshov algorithm to trans...