Singular

7.7.9 freegb_lib

Library:

freegb.lib

Purpose:

Compute two-sided Groebner bases in free algebras via letterplace approach

Authors:

Viktor Levandovskyy, viktor.levandovskyy@math.rwth-aachen.de Grischa Studzinski, grischa.studzinski@math.rwth-aachen.de

Overview:

For the theory, see chapter 'Letterplace' in the @sc{Singular} Manual

Support: Joint projects LE 2697/2-1 and KR 1907/3-1 of the Priority Programme SPP 1489: 'Algorithmische und Experimentelle Methoden in Algebra, Geometrie und Zahlentheorie' of the German DFG
and Project II.6 of the transregional collaborative research centre SFB-TRR 195 'Symbolic Tools in Mathematics and their Application' of the German DFG

Procedures:

7.7.9.0. makeLetterplaceRing		creates a ring with d blocks of shifted original variables
7.7.9.0. letplaceGBasis		computes two-sided Groebner basis of a letterplace ideal I up to a degree bound
7.7.9.0. lpNF		two-sided normal form of f with respect to ideal I
7.7.9.0. setLetterplaceAttributes		supplies ring R with the letterplace structure
7.7.9.0. freeGBasis		computes two-sided Groebner basis of an ideal, encoded via list L, up to degree n
7.7.9.0. lpMult		letterplace multiplication of letterplace polynomials
7.7.9.0. shiftPoly		compute the i-th shift of letterplace polynomial p
7.7.9.0. lpPower		natural power of a letterplace polynomial
7.7.9.0. lieBracket		compute Lie bracket ab-ba of two letterplace polynomials
7.7.9.0. lp2lstr		convert a letterplace ideal into a list of modules
7.7.9.0. lst2str		convert a list (of modules) into polynomials in free algebra via strings
7.7.9.0. mod2str		convert a module into a polynomial in free algebra via strings
7.7.9.0. vct2str		convert a vector into a word in free algebra
7.7.9.0. serreRelations		compute the homogeneous part of Serre's relations associated to a generalized Cartan matrix A
7.7.9.0. fullSerreRelations		compute the ideal of all Serre's relations associated to a generalized Cartan matrix A
7.7.9.0. isVar		check whether p is a power of a single variable
7.7.9.0. ademRelations		compute the ideal of Adem relations for i<2j in char 0