### 7.7.8 freegb_lib

Library:
  freegb.lib
Purpose:
  Compute two-sided Groebner bases in free algebras via
  letterplace
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

Procedures:

> 7.7.8.0. makeLetterplaceRing |  | creates a ring with d blocks of shifted original variables
> 7.7.8.0. letplaceGBasis |  | computes two-sided Groebner basis of a letterplace ideal I up to a degree bound
> 7.7.8.0. lpNF |  | normal form of f with respect to ideal I
> 7.7.8.0. freeGBasis |  | computes two-sided Groebner basis of an ideal, encoded via list L, up to degree n
> 7.7.8.0. setLetterplaceAttributes |  | supplies ring R with the letterplace structure
> 7.7.8.0. lpMult |  | letterplace multiplication of letterplace polynomials
> 7.7.8.0. shiftPoly |  | compute the i-th shift of letterplace polynomial p
> 7.7.8.0. lpPower |  | natural power of a letterplace polynomial
> 7.7.8.0. lp2lstr |  | convert letter-place ideal to a list of modules
> 7.7.8.0. lst2str |  | convert a list (of modules) into polynomials in free algebra
> 7.7.8.0. mod2str |  | convert a module into a polynomial in free algebra
> 7.7.8.0. vct2str |  | convert a vector into a word in free algebra
> 7.7.8.0. lieBracket |  | compute Lie bracket ab-ba of two letterplace polynomials
> 7.7.8.0. serreRelations |  | compute the homogeneous part of Serre's relations associated to a generalized Cartan matrix A
> 7.7.8.0. fullSerreRelations |  | compute the ideal of all Serre's relations associated to a generalized Cartan matrix A
> 7.7.8.0. isVar |  | check whether p is a power of a single variable
> 7.7.8.0. ademRelations |  | compute the ideal of Adem relations for i<2j in char 0

See also: LETTERPLACE; fpadim_lib.

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