### 7.10.4 freegb_lib

Library:
  freegb.lib
Purpose:
  Two-sided Groebner bases in free algebras and tools via Letterplace approach
Authors:
  Viktor Levandovskyy, viktor.levandovskyy at math.rwth-aachen.de
  Karim Abou Zeid, karim.abou.zeid at rwth-aachen.de
  Grischa Studzinski, grischa.studzinski at math.rwth-aachen.de

Overview:
  For the theory, see chapter 'Letterplace' in the Singular Manual.

  This library provides access to kernel functions and also contains legacy code (partially as static procedures) for compatibility reasons.

  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:

> 7.10.4.1 isFreeAlgebra |  | check whether r is a letterplace ring (free algebra)
> 7.10.4.2 lpDegBound |  | returns the degree bound of a letterplace ring
> 7.10.4.3 lpVarBlockSize |  | returns the size of the letterplace blocks
> 7.10.4.4 lpNcgenCount |  | returns the number of ncgen variables
> 7.10.4.5 lpDivision |  | two-sided division with remainder
> 7.10.4.6 lpGBPres2Poly |  | reconstructs a polynomial from the output of lpDivision
> 7.10.4.7 isOrderingShiftInvariant |  | tests shift-invariance of the monomial ordering
> 7.10.4.8 makeLetterplaceRing |  | (deprecated, use freeAlgebra) creates a Letterplace ring out of given data
> 7.10.4.9 letplaceGBasis |  | (deprecated, use twostd) two-sided Groebner basis of a letterplace ideal I
> 7.10.4.10 lieBracket |  | (deprecated, use bracket) iterated Lie bracket of two letterplace polynomials
> 7.10.4.11 setLetterplaceAttributes |  | (for testing purposes) supplies ring R with the letterplace structure
> 7.10.4.12 testLift |  | verify the output of lift
> 7.10.4.13 testSyz |  | verify the output of syz

See also: LETTERPLACE; fpadim_lib; fpalgebras_lib; fpaprops_lib.

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