Singular Manual: freegb_lib

> | ### 7.7.4 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:
> 7.7.4.1 makeLetterplaceRing |  | creates a Letterplace ring out of given data
> 7.7.4.2 setLetterplaceAttributes |  | supplies ring R with the letterplace structure
> 7.7.4.3 lieBracket |  | Lie bracket ab-ba of two letterplace polynomials
> 7.7.4.4 letplaceGBasis |  | two-sided Groebner basis of a letterplace ideal I
> 7.7.4.5 lpDivision |  | two-sided division with remainder
> 7.7.4.6 lpGBPres2Poly |  | reconstructs a polynomial from the output of lpDivision
> 7.7.4.7 isOrderingShiftInvariant |  | tests shift-invariance of the monomial ordering
> 7.7.4.8 isVar |  | check whether p is a power of a single variable
> 7.7.4.9 lpLmDivides |  | tests whether there exists q in I, such that LM(q)|LM(p)
> 7.7.4.10 lpVarAt |  | returns the variable (as a poly) at position pos of the poly p
See also: LETTERPLACE; fpadim_lib; fpalgebras_lib; fpaprops_lib.

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