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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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