Singular

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