Top
Back: primdecMon
Forward: setBaseMultigrading
FastBack: monomialideal_lib
FastForward: paraplanecurves_lib
Up: Experimental libraries
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

D.15.5 multigrading_lib

Todos/Issues:

Library:
multigrading.lib
Purpose:
Multigraded Rings

Authors:
Rene Birkner, rbirkner@math.fu-berlin.de
Lars Kastner, lkastner@math.fu-berlin.de
Oleksandr Motsak, U@D, where U={motsak}, D={mathematik.uni-kl.de}

Overview:
This library allows one to virtually add multigradings to Singular. For more see http://code.google.com/p/convex-singular/wiki/Multigrading For theoretical references see:
E. Miller, B. Sturmfels: 'Combinatorial Commutative Algebra' and M. Kreuzer, L. Robbiano: 'Computational Commutative Algebra'.

Note:
'mDegBasis' relies on 4ti2 for computing Hilbert Bases.

Procedures:

D.15.5.1 setBaseMultigrading  attach multiweights/torsion matrices to the basering
D.15.5.2 getVariableWeights  get matrix of multidegrees of vars attached to a ring
D.15.5.3 getTorsion  get torsion matrix attached to a ring
D.15.5.4 setModuleGrading  attach multiweights of units to a module and return it
D.15.5.5 getModuleGrading  get multiweights of module units (attached to M)
D.15.5.6 mDeg  compute the multidegree of A
D.15.5.7 mDegBasis  compute all monomials of multidegree d
D.15.5.8 mDegPartition  compute the multigraded-homogenous components of p
D.15.5.9 isTorsionFree  test whether the current multigrading is torsion free
D.15.5.10 isTorsionElement  test whether p has zero multidegree
D.15.5.11 isHomogenous  test whether 'a' is multigraded-homogenous
D.15.5.12 equalMDeg  test whether e1==e2 in the current multigrading
D.15.5.13 mDegGroebner  compute the multigraded GB/SB of M
D.15.5.14 mDegSyzygy  compute the multigraded syzygies of M
D.15.5.15 mDegResolution  compute the multigraded resolution of M
D.15.5.16 defineHomogenous  get a torsion matrix wrt which p becomes homogenous
D.15.5.17 pushForward  find the finest grading on the image ring, homogenizing f
D.15.5.18 hermite  compute the Hermite Normal Form of a matrix
D.15.5.19 hilbertSeries  compute the multigraded Hilbert Series of M


Top Back: primdecMon Forward: setBaseMultigrading FastBack: monomialideal_lib FastForward: paraplanecurves_lib Up: Experimental libraries Top: Singular Manual Contents: Table of Contents Index: Index About: About this document
            User manual for Singular version 3-1-2, Oct 2010, generated by texi2html.