Singular

D.15.10 gradedModules_lib

Library:

gradedModules.lib

Purpose:

Operations with graded modules/matrices/resolutions

Authors:

Oleksandr Motsak <U@D>, where U=motsak, D=mathematik.uni-kl.de
Hanieh Keneshlou <[email protected]>

Overview:

The library contains several procedures for constructing and manipulating graded modules/matrices/resolutions. Basics about graded objects can be found in [MO].

Note:

set assumeLevel to positive integer value in order to auto-check all assumptions.

References:

[MO] Motsak, O.: Non-commutative Computer Algebra with applications: Graded commutative algebra and related structures in Singular with applications, Ph.D. thesis, TU Kaiserslautern, 2010

Procedures:

D.15.10.1 grobj		construct a graded object
D.15.10.2 grtest		check whether A is a valid graded object
D.15.10.3 grdeg		compute graded degrees of columns of M
D.15.10.4 grview		view the graded structure of M
D.15.10.5 grshift		shift graded module M by d
D.15.10.6 grzero		presentation of S(0)^1, where S = basering
D.15.10.7 grtwist		presentation of S(d)^r, where S = basering
D.15.10.8 grsum		direct sum of two graded modules M + N
D.15.10.9 grpower		direct p-th power of graded module M
D.15.10.10 grorder		reorder cols/rows of M for correct graded-block-structure
D.15.10.11 grtranspose		reordered graded transpose of M
D.15.10.12 TestGRRes		compute/order/transpose a graded resolution of I