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D.15.10 gradedModules_lib

Operations with graded modules/matrices/resolutions
Oleksandr Motsak <U@D>, where U=motsak, D=mathematik.uni-kl.de
Hanieh Keneshlou <hkeneshlou@yahoo.com>

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

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

[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


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