> | ### 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 <hkeneshlou@yahoo.com> 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

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