# Singular

#### D.15.20.5 grshift

Procedure from library `gradedModules.lib` (see gradedModules_lib).

Usage:
grshift(A, d), graded objects A, int d

Return:

Purpose:
shift the grading on A by d: A(i) -> A(i+d)

Example:
 ```LIB "gradedModules.lib"; ring r=32003,(x,y,z),dp; module A = grobj( module([x+y, x, 0, 0], [0, x+y, y, 0]), intvec(0,0,0,1) ); grview(A); ==> Graded homomorphism: r^3 + r(-1) <- r(-1)^2, given by a matrix, with degr\ ees: ==> ..1 ..2 .... ==> --- --- +... ==> 0 : 1 - |..1 ==> 0 : 1 1 |..2 ==> 0 : - 1 |..3 ==> 1 : - - |..4 ==> === === ==> 1 1 module S = grshift( A, 6); grview(S); ==> Graded homomorphism: r(6)^3 + r(5) <- r(5)^2, given by a matrix, with deg\ rees: ==> ..1 ..2 .... ==> --- --- +... ==> -6 : 1 - |..1 ==> -6 : 1 1 |..2 ==> -6 : - 1 |..3 ==> -5 : - - |..4 ==> === === ==> -5 -5 grview( grshift( grzero(), 100 ) ); // does nothing... ==> !! Warning: shifting '0 <- 0' leaves it as it unchanged! ==> Graded homomorphism: 0 <- 0, given by zero (0^2) matrix. ```