# Singular

#### D.15.18.18 grsyz

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

Usage:

Return:

Purpose:
 ```LIB "gradedModules.lib"; ring r=32003,(x,y,z),dp; module A = grgroebner( grobj( module([x+y, x, 0, 3], [0, x+y, y, 2], [y, y, z, 1]), intvec(0,0,0,1) ) ); grview(A); ==> Graded homomorphism: r^3 + r(-1) <- r(-1)^3 + r(-2) + r(-3), given by a m\ atrix, with degrees: ==> ..1 ..2 ..3 ..4 ..5 .... ==> --- --- --- --- --- +... ==> 0 : 1 1 1 2 - |..1 ==> 0 : 1 - 1 - - |..2 ==> 0 : 1 1 1 2 3 |..3 ==> 1 : 0 0 0 1 2 |..4 ==> === === === === === ==> 1 1 1 2 3 grview(grsyz(A)); ==> Graded homomorphism: r(-1)^3 + r(-2) + r(-3) <- r(-2) + r(-3), given by a\ matrix, with degrees: ==> ..1 ..2 .... ==> --- --- +... ==> 1 : 1 - |..1 ==> 1 : 1 2 |..2 ==> 1 : 1 - |..3 ==> 2 : 0 1 |..4 ==> 3 : - 0 |..5 ==> === === ==> 2 3 module X = grgroebner( grobj( module([x]), intvec(2) ) ); grview(X); ==> Graded homomorphism: r(-2) <- r(-3), given by a diagonal matrix, with deg\ rees: ==> .1 ... ==> -- +.. ==> 2 : 1 |.1 ==> == ==> 3 // syzygy module should be zero! grview(grsyz(X)); ==> Graded homomorphism: r(-3) <- 0, given by zero (1 x 0) matrix. ```