# Singular

#### D.15.18.3 grdeg

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

Usage:
grdeg(M), graded object M

Return:
intvec of degrees

Purpose:
graded degrees of columns (generators) of M, describing the source of M

Assume:
M must be a graded object (matrix/module/ideal/mapping)

Note:
if M has zero cols it shoud have attrib(M,'degHomog') set.

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 B = grobj( module([0,x,y]), intvec(15,1,1) ); grview(B); ==> Graded homomorphism: r(-15) + r(-1)^2 <- r(-2), given by a matrix, with d\ egrees: ==> ..1 .... ==> --- +... ==> 15 : - |..1 ==> 1 : 1 |..2 ==> 1 : 1 |..3 ==> === ==> 2 module D = grsum( grsum(grpower(A,2), grtwist(1,1)), grsum(grtwist(1,2), grpower(B,2)) ); grview(D); ==> Graded homomorphism: ==> r^3 + r(-1) + r^3 + r(-1) + r(1) + r(2) + r(-15) + r(-1)^2 + r(-15) + r(-\ 1)^2 <- ==> r(-1)^4 + r(-2)^2, given by a matrix, with degrees: ==> ..1 ..2 ..3 ..4 ..5 ..6 .... ==> --- --- --- --- --- --- +... ==> 0 : 1 - - - - - |..1 ==> 0 : 1 1 - - - - |..2 ==> 0 : - 1 - - - - |..3 ==> 1 : - - - - - - |..4 ==> 0 : - - 1 - - - |..5 ==> 0 : - - 1 1 - - |..6 ==> 0 : - - - 1 - - |..7 ==> 1 : - - - - - - |..8 ==> -1 : - - - - - - |..9 ==> -2 : - - - - - - |.10 ==> 15 : - - - - - - |.11 ==> 1 : - - - - 1 - |.12 ==> 1 : - - - - 1 - |.13 ==> 15 : - - - - - - |.14 ==> 1 : - - - - - 1 |.15 ==> 1 : - - - - - 1 |.16 ==> === === === === === === ==> 1 1 1 1 2 2 grdeg(D); ==> 1,1,1,1,2,2 def D10 = grshift(D, 10); grview(D10); ==> Graded homomorphism: ==> r(10)^3 + r(9) + r(10)^3 + r(9) + r(11) + r(12) + r(-5) + r(9)^2 + r(-5) \ + r(9)^2 <- ==> r(9)^4 + r(8)^2, given by a matrix, with degrees: ==> ...1 ...2 ...3 ...4 ...5 ...6 ..... ==> ---- ---- ---- ---- ---- ---- +.... ==> -10 : 1 - - - - - |...1 ==> -10 : 1 1 - - - - |...2 ==> -10 : - 1 - - - - |...3 ==> -9 : - - - - - - |...4 ==> -10 : - - 1 - - - |...5 ==> -10 : - - 1 1 - - |...6 ==> -10 : - - - 1 - - |...7 ==> -9 : - - - - - - |...8 ==> -11 : - - - - - - |...9 ==> -12 : - - - - - - |..10 ==> 5 : - - - - - - |..11 ==> -9 : - - - - 1 - |..12 ==> -9 : - - - - 1 - |..13 ==> 5 : - - - - - - |..14 ==> -9 : - - - - - 1 |..15 ==> -9 : - - - - - 1 |..16 ==> ==== ==== ==== ==== ==== ==== ==> -9 -9 -9 -9 -8 -8 grdeg(D10); ==> -9,-9,-9,-9,-8,-8 ```