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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