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D.15.10.3 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

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);
==>        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);
==>        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);
==>        1   2   3   4   5   6   7   8     
==>      --------------------------------    
==>   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  -1  -2   2   2     
grdeg(D);
==> 1,1,1,1,-1,-2,2,2
def D10 = grshift(D, 10);
grview(D10);
==>          1    2    3    4    5    6    7    8      
==>       ----------------------------------------     
==>  -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  -11  -12   -8   -8      
grdeg(D10);
==> -9,-9,-9,-9,-11,-12,-8,-8