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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
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