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D.15.5.3 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 should 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
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