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D.15.6.4 grview
Procedure from library gradedModules.lib (see gradedModules_lib).
- Usage:
- grview(M), graded object M
- Return:
- nothing
- Purpose:
- print the degree/grading data about the GRADED matrix/module/ideal/mapping object M
- Assume:
- M must be graded
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
ring R = 0,(w,x,y,z), dp; def I = grobj( ideal(y2-xz, xy-wz, x2z-wyz), intvec(0) );
list res1 = grres(I, 0); // non-minimal
grview(res1);
==> Graded resolution:
==> R <-- d_1 --
==> R(-2)^2 + R(-3) <-- d_2 --
==> R(-3) + R(-4) <-- d_3 --
==> 0, given by maps:
==> d_1 :
==> Graded homomorphism: R <- R(-2)^2 + R(-3), given by a matrix, with degree\
s:
==> .1 .2 .3 ...
==> -- -- -- +..
==> 0 : 2 2 3 |.1
==> == == ==
==> 2 2 3
==> d_2 :
==> Graded homomorphism: R(-2)^2 + R(-3) <- R(-3) + R(-4), given by a matrix,\
with degrees:
==> .1 .2 ...
==> -- -- +..
==> 2 : 1 2 |.1
==> 2 : 1 2 |.2
==> 3 : 0 1 |.3
==> == ==
==> 3 4
==> d_3 :
==> Graded homomorphism: R(-3) + R(-4) <- 0, given by zero (2 x 0) matrix.
print(betti(res1,0), "betti");
==> 0 1 2
==> ------------------------
==> 0: 1 - -
==> 1: - 2 1
==> 2: - 1 1
==> ------------------------
==> total: 1 3 2
==>
list res2 = grres(grshift(I, -10), 0, 1); // minimal!
grview(res2);
==> Graded resolution:
==> R(-10) <-- d_1 --
==> R(-12)^2 <-- d_2 --
==> R(-14) <-- d_3 --
==> 0, given by maps:
==> d_1 :
==> Graded homomorphism: R(-10) <- R(-12)^2, given by a matrix, with degrees:
==> ..1 ..2 ....
==> --- --- +...
==> 10 : 2 2 |..1
==> === ===
==> 12 12
==> d_2 :
==> Graded homomorphism: R(-12)^2 <- R(-14), given by a matrix, with degrees:
==> ..1 ....
==> --- +...
==> 12 : 2 |..1
==> 12 : 2 |..2
==> ===
==> 14
==> d_3 :
==> Graded homomorphism: R(-14) <- 0, given by zero (1 x 0) matrix.
print(betti(res2,0), "betti");
==> 0 1 2
==> ------------------------
==> 10: 1 - -
==> 11: - 2 -
==> 12: - - 1
==> ------------------------
==> total: 1 2 1
==>
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