# Singular

#### D.15.18.4 grview

Procedure from library `gradedModules.lib` (see gradedModules_lib).

Usage:

Return:
nothing

Purpose:

Assume:
 ```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 ==> ```