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
==>