LIB "gradedModules.lib";
ring r=32003, x(0..4),dp;
def A=grtwist(3,1);
grview(A);
==> Graded homomorphism: r(1)^3 <- 0, given by zero (3 x 0) matrix.
def T=KeneshlouMatrixPresentation(intvec(0,1,0,0,0));
grview(T);
==> Graded homomorphism: r(-1)^10 <- r(-2)^10, given by a square matrix, with\
    degrees: 
==>      ..1 ..2 ..3 ..4 ..5 ..6 ..7 ..8 ..9 .10 ....
==>      --- --- --- --- --- --- --- --- --- --- +...
==>   1 :  1   1   -   -   1   -   -   -   -   - |..1
==>   1 :  1   -   1   -   -   1   -   -   -   - |..2
==>   1 :  1   -   -   1   -   -   1   -   -   - |..3
==>   1 :  -   1   1   -   -   -   -   1   -   - |..4
==>   1 :  -   1   -   1   -   -   -   -   1   - |..5
==>   1 :  -   -   1   1   -   -   -   -   -   1 |..6
==>   1 :  -   -   -   -   1   1   -   1   -   - |..7
==>   1 :  -   -   -   -   1   -   1   -   1   - |..8
==>   1 :  -   -   -   -   -   1   1   -   -   1 |..9
==>   1 :  -   -   -   -   -   -   -   1   1   1 |.10
==>      === === === === === === === === === ===     
==>        2   2   2   2   2   2   2   2   2   2     
def F=grlifting3(T,A);
==>            0     1     2     3
==> ------------------------------
==>     1:    10    10     5     1
==> ------------------------------
==> total:    10    10     5     1
==> 
==>            0
==> ------------
==>    -1:     3
==> ------------
==> total:     3
==> 
==> t:  1
==> Graded homomorphism: r(1)^3 <- r(-1)^10, given by a matrix, with degrees: 
==>      ..1 ..2 ..3 ..4 ..5 ..6 ..7 ..8 ..9 .10 ....
==>      --- --- --- --- --- --- --- --- --- --- +...
==>  -1 :  2   2   2   2   2   2   2   2   2   2 |..1
==>  -1 :  2   2   2   2   2   2   2   2   2   2 |..2
==>  -1 :  2   2   2   2   2   2   2   2   2   2 |..3
==>      === === === === === === === === === ===     
==>        1   1   1   1   1   1   1   1   1   1     
grview(F);
==> Graded resolution: 
==> r(1)^3 <-- d_1 --
==> r(-1)^10, given by maps: 
==> d_1 :
==> Graded homomorphism: r(1)^3 <- r(-1)^10, given by a matrix, with degrees: 
==>      ..1 ..2 ..3 ..4 ..5 ..6 ..7 ..8 ..9 .10 ....
==>      --- --- --- --- --- --- --- --- --- --- +...
==>  -1 :  2   2   2   2   2   2   2   2   2   2 |..1
==>  -1 :  2   2   2   2   2   2   2   2   2   2 |..2
==>  -1 :  2   2   2   2   2   2   2   2   2   2 |..3
==>      === === === === === === === === === ===     
==>        1   1   1   1   1   1   1   1   1   1     
def R=KeneshlouMatrixPresentation(intvec(0,0,0,2,0));
def S=KeneshlouMatrixPresentation(intvec(1,2,0,0,0));
def H=grlifting3(R, S);
==>            0     1
==> ------------------
==>     1:    10     2
==> ------------------
==> total:    10     2
==> 
==>            0     1     2     3
==> ------------------------------
==>     0:     1     -     -     -
==>     1:    20    20    10     2
==> ------------------------------
==> total:    21    20    10     2
==> 
==> t:  2
==> Graded homomorphism: r(-2)^20 <- r(-2)^2, given by a matrix, with degrees\
   : 
==>      ..1 ..2 ....
==>      --- --- +...
==>   2 :  0   0 |..1
==>   2 :  0   0 |..2
==>   2 :  0   0 |..3
==>   2 :  0   0 |..4
==>   2 :  0   0 |..5
==>   2 :  0   0 |..6
==>   2 :  0   0 |..7
==>   2 :  0   0 |..8
==>   2 :  0   0 |..9
==>   2 :  0   0 |.10
==>   2 :  0   0 |.11
==>   2 :  0   0 |.12
==>   2 :  0   0 |.13
==>   2 :  0   0 |.14
==>   2 :  0   0 |.15
==>   2 :  0   0 |.16
==>   2 :  0   0 |.17
==>   2 :  0   0 |.18
==>   2 :  0   0 |.19
==>   2 :  0   0 |.20
==>      === ===     
==>        2   2     
==> k:  1
==> Graded homomorphism: r + r(-1)^20 <- r(-1)^10, given by a matrix, with de\
   grees: 
==>      ..1 ..2 ..3 ..4 ..5 ..6 ..7 ..8 ..9 .10 ....
==>      --- --- --- --- --- --- --- --- --- --- +...
==>   0 :  -   -   -   -   -   -   -   -   -   - |..1
==>   1 :  0   0   0   -   -   0   0   0   -   - |..2
==>   1 :  0   0   -   0   -   0   0   -   0   - |..3
==>   1 :  0   0   -   -   0   0   0   -   -   0 |..4
==>   1 :  0   -   0   0   -   0   -   0   0   - |..5
==>   1 :  0   -   0   -   0   0   -   0   -   0 |..6
==>   1 :  0   -   -   0   0   0   -   -   0   0 |..7
==>   1 :  -   0   0   0   -   -   0   0   0   - |..8
==>   1 :  -   0   0   -   0   -   0   0   -   0 |..9
==>   1 :  -   0   -   0   0   -   0   -   0   0 |.10
==>   1 :  -   -   0   0   0   -   -   0   0   0 |.11
==>   1 :  0   0   0   -   -   0   0   0   -   - |.12
==>   1 :  0   0   -   0   -   0   0   -   0   - |.13
==>   1 :  0   0   -   -   0   0   0   -   -   0 |.14
==>   1 :  0   -   0   0   -   0   -   0   0   - |.15
==>   1 :  0   -   0   -   0   0   -   0   -   0 |.16
==>   1 :  0   -   -   0   0   0   -   -   0   0 |.17
==>   1 :  -   0   0   0   -   -   0   0   0   - |.18
==>   1 :  -   0   0   -   0   -   0   0   -   0 |.19
==>   1 :  -   0   -   0   0   -   0   -   0   0 |.20
==>   1 :  -   -   0   0   0   -   -   0   0   0 |.21
==>      === === === === === === === === === ===     
==>        1   1   1   1   1   1   1   1   1   1     
// grview(H);
// 2nd module does not lie in the first:
// def H=grlifting3(S, R);
//def I=KeneshlouMatrixPresentation(intvec(2,3,0,6,2));
//def J=KeneshlouMatrixPresentation(intvec(4,0,1,2,1));
//def N=grlifting3(I,J); grview(N);