LIB "gradedModules.lib";
//  if( defined(assumeLevel) ){ int assumeLevel0 = assumeLevel; } else { int assumeLevel; export(assumeLevel); }; assumeLevel = 5;
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 C = grsum(A,B);
print(C);
==> x+y,0,  0,
==> x,  x+y,0,
==> 0,  y,  0,
==> 0,  0,  0,
==> 0,  0,  0,
==> 0,  0,  x,
==> 0,  0,  y 
homog(C);
==> 1
grview(C);
==> Graded homomorphism: r^3 + r(-1) + r(-15) + r(-1)^2 <- r(-1)^2 + r(-2), g\
   iven by a matrix, with degrees: 
==>      ..1 ..2 ..3 ....
==>      --- --- --- +...
==>   0 :  1   -   - |..1
==>   0 :  1   1   - |..2
==>   0 :  -   1   - |..3
==>   1 :  -   -   - |..4
==>  15 :  -   -   - |..5
==>   1 :  -   -   1 |..6
==>   1 :  -   -   1 |..7
==>      === === ===     
==>        1   1   2     
module D = grsum(
grsum(grpower(A,2), grtwist(1,1)),
grsum(grtwist(1,2), grpower(B,2))
);
print(D);
==> x+y,0,  0,  0,  0,0,
==> x,  x+y,0,  0,  0,0,
==> 0,  y,  0,  0,  0,0,
==> 0,  0,  0,  0,  0,0,
==> 0,  0,  x+y,0,  0,0,
==> 0,  0,  x,  x+y,0,0,
==> 0,  0,  0,  y,  0,0,
==> 0,  0,  0,  0,  0,0,
==> 0,  0,  0,  0,  0,0,
==> 0,  0,  0,  0,  0,0,
==> 0,  0,  0,  0,  0,0,
==> 0,  0,  0,  0,  x,0,
==> 0,  0,  0,  0,  y,0,
==> 0,  0,  0,  0,  0,0,
==> 0,  0,  0,  0,  0,x,
==> 0,  0,  0,  0,  0,y 
homog(D);
==> 1
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     
module F = grobj( module([x,y,0]), intvec(1,1,5) );
grview(F);
==> Graded homomorphism: r(-1)^2 + r(-5) <- r(-2), given by a matrix, with de\
   grees: 
==>      ..1 ....
==>      --- +...
==>   1 :  1 |..1
==>   1 :  1 |..2
==>   5 :  - |..3
==>      ===     
==>        2     
module T = grsum( F, grsum( grtwist(1, 10), B ) );
grview(T);
==> Graded homomorphism: r(-1)^2 + r(-5) + r(10) + r(-15) + r(-1)^2 <- r(-2)^\
   2
==> , given by a matrix, with degrees: 
==>       ...1 ...2 .....
==>       ---- ---- +....
==>    1 :   1    - |...1
==>    1 :   1    - |...2
==>    5 :   -    - |...3
==>  -10 :   -    - |...4
==>   15 :   -    - |...5
==>    1 :   -    1 |...6
==>    1 :   -    1 |...7
==>       ==== ====      
==>          2    2      
//  if( defined(assumeLevel0) ){ assumeLevel = assumeLevel0; } else { kill assumeLevel; } // restore the state of aL