Singular

LIB "tateProdCplxNegGrad.lib";
intvec f = 1,1;
def (S,E) = productOfProjectiveSpaces(f);
intvec low = -3,-3;
intvec high = 3,3;
setring(S);
module M = 0;
intmat MGrading[2][1] = -1,-1;
M = setModuleGrading(M,MGrading);
multigradedcomplex tate;
(E,tate) = tateResolution(M,low,high);
setring(E);
ring Z = cohomologyMatrixFromResolution(tate,low,high);
setring(Z);
print(cohomologymat);
==> 5h,0,5,10,15,20,25,
==> 4h,0,4,8, 12,16,20,
==> 3h,0,3,6, 9, 12,15,
==> 2h,0,2,4, 6, 8, 10,
==> h, 0,1,2, 3, 4, 5, 
==> 0, 0,0,0, 0, 0, 0, 
==> h2,0,h,2h,3h,4h,5h 
setring(E);
intvec  c= 0,-3;
intvec J = 1;
multigradedcomplex U = strand(tate,c,J);
U;
==> 0  <--  E^10  <--  E^8  <--  E^6  <--  E^4  <--  E^2  <--  E^2  <--  E^4 \
    <--  E^6  <--  E^8  <--  E^10
==> -4      -3         -2        -1        0         1         2         3   \
         4         5         6
==> 
Z = cohomologyMatrixFromResolution(U,low,high);
setring(Z);
print(cohomologymat);
==> 0,0,0,10,0,0,0,
==> 0,0,0,8, 0,0,0,
==> 0,0,0,6, 0,0,0,
==> 0,0,0,4, 0,0,0,
==> 0,0,0,2, 0,0,0,
==> 0,0,0,0, 0,0,0,
==> 0,0,0,2h,0,0,0