D.15.21.8 cohomologyMatrixFromResolution

Usage:

cohomologyMatrixFromResolution(T,low,high); T multigradedcomplex, low intvec, high intvec

Purpose:

computes the cohomology matrix corresponding to the multigraded complex T (part of a Tate resolution)

Assume:

T is a multigraded complex representing a part of a Tate resolution (for example output of tateResolution), basering is E

Return:

ring Z in which cohomology matrix lives, it is exported in the variable cohomologymat, cohomologymat stores information in the range between low and high

LIB "tateProdCplxNegGrad.lib";
intvec c = 1,1;
def (S,E) = productOfProjectiveSpaces(c);
intvec low = -3,-3;
intvec high = 3,3;
setring(S);
module M = 0;
intmat grading[2][1] = -1,-1;
M = setModuleGrading(M,grading);
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