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D.15.21.10 cohomologyHashTable

Procedure from library tateProdCplxNegGrad.lib (see tateProdCplxNegGrad_lib).

Usage:
cohomologyHashTable(M,L,low,high); M module, low intvec, high intvec

Purpose:
computes hashtable of sheaf cohomology groups of twists in the range between between low and high corresponding to coker(M)

Assume:
M module representing a sheaf F on the product of t projective spaces, note that at the moment M is a module over S,

Return:
cohomologytable where cohomologytable is a hash table with integer vectors in ZZ^{t+1} as keys, entries can be accessed via cohomologytable*(c_1,...,c_t,i) = dim(H^i(F(c_1,...,c_t)))

Note:
this function works for arbitrary products P^{n_1} x \cdots x P^{n_t} and corresponding Z^t-gradings

Example:
 
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);
def cohomologytable = cohomologyHashTable(M,low,high);
print(cohomologytable);
intvec d = 3,3,0;
cohomologytable*d;
def (Z,eulerTable) = eulerPolynomialTable(M,low,high);
setring(Z);
print(eulerTable);


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