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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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