Singular Manual: cohomologyHashTable

| #### D.15.24.10 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);

User manual for Singular version 4.3.2, 2023, generated by texi2html.