Singular Manual: dimH

| #### D.5.18.10 dimH Procedure from library `sheafcoh.lib` (see sheafcoh_lib). Usage: dimH(i,M,d); M module, i,d int Assume: `M` is graded, and it comes assigned with an admissible degree vector as an attribute, `h>=l`, and the basering `S` has `n+1` variables. Return: int, vector space dimension of for F the coherent sheaf on P^n associated to coker(M). Note: The procedure is based on local duality as described in [Eisenbud: Computing cohomology. In Vasconcelos: Computational methods in commutative algebra and algebraic geometry. Springer (1998)]. Example:
    LIB "sheafcoh.lib";
    ring R=0,(x,y,z,u),dp;
    resolution T1=mres(maxideal(1),0);
    module M=T1[3];
    intvec v=2,2,2,2,2,2;
    attrib(M,"isHomog",v);
    dimH(0,M,2);
    ==> 6
    dimH(1,M,0);
    ==> 1
    dimH(2,M,1);
    ==> 0
    dimH(3,M,-5);
    ==> 36
See also: sheafCoh; sheafCohBGG.

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