| #### D.15.24.13 regionComplex Procedure from library `tateProdCplxNegGrad.lib` (see tateProdCplxNegGrad_lib). Usage: regionComplex(T,d,I,J,K); T multigradedcomplex, d intvec, I intvec, J intvec, K intvec Purpose: compute the region complex of T w.r.t. the sets I,J,K and the vector d Assume: I,J,K are intvecs representing disjoint subsets of {1,...,t}, T is a complex in ring E, zero represents the empty set Return: multigraded complex which is the region complex T_d(I,J,K) of T Example:
    LIB "tateProdCplxNegGrad.lib";
    intvec f = 1,1;
    def (S,E) = productOfProjectiveSpaces(f);
    intvec low = -3,-3;
    intvec high = 3,3;
    setring(S);
    module M = 0;
    intmat MGrading[2][1] = -1,-1;
    M = setModuleGrading(M,MGrading);
    multigradedcomplex tate;
    (E,tate) = tateResolution(M,low,high);
    setring(E);
    tate;
    ring Z = cohomologyMatrixFromResolution(tate,low,high);
    setring(Z);
    print(cohomologymat);
    setring(E);
    intvec  c= 0,-3;
    intvec I = 0;
    intvec J = 0,1;
    intvec K = 0,2;
    multigradedcomplex U = regionComplex(tate,c,I,J,K);
    U;
    Z = cohomologyMatrixFromResolution(U,low,high);
    setring(Z);
    print(cohomologymat);
    setring(E);
    multigradedcomplex V = regionComplex(tate,c,I,J,J);

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