| #### D.15.24.6 tateResolution Procedure from library `tateProdCplxNegGrad.lib` (see tateProdCplxNegGrad_lib). Usage: tateResolution(M,low,high); M module, L list, low intvec, high intvec Purpose: compute tate resolution of coker(M) where M is Z^t-graded S-module Assume: M a module over multigraded ring S Return: (E,tate), tate a multigradedcomplex, E the ring in which tate has to be viewed, however note that tate is not ring dependent Example:
    LIB "tateProdCplxNegGrad.lib";
    // example 1
    intvec c1 = 1,1,1;
    intvec low1 = 0,0,0;
    intvec high1 = 0,1,0;
    def (S1,E1) = productOfProjectiveSpaces(c1);
    setring(S1);
    module M1 = 0;
    intmat grading1[3][1] = -1,-1,-1;
    M1 = setModuleGrading(M1,grading1);
    multigradedcomplex tate1;
    (E1,tate1) = tateResolution(M1,low1,high1);
    setring(E1);
    tate1;
    tate1.differentials;
    // example 2
    intvec c2 = 1,2;
    def (S2,E2) = productOfProjectiveSpaces(c2);
    setring(S2);
    intvec low2 = -3,-3;
    intvec high2 = 0,0;
    module M2 = x(0)(0),x(1)(0)^3 + x(1)(1)^3 +x(1)(2)^3;;
    intmat grading2[2][1] = 0,0;
    M2 = setModuleGrading(M2,grading2);
    multigradedcomplex tate2;
    (E2,tate2) = tateResolution(M2,low2,high2);
    setring(E2);
    tate2;
    // example 3
    intvec c3 = 1,1;
    def (S3,E3) = productOfProjectiveSpaces(c3);
    intvec low3 = -3,-3;
    intvec high3 = 3,3;
    setring(S3);
    module M3 = 0;
    intmat grading3[2][1] = -1,-1;
    M3 = setModuleGrading(M3,grading3);
    multigradedcomplex tate3;
    (E3,tate3) = tateResolution(M3,low3,high3);
    setring(E3);
    tate3;

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