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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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