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restart loadPackage "Dmodules" ------------------------------------------------------------------------- -- Computation of the local cohomology CCs at the ideal -- generated by the minors of 2x3 matrix of indeterminates W = QQ[x_1..x_6, a_1..a_6]; I = minors(2, matrix{{x_1, x_2, x_3}, {x_4, x_5, x_6}}); cc = {ideal W => 1}; B = populateCechComplexCC(I,cc) scan(keys B, k->print (k=>B#k)) -- CCs of Cech complex BEFORE pruning pruneCechComplexCC B scan(keys B, k->if #B#k>0 then print (k=>B#k)) -- ................... AFTER ........ W = QQ[x_1..x_4, a_1..a_4]; I = minors(2, matrix{{x_1, x_2, x_3}, {x_2, x_3, x_4}}); cc = {ideal W => 1}; B = populateCechComplexCC(I,cc) scan(keys B, k->print (k=>B#k)) -- CCs of Cech complex BEFORE pruning pruneCechComplexCC B scan(keys B, k->if #B#k>0 then print (k=>B#k)) -- ................... AFTER ........ ----------------------------------------------------------------------------- -- Lyubeznik numbers CCH2 = B#{0,1} -- CC(H^2_I(R)) I = ideal (x_1..x_6) ssets = (toList subsets set(0..5)) / sort@@toList; -- subsets of {0,...,5} Dtrace 2 B = populateCechComplexCC(I,CCH2) scan(keys B, k->print (k=>B#k)) pruneCechComplexCC B scan(keys B, k->if #B#k>0 then print (k=>B#k)) ------------------------------------ -- Brianson-Maisonobe-Merle formula S = QQ[x,y,z,a,b,c] cc = BMM({ideal S=>1},x^3+y^3+z^3)