-------------------------------------------------------------------------
-- Computation of the local cohomology CCs at the ideal
-- generated by the minrs of 2x3 matrix of indeterminates
restart
load "it.m2"
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}});
inds = {{},{0},{1},{2},{0,1},{0,2},{1,2},{0,1,2}} -- nonempty subsets of {0,1,2} 
B = new MutableHashTable from {{}=>{ideal W=>1}}
scan(drop(inds,1), i -> (
     J := B#{}#0#0;	  
     f := I_(last i);
     if #i>1 then J = B#(drop(i,-1)); 
     << "localization " << i << ": " << (time B#i = BMM(J,f)) << endl;
     )); 
scan(inds, k->print (k=>B#k)) -- CCs of Cech complex BEFORE pruning
PruneCechComplexCC B 
scan(inds, k->print (k=>B#k)) -- ................... AFTER ........

-----------------------------------------------------------------------------
-- Lyubeznik numbers

CCH2 = B#{0,1} -- CC(H^2_I(R))

inds = {};
scan(6, i->inds = inds | subsets(6,i+1))

I = ideal (x_1..x_6)
B = new MutableHashTable from {{}=>CCH2}
scan(inds, i -> (
     J := B#{}#0#0;	  
     f := I_(last i);
     if #i>1 then J = B#(drop(i,-1)); 
     << "localization " << i << ": " << (time B#i = BMM(J,f)) << endl;
     )); 
scan(inds, k->print (k=>B#k))
PruneCechComplexCC B 
scan(inds, k->print (k=>B#k))