--5/30/06
--author:Jessica Sidman
--Goal:  Taking Seth's suggestion:  Can we integrate into the prolongation space?
--i.e., Let A be a space of quadrics and A_i be this set integrated with respect
--to x_i.  The interseciton of the A_i's is the prolongation.



--8/06
--Write a quick monomial integration function.  (with help from Mike Stillman)

load "intersection.m2"

integration = (i,f) ->(
     S:=ring f;
    sum apply (terms f, g -> (1/((flatten exponents g)_i+1)) * g*S_i)
     )

--A is a list of forms of degree d; 
prolong = (A) ->(
     S:= ring A_0;
     n:= numgens S;
     d:= (degree(A_0))_0;
     L :={};
     
     for i from 0 to (n-1) do(
	 M := ideal drop (flatten entries vars S, {i,i});
	 intA:=ideal apply(A, f -> integration(i, f))+M^(d+1);
	 L = append(L, intA);
	  );
     << "d = " << d << endl;
     LL = L;
     --GenList := flatten entries mingens intersection(L, DegreeLimit=>d+1)
     --GenList := flatten entries mingens inter(d+1,L) -- MES version 1
     GenList := flatten entries mingens intersectSpaces(d+1,L) -- MES version 2
  --   degList := {};
    -- for i from 0 to #GenList-1 do(
      --    if (degree GenList_i)_0 == d+1 then degList = append(degList, GenList_i);    
        --  );
    -- degList
)

end
restart

--8/14/06
--Note:  The time used comments here refer to an old intersection routine
--before Mike added the intersectSpaces code.


n= 14
S = QQ[x_0..x_n,MonomialSize=>8]

M = genericSkewMatrix(S,x_0, 6)
I = pfaffians(4,M);
dim I
time I1 = prolong(flatten entries mingens I);   -- used 64.72 seconds

n= 20
S = QQ[x_0..x_n,MonomialSize=>8]

M = genericSkewMatrix(S,x_0, 7)
I = pfaffians(4,M);
dim I
time I1 = prolong(flatten entries mingens I);  -- used 1529.43 seconds
I1 = ideal I1
betti I1


n= 28
S = QQ[x_0..x_n,MonomialSize=>8]

M = genericSkewMatrix(S,x_0, 8)
I = pfaffians(4,M);
dim I
time I1 = prolong(flatten entries mingens I);  -- used
I1 = ideal I1
betti I1