Graded Betti numbers of Ideals of Fat Points

I(Z) = Ideal of fat point scheme Z supported at n general points of P2

Write down graded Betti numbers of minimal free resolution
        0 → F1 → F0 → I(Z) → 0
of the ideal I(Z) for Z = m1p1 + ... + mnpn for general points pi of the plane.

To run examples on your own computer, click here to obtain the Macaulay script used.

Note: The result is correct when the number of points is at most 8.
The result may be only conjectural for more than 8 points, assuming when
necessary the SHGH Conjecture and the Omega Conjecture.


This version is taciturn:

Enter up to 50 nonnegative integer multiplicities mi (separated by spaces, no returns, no multiplicity bigger than 230):

This version is verbose:

Enter up to 50 nonnegative integer multiplicities mi (separated by spaces, no returns, no multiplicity bigger than 230):