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 → F_{1} → F_{0} → I(Z) → 0
of the ideal I(Z) for Z = m_{1}p_{1} + ... + m_{n}p_{n}
for general points p_{i} 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 m_{i} (separated by spaces, no returns, no multiplicity bigger than 230):

This version is verbose:

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