If p = mfBound M, then the p-th syzygy of M, which is computed by highSyzygy(M), should (this is a conjecture) be a "high Syzygy" in the sense required for matrixFactorization. In examples, the estimate seems sharp (except when M is already a high syzygy).

The actual formula used is:

mfBound M = max(2*r_{even}, 1+2*r_{odd})

where r_{even} = regularity evenExtModule M and r_{odd} = regularity oddExtModule M. Here evenExtModule M is the even degree part of Ext(M, (residue class field)).

- highSyzygy -- Returns a syzygy module one beyond the regularity of Ext(M,k)
- evenExtModule -- even part of Ext^*(M,k) over a complete intersection as module over CI operator ring
- oddExtModule -- odd part of Ext^*(M,k) over a complete intersection as module over CI operator ring
- matrixFactorization -- Maps in a higher codimension matrix factorization

- mfBound(Module)

The object mfBound is a method function.