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CompleteIntersectionResolutions :: mfBound

mfBound -- determines how high a syzygy to take for "matrixFactorization"



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)).

See also

Ways to use mfBound :

For the programmer

The object mfBound is a method function.