dual I





For a general monomial ideal, the Alexander dual defined as follows: Given two list of nonnegative integers a and bfor which a_i >= b_i for all i let a\b denote the list whose ith entry is a_i+1b_iif b_i >= 1and 0otherwise. The Alexander dual with respect to a is the ideal generated by a monomial x^a\b for each irreducible component (x_i^b_i) of I. If a is not provided, it is assumed to be the least common multiple of the minimal generators of I.




One always has dual( dual(I, a), a) == I however dual dual Imay not equal I.




See Ezra Miller's Ph.D. thesis 'Resolutions and Duality for Monomial Ideals'.
Implemented by Greg Smith.
The computation is done by calling the frobby library, written by B. H. Roune; setting gbTrace to a positive value will cause a message to be printed when it is called.