r = regularity C
r = regularity(C, Weights => w)
For a free chain complex C, the regularity r is the smallest number so that each basis element of C_i has degree at most i+r. For an ideal I, regularity is one plus the regularity of the minimal free resolution of the quotient of the ambient ring by I. For a module M, regularity is the regularity of a minimal free resolution of M.







The regularity is the label of the last row in the Betti diagram of a chain complex. However, this depends on the total degree weights in the Betti tally, which are computed based on the heft vector of the underlying ring. To adjust this vector, a vector w whose length is the same as the degree length of the ring can be provided using the option Weights. The dot products of w with the multidegrees in the tally will be used in the resulting computation.





The object regularity is a method function with options.