# residualCodims -- a list of possible residual intersection codimensions

## Synopsis

• Usage:
L = residualCodims I
• Inputs:
• I, ,
• Outputs:
• L, a list, a list of integers s such that I localized at any prime of codimension s-1 in the ambient ring has at most s generators. The range of values is from codim I + 1 to the dimension of the ring + 1.

## Description

For each s computes the maximum, over all monomial primes P with codimension s-1 in the ambient ring, of the minimal size of a generating set of I localized at P. If this number is less than s, then s is included in the list.

The values s returned are the numbers such that an s-residual intersection of I exists.

 i1 : R = ZZ/101[a,b,c]; i2 : I = monomialIdeal{a*b,b*c^2} 2 o2 = monomialIdeal (a*b, b*c ) o2 : MonomialIdeal of R i3 : residualCodims I o3 = {2, 3, 4} o3 : List