residualCodims -- a list of possible residual intersection codimensions

Synopsis

Usage:

L = residualCodims I
Inputs:
- I, a monomial ideal,
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

Ways to use residualCodims :

residualCodims(MonomialIdeal)

For the programmer

The object residualCodims is a method function.

residualCodims -- a list of possible residual intersection codimensions

Synopsis

Description

See also

Ways to use residualCodims :

For the programmer