vasconcelosDegree -- Vasconcelos function of an ideal

Synopsis

Usage:

vasconcelosDegree(d,r,I)
Inputs:
- d, an integer,
- r, an integer,
- I, an ideal,
Outputs:
- an integer,

Description

Returns the value of the Vasconcelos function of the ideal I on the parameters d and r. In the case of a graded unmixed radical ideal I, the Vasconcelos function is equal to the generalized minimum distance function genMinDisIdeal. The Vasconcelos function computes the minimum value of the degree of I minus the degree of the ideal generated by r-tuples of polynomials of degree at most d that are linearly independent modulo the ideal I. More information about the Vasconcelos function can be found in Definition 3.4 at https://arxiv.org/pdf/1812.06529v1.pdf.

i1 : K=QQ;

i2 : R=K[t1,t2,t3];

i3 : I=ideal(t1^3,t2*t3);

o3 : Ideal of R

i4 : vasconcelosDegree(1,1,I)

o4 = infinity

o4 : InfiniteNumber

Ways to use vasconcelosDegree :

vasconcelosDegree(ZZ,ZZ,Ideal)

For the programmer

The object vasconcelosDegree is a method function.