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# vNumber -- the v-number of a graded ideal

- Usage:
    `vNumber(I)`
- Inputs:
  - I, an ideal,
- Outputs:
  - an integer,

## Description

Returns the v-number of a graded ideal I. This invariant is used to express the regularity index of the generalized minimum distance function of the ideal I on the parameter $r=1$ genMinDisIdeal. Moreover, the v-number has other combinatorial implications. More information about the v-number can be found in Definition 4.1 at https://arxiv.org/pdf/1812.06529v1.pdf.

    i1 : K=ZZ/3;

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

    i3 : I=ideal(t1*t2^2-t1^2*t2,t1*t3^3-t1^3*t3,t2*t3^3-t2^3*t3);

    o3 : Ideal of R

    i4 : vNumber(I)

    o4 = 3

## Ways to use vNumber:

- `vNumber(Ideal)`

## For the programmer

The object vNumber is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/CodingTheory.m2:3812:0.