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VNumber -- a package for computing the v-number and v-function

Description

VNumber is a package for computing the v-number of homogeneous ideals and v-function of monomial ideals

Authors

Version

This documentation describes version 1.0 of VNumber.

Citation

If you have used this package in your research, please cite it as follows:

@misc{VNumberSource,
  title = {{VNumber: compute v-number of homogeneous ideals and v-function of monomial ideals. Version~1.0}},
  author = {Antonino Ficarra and Emanuele Sgroi},
  howpublished = {A \emph{Macaulay2} package available at
    \url{https://github.com/Macaulay2/M2/tree/master/M2/Macaulay2/packages}}
}

Exports

  • Functions and commands
    • isStablePrime -- test whether a prime ideal is a stable prime of a ideal $I$
    • reesMap -- compute the Rees map of $I$
    • soc -- compute the $\text{Soc}_\mathfrak{p}^*(I)$, where $I$ is a monomial ideal
    • stableMax -- compute the set of stable primes of a monomial ideal that are maximal with respect to the inclusion.
    • stablePrimes -- compute the set of stable primes of a monomial ideal
    • vFunction -- compute the $\text{v}$-function of monomial ideal $I$
    • vFunctionP -- compute the $\text{v}_\mathfrak{p}$-function of monomial ideal $I$
    • vNumber -- compute the $\text{v}$-number of homogeneous ideal $I$
    • vNumberP -- compute the $\text{v}_\mathfrak{p}$-number of homogeneous ideal $I$
  • Methods
    • isStablePrime(Ideal,Ideal) -- see isStablePrime -- test whether a prime ideal is a stable prime of a ideal $I$
    • reesMap(Ideal) -- see reesMap -- compute the Rees map of $I$
    • soc(Ideal,Ideal) -- see soc -- compute the $\text{Soc}_\mathfrak{p}^*(I)$, where $I$ is a monomial ideal
    • stableMax(Ideal) -- see stableMax -- compute the set of stable primes of a monomial ideal that are maximal with respect to the inclusion.
    • stablePrimes(Ideal) -- see stablePrimes -- compute the set of stable primes of a monomial ideal
    • vFunction(Ideal) -- see vFunction -- compute the $\text{v}$-function of monomial ideal $I$
    • vFunctionP(Ideal,Ideal) -- see vFunctionP -- compute the $\text{v}_\mathfrak{p}$-function of monomial ideal $I$
    • vNumber(Ideal) -- see vNumber -- compute the $\text{v}$-number of homogeneous ideal $I$
    • vNumberP(Ideal,Ideal) -- see vNumberP -- compute the $\text{v}_\mathfrak{p}$-number of homogeneous ideal $I$
  • Symbols
    • control -- optional argument for vFunctionP and vFunction

For the programmer

The object VNumber is a package, defined in VNumber.m2.

The source of this document is in VNumber.m2:547:0.