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SymbolicPowers :: SymbolicPowers

SymbolicPowers -- A package for computing symbolic powers of ideals


This package gives the ability to compute symbolic powers, and related invarients, of ideals in a polynomial ring or a quotient of a polynomial ring. For example, in the context of the default behavoir, symbolicPower assumes the following definition of the symbolic power of an ideal I ,

I(n) = ∩p ∈Ass(R/I)(InRp ∩R ),

as defined by M. Hochster and C. Huneke.

Alternatively, as defined in Villarreal, symbolicPower has the option to restrict to minimal primes versus use all associated primes with UseMinimalPrimes.In particular, the symbolic power of an ideal I is defined as

I(n) = ∩p ∈Min(R/I)(InRp ∩R ),

where Min(R/I) is the set of minimal primes in I .

  • M. Hochster and C. Huneke. Comparison of symbolic and ordinary powers of ideals. Invent. Math. 147 (2002), no. 2, 349–369.
  • R. Villarreal. Monomial algebras. Second edition. Monographs and Research Notes in Mathematics. CRC Press, Boca Raton, FL, 2015. xviii+686 pp. ISBN: 978-1-4822-3469-5.
  • Hailong Dao, Alessandro De Stefani, Eloísa Grifo, Craig Huneke, and Luis Núñez-Betancourt.Symbolic powers of ideals,


The following people have generously contributed code or worked on our code at various Macaulay2 workshops.
  • Ben Drabkin
  • Alexandra Seceleanu
  • Branden Stone

A Quick Introduction

Other Related Examples



This documentation describes version 1.0 of SymbolicPowers.

Source code

The source code from which this documentation is derived is in the file SymbolicPowers.m2.