MinimalPrimes -- minimal primes and radical routines for ideals

Description

Find the minimal primes of an ideal in a polynomial ring over a prime field, or a quotient ring of that. These are the geometric components of the corresponding algebraic set.

Multiple strategies are implemented via hooks. In many cases the default Birational strategy is much faster, although there are cases when the Legacy strategy does better. For a monomial ideal, a more efficient algorithm is used instead.

minprimes and decompose are synonyms for minimalPrimes.

Caveat

Only works for ideals in (commutative) polynomial rings or quotients of polynomial rings over a prime field, might have bugs in small characteristic and larger degree (although, many of these cases are caught correctly).

Authors

Version

This documentation describes version 0.10 of MinimalPrimes.

Source code

The source code from which this documentation is derived is in the file MinimalPrimes.m2. The auxiliary files accompanying it are in the directory MinimalPrimes/.

Exports

Types
- Hybrid -- the class of lists encapsulating hybrid strategies
Functions and commands
- minimalPrimes -- minimal primes of an ideal
- radical -- the radical of an ideal
- radicalContainment -- whether an element is contained in the radical of an ideal
Methods
- isPrime(Ideal) -- whether an ideal is prime
- decompose(Ideal) -- see minimalPrimes -- minimal primes of an ideal
- minimalPrimes(Ideal) -- see minimalPrimes -- minimal primes of an ideal
- radical(Ideal) -- see radical -- the radical of an ideal
- radicalContainment(Ideal,Ideal) -- see radicalContainment -- whether an element is contained in the radical of an ideal
- radicalContainment(RingElement,Ideal) -- see radicalContainment -- whether an element is contained in the radical of an ideal

For the programmer

The object MinimalPrimes is a package.