ideals

ideals

An overview

In Macaulay 2, once a ring (see rings) is defined, ideals are constructed in the usual way by giving a set of generators.

creating an ideal

conversions

ideals to and from matrices

ideals to and from modules

basic operations on ideals

sums, products, and powers of ideals

equality and containment

extracting generators of an ideal

dimension, codimension, and degree

components of ideals

intersection of ideals

ideal quotients and saturation

radical of an ideal

minimal primes of an ideal

associated primes of an ideal

primary decomposition

Groebner bases and related computations

For those operations where we consider an ideal as a module, such as computing Hilbert functions and polynomials, syzygies, free resolutions, see modules I.

For additional common operations and a comprehensive list of all routines in Macaulay 2 which return or use ideals, see Ideal.