documentation:release:4.0:ideal:ideal

Available versions of this document: latest release, release 4.13, release 4.12, release 4.11, release 4.10, release 4.9, release 4.8, release 4.7, release 4.6, release 4.5, release 4.4, release 4.3, release 4.2, release 4.1, release 4.0, release 3.6, release 3.5, nightly master

Reference documentation for older polymake versions: release 3.4, release 3.3, release 3.2

BigObject Ideal

from application ideal

An ideal in a polynomial ring.

Properties of an ideal computed via commutative algebra.


DEPTH

The depth of the ideal.

Type:
Int
depends on extension:

DIM

The dimension of the ideal, i.e. the Krull dimension of Polynomial ring/Ideal.

Type:
Int
depends on extension:

GROEBNER

Subobject containing properties that depend on the monomial ordering of the ring.

Type:
depends on extension:

HILBERT_POLYNOMIAL

The Hilbert polynomial of the ideal. For toric ideals this is linked with the Ehrhart polynomial.

Type:

HOMOGENEOUS

True if the ideal can be generated by homogeneous polynomials.

Type:

MONOMIAL

True if the ideal can be generated by monomials.

Type:

N_VARIABLES

The number of variables of the polynomial ring containing the ideal.

Type:
Int

PRIMARY

True if the ideal is a primary ideal. I.e. its RADICAL is PRIME and in the quotient ring by the ideal every zero divisor is nilpotent.

Type:

PRIMARY_DECOMPOSITION

An array containing the primary decomposition of the given ideal, i.e. the contained ideals are PRIMARY and their intersection is the given ideal.

Type:
depends on extension:

PRIME

True if the is ideal a prime ideal.

Type:

RADICAL

The radical of the ideal.

Type:
depends on extension:

ZERO

True if the ideal is the zero ideal.

Type:

Properties defining an ideal.


GENERATORS

A set of generators usually given by the user and not unique.

Type:

SATURATION

UNDOCUMENTED

from extension:

SOLVE

UNDOCUMENTED

from extension:

contains_monomial(String s)

Check via saturation whether the ideal contains a monomial. Returns a monomial from the ideal or the trivial monomial if there is none.

Parameters:

String s: Optional term order (see ORDER_NAME) for intermediate Groebner bases, default: “dp”

Returns:
from extension:

  • documentation/release/4.0/ideal/ideal.txt
  • Last modified: 2020/01/22 09:02
  • by 127.0.0.1