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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
Commutative algebra
Properties of an ideal computed via commutative algebra.

DEPTH
The depth of the ideal.
 Type:
 depends on extension:

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

PRIMARY
True if the ideal is a primary ideal. I.e. its
RADICAL
isPRIME
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:
Input properties
Properties defining an ideal.

GENERATORS
A set of generators usually given by the user and not unique.
 Type:
Methods
no category

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 (seeORDER_NAME
) for intermediate Groebner bases, default: “dp” Returns:
 from extension: