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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: