from application ideal
An ideal in a polynomial ring.
Properties of an ideal computed via commutative algebra.
DEPTHThe depth of the ideal.
DIMThe dimension of the ideal, i.e. the Krull dimension of Polynomial ring/Ideal.
GROEBNERSubobject containing properties that depend on the monomial ordering of the ring.
HILBERT_POLYNOMIALThe Hilbert polynomial of the ideal. For toric ideals this is linked with the Ehrhart polynomial.
HOMOGENEOUSTrue if the ideal can be generated by homogeneous polynomials.
MONOMIALTrue if the ideal can be generated by monomials.
N_VARIABLESThe number of variables of the polynomial ring containing the ideal.
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.
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.
PRIMETrue if the is ideal a prime ideal.
RADICALThe radical of the ideal.
ZEROTrue if the ideal is the zero ideal.
Properties defining an ideal.
GENERATORSA set of generators usually given by the user and not unique.
SATURATIONUNDOCUMENTED
SOLVEUNDOCUMENTED
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.
String s: Optional term order (see ORDER_NAME) for intermediate Groebner bases, default: “dp”