Subsections

• Related Structures
• Numerical Invariants
• Ring Predicates and Booleans

The main structure related to a polynomial ring is its coefficient ring. Multivariate polynomial rings belong to the Magma category RngMPol.

Category(P) : RngMPol -> Cat

Parent(P) : RngMPol -> Pow

PrimeRing(P) : RngMPol -> Rng

CoefficientRing(P) : RngMPol -> Rng

Return the coefficient ring of polynomial ring P.

Note that the # operator only returns a value for finite (quotients of) polynomial rings.

Characteristic(P) : RngMPol -> RngIntElt

# P : RngMPol -> RngIntElt

Return the number of indeterminates of polynomial ring P over its coefficient ring.

The usual ring functions returning Boolean values are available on polynomial rings.

IsCommutative(P) : RngMPol -> BoolElt

IsUnitary(P) : RngMPol -> BoolElt

IsFinite(P) : RngMPol -> BoolElt

IsOrdered(P) : RngMPol -> BoolElt

IsField(P) : RngMPol -> BoolElt

IsEuclideanDomain(P) : RngMPol -> BoolElt

IsPID(P) : RngMPol -> BoolElt

IsUFD(P) : RngMPol -> BoolElt

IsDivisionRing(P) : RngMPol -> BoolElt

IsEuclideanRing(P) : RngMPol -> BoolElt

IsPrincipalIdealRing(P) : RngMPol -> BoolElt

IsDomain(P) : RngMPol -> BoolElt

P eq Q : RngMPol, RngMPol -> BoolElt

P ne Q : RngMPol, RngMPol -> BoolElt