Subsections

• Related Structures
• Invariants
• Ring Predicates and Booleans

Category(R) : FldFun -> Cat

Parent(R) : FldFun -> Pow

PrimeRing(R) : FldFun -> Rng

Given the rational function field F this returns the polynomial ring from which F was constructed as its field of fractions.

CoefficientRing(F) : FldFun -> Rng

The coefficient ring of the (ring of integers of) the rational function field F.

The rank (number of indeterminates) of the rational function field F.

Given the rational function field F for which the coefficients come from a field, this returns the valuation ring of F with respect to the valuation given by the degree. This valuation ring consists of those rational functions g/h for which the degree of h is greater than or equal to that of g.

ValuationRing(F, f) : FldFun -> RngVal

Given the rational function field F for which the coefficients come from a field, and an irreducible polynomial f in the ring of integers of F, this returns the valuation ring of F with respect to the valuation associated with f. This valuation ring consists of those rational functions g/h for which f| h but f not| g.

Characteristic(F) : FldFun -> FldFunElt

IsCommutative(F) : FldFun -> BoolElt

IsUnitary(F) : FldFun -> BoolElt

IsFinite(F) : FldFun -> BoolElt

IsOrdered(F) : FldFun -> BoolElt

IsField(F) : FldFun -> BoolElt

IsEuclideanDomain(F) : FldFun -> BoolElt

IsPID(F) : FldFun -> BoolElt

IsUFD(F) : FldFun -> BoolElt

IsDivisionRing(F) : FldFun -> BoolElt

IsEuclideanRing(F) : FldFun -> BoolElt

IsPrincipalIdealRing(F) : FldFun -> BoolElt

IsDomain(F) : FldFun -> BoolElt

F eq G : FldFun, Rng -> BoolElt

F ne G : FldFun, Rng -> BoolElt