Structure Predicates

IsField(R) : FldFun -> BoolElt

IsEuclideanDomain(R) : FldFun -> BoolElt

IsField(O) : RngFunOrd -> BoolElt

IsPID(R) : FldFun -> BoolElt

IsUFD(R) : FldFun -> BoolElt

IsDivisionRing(R) : FldFun -> BoolElt

IsEuclideanRing(R) : FldFun -> BoolElt

IsDivisionRing(O) : RngFunOrd -> BoolElt

IsPrincipalIdealRing(R) : FldFun -> BoolElt

IsDomain(R) : FldFun -> BoolElt

IsDomain(O) : RngFunOrd -> BoolElt

F eq G : FldFunG, FldFunG -> BoolElt

F ne G : FldFunG, FldFunG -> BoolElt

O1 eq O2 : RngFunOrd, Rng -> BoolElt

O1 ne O2 : RngFunOrd, Rng -> BoolElt

IsGlobal(F) : FldFun -> BoolElt

Returns true if and only if the algebraic function field F/k is global, i.e. the constant field is a finite field; false otherwise.

IsRationalFunctionField(F) : FldFunG -> BoolElt

Return true if F is isomorphic to a rational function field, (i.e. F is only trivially algebraic).

IsFiniteOrder(O) : RngFunOrd -> BoolElt

Given an order O of a function field, return true if and only if the bottom coefficient ring of O is a polynomial ring.

IsEquationOrder(O) : RngFunOrd -> BoolElt

Given an order O of a function field, return true if and only if the order O is an equation order (i.e. it has been defined by a polynomial and so has a power basis).

IsAbsoluteOrder(O) : RngFunOrd -> BoolElt

Return false if O is an extension of another order, otherwise true.

IsMaximal(O) : RngFunOrd -> BoolElt

Given an order O of a function field, return true if and only if the order O is maximal in its field of fractions.

IsTamelyRamified(O) : RngFunOrd -> BoolElt

Return whether O is tamely ramified, i.e. no prime ideal of O has residue field with characteristic dividing its ramification index.

IsTotallyRamified(O) : RngFunOrd -> BoolElt

Return whether there is an ideal of O which is totally ramified, i.e. its ramification index is equal to the degree of O over its coefficient ring.

IsUnramified(O) : RngFunOrd -> BoolElt

Return whether a finite order O is unramified at the finite places and whether an infinite order O is unramified at the infinite places.

IsWildlyRamified(O) : RngFunOrd -> BoolElt

Return whether there is a prime ideal of O which is wildly ramified, i.e. its ramification index is divisible by the characteristic of its residue class field.