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
Return whether O1 is a subset of O2.
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.
Return true if the function field F is isomorphic to a rational function field,
(i.e. F is only trivially algebraic).
Given an order O of a function field, return
true if and only if the bottom coefficient ring of O
is a polynomial ring.
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).
Return false if the order O is an extension of another order, otherwise
true.
Given an order O of a function field, return
true if and only if the order O is maximal in its field of fractions.
Return whether the order O is tamely ramified, i.e. no prime ideal of O has residue
field with characteristic dividing its ramification index.
Return whether there is an ideal of the order O which is totally ramified, i.e.
its ramification index is equal to the degree of O over its coefficient
ring.
Return whether a finite order O is unramified at the finite places and
whether an infinite order O is unramified at the infinite places.
Return whether there is a prime ideal of the order O which is wildly ramified, i.e.
its ramification index is divisible by the characteristic of its residue
class field.
Tests if the global function field K is, in its current representation,
a Kummer extension. More specific, this function tests if the defining
polynomial is of the form xr - a for some r coprime to the characteristic
and if r divides the order of the multiplicative group of the constant
field, ie. if the coefficient ring of K contains a primitive r-th root
of unity. In case K is in Kummer representation, the element a is returned
as a second return value.
Tests if a global function field K is, in its current representation,
a Artin-Schreier extension, ie. if the defining polynomial of K is
of the form xp - x - a where p is the characteristic of K. In this case,
the element a is returned as a second return value.
V2.28, 13 July 2023