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 multipicative 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.[Next][Prev] [Right] [Left] [Up] [Index] [Root]