|
|
Next: Arithmetic Fields (Local)
Up: Arithmetic Fields (Global)
Previous: Algebraic Number Fields
Algebraic Function Fields
Removals and Changes:
- Removed an unnecessary restriction on orders being maximal when testing
whether ideals are prime and in some operations on prime ideals.
- GaloisGroup of a global function field has been reimplemented.
- The MaximalOrder computation in Kummer extensions has been sped up
by avoiding the construction of intermediate p-maximal orders. (V2.15-3)
- The application of the residue field map to inputs with denominators has
been improved. (V2.15-6)
- Some expensive computations with orders have been avoided which has
considerable effect in maximal order computations. (V2.15-6)
New Features:
- A new algorithm has been implemented for the computation of p-maximal and
maximal orders in Artin-Schreier extensions.
- Computing a prime decomposition of a prime which totally ramifies in an
Artin-Schreier or a Kummer extension now uses a similar algorithm to that
implemented for computation of p-maximal and maximal orders.
- The algorithm of Klüners and van Hoeij for computing subfields of a
generic field has been implemented and is used to compute the
Subfields of a global function field.
- InfiniteDivisor, FiniteDivisor, FiniteSplit of a divisor
have been added.
- A sub constructor has been added for function fields.
Bug Fixes:
- The ext<> constructor for infinite orders of function fields has been
fixed.
- It is now possible to take the Valuation of a rational function at a
place, after the fix of an input check. (V2.15-3)
- The computation of p-maximal orders of function fields which are a
direct Kummer extension of a rational function field has been fixed. (V2.15-6)
- A problem with product representations has been fixed. (V2.15-7)
- Some bugs resulting in incorrect answers from Expand and the application
of completion maps have been fixed. (V2.15-8, V2.15-10)
Next: Arithmetic Fields (Local)
Up: Arithmetic Fields (Global)
Previous: Algebraic Number Fields
|
|
