Next: Arithmetic Fields (Local)
Up: Arithmetic Fields (Global)
Previous: Characters and Artin Representations
Algebraic Function Fields
New Features:
- The intrinsics MaximalOrderFinite and MaximalOrderInfinite now
apply to abelian extensions of function fields. These intrinsics can be
much faster than the same intrinsics applied directly to the function field of
the abelian extension.
- When computing the GaloisGroup of a polynomial over a function field
having characteristic 2
, two more invariants are now available, similarly
to the odd characteristic cases.
One of these invariants is used to decide whether the Galois
group is a subgroup of An
.
- When computing the GaloisGroup of a polynomial over a function field
having prime characteristic, invariants with coefficients in Fq[t]
are now
available.
- A function field may now be constructed from a sequence of multivariate
polynomials. The resulting field will have a similar representation to that
constructed from one multivariate polynomial.
- Embed can now be applied to function fields represented as an extension
by multiple defining polynomials.
Changes and Removals:
- Improvements have been made to the computation of maximal orders of
Artin-Schreier extensions. The application of this more efficient
algorithm is restricted to fields whose constant field is perfect as
these are the fields for which the algorithm is known to always work.
- When computing the GaloisGroup of a reducible polynomial over a function
field of prime characteristic the descent step has been split so that it is
only performed for those factors whose splitting fields may have non-trivial
intersection.
- The order of the variables (when there are at least two) in
RationalFunction has been reversed back to what it was in Magma V2.10.
Now the first variable corresponds to
the primitive element of the topmost extension.
Bug Fixes:
- Compatibility of modules over maximal orders has been fixed.
- The PrimitiveElement of an order is now integral.
Next: Arithmetic Fields (Local)
Up: Arithmetic Fields (Global)
Previous: Characters and Artin Representations