Change log for Magma V2.16-4 (Released 24/12/2009)

Algebraic Function Fields

·The computation of the Galois group or subfields of global function fields has been improved.

·A bug in the computation of maximal orders has been fixed. For some orders the Artin-Schreier algorithm was being used when the extension was not Artin-Schreier.

Complex Numbers

·Magma has been updated to use MPC 0.8.1. Inverse trigonometric functions for complex numbers and powering of complex numbers now uses the MPC implementation of this functionality.

Elliptic Curves

·A bug that could occasionally cause the discrete logarithm to incorrectly report failure has been fixed.

·A bug when quotienting out by elements in 4-descent was patched.

·The manner in which 2-covers are added has been corrected.

·The ability to translate by 2-torsion with Heegner descent on covers has been added.

·The condition of nonzero element in TwoCover has been changed to require nonzero norm instead.

·Some improvements have been made for curves defined over real fields, so that basic point creation and arithmetic has some chance of working.

Graphs

·Interfaces to databases of various small graphs have been added. These databases may be downloaded from the Optional Databases section of the Magma download page, and are based on graph data made available by Brendan McKay.

Lazy Power Series Rings

·A bug in Coefficients when the range was empty has been fixed.

Orders of Associative Algebras

·A bug in determining equality of orders over the integers has been fixed.

Polynomial Rings

·A slowdown in resultant computation has been fixed. Reported by V. Vitse.

Sequences

·Sort and ParallelSort of sequences handle sequences with many repeated elements significantly better now.

·A crash that could arise when creating sequences of multiset items (using the double-hat operator) has been fixed. Reported by C. Quitte.