Change log for Magma V2.13-8 (Released 19/12/2006)

Arithmetic Geometry

·Some bugs in the characteristic two canonical lift code for point-counting on hyperelliptic curves/Jacobians have been fixed.

Elliptic Curves

·In TwoSelmerGroup for curves over number fields, some further precision problems have now been handled.

Finite Fields

·A bug in IsPower(a, n) for large values of n over large fields has been fixed. Arbitrarily large n is now supported for the first time. Bug reported by Eamonn O'Brien.

Galois Groups

·A bug in the Galois group package that would occasionally introduce an infinite loop using more and more memory has been fixed.

Groups

·Two functions called Transversal have been added for the class of finite finitely-presented Coxeter groups. These give minimal length right- and double-coset representatives for standard parabolic subgroups (specified by a set of integers). Algorithms supplied by Bob Howlett.

·For matrix groups, a bug in the implementation of the Murray-O'Brien base point selection method has been fixed. Bug reported by Eamonn O'Brien.

·A bug in the recognition of non-generic orthogonal plus matrix groups over finite fields has been fixed. Bug reported by Mark Stather.

Module Theory

·A bug in the Meataxe algorithm in rare cases involving the endomorphism ring has been fixed (the bug was only in V2.13).

Number Fields

·Generators of a fractional ideal in non-maximal order would return an inconsistent eltseq. This has been fixed.

·Decomposition of elements of field of fractions of non-maximal orders would cause an internal error to be triggered. The decomposition of such elements (into prime ideals) has been disabled as it is in general not unique.

Polynomials

·A bug in polynomial factorization over integers, where a reducible polynomial was very occasionally considered irreducible, has been fixed.