Change log for Magma V2.15-6 (Released 16/2/2009)

Algebraic Curves

·The maximal order fix for function fields has also fixed a bug that was causing crashes in calls to LPolynomial and ZetaFunction for general algebraic curves. Additionally, a confusing runtime error message for these functions, telling the user that the constant field is too large, has been amended. The actual size parameter that limits the function field method is the field size to the power of the genus: the approximate number of rational points of the Jacobian.

Coding Theory

·MinimumWeight was incorrectly disallowing codes over finite residue rings. The false check has been fixed. Reported by M. Harada.

Commutative Algebra

·A crash in PrimaryDecomposition over very small finite fields has been fixed.

Diophantine Equations

·The restriction on Thue equations that the right-hand side should be less than 230 has been lifted. Requested by O. Phuksuwan.

Function Fields

·A bug in the computation of norm groups of an abelian extension caused runtime errors if the group has trivial conductor.

·Improvements have been made to the application of the residue field map at places where the input had valuation in its denominator. Reported by M. Grassl.

·Improvements have also been made to avoid expensive computations with orders. This has a considerable effect in maximal order computations.

·The p-maximal orders of function fields in absolute representation have been fixed.

Galois Groups

·The computation of GaloisSplittingField of a polynomial defined over a quadratic field or an order was not possible. Bug found by G. Wiese.

Groups

·A crash when doing calculations with very many pc-groups has been addressed.

·A runtime error when the Generators parameter for RandomProcess was used and did match with the WordGroup parameter but not the number of generators of the group has been fixed. Bug reported by Eamonn O'Brien.

·When testing for trivial matrix groups in the cohomology package, infinite groups caused errors.

·Trying to "clean up" a representation of an infinite group caused an infinite loop.

·A crash in Subgroups (reported with group 2.PSL(3,5).2) has been fixed.

Modular Symbols

·A slowdown and leak in ModularSymbols has been fixed. Reported by P. Elbaz-Vincent.

Number Fields

·A bug in certain computations with trivial RayClassGroups has been fixed. Reported by S. Donnelly.

·A few functions were using Generators (a set) instead of GeneratorsSequence (a sequence) which caused a variety of class field related functions to compute the automorphism group of an abelian extension to abort.

·Improvements have been made to the application of the residue field map at places where the input had valuation in its denominator. Reported by M. Grassl.

·Improvements have also been made to avoid expensive computations with orders. This has a considerable effect in maximal order computations.

Quadratic Fields

·A bug related to the conversion between ideals and quadratic forms has been fixed. Without this fix, IsPrincipal could return non-integral generators for integral ideals. Reported by M. Kirschmer and L. Wilson.