Change log for Magma V2.14-7 (Released 6/12/2007)

Associative Arrays

·Some crashes in associative arrays have been fixed. Reported by T. Ekedahl.

Elliptic Curves

·Several kinds of runtime and internal errors in CasselsTatePairing have been fixed.

Groups

·A bug in the construction of inclusion and projection maps for direct products of sequences of pc-groups has been fixed. Reported by E. O'Brien.

·A problem with HasComplement for finite abelian groups has been fixed. Without this fix, the algorithm would fail in certain examples and trigger a runtime error.

·The function PCGroup now respects the Check parameter properly. Some crashes with large presentations are also fixed. Reported by M. Newman.

·A bug in the solvable quotient has been fixed. Without the fix, AbsolutelyIrreducibleModulesSchur would trigger internal errors for certain inputs. Reported by A. Previtali.

Hyperelliptic Curves

·The map returned by TwoSelmerGroup (or TwoSelmerGroupData) is now correct. (Previously, the map sometimes failed to send the group generators to independent elements).

Invariant Theory

·The function FundamentalInvariants has been fixed to use the new IrreducibleSecondaryInvariants code in the non-modular case. Reported by G. Kemper.

Local Fields

·A bug in the coercion of squences into infinite precision fields has been fixed. Without the fix, the precision in ramified extensions would be too small.

·A bug in Kernel for matrices over p-adic rings has been fixed. Without the fix, Magma would trap internal errors. Reported by G. Chatel.

Number Fields

·A bug in the computation of traces of elements in relative extensions of number fields defined by non-monic, non-integral polynomials has been fixed. The old code could return wrong answers. Reported by L. Wilson.

·A bug in the computation of inverses of isomorphisms of absolute simple number fields has been fixed. In certain situations where one of the input fields has a non-monic, non-integral defining polynomial the map returned was wrong. Reported by M. Kirschmer.

·A bug in the internal handling of non-canonically generated prime ideals has been fixed. Without this fix, Magma would dump a lot of information on certain input and terminate with an internal error. Rported by J. Voight.

·A bug in the internal handling of certain non-simple fields has been fixed. The use of sparse cyclotomic fields in quarterion algebras and non-cimple number fields in Decomposition can, under certain circumstances, result in runtime errors. Reported by A. Previtali.

·A problem in the internal precision handling of p-adic completions of number fields has been fixed. Pre-images under the completion of fields were sometimes returned with insufficient precision.

·The function Extends to compare places of number fields was wrong for certain finite places and complex infinite ones.

·The function DecompositionType for abelian extensions can now also handle infinite places.

·A problem in the handling of infinite places in SplittingField has been fixed. Without this fix, certain input would result in infinite loops.

Polynomials

·A crash in multivariate GCD has been fixed (called from primary decomposition).

·Crashes in multivariate resultant have been fixed. Reported by M. Watkins.

Quaternion Algebras

·A bug in HilbertSymbol, involving ramified extensions, has been fixed.