Change log for Magma V2.21-8 (Released 13/11/2015)

Abelian Fields

·A problem with Discriminant has been fixed.

Algebraic Number Fields

·A bug in WeakApproximation given ideals of an order of a number field in relative representation has been fixed. This bug only occurred when the ramification degree of the ideal over its minimal prime integer was different to the ramification degree of the relative representation of the ideal. Reported by M. Kirschmer.

·Given a number field represented relatively as an extension of another number field, a more reliable method to compute an isomorphic field which is an extension of Q is now always used - an optimized representation is no longer attempted. Reported by D. Mayer.

Algebraic Surfaces

·A bug has been fixed in ArithmeticGenusOfDesingularization which caused some incorrect results for surfaces that had been formally desingularized. Reported by M.J. Martins.

·Some major speedups have been achieved in the main function FormallyResolveProjectiveHypersurface and also in the HomAdjoints function and the algorithms which depend heavily on this (such as ArithmeticGenusOfDesingularization, GeometricGenusOfDesingularization, PlurigenusOfDesingularization). Example input provided by M.J. Martins.

Commutative Algebra

·A hang in Groebner basis computation with local orders over number fields has been fixed. Reported by C. Rito.

·A crash in Groebner basis interreduction on 32-bit processors has been fixed.

Elliptic Curves

·The third return value for MordellWeilGroup and similar functions was always true due to a typo comparing the lower bound to the known number of generators, rather than the upper bound. Reported by B. Matschke.

·A bug with HeegnerPoint when computing more than 2^30 primes was fixed. Noted by B. Matschke (and others in years past).

General Local Fields

·A RamifiedRepresentation of a general local field can be constructed but sometimes there is not enough precision in the coefficients of the defining polynomial of the field for the mapping into this ramified representation to be successfully applied. The handling of the failure of this mapping has been improved so that an error message is given when neccessary.

Hyperelliptic Curves

·A problem with IgusaClebschInvariants in some cases was resolved. Reported by J. Voight.

L-Series

·The EulerFactors for an L-series that had been Translated were always computed to maximal precision, rather than to the amount of terms needed. Noted by D. Roberts.

·Some internal changes were made so that LCfRequired is more consistent with Translated L-series.

Lattice Reduction

·A problem with the TimeLimit vararg in LLL was fixed. Reported by M. Stoll.

Local Fields

·IsWildlyRamified for extensions of p-adic fields has been corrected. Reported by A.S. Elsenhans.

System

·A bug that could cause errors raised by require to report the wrong intrinsic name in some circumstances has been fixed.