Change log for Magma V2.20-7 (Released 25/6/2014)

Aggregates

·A bug that could cause rare crashes in certain multisets has been fixed. Reported by S. Kionke.

Class Field Theory

·It is now possible to directly compute the abelian extension (FldAb) corresponding to a Hecke character (over a number field), and vice-versa.

Coding Theory

·A bug in SpanZ2CodeZ4 when delta = 0 has been fixed. Reported by N. Aydinn.

Coherent Sheaves

·A bug has been fixed that resulted in the canonical sheaf having the wrong grading in some cases after calls to IsGorenstein. Reported by E. Rains.

Commutative Algebra

·A crash in FreeResolution for modules over non-prime fields of characteristic 2 has been fixed. Reported by I. Soprunov.

Cones

·MinimalRGenerators now uses Fourier-Motzkin elimination by default. Similarly, ZGenerators now uses Hemmecke's method by default. Previous versions would use a heuristic based on computing the SimplicialSubdivision of the cone to choose the most appropriate algorithm, however this scales poorly with the complexity of the cone. The optional algorithm parameter is deprecated and will be removed from these two intrinsics in a future patch release.

Elliptic Curves

·A bug in HasComplexMultiplication that caused runtime errors in some cases has been fixed. Reported by W. Moore.

·A bug in LFunction for elliptic curves over rational function fields (over finite fields) has been fixed and a slight speed-up has also been introduced.

·A runtime error has been fixed in reduction of genus one models over certain number fields. This affected MordellWeilShaInformation for those fields. Reported by Kazuo Matsuno.

Groups

·A crash when computing the derived series of a permutation group has been fixed. Bug reported by Eamonn O'Brien (as a crash when computing CompositionTree of a matrix group).

·The GeneratorOrder parameter of the AutomaticGroup function now accepts a sequence of integers (generator numbers and their negatives) as input. Response to crash in calculator.

·A crash when computing the conjugacy classes of a permutation group has been fixed. Bug reported by Eamonn O'Brien.

Hypergeometric motives

·The EulerFactor intrinsic was returning polynomials over the rational field instead of the integers in some cases (particularly at multiplicative primes).

·The Weight01 vararg to LSeries has been modified to allow a weight dependent on the number of trivial cyclotomics in the data.

·The Character of hypergeometric data at a given t-value (including t = 1) can now be obtained directly.

·A database of wild prime information at t = 1 for small degrees has been computed, for instance containing all 147 examples in degree 5, and the 23/287/487 examples for degree 6 in weights 0/1/3.

L-series

·A bug with TensorProduct concerning Artin representations has been fixed. This could also afflict elliptic curves over number fields which internally use these. Noted in part by J. Cremona and W. Moore.

·Division by the trivial L-series is now possible in any weight.

·Utility intrinsics to ChangeLocalInformation and CopyCoefficients between L-functions are now provided, to ease the difficulties in numerically determining bad Euler factors.

·The HodgeStructure of various objects have been added, such as elliptic curves, Hilbert modular forms, and Artin representations.

·An intrinsic for the Degree of a HodgeStructure has been added.

·Various issues with precision have been remedied.

·Translate now tries to translate the residues (in addition to poles).

·An experimental intrinsic CFENew has been added that uses a dynamic method (relative precision of summands versus sum) to determine how many terms to use in checking the functional equation. Comparatively the intrinsic CheckFunctionalEquation simply uses LCfRequired to get the required number of coefficients (usually a good factor larger).

Number Fields

·A problem that was introduced in version 2.20-6 has been fixed: RayClassGroup did not use a "current" (already computed) class group, but instead performed a full unconditional proof. Note: this behavior can be overcome in version 2.20-6 by using SetClassGroupBounds("GRH"). Reported by Armand Brumer.

·Some problems with linear algebra over the 1st CyclotomicField have been fixed.

Rings

·The ChangeRing intrinsic can now be applied to a multivariate polynomial. Requested by A. Sutherland.