Change log for Magma V2.20-3 (Released 30/1/2014)

Abelian Extensions of Function Fields

·Hermite computations in the computation of maximal orders of abelian extensions of global function fields and of extensions defined by a Witt vector have been improved and also computed less often. An unneccessary discriminant computation has also been avoided.

Aggregates

·The speed of Flat has been improved; additionally, it nows handles embedded null sequences more gracefully. Speed issues reported by U. Thiel.

Artin Representations

·A bug with degree 0 representations over the rationals was fixed.

·IsZero can now be applied to an Artin representation directly.

·The sum of an empty sequence of Artin representations over Q now works.

Coding Theory

·The intrinsic RegularLDPCEnsemble now returns a regular LDPC ensemble, as opposed to an approximately regular one. Also IrregularLDPCEnsemble now better matches the provided distribution. Reported by O. Orciere.

·Some minor leaks in cyclic code creation have been fixed.

Complex Numbers

·Two fixes to Roots of a complex polynomial were made, one to delimit an infinite loop, and the other to try to handle multiple roots more gracefully.

Function Fields

·StrongApproximation has been made more efficient.

Hypergeometric Motives

·The default printing has been changed to use cyclotomic indices. The alpha/beta printing (which is not so useful over the rationals) can be obtained via a vararg Print when initialising the data.

·The HodgeStructure of odd weight data is now directly obtainable, without specifying a t-value.

·A runtime error is now triggered for tame Euler factors that are too hard to compute to high precision (rather than a crash).

·The initialisation of large degree data is now more efficient, as large cyclotomics are avoided and the GammaArray length is not artifically lengthened during the pre-computation.

·A vararg Weight01 has been added to the LSeries creation intrinsic, which takes the Tate twist (via Translate) of the LSeries to make it have (motivic) weight 0 or 1.

·A vararg QuadraticTwist has been added to the LSeries creation intrinsic, which can be specified either as a nonzero rational or as a real Dirichlet character, or alternatively via the boolean true, when Magma will then use a default twisting factor that aims to help some deformation theory work out.

·Some functionality for non-disjoint hypergeometric data is now available. In particular, the LSeries intrinsic now returns two L-series, the first corresponding to the disjoint data, and the second corresponding to an Artin representation for the common data.

I/O

·The version of ReadBytes which takes an exact length now works as advertised, instead of returning short reads.

L-Series

·The TensorProduct of two LSeries with integral coefficients should now keep this integrality at the EulerFactor for every prime. There was a bug in the case where one constituent had degree 1. Reported by D. Roberts.

·The case of a tensor product when a bad prime has both constituents with a degree 1 factor is now handled automatically (thanks to Tim and Vladimir Dokchitser).

·The HodgeStructure printing has changed, so that repeated (p,q) pairs appear with a multiplicand in front.

·The RootNumber at infinity of a Hodge structure is now available, returned as an element of the 4th cyclotomic field.

·Calling LSeries on the rationals will now give RiemannZeta.

Matrices

·A crash involving indexing of a matrix with very many rows has been fixed.

·A problem with matrix multiplication over rational function fields (where entries were not standardized so wrong results could arise occasionally) has been fixed. Reported by E. Schost.

p-adics

·One can now compute the PowerRelation for an element of Qp.