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Magma V2.20-3 Patch Notes

Patch release for Magma V2.20-3. Updated areas: Abelian Extensions of Function Fields, Aggregates, Artin Representations, Coding Theory, Complex Numbers and 6 more.

11 areas

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 \(\mathbb{Q}\) 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

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 \(\mathbb{Q}_p\).

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