Magma V2.20-3 Patch Notes

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¶

• 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 $\mathbb{Q}_p$.