Change log for Magma V2.21-6 (Released 10/9/2015)

Aggregates

·MultisetToSequence has been added. Requested by M. Zieve.

Algebraic Function Fields

·Computations of Subfields have had some efficiency improved by not checking known irreducible factors for irreducibility when they are used in the calculation of subfields to define a function field.

·The computation of the GaloisGroup of a polynomial has been improved by choosing a prime which has been checked to be fine to use with all subfields involved in the calculation.

·WeakApproximation has been implemented for ideals of orders represented in a relative representation. Requested by M. Kirschmer.

·A crash in WronskianOrders has been fixed.

Algebraic Number Fields

·Computations of Subfields and GaloisGroups of number fields defined by a polynomial over an order rather than a field have benefited from improved denominator handling. This includes computations of GaloisGroups of polynomials over orders.

·Computations of Subfields have had some efficiency improved by not checking known irreducible factors for irreducibility when they are used in the calculation of subfields to define a number field.

·The computation of the GaloisGroup of a polynomial (especially a reducible polynomial) has been improved by choosing a prime which has been checked to be fine to use with all subfields involved in the calculation.

·WeakApproximation has been implemented for ideals of orders represented in a relative representation. Requested by M. Kirschmer.

·A fix has been made to CyclotomicUnits. Reported by M. Kirschmer.

·A fix has been made to GaloisProof. Reported by J. KlÃ¼ners.

Dirichlet and Hecke Characters

·A problem with a Grossencharacter of negative weight has been fixed.

·Dirichlet and Hecke characters should now retain their ambient subgroups when multiplied by elements in the same subgroup.

·The TateTwist intrinsic can now be used to get a Hecke character corresponding to twisting by the norm, which internally is of the type GrossenChar. This can be done over any field (not just CM).

·The printing with Grossencharacters has been changed.

·Intrinsics for the local Components of characters have now been added, and allow a place or prime ideal to be specified.

·Intrinsics for the local RootNumbers of Hecke and Grossencharacters have now been added, and allow a place or prime ideal to be specified. The global root number can also be obtained in this manner.

·A new intrinsic QuadraticCharacter has been added, to be able to obtain the Hecke character corresponding to a quadratic extension.

Graphs

·Spectrum of a graph no longer returns the wrong type of complex numbers.

Groups

·The code for finding the PCGenerators of a GrpMatUnip has been improved to remove considerable redundancy. Reported by E. O'Brien.

·Fixed a rare crash in UpperCentralSeries. Reported by S. Elsenhans.

·Characters or sequences of characters may now be coerced into appropriate matrix spaces over the complex numbers, and this is considerably faster than coercing each element of the character table.

·A problem with CohomologicalDimension involving symplectic groups has been fixed. Reported by A. Brumer.

Hodge Structures

·The convention for RootNumber of a HodgeStructure has been changed, taking the reciprocal of that given by Deligne. The code for Artin representations has been changed to reflect this.

·The output of CriticalPoints has been modified to be symmetric, and the intrinsic is now documented. Reported by D. Loeffler.

Hypergeometric Motives

·A complementary package for Jacobi sum motives and their Kummer twists has now been added. The most notable feature of this is the ability to identify these motives with a Grossencharacter, following Weil.

·A incorrect answer for EulerFactor at a tame prime when 1 was in the cyclotomic data for the alpha's has been corrected.

Local Fields

·Gamma of a 2-adic integer now has its output precision calculated more precisely. Determined in discussions with B. Allombert.

·More error checking has been added to the computation of Roots of a polynomial over a local ring or field.

·Various speed improvements have been made to p-adic Gamma.

·The formula for the Discriminant of a relative extension has been corrected.

·An error when using AutomorphismGroup has been remedied (the Generic Group code was called with a nontrivial automorphism being specifed as the group identity).

·An incorrect increase in default precision of a Completion of a number field, seen when computing preimages using the completion mapping has been fixed.

Polynomial Rings

·div:= has been fixed to make it consistent with div. Reported by M. Zieve.

·The previous functionality of Denominator for multivariate polynomials is now implemented by CoefficientDenominator. The intrinsic CoefficientNumerator has been added to match. The intrinsics Denominator and Numerator for multivariate polynomials now work with the polynomial interpreted as a rational function with denominator 1. Reported by M. Zieve and M. Kirschmer.

·A crash in Roots for polynomials over number fields has been fixed. Reported by M. Kirschmer.

·The XGCD algorithm has been improved for univariate polynomials over rational function fields to avoid bad coefficient blowup. Issue reported by M. Massierer.

System

·Fixed a bug that could erroneously cause out of memory errors when using printf or similar to produce strings of over a gigabyte in size.

·Improved the speed of concatenating a sequence of many strings.