Change log for Magma V2.22-7 (Released 16/12/2016)

Algebraic Number Fields

·Divisors of elements of orders of algebraic number fields now gives an error when presented with an input of zero. Reported by M. Cuntz.

Artin Representations

·A precision-based bug when computing local data at bad primes was fixed.

Binary Quadratic Forms

·The Distance intrinsic on a single form has been removed.

·Reduction now does not compute or return the transformation matrix if the results are being printed or only the first return value is used.

·Reduction has been sped up.

·A bug has been fixed in IsEquivalent that could have caused the resulting transformation matrix to not be correct.

·IsEquivalent now allows returning transformation matrices in the real case. If non-narrow equivalence has been asked for, then the resulting transformation may produce the complementary form <-a, b, -c>.

·IsEquivalent has been sped up.

Elliptic Curves

·The Cremona database of elliptic curves of small conductor has been updated to conductor 399,999.

·A problem with AnalyticRank for elliptic curves over number fields with even degree was fixed. Reported by D. Lorenzini.

·A problem with EulerFactor for elliptic curves over number fields with nontrivially intersecting ramification was fixed. This also appeared in EulerFactor for an elliptic curve twisted by an Artin representation, giving a result in a cyclotomic field rather than a complex field. Reported by D. Lorenzini.

Galois Groups

·Some improvements have been made to the computation of Galois groups.

·A bug in SolveByRadicals for non-monic polynomials has been fixed. Reported by P. Lisonek and fixed by Stephan Elsenhans.

·The intrinsic GaloisSplittingField now applies to polynomials over number fields. This used to be the case but was removed probably by error for a time. Reported by J. Sijsling.

·A bug involving Galois groups over function fields was fixed. Reported by B. Naskrecki.

Groups

·Some missing checks have been added to prevent creating matrix groups over inexact rings such as the real numbers.

·An infinite loop which can arise when computing normalizers and the trivial subgroup of a pc-group has been fixed. Bug reported by T. Dokchitser.

Hyperelliptic Curves

·RichelotIsogenousSurfaces has been patched, in particular for cases where the same codomain was listed 3 times rather than 3 different ones.

Hypergeometric Motives

·A problem with the computation of the conductor in the identification of the Grossencharacter of a Jacobi motive over Q(zeta_4) was fixed.

L-series

·A bug with the TateTwist of a Grossencharacter with nontrivial Dirichlet component has been fixed.

Lattices

·Bugs arising from computing Coordinates for vectors in lattices over a real field have been fixed.

Laurent Series Rings

·The hom constructor is now supported for Laurent series rings.

Local Fields

·A possible crash when powering by large exponents has been fixed.

·A crash involving HenselLift was changed to give a runtime error.

Matrix Groups

·IrreducibleSubgroups has been updated to include the insoluble irreducible subgroups of degree 3; the code was prepared by Barry Hurley. This generalises and replaces the function IrreducibleSolubleSubgroups.

·This patch release includes a new version of the CompositionTree package which contains more efficient versions of the ClassicalRewriting intrinsics (Csaba Schneider) and the RecogniseSmallDegree intrinsic (Eamonn O'Brien).

·A crash in the intrinsic SuzukiConjugacyClasses has been fixed by Henrik Baarnhielm.

·A crash in IsAbsolutelyIrreducible has been fixed.

Polynomials

·The SmallRoots intrinsic no longer crashes when X is 0.

Real Numbers

·ExponentialIntegral now accepts negative arguments.

·ExponentialIntegral, LogIntegral, and DawsonIntegral should be slightly more accurate in some cases.

Rings

·The functions IsFinite and # for rings now give a proper error message if an algorithm is not available (instead of sometimes returning false). Issue reported by S. Szabo.

Schemes

·A bug in Reduction for schemes has been fixed. Reported by S. Vishkautsan.

Symmetric Functions

·Coercion of symmetric functions into suitable polynomials rings has been made more flexible. Reported by T. Coates.