Change log for Magma V2.23-7 (Released 22/12/2017)

Arithmetic Fuchsian Groups

·A bug with FundamentalDomain when an isometric circle meets the real axis at a right angle was fixed. Reported by A. Page.

Artin Representations

·An incorrect answer (due to too low of precision) for various Frobenius computations (particularly at 2) has been fixed. Reported by J. Jones.

Character Theory

·A crash in IsConjugate for characters for a small soluble group hash been fixed. Reported by A. Previtali.

Complex Fields

·Problems in Roots for polynomials over complex fields have been fixed. Reported by J. Voight and M. Grassl.

Dirichlet and Hecke Characters

·The evaluation functions previously coerced 1 and -1 to the Integers; this has been removed in the case that the evaluations are not elements of a cyclotomic field in the first place, thus making the usage of SetTargetRing (e.g. for a finite field) give more uniform answers. Noted by L. Dembele.

Groebner Bases

·The FGLM algorithm has been non-trivially improved for ideals defined over medium prime finite fields. Issue reported by M. Grassl.

·A crash in GB computation for ideals defined over number fields with multiple relative levels has been fixed. Reported by M. Grassl.

Hypergeometric Motives

·Identifying a hypergeometric motive which is a hyperelliptic curve now automatically sets the LocalData parameter to "Ogg" in its L-series. Reported by J. Jones.

KG-Modules

·A package implemented by Peter Brooksbank, based on a new algorithm due to him and Eugene Luks for testing two KG-modules for isomorphism, has been installed. The algorithm is superior to the existing algorithm of Allan Steel in the case of difficult reducible KG-modules. There are three new intrinsics:

·- SummandIsomorphism(M, N) determines the unique maximal isomorphic summands of KG-modules M and N;

·- RelativeDecomposition(M, T) finds the direct sum decomposition of KG-module M into N + K, where K is minimal with respect to containing the KG-module T;

·- SocleRecursive(M) finds the socle of KG-module M.

·A hang in the intrinsic IsIsomorphic for KG-modules over finite fields has been fixed. At the same time, the algorithm has been sped up in the case of difficult isomorphism computations for reducible KG-modules through use of the package described above. A particularly difficult example for the existing isomorphism algorithm was provided by Dave Benson.

·An intrinsic InjectiveHull which computes the injective hull of a KG-module over a finite field has been installed. This was suggested by Dave Benson and implemented by Derek Holt.

L-series

·Taking an EulerFactor of the trivial (unital) L-series no longer gives an error. Reported by J. Jones.

Language

·The and:= and or:= operators now shortcircuit (do not evaluate the RHS) when the LHS is already false or true, respectively. Issue reported by C. Doris.

Lattices

·The MinkowskiGramReduction intrinsic has been internally changed to compute successive minima via LLL and HKZ rather than call SuccessiveMinima.