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Magma V2.23-7 Patch Notes

Patch release for Magma V2.23-7. Updated areas: Arithmetic Fuchsian Groups, Artin Representations, Character Theory, Complex Fields, Dirichlet and Hecke Characters and 6 more.

11 areas

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:

    • 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;

  • 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

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