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Magma V2.18-2 Patch Notes

Patch release for Magma V2.18-2. Updated areas: Algebraic Function Fields, Algebraic Number Fields, Commutative Algebra, Elliptic Curves, Global Arithmetic Fields and 5 more.

10 areas

Algebraic Function Fields

  • The arithmetic of elements in different fields of fractions of orders has been fixed.

  • The computation of a maximal order in an Artin-Schreier extension has been improved.

Algebraic Number Fields

  • Fixes have been made to Subfields of extensions of Q. Reported by J. Klüners.

Commutative Algebra

  • A crash in FreeResolution for modules over number fields has been fixed. Reported by H. Campbell.

Elliptic Curves

  • The database of elliptic curves over \(\mathbb{Q}\) of small conductor, constructed by John Cremona, has been updated to include curves representing all isogeny classes for all conductors less than 210000.

Global Arithmetic Fields

  • A check for fields defined by a sequence of polynomials has been added to Subfields. Reported by J. Voight.

  • A fix has been made to meet for an order with a field.

  • A fix has been made to GaloisGroup computations. Reported by J. Klüners.

Group Algebras

  • A crash when computing RegularRepresentation of a group algebra over a multivariable polynomial ring has been trapped to give a runtime error instead. The algorithm is only implemented for base rings that are fields or Euclidean domains. Reported by S. Humphries.

Matrix Groups

  • A bug in the machinery for recognising classical groups, which caused a proper subgroup of \(Ømega(3, 7^2)\) to be incorrectly identified as the full group, has been fixed.

  • A bug in the machinery for performing Aschbacher analysis on a matrix group over a finite field, whereby a group of order 16 in \(GL(3, 7^2)\) was not identified as a subgroup of the normaliser of an extraspecial group, has been fixed.

Representation Theory

Series Rings

  • ChangeExponentDenominator on a series has been fixed to ensure that the resulting series is normalized.

p-Groups

  • A revised version of the intrinsic ClassTwo, which counts the set of p-class 2 d-generator groups, prepared by Michael Vaughan-Lee, exploits types of matrices to greatly reduce the cputime.

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