Change log for Magma V2.19-4 (Released 5/3/2013)

Algebraic Number Fields

·The check on the Al parameter to Subfields has been improved.

·A bug has been fixed in RelativeField when the first argument is a degree 1 extension of Q.

·A bug has been fixed in the KluenersvanHoeijSubfields algorithm.

·Subfields are now returned in the same order each time they are requested for a field.

Class Field Theory for Global Function Fields

·The computation of maximal orders of class fields of function fields has been improved.

Commutative Algebra

·A bug when computing GrÃ¶bner bases of the integers has been fixed. Reported by E. Rains.

General Local Fields

·A bug has been fixed when an attempt is made to construct a local field from a reducible polynomial. Reported by Lassina Dembele.

Groups

·Two bugs in LowIndexNormalSubgroups have been fixed. Bugs reported by Primoz Potocnik.

·A bug in pQuotient has been fixed. The bug may have caused crashes or incorrect answers to be returned.

·The Magma level printing of pc-groups has been changed to use the CompactPresentation format, and the Magma level printing of elements of a pc-group within sets and sequences has been changed to use the Eltseq format. This has the advantage that Magma will read such sets and sequences correctly, and the disadvantage that the printing is not easily human readable.

·A crash in RepresentativeCocycles for a pc-group has been fixed. Bug reported by Stephen Humphries.

Number Fields

·Additional functionality has been provided for characters over number fields with TotallyUnitTrivialSubgroup for Dirichlet characters, NormInduction for Hecke characters, and also GrossenTwist for Grossencharacters.

Polynomials

·A fix to GaussianBinomial was made to automatically coerce an element from a polynomial ring into a function field. The same is also now done for GaussianFactorial and GaussNumber.

Polytopes

·A particular sequence of transformations on the Zero element of a toric lattice could result in IsPrimitive giving an incorrect answer; this has now been corrected.

·Under very special conditions, isomorphism testing of rational polytopes could fail with an assertion error. This has now been fixed. Reported by Antonio Laface and Damiano Testa.

·A bug has been fixed in IsEquivalent when analysing rational polytopes of non-zero codimension.

·The computation of the automorphism group of a polytope has been improved.

Representation Theory

·A crash (runtime error) while computing SchurIndices has been fixed. Bug reported by Alex Bartel.

Toric Geometry

·The new fan constructor FanWithWeights has been added. This allows the creation of a fan based on the given weights and optional ample divisor.

·The choice of generators selected by QuotientGradings has been improved. Suggested by Antonio Laface and Damiano Testa.

·Attempts to construct a fan from contradictory cone data now gives the explanation of what went wrong as part of the error message, rather than as a separate piece of output.

·The computation time required by IsFano has been significantly reduced. A new intrinsic IsWeakFano has been added.