Change log for Magma V2.18-8 (Released 4/7/2012)

Admissible Representations

·When creating a LocalComponent, there is now an option to set CheckMinimal to false: in this case, the input will be assumed to be minimal, skipping the potentially expensive check.

Aggregates

·A crash associated with use of coproducts has been fixed. Reported by E. O'Brien as a crash in CompositionTree.

·A bug in associative arrays that could cause crashes when keys of different universes are used has been fixed.

Algebraic Function Fields

·A fix has been made to memory management in the computation of MaximalOrders in Artin-Schreier extensions.

·Computations involving kernels of matrices over function fields whose constant field is not a finite field or the rationals have been fixed.

Algebraic Number Fields

·A fix has been made to memory management in the computation of roots of elements in number fields.

·The torsion unit computation has been fixed.

·A fix has been made to memory management in a part of the ClassGroup and UnitGroup computations where the class group is computed using the Sieving algorithm.

·A fix has been made to computations of polynomial GCDs over fields of fractions of non-equation orders when the subresultant algorithm was used. Reported by N. Bruin.

·The computation of Subfields using the KlÃ¼ners-van Hoeij algorithm has been improved in the areas of the prime selection and gradual LLL_with_removals computations. The choice between the KlÃ¼ners-van Hoeij algorithm and the KlÃ¼ners algorithm has also been improved.

·Testing a large ideal of a non-maximal order for being principal has been fixed.

·A fix has been made to AbsoluteOrder.

·A leak has been fixed in Factorization of elements of quadratic fields. Reported by R. Broker.

Binary Quadratic Forms

·The commands PicardGroup for quadratic nonmaximal orders and ClassGroup for quadratic forms for nonfundamental discriminants had been returning incorrect answers for some time. This has been corrected. Reported by John Voight.

Class Field Theory

·A fix has been made to the computation of a MaximalOrder for fields constructed as (ray) class fields. Reported by D. Mayer.

Coding Theory

·A bug in AutomorphismGroup for codes over non-binary finite fields would cause the computation to be done over the less efficient choice out of the code and its dual. This bug has been fixed. Reported by M. Grassl.

Commutative Algebra

·A bug in RegularSequence has been fixed. Reported by Claude Quitte.

·A bug in Homogenization has been fixed. Reported by Damiano Testa and Tony Varilly-Alvarado.

Cones and Polyhedra

·Fixed a potential crash when taking -P of a polyhedron P. Reported by T. Coates.

·Added Representative for a cone C, so correcting unexpected behaviour. Reported by T. Coates.

Curves

·The restriction that the degree of the place input to Expand is 1 has been removed (now consistent with Expand taking a place of an algebraic function field). Reported by M. Grassl.

·Completion of a function field of a curve at a place is now directly available.

Cyclotomic Fields

·Coercion between Cyclotomic fields when only one of the fields has sparse representation has been fixed.

Elliptic Curves

·A bug in the elliptic curve rank computation (for elliptic curves defined over the rational field) has been fixed; this bug could cause some covering curves to be erroneously discarded as not contributing to the 2-Selmer group, and thus may under-report the upper bound on the rank or fail with a warning about a missing quartic. This bug does not affect curves with rational 2-torsion. Reported by E. Rains.

·A bug in the elliptic curve Chabauty routine has been fixed. Reported by Enrique Gonzalez-Jimenez.

·The elliptic curve database now includes all curves of conductor up to 240,000.

Groebner Bases

·A crashes in computing Groebner bases for ideals over number fields has been fixed. Reported by T. Fisher.

·A bug in EasyBasis that was occasionally producing incorrect results has been fixed.

Groups

·A crash in the CharacterTable function has been fixed. Reported by E. O'Brien.

·The stored name for PrimitiveGroup(64, 41) has been changed to 2^6:PGL(2,7). (It was 2^6:GL(3,2), which is half the order of the stored group.) Reported by J. Schmidt.

·A bug in RecogniseClassical has been fixed. A non-classical group was incorrectly identified as Omega(3, 9). Fix provided by Alice Niemeyer.

Incidence Geometry

·A new function is included for coset geometries. Dimitri Leemans has supplied a LocallySArcTransitive function. This returns the largest integer s such that the given coset geometry is locally s-arc-transitive but not locally (s+1)-arc-transitive.

LSeries

·Taking the TensorProduct now always gives a Conductor that is a RngIntElt â€“ previously it could occasionally be a FldRatElt, which could later cause problems.

Modular Curves

·An bug has been fixed in the Isogeny and SubgroupScheme intrinsics which produced incorrect results for input elliptic curves not of the form y2=x3 + Ax + B.

Modular Forms

·Runtime errors occuring for weight one forms have been fixed. Reported by David Loeffler and others.

·A runtime error in Newforms(I, M) has been fixed. Reported by Kartik Prasanna.

·IsTwist and IsMinimalTwist now use sharp bounds (as in Loeffler-Weinstein), making them massively faster. Since V2.18 very crude bounds had been used, and prior to V2.18 there were occasional errors.

Schemes

·A problem in IsNode and TangentCone has been fixed that was causing a large slowdown in some cases by inefficient translation to the origin. Reported by Pietro Mercuri and David Kohel.

Series Rings

·When evaluating a power series at another power series, the precision of the result could have been set lower than it should be. This has now been fixed.