Change log for Magma V2.16-8 (Released 30/4/2010)

Algebraic Curves

·A bug in CartierRepresentation with a multiplicity argument has been fixed. Reported by A. Elkin.

Brandt Modules

·For HeckeOperator at a ramified prime, an infinite loop occurred with the ComputeGrams option. This case is disallowed. Reported by K. Buzzard.

Characters of Groups

·A bug causing a crash has been fixed in the SchurIndex function.

Coding Theory

·The dimension of quantum codes over extensions of degree larger than two was incorrectly calculated. This has been fixed; the dimension of a quantum code is now returned as a rational. Reported by M. Grassl.

·The computation of the MacWilliams transform (of a weight distribution) has been mildly sped up.

·The intrinsic NumberOfWords as applied to a linear code will now use the weight distribution where this is expected to be faster. (In practice, when the dual is small.)

Coherent Sheaves

·A bug in the computation of the maximal module of a sheaf (accessed by, eg, FullModule) has been fixed. Reported by E. Rains.

Cryptography

·Fixed a bug in the hexadecimal digit conversion used by SHA1, which would cause incorrect results whenever the input contained alphabetic characters. (i.e., aâ€“f or Aâ€“F.) Reported by F. Hess.

Elliptic Curves

·Fixed a minor bug with Hints in 4-descent, to simply re-call the function when the x-coordinates are not distinct. An example with SetSeed(1) would be for FourDescent(x^4 - 2*x^3 + 7*x^2 + 6*x + 9) at p = 3.

Finite Fields

·A bug in CommonOverfield has been fixed. Reported by E. ThomÃ©.

Galois Groups

·A fix has been made to GaloisGroup for a function field of characteristic p. The problem may have only occurred for small p. Reported by F. MÃ¶ller.

·A fix has been made to GaloisGroup for a function field of characteristic 2. Reported by F. MÃ¶ller.

·A problem with a wrong bound in GaloisSubfieldTower has been fixed. In same (very rare) cases where the bound was actually sharp the reconstruction failed. Reported by M. Watkins.

Groups

·The simple group recognition code for Sp4 in characteristic 2, SU3, and SU4 has been revised by Peter Brooksbank, fixing a number of bugs.

·A bug giving an infinite loop in the Simplify command for finitely presented groups has been fixed. Bug reported by S. Humphries.

·A bug causing a crash in LowIndexSubgroups has been fixed. Fixed by Derek Holt.

·A bug in ClassicalMaximals has been fixed. There was a missing maximal subgroup of U(5,2) (missing group isomorphic to L(2,11)). Fixed by D. Holt.

·Bugs in the standard form functions UnitaryForm and QuadraticForm have been fixed. There were problems producing standard forms of odd degree. Fixed by D. Holt.

·The function IsHomomorphism for matrix groups is described in the manual but was not implemented. It is now implemented. Reported by A. Munemasa.

·A bug in the MaximalSubgroups code for families PSp(4,q), PSU(3,q), and PSU(4,q) has been rectified. The bug caused an infinite loop, but no incorrect results were returned. F. by Derek Holt.

·The quotient group constructor G/N has been extended to return the quotient group and, when two return values are assigned, the corresponding epimorphism.

·A spurious line in the printing of a subgroup lattice has been removed. Also the order of printing has been reversed, so the whole group, and then maximal subgroups, come at the top.

Hilbert modular forms

·A failure in HilbertCuspForms over NumberField(x^2-2869) has been fixed. Reported by J. Bryk.

Lattices

·A bug in the computation of the inverse of the quotient map of a lattice by a sublattice has been fixed. Bug reported by N. Scheithauer.

Lists

·Indexing a list by a sequence now works for ranged sequences as well.

Local Fields

·(Trivial) code to access the Frobenius of a local field has been added. Reported by A. Elkin.

·New code to obtain the Verschiebung of a local field has been added. Requested by A. Elkin.

Matrices

·When creating a matrix by coercion of a sequence into the parent structure, the sequence is now allowed to be a sequence of sequences.

Number Fields

·Fixed a bug in IsPrincipal for fractional ideals in non-maximal orders. In this case sometime principality would not get recognized or wrong generators could be returned. Reported by M. Kirschmer and J. KlÃ¼ners.

·A problem in the code for the norm computation of elements in product representation could sometimes produce inconsistent results.

·A problem in the prime decomposition code would sometimes use special methods for Kummer extensions when not appropriate, resulting in ideals that are wrongly labelled prime.

·Added a function to obtain ring class fields from non-maximal orders.

·Fixed the code for Hilbert90 which would occasionally generate errors for correct input. Also, the result would frequently lie in a different ring from the input.

·The code for computing the gcd of a sequence of algebraic numbers had difficulties with short lists and lists containing too many zero elements. In this case a runtime error would be triggered.

·The function UnitGroupAsSubgroup was trying to use a variable before assigning it, resulting in runtime errors. Reported by J. KlÃ¼ners.

Polynomial Rings

·A crash when computing the cardinality of a module over a residue ring has been fixed. Reported by M. Grassl.

·A crash when computing the roots of a polynomial over a local ring which it could not be coerced into has been fixed.

·A crash when calling multivariate GCD over several different finite fields has been fixed. Reported by T. Fisher.

Quaternion Algebras

·LeftIdealClasses now return left ideals not right ideals. Reported by K. Buzzard.

·Several bugs in MaximalOrder and HilbertSymbol for quaternion algebras have been fixed. Reported by J. Sisling, S. Donnelly.

·Enumerate also works for quaternion orders and ideals over Z.

Schemes

·Various changes have been made to PointSearch. The first is to allow the user to avoid singularity checks via a flag. The second is a bug fix for umbilical points that could cause some small points to be missed. This was reported by T. Fisher and N. Bruin.

·A long-standing issue with IsProjective, IsAffine, and EmptySubscheme in which incorrect answers could be returned in certain exceptional cases has been fixed. These intrinsics now take advantage of the toric geometry package when appropriate.

Simplicial Complexes

·A bug in the computation of the boundary maps of the chain complex of a simplicial complex has been fixed. Bug reported by S. Humphries.

System

·Fixed a bug that could occur under rare circumstances when package code called an eval which triggered the load of other package code.