Change log for Magma V2.15-10 (Released 12/6/2009)

Elliptic Curves

·Over GF(p), for a prime p of bit length less than 50, Magma now uses a fast internal BSGS for point counting rather than going through SEA. This is also used if the j-invariant of the curve lies in the base field and the characteristic is as above.

·A bug in SEA has been fixed that caused (very rare) runtime errors in the processing of Elkies primes.

Function Fields

·Some bugs in the application of completion maps have been fixed. Reported by B. Wardemann.

·A speedup in arithmetic has been achieved for sums of elements with denominators differing greatly in size. Problem reported by E. O'Brien.

Galois Groups

·A badly chosen prime was unneccessarily slowing down the computation of the roots of a polynomial with galois group An or Sn.

Groups

·The IsNormal command for fp-groups has been corrected to use the inverses of the group generators as well as the generators when conjugating, possibly correcting results for infinite groups. Bug reported by A. Previtali.

·Filtering in the Subgroups command has been fixed, particularly for finding simple subgroups. Bug reported by J. Schmidt.

·A bug in permutation groups, triggered when applying IsConjugate to a pair of sequences longer than the base length of the group, has been fixed. Bug reported by V. Gebhardt.

·A crash when computing the kernel of a homomorphism with domain an infinite abelian group has been fixed. Bug reported by S. Siksek.

·The constructions of the various projective orthogonal groups as permutation groups (functions PGO, PSO, POmega, PGOPlus, PSOPlus, POmegaPlus, PGOMinus, PSOMinus, POmegaMinus) have been adjusted so that all are subgroups of the corresponding PGO group.

Hyperelliptic Curves

·A bug occurring in CanonicalHeight has been fixed. Reported by A. Brumer.

Incidence Structures

·A crash in BlockGroup of an incidence structure has been fixed. Bug reported by A. Munemasa.

Local Fields

·A bug in the creation of an arbitrary local field as an extension of a ramified extension which was an extension of an unramified extension has been fixed.

Modules over Dedekind Domains

·A problem involving zero-ideals was causing internal errors in ElementaryDivisors, reported by M. H. Sengun.

Number Fields

·A bug in accessing individual coefficients of number field elements using square brackets has been fixed. The bug could result in memory corruption. Reported by M. Grassl.

·A bug in CoprimeBasis on trivial input would cause runtime errors because of untyped empty sequences.

·A bug in FixedField when the group is trivial was fixed.

·The creation of zero ideals via 0*R where R is an order is now permitted.

Quadratic Fields

·A badly chosen square root in the conversion between ideals and quadratic fields would sometimes result in the conjugate ideal being used.

·The subconstructor for orders of quadratic fields has been fixed to allow more general constructs. Reported by J. Voight.