Change log for Magma V2.15-8 (Released 30/3/2009)

Coding Theory

·A crash in LDPCDecode has been fixed. Reported by M. Grassl.

Elliptic Curves

·TwoDescent has been modified to also return maps. Similarly with TwoCover.

·DualIsogeny has been rewritten. Previously it was correct only up to an automorphism; now the composite of the given and its dual is guaranteed to equal multiplication by m, where m is the degree of the isogeny.

·Some errors in IsogenyFromKernel have been corrected.

·PushThroughIsogeny now works faster.

·Improved the equality comparison of isogenies so that different presentations of the same isogeny are correctly identified as equal more often.

·Improved the speed of MultiplicationByMMap for larger values of m, and fixed several bugs in the characteristic 2 case.

·A change to the amount of real precision in QuarticReduce was made, which was a problem in some cases of using the descent machinery.

·An bug has been fixed concerning reduction of plane cubics (occurring as genus one models of degree 3, or as curves returned by ThreeDescent).

Function Fields

·Some incorrect answers from Expand and the application of completion maps have been fixed. Reported by G. Moehlmann.

Galois Groups

·A crash in SolveByRadicals has been fixed. Reported by A. Previtali.

Groups

·A crash when comparing two group homomorphisms for equality has been corrected. Bug reported by S. Guest.

·A bug when computing conjugacy classes of a matrix group has been corrected. Bug reported by S. Guest.

·A crash computing NormalLattice of a matrix group has been fixed. Bug reported by H. Coutts.

Hilbert Modular Forms

·A serious oversight in the initial choices has been corrected. This would only have affected Hecke operators at primes dividing the level. (The choice of right ideal classes for a definite quaternion order was not made carefully enough.)

·The precomputation phase is now massively faster for number fields of degree  â‰¥ 8, due to greater care in lattice searches.

Hyperelliptic Curves

·The intrinsics taking a sequence of 3 G2 invariants now accept sequences of integers which are converted to rationals. The geometric autorphism groups returned for genus 2 curves are now permutation groups (GrpPerm) rather than finitely-presented groups (GrpFP).

Invariant Theory

·A bug in FundamentalInvariants for invariant rings of reductive groups has been fixed. Reported by M. Vogt.

Lattices

·A long-standing bug in the 2-adic genus of a lattice was fixed; e.g., pAdicDiagonalization(LatticeWithGram(DiagonalMatrix([4,6])),2) gave the wrong result. Reported by N. Scheithauer.

·A crash in ShortestVectors has been fixed. Reported by R. Marinier.

·A crash when taking an ActionGenerator of a G-Lattice has been fixed. Bug reported by M. Watkins.

Polynomial Rings

·A crash when creating polynomial rings over fields of fractions has been fixed. Reported by K. Binder.

·A crash when computing the discriminant of the zero multivariate polynomial has been fixed. Reported by A. Brumer.

·An incorrect result for squarefree factorization of bivariate polynomials in small characteristic has been fixed. Reported by P. Lisonek.

Real Numbers

·A convergence problem when using Root in fixed low-precision real fields has been fixed. Reported by R. Cossett.

Sparse Matrices

·A bug in ModularSolution would result in a crash whenever Lanczos was selected without also selecting verbose output. Reported by C. Diem.