Change log for Magma V2.13-9 (Released 22/1/2007)

Algebraic Curves

·An incorrect filename bug has been fixed in the AutomorphismGroup functions.

Algebras

·A missing check in algebra coercion has been installed. Bug reported by M. Grassl.

·For quaternion algebras over number fields, the handling of real places has been fixed; the provious version would produce errors.

Arithmetic Geometry

·Jacobians of hyperelliptic curves: bugs have been fixed in TorsionSubgroup, TwoSelmerGroup and RankBounds. Reported by A. Brumer.

·Elliptic curves over number fields: TwoSelmerGroup has been made more efficient in the case of largish degree number fields (because certain p-adic calculations can now be done using less precision).

·The constructor EllipticCurve(C,pt) has had special cases added to deal with quadric intersections, and hyperelliptic curves in characteristic 2. The corrects a bug that arose when ZetaFunction was called for certain genus one curves over finite fields of characteristic 2.

Coding Theory

·A bug in meet for 4 codes has been fixed. Reported by G. Nebe.

·A bug which caused MinimumLeeWeight to return incorrect results for 4 codes having full rank has been fixed. Reported by N. Aydin.

Groebner Bases

·A bug in the F4 algorithm when solving systems with 32 variables over GF(2) has been fixed. Reported by Y. Seurin.

Group Theory

·A proper error test has been installed for ElementaryAbelianSeries applied to matrix groups.

·Algorithms have been installed for computing the soluble radical and radical quotient of matrix groups over rings of integers modulo n (type RngIntRes). This allows SolubleRadical, RadicalQuotient, ElementaryAbelianSeries, IsIsomorphic, AutomorphismGroup and Subgroups to be applied to this class of matrix group.

·A memory explosion when computing image and kernel of a homomorphism with domain a matrix group has been fixed. Bug reported by Derek Holt.

·A bug in the storing of characters with a group has been rectified. Bug reported by Markus Grassl.

·Routines for computing minimal coset and double coset representatives of standard parabolic subgroups in a GrpFPCox have been revised to include a length limit. These routines can now be applied to infinite Coxeter groups. Algorithms supplied by Bob Howlett.

·A crash in ToddCoxeter, when the coset table could not be constructed, has been removed; the function now correctly returns 0 in such a case. Bug reported by Mike Newman.

Invariant Theory

·A bug in computing invariants of the trivial matrix group, which occurred on Sun Sparcs, has been fixed. Reported by F. Quiring.

·The algorithms for computing primary and secondary invariants have been improved significantly.

Lie Theory

·A bug in StandardAction for certain Coxeter groups has been fixed. Reported by M. Grassl.

Local Rings

·Some fixes have been made to Factorization for polynomials over local rings and series rings.

·GaloisImage for default UnramifiedExtensions has been rewritten and is now much faster for large degree extensions.

·The constructor for UnramifiedExtension with Cyclotomic=true has been heavily speeded-up for small prime characteristics following updates to the Teichmuller lift code which gives the cyclotomic generator.

Mappings

·A bug where the type of a composite map was set incorrectly has been fixed. Bug reported by Mike Newman.

Module Theory

·A bug in the Meataxe, in the hard case where the endomorphism ring was needed, has been fixed. Reported by E. O'Brien.

Number Fields

·A bug in the code used for subset relations of orders has been fixed. Occasionally this would trigger internal errors even in standard computations of maximal orders.

Polynomial Rings

·Bugs in SquarefreePart in positive characteristic have been fixed. Reported by M. Grassl.

·A bug in polynomial quotient rings over integer residue rings has been fixed. Reported by H. Hubrechts.

Subgroups of $\mathrm{PSL}_2(\mathbb{Z})$

·A large class of congruences subgroups, defined with a character chi via CongruenceSubgroup([N,N,1],chi), had been wrongly recognised as being equal to Gamma1(N). This has been corrected and several other adjustments made so that the available functionality (including Index, FareySequence and Genus) is fully correct for all subgroups constructed using CongruenceSubgroup.