Title: Change log for Magma V2.19-5
Author: Computational Algebra Group

Change log for Magma V2.19-5 (Released 11/4/2013)

Algebraic Curves

•The new intrinsics IntersectionNumbers have been exported.

•The Automorphisms intrinsic has been sped-up when the argument is a CrvHyp by linking to the special hyperelliptic curve code for automorphisms. Changed after a report from John Doyle.

Algebraic Function Fields

•The Poles of an element which has denominator with respect to the finite maximal order which is not squarefree has been fixed. Reported by M. Derickx.

Coding Theory

•A possible crash in BCHCode for dimensions near 2^15 (or greater) has been fixed. Reported by Darcy Best.

Elliptic Curves

•A runtime error which occurred in one case of AutomorphismGroup has been fixed. Reported by Ben Smith.

Galois Groups

•The Bound computation for ProdSum invariants of type RngSLPolElt has been fixed.

•Evaluation of RngSLPolElt at sequences not represented explicitly has been fixed.

•The efficiency of invariants has been improved, especially computing Bound and NumberOfOperations of such.

•A few improvements have been made to the computation of Galois groups of polynomials over characteristic p function fields.

Groebner Bases

•A crash when computing sygyzies over polynomial rings over residue class fields has been fixed. Reported by F. Lunnon.

Groups - Finite

•The database of irreducible quasisimple matrix groups having degrees up to 100 has had a number of small errors corrected. In some cases these errors prevented a group from being read from the database. In addition, the group 3U35 in degree 48 is included for the first time. The problems were reported by Claus Fieker. The errors were corrected by Derek Holt; the missing representation of 3U35 was constructed by Allan Steel.

•A new function ClassicalRewrite has been added to the CompositionTree package which allows the user to write an arbitrary element of a classical group as an SLP in its standard generators. A special version, ClassicalRewriteNatural, performs the same task for a classical group in its natural representation. The new code was prepared by Csaba Schneider.

•A bug causing a crash in LowIndexSubgroups when applied to a permutation group has been fixed.

Groups - Finitely Presented

•A crash when the intrinsic Homomorphisms was applied to a finitely-presented Coxeter group has been fixed. This also fixes a crash when applying SimpleQuotients to such a group.

Groups - Soluble

•A bug whereby an incomplete subgroup lattice of a pc-group was stored in the group as if it were the complete subgroup lattice has been fixed. This led to subsequent calls to Subgroups intrinsics returning incomplete answers. Bug reported by Gabriel Verret.

•A bug (giving a runtime error) in the routines for computing cohomology of pc-groups has been fixed. Bug reported by Stephen Humphries, fixed by Eamonn O'Brien and Ronan Egan.

Hyperelliptic Curve

•A runtime error which occurred in RankBound has been fixed. Reported by Jeremy Rouse

LSeries

•The LSeries of a real Dirichlet character could return the values -1, 0, and +1 in a cyclotomic field (rather than the integers) when defined via a large DirichletGroup. Reported by T. Ward.

Local Rings and Fields

•Direct coercion has been enabled, for instance, from a p-adic ring or field into an extension of a p-adic ring or field of a differing precision. Reported by Tim Dokchitser.

Matrices

•A bug in OrthogonalizeGram for matrices over a non-rational field has been fixed.

Multivariate Polynomial Rings

•A bug in DiagonalForm for quadratic polynomial forms which was itself caused by a bug in OrthogonalizeGram has been fixed.

Number Fields

•In ClassGroup, occasionally an internal error occurred with the message "Bug in class group/unit computations!". This has been fixed. Reported by Daniel Mayer.

•ClassGroup for fields of large degree was getting stuck unnecessarily (attempting to compute field automorphisms), even when the (heuristic) class group computation is in fact feasible. This no longer occurs.

•The GrossenTwist intrinsic erroneously had its return type given as the non-existent "Grossenchar" rather than GrossenChar. Reported by D. R. Kohel.

•A repeated instance of an automorphism has been removed when Automorphisms is applied to a field of fractions of an order.

Polynomials

•A patch for a problem with complex Roots was made, though the fix is only for the given case, and may cause problems elsewhere.

•Slowness when performing polynomial operations over large residue class rings has been fixed. Reported by J. Klueners.

Schemes

•A memory bug in the construction of scheme maps has been fixed. Reported by Claude Quitte.

•Checking for projective spaces which are not scrolls has been improved.

Sets

•The construction of a set now insists that coercion of something into that universe is possible so that empty sets cannot be constructed when the universe does not have a corresponding element type.

Surfaces

•A bug in HasOnlySimpleSingularities and IsSimpleSurfaceSingularity has been fixed. Reported by Eric Rains.

•An error in the signature for IsSimpleSurfaceSingularity has been fixed. Occasional crashes caused by a bug in DiagonalForm (see below) have been eliminated.

•New surface constructors, RationalRuledSurface, RandomCompleteIntersection and KummerSurfaceScheme have been exported.