Change log for Magma V2.15-13 (Released 28/8/2009)

Arithmetic Geometry

·A problem with TensorProduct with LSeries has been fixed. The "weight" of the tensor product should now be correct for GL(2) (for instance, when tensoring two elliptic curves, or more generally two modular forms).

·A problem with PointSearch on a Scheme has been fixed. Magma would occasionally choose primes of bad reduction in its p-adic methods. Reported by K. Doerksen.

·Another problem with PointSearch on a scheme has been fixed. Magma would occasionally miss points where many derivatives vanished. An Example is: -X4 â€“ 4X3Z â€“ 2X2Z2 â€“ Y2Z2 â€“ 4XZ3 â€“ Z4 where the point (-1 : 2 : 1) was missed. The singular point (0 : 1 : 0) was also missed, and this was additionally fixed. Reported by P. Birkner.

Commutative Algebra

·The function MinimalBasis has been improved so that if the input is inhomogeneous, a grading is first sought so that a homogeneous input basis is used if possible. Issue reported by M. Reid.

Complex Fields

·Tan and Cot of complex numbers have been corrected.

Coxeter Groups

·Error messages of the form "Not a reflection group" have been changed to "Not a real reflection group" as appropriate.

·Reflection groups can now be defined over number fields of categories other than FldRat, FldCyc, and FldNum (for example FldQuad).

·BasicDegrees and BasicCodegrees work for complex reflection groups as well as real reflection groups.

·BasicDegrees and GroupOfLieType fixed for toral root data (BasicDegrees was returning [1] rather than an empty sequence).

Finite Fields

·The parameters Check and Optimize are now allowed in the ExtensionField constructor.

Function Fields

·A problem in the computation or Ray class groups in relative extensions has been fixed. Reported by A. Rigato.

Galois Groups

·A problem in the computation of the Galois group of a reducible polynomial has been fixed. Without this fix, Magma could trigger an error if at least one of the factors has a Galois group isimorphic to Sn or An. Reported by K. Morgan.

·The computation of relative invariants for intransitive groups has been changed.

Graphs

·A memory problem when dealing with edge labelled graphs has been fixed. Bug reported by E. O'Brien (when working with Cayley graphs).

Groups

·A bug in computing Subgroups, where many subgroups of large groups were missed, has been fixed.

·A bug in Extension of pc-groups, which did not allow elements of the automorphism group to be used to specify data, has been fixed. Bug reported by K. Andersen.

·The IsFree intrinsic has been modified to return true when applied to the trivial abelian group.

·A bug in the Homomorphisms function has been fixed so that domain a free group no longer gives an error message. Bug reported by E. O'Brien.

·A bug in the IsSoluble function for matrix groups has been fixed. Previously it could return true even though the routine had failed to find an answer. Now this is detected and an error results. Bug reported by D. Flannery.

·A bug in the Representations function, applied to a character of a pc-group, has been fixed.

·A bug while using the rewriting Todd-Coxeter (RACE), which caused a very large memory request, has been fixed.

·When computing PQuotient of a fp-group, in the case where no quotient map is requested and no presentation is stored, a cheaper rewriting scheme has been adopted to save time. Following alert from M. Newman.

·A slowness problem when many group homomorphisms are created has been fixed. Problem reported by M. Grassl.

Groups of Lie type

·Order fixed for toruses.

IncidenceGeometry

·Incidence geometries created from coset geometries can now be constructed using sparse graphs.

Integer Ring

·A bug involving multiplicities in CoprimeBasis has been fixed.

Lattices

·Some bugs in ClosestVectors for lattices with very large entries have been fixed.

Matrix Spaces

·Better support for action of matrix space elements on module elements and submodules has been added (image of submodule, preimage of element and submodule).

Number Fields

·A problem in the computation of maximal orders of abelian extensions has been fixed. In the case that the extension is of exponent 2, wrong (too small) maximal orders were returned on occaison.

Polynomial Rings

·A crash in multivariate factorization with high degree polynomials has been fixed and related speedups have been achieved. Reported by M. Grassl.

Series Rings

·A bug has been fixed in Roots of polynomials over series rings with low precision.

·Coercion of rational functions into series rings over the integer ring has been fixed (this involved the removal of wrong coercions). Reported by R. Zeier.

p-adic Rings

·A problem in the p-adic factorisation has been fixed.