Title: Change log for Magma V2.17-10
Author: Computational Algebra Group

Change log for Magma V2.17-10 (Released 29/7/2011)

Algebraic Function Fields

•A fix has been made to RayResidueRing. Reported by V. Ducet.

•Places of degree of a function field in relative extension representation has been improved to return large degree places over small degree places. These were previously missed.

Basic Algebras

•A crash in SimpleModule for basic algebras over number fields has been fixed. Reported by M. Towers.

Coding Theory

•Fixed a memory leak in the minimum weight computation of codes. Reported by M. Grassl.

•Fixed an occasional crash in the intersection of a linear and an additive code. Reported by M. Grassl.

Coxeter Groups

•Fixed the return type of Identity for finitely presented Coxeter groups.

Cyclotomic Fields

•Fixes have been made to coercion involving cyclotomic fields.

•RootOfUnity has been improved for large cyclotomic fields.

Elliptic Curves

•The CasselsTatePairing for curves over number fields was incorrect (due to the incorrect HilbertSymbol).

•The CasselsTatePairing on 4-coverings was incorrect for some elliptic curve that have a single rational 2-torsion point.

•A bug in Twists has been corrected (in the easy case, sometimes multiple representatives of the same isomorphism class were returned).

Finite Geometry

•A crash in the memory management of finite planes has been fixed.

Global Arithmetic Fields

•A fix has been made to elements of global arithmetic fields. Reported by V. Ducet.

•A fix has been made to the coercion of elements involving non-simple fields. Reported by V. Ducet.

Graphs

•A possible crash when deleting a subgraph of another graph has been fixed. Reported by E. O'Brien.

Groups

•A memory management problem to do with groups and their subgroups has been fixed.

•The permutation and matrix group function Subgroups has had an extra parameter, IndexEqual, added. The pc-group version of Subgroups already had this parameter. This brings them closer together.

•A crash computing a permutation representation of a group automorphism group has been fixed. Bug reported by D. Howden.

•The warning message about large numbers of groups from the SmallGroups command is now completely disabled by setting the parameter Warning to false. Up till now the parameter was ignored for over 100,000 groups.

Modular Symbols

•IsTwist and IsMinimalTwist failed to identity twists in some cases.

Number Fields

•Prime selection for the computation of Subfields has been improved. Reported by M. Grassl.

•Computation of Absolute orders has been fixed. Reported by D. Holmes.

•HilbertSymbol was incorrect (for odd primes); it has been replaced by faster code.

Polynomials

•Exponentiation of polynomials in characteristic p has been sped up. Reported by M. Zieve.

•I/J and quo is now allowed when I is not the full polynomial ring.

Quaternion Algebras

•QuaternionicComplement now handles algebras with non-orthogonal basis. This fixes bugs in several routines, such as isomorphism testing, for such algebras. Reported by D. Kohel.

•HilbertSymbol was incorrect (for odd primes); it has been replaced by faster code.

System

•Added the intrinsic GetTempDir to obtain the directory some functions are using to store files temporarily. On Unix-like systems this is the value of the environment variable MAGMA_TEMP_DIR, if set, and /tmp otherwise.