Change log for Magma V2.15-5 (Released 23/1/2009)

Algebraic Curves

·A sporadic bug in Genus introduced into the latest major release has been fixed. Reported by B. Smith.

Coding Theory

·A crash when printing a code defined over a large finite field extension has been fixed. Reported by A. Previtali.

Elliptic Curves

·A bug in QuadraticTwist and QuadraticTwists that gave the wrong answer for some curves with j=1728 (namely those over a finite field of size = 3 mod 4) has been fixed. A further change is that QuadraticTwist(E) now has a second, boolean return value. For certain curves with j=0 over finite fields of characteristic 2, no quadratic twist (ie a curve isomorphic to the original over the quadratic extension of the base field but not over the base field) exists. In these cases, the returned curve is isomorphic to the original and the second return value is false. In all other cases the return value is the unique (up to isomorphism) quadratic twist and the second return value is true. Reported by H. Hubrechts.

·WeilDescent had a bug that returned an incorrect divisor map when the descended curve wasn't of hyperelliptic type. This has now been fixed.

Groups

·A crash when computing conjugacy classes of matrix groups with base ring the integers modulo N has been fixed.

·A crash when computing subgroups of Coxeter groups with type GrpPermCox has been fixed.

·A bug in the PC-group function IsConditioned has been fixed. The bug caused some presentations that were not conditioned to be treated as a conditioned, and may have been the cause of many problems. Bug (manifesting as a crash in CharacterTable) reported by S. Humphries.

Hyperelliptic Curves

·A bug that caused a rare crash in computing the orders of jacobians or Euler factors of genus 2 hyperelliptic curves has been fixed. Reported by S. Siksek.

Rings

·A bug in Ngens would trigger user errors whenever a ring with 0 generators was used. Reported by E. O'Brien.

Schemes

·A bug in SingularSubscheme that caused an error for non-reduced schemes whose singular subscheme is the entire scheme, has been fixed. Reported by F. Gounelas.