Magma V2.13-8 Patch Notes

Arithmetic Geometry¶

• Some bugs in the characteristic two canonical lift code for point-counting on hyperelliptic curves/Jacobians have been fixed.

Elliptic Curves¶

• In TwoSelmerGroup for curves over number fields, some further precision problems have now been handled.

Finite Fields¶

• A bug in IsPower(a, n) for large values of n over large fields has been fixed. Arbitrarily large n is now supported for the first time. Bug reported by Eamonn O'Brien.

Galois Groups¶

• A bug in the Galois group package that would occasionally introduce an infinite loop using more and more memory has been fixed.

Groups¶

• Two functions called Transversal have been added for the class of finite finitely-presented Coxeter groups. These give minimal length right- and double-coset representatives for standard parabolic subgroups (specified by a set of integers). Algorithms supplied by Bob Howlett.
• For matrix groups, a bug in the implementation of the Murray-O'Brien base point selection method has been fixed. Bug reported by Eamonn O'Brien.
• A bug in the recognition of non-generic orthogonal plus matrix groups over finite fields has been fixed. Bug reported by Mark Stather.

Module Theory¶

• A bug in the Meataxe algorithm in rare cases involving the endomorphism ring has been fixed (the bug was only in V2.13).

Number Fields¶

• Generators of a fractional ideal in non-maximal order would return an inconsistent eltseq. This has been fixed.
• Decomposition of elements of field of fractions of non-maximal orders would cause an internal error to be triggered. The decomposition of such elements (into prime ideals) has been disabled as it is in general not unique.

Polynomials¶

• A bug in polynomial factorization over integers, where a reducible polynomial was very occasionally considered irreducible, has been fixed.