Change log for Magma V2.16-7 (Released 25/3/2010)

Algebraic Geometry

·HeightOnAmbient now works over a number field defined by a non-monic integral polynomial. Reported by T. Fisher.

Commutative Algebra

·A crash in IsRadical for ideals in a direct product of an affine and a projective space has been fixed. Reported by B. Smith.

Cones and Fans

·Fixed a minor bug when calculating the preimage in a very special case.

Cones and Polyhedra

·An internal change to the code structure prevented the user from defining an EmptyPolyhedron, with corresponding problems when performing calculations on toric divisors. This has been fixed.

Elliptic Curves

·Bugs in Chabauty for elliptic curves have been corrected. Reported by N. Bruin.

Galois Groups

·An incorrect assertion in GaloisGroup for a reducible polynomial has been removed.

·A fix has been made to GaloisGroup of a function field of characteristic p. The problem may have only occurred for small p. Reported by Florian MÃ¶ller.

·A fix has been made to GaloisGroup of a function field of characteristic 2. Reported by Florian MÃ¶ller.

Groups

·A crash when computing image or kernel of homomorphisms involving the GrpAuto type has been fixed. Reported by D. Holt.

·A crash in IdentifyGroup has been fixed. Reported by M. Conder.

·A bug in computing pCentralSeries has been fixed. This bug also affected code dependent on pCentralSeries, such as pClass and IsIsomorphic for p-groups. Bug reported by Marston Conder as failure in IsIsomorphic. Thanks to Eamonn O'Brien for finding the dependence on the pCentralSeries problem.

Lattices

·The EnumerationCost function for a short lattice vector enumeration with pruning was taking more time than it should. This was due to an overly pessimistic analysis of the underlying Monte Carlo algorithm. This has been fixed.

·When using the short lattice vector enumeration functions with real lattices, far too much memory was allocated. This is now fixed. Associative Algebras

·Sometimes a wrong discriminant was stored during a maximal order computation. Reported by J. Sijsling.

Number Fields

·The '@' evaluation intrinsic for a Grossencharacter now properly passes the Precision parameter to the evaluation of the infinite place(s).

·The 'in' intrinsic to test whether elements are in ideals now tries to apply automatic coercion of the element into the number field containing the ideal first.

·An error has been corrected in pSelmerGroup for a number field of degree 1 (the sign had been forgotten). Reported by S. Siksek.

Toric Geometry

·In the unusual case where the associated fan is not generated by cones of maximum dimension in the ambient lattice, previous divisor calculations were suspect. They have been fixed with this patch. Affected intrinsics are IsQCartier and IsPrincipal, along with any intrinsic that made use of them.

·GCD for multivalued sections was doing much more work than was necessary, slowing down the general mapping machinery between toric varieties. This has been corrected.