Change log for Magma V2.12-19 (Released 10/2/2006)

Algebraic Geometry

·If called with an affine argument X, ArithmeticGenus now returns the arithmetic genus of the projective closure of X.

Arithmetic Geometry

·In Order, ZetaFunction and EulerFactor for hyperelliptic curves or their Jacobians, the lower size bound for the switch to Kedlaya's algorithm has been increased so that generic group order algorithms are used for orders less than around 1015 even in small (odd) characteristic.

·Two-Selmer groups of Jacobians: Revisions have been made to the procedures for determining the local groups J(K)â�„pJ(K). Corrections have been made to fix bugs in TwoSelmerGroupData that arose with curves such as y2 = (x2+31)(x4+312) (reported by John Merriman). Fixes have also been made to TwoSelmerGroup to repair problems that showed up with many curves, for instance y2 = x5 â€“ 2. This intrinsic should now be reliable at least for curves over Q given by minimal models. More convenient optional parameters have been provided for TwoSelmerGroupData for controlling the class group computations.

·Creating points on Jacobians from divisors: The new intrinsic JacobianPoint(J::JacHyp, D::DivCrvElt) returns the point on the Jacobian J (of a hyperelliptic curve C) associated to the divisor D on C. If D does not have degree 0, then a suitable multiple of the divisor at infinity is subtracted. When the divisor at infinity on C has even degree, D is required to have even degree. The function works for any divisor such that the corresponding point is definable in Magma. It is not implemented in characteristic 2.

·A bug in TorsionSubgroup for Jacobians has been fixed.

Commutative Algebra

·A bug in factorization of polynomials over number fields has been fixed. Reported by M. Grassl.

·Some bugs have been fixed in Normalization for affine algebras and a number of other changes have been made to improve its efficiency. A verbose flag IntCl has been added to follow the stages of the computation.

Function Fields

·The parameter Check on ext of orders of function fields has been fixed to default to true.

Graphs

·The error resulting from constructing a graph with too many vertices has been modified from an internal error to a runtime error.

Groups

·A bug in MaximalSubgroups has been fixed. The bug may have caused subgroups of groups with composition factors PSL(3,p) or PSU(3,p) to be missed.

·Two bugs in ConjugacyClasses have been fixed. The bugs occurred when the TFAl option was set to other than Default.

·Using IsIsomorphic on an insoluble group and a pc-group is now corrected. Bug reported by Kasper Andersen.

·The functions Agemo and Omega (p-groups) have been extended to allow 0 as 2nd argument. A bug in Omega has been fixed. Bug reported and extension requested by Kasper Andersen.

·Attempts to use IdentifyGroup on groups of order p7 no longer crash, but still return a runtime error, as this is not yet implemented.

Integers

·Ceiling, Floor, ContinuedFraction and BestApproximation now operate directly on integers (trivially of course). This fixes problems with insufficient precision after the conversion to reals.

·NthPrime(3) has been fixed (to return 5, not 6).

Matrix Lie Algebras

·A bug in ChangeRing has been fixed.

Number Fields

·The function NormEquation would in certain cases return a Raw representation of a solution when an explicit solution was asked for. This mainly affected relative norm equations and in particular, norm equations involving Abelian extensions (class fields).

·The function Embed would cause an internal error rather than a user error when called to create an embedding of a relative extension when the embedding of the coefficient ring was not there.

·AbsoluteAlgebra now accepts a RngMPolRes, not only a RngUPolRes.

·SafeUniformiser now works for relative extensions.

Polynomial Rings

·A bug in XGCD for rational polynomials has been fixed.

·A bug in Factorization for integral/rational multivariate polynomials has been fixed. Reported by N. Bruin.

Rational Numbers

·ContinuedFraction and BestApproximation has been provided for rational numbers directly instead of converting to real numbers first.