Change log for Magma V2.19-8 (Released 23/7/2013)

Algebraic Function Fields

·The prime selection when computing GaloisGroups of polynomials over function fields of prime characteristic has been improved.

·The computation of transformations in one place of the Galois group computation for reducible polynomials has been improved to avoid infinite loops.

Commutative Algebra

·Some bugs in PrimaryDecomposition and Radical involving ideals with graded orders have been fixed.

Curves

·A bug in the arithmetic and construction of automorphisms in the curve automorphism group machinery has been fixed. Reported by J. Rouse.

·A bug in the preimage of a map between a function field of a curve and its representation as an algebraic function field has been fixed. Reported by J. Rouse.

·A bug in the conversion of function field places to curve places in WeierstrassPlaces of a divisor of a curve has been fixed. Reported by M. Derickx.

Integer Factorization

·A problem with not detecting powers when stored factors were used has been resolved. For instance, pq2 where p was stored, and q large, say p is 1015 + 37 and q is 1050 + 151.

Matrices

·Some crashes involving huge matrices over medium prime finite fields have been fixed.

Orders and Algebraic Fields

·Fixed a possible crash in IsPrincipal calculations applied to order ideals.

·A few fixes supplied by J. KlÃ¼ners have been made to GaloisGroup computations.

·A fix has been made to CharacteristicPolynomial so that properties of related orders are not altered during the computation. Reported by E. Thome.

System

·The Intel 64 AVX version has been sped up for several types of Groebner basis and linear algebra computations (up to 1.5 times faster in some cases).

·User-defined types may now define a Compare intrinsic that will be used by system sorting operations.