Change log for Magma V2.11-3 (Released 27/7/2004)

Commutative Algebra

·A bug in the new multivariate factorization algorithm has been fixed.

·A bug when computing the reduced GrÃ¶bner basis with field polynomials over GF(2) has been fixed.

·A bug when computing GrÃ¶bner bases over p-adic rings has been fixed.

Elliptic Curves

·A crash in PseudoMordellWeilGroup has been fixed.

·LocalInformation of elliptic curves over number fields now returns the prime ideal rather than its characteristic (amongst the other information).

Groups

·An intrinsic CosetIntersection which finds the intersection of the cosets associated with two subgroups of a finitely presented abelian group has been provided.

·The sorting of class tables of PC-groups has been fixed so that the classes are reliably sorted by element order and then class size. This resolves a bug in PowerMap that occurred when this failed for PC-groups with large classes.

·The verbose flag Classes now gives information on the progress of the PC-group class table algorithms.

·A bug that occurred when finding the complements of a normal subgroup of a permutation group has been fixed.

·Evaluating the class map of a permutation group has been made more efficient.

·A bug in the Homomorphisms intrinsic for finitely presented groups has been fixed. The bug caused a crash when an FP-group with 32 generators was input. Bug reported by Eamonn O'Brien.

·The conjugacy classes of a permutation group may now be asserted to be an ordinary sequence of 3-tuples, not necessarily one constructed by a call to ConjugacyClasses.

·Maximal subgroups of PSL(11,2) corrected to include two classes of M24, conjugate under an outer automorphism. They do not extend to maximal subgroups of the automorphism group. Bug reported by Colva Roney-Dougal.

·Primitive groups database - Added a group of degree 574 (which is not in the Dixon and Mortimer list). The group is isomorphic to PSL(2,41), with point stabilizer A5. The automorphism group does not have a corresponding primitive representation. Bug reported by Colva Roney-Dougal.

·A bug when assigning indexed generator names for a braid group (assignment of the form B<[a]> := BraidGroup(5);) has been fixed. Reported by Scott Murray.

Hyperelliptic Curves

·An error that occurred in the scaling of solutions by the intrinsic HyperellipticHasPoint has been fixed.

·An error in the intrinsic Covariant, which given a binary form with real coefficients returns its covariant in the upper half-plane, has been fixed.

·There now exists a group law on Jacobians of hyperelliptic curves which have 2 rational points at infinity.

Incidence Structures

·A bug where IsDesarguesian applied to a finite affine or projective plane gave false negatives has been fixed. The same bug may also have given false negatives when testing isomorphism of finite projective planes. The speed of the IsDesarguesian function has also been increased.

·A bug in HadamardInvariant for 64-bit versions of Magma (Compaq/DEC Alpha or SPARC/Solaris) has been fixed. The sequences returned without this fix are essentially garbage. No 32-bit versions have this bug. Reported by Ilias Kotsireas.

·A bug in the Hadamard matrix database creation routines has been fixed. Without this fix, the matrices were always stored in the form they were given, even if the canonical forms are supposed to be stored.

·203 new Hadamard matrices of degree 56 and one of degree 72 have been added to the standard database. These matrices were constructed by Ilias Kotsireas using the distributed computing resources of SHARCnet.

Lie Groups

·A dramatically faster method for computing the left and right descent sets of an element of a finitely presented Coxeter group (suggested by Derek Holt) has been installed. The time taken for an example reported by Tim Honeywill dropped from 3.5 days to 80 seconds.

·A bug in the application of the function returned by RowReductionHomomorphism has been fixed.

Modules

·An error that could result in the elementary divisors of a sparse matrix being computed incorrectly has been fixed. Reported by Markus Grassl.

·Several minor memory allocation problems that can lead to unneccessary large amounts of memory to be used for real lattices have been fixed.

·A bug that prevented ExteriorPower of a G-module from being called has been fixed. Reported by Eamonn O'Brein.

Rings and Fields

·An error occurring under certain conditions when echelonizing a matrix over a number field has been fixed.

·A problem with DedekindEta where the input does not lie in a Laurent series ring has been fixed.

·An error when creating an order of a function field given a coefficient ring and a sequence of function field elements has been fixed.

·Several minor memory allocation problems that can lead to unneccessary large amounts of memory being used for number field computations have been fixed.

·A problem causing internal errors when applying ResidueClassField to an infinte place of a number field has been fixed.

Schemes

·The attempted creation of a map to a projective scheme which is not a scroll where the defining equations are not expressible as polynomials now produces a run-tme error.

Sets and Sequences

·SetToSequence now handles a null indexed set correctly.

System

·The routines for sockets are now available (UNIX platforms only).