Change log for Magma V2.20-5 (Released 14/4/2014)

Binary Quadratic Forms

·For positive discriminants (with fundamental unit of norm 1), the behaviour of ReducedForms and ReducedOrbits was illogical and has been changed: now every form is equivalent to a reduced form. Note: confusion arises from the fact that the ClassGroup of binary quadratic forms in Magma is not the most natural one in the context of forms, and this was never documented. Problems reported by V. Genz.

Commutative Algebra

·A bug in IsPrime for a certain ideal has been fixed. Reported by A. Laface.

Elliptic Curves

·A bug (runtime error due to unassigned variable) has been fixed in MordellWeilShaInfo(E : ShaInfo := true) for E over number fields. Reported by Dan Yasaki.

Finite Fields

·A crash in discrete logarithms for non-prime finite fields in higher characteristic has been fixed. Reported by N. Freitas.

Groups

·A bug in PCGroup applied to a GrpFP has been fixed. The bug caused incorrect results to be returned when PCGroup was applied to an fp-group which did not have a presentation computed. The bug was reported by W. Becker.

·A bug in the computation of the centralizer of a finite subgroup of SL(n,) has been fixed. Bug reported by Tamas Korodi.

·Unwanted printing in the NilpotentQuotient has been turned off. Bug reported by E. O'Brien.

·The printing of a group character table has been fixed. In the past, the formatting of the character table caused integer character values over 2^30 (including large character degrees) to be incorrectly printed. This has been corrected. There was no problem in the printing of an individual character. Bug reported by E. O'Brien.

Invariant Rings

·A proper check has been included so that the base ring of an invariant ring is always a field. Reported by H. Roozbehan.

Modules

·A bug in Norm for vectors over orders of cyclotomic fields has been fixed. Reported by D. Dursthoff.

Number Fields

·Upgrades to the class group algorithm are included, so that the ClassGroup (under GRH) is now faster for difficult examples (i.e. large discriminant).

·SUnitGroup is now feasible for fields where the class group computation uses a large factor base.

·Various problems with computations involving units have been fixed. In occasional instances, a crash (internal error) was encountered. In other occasional instances, an incorrect answer was returned, such as a false unit, or an incorrect ideal generator. Reported by J. Klueners and M. Stoll.

·Slowness in producing the IndependentUnits for some fields has been improved. Reported by M. Stoll.

·A bug has been fixed which caused the Regulator of particular quadratic fields to be wrong (due to total loss of precision). Reported by J. Jones.

·Algorithms for unit groups that were selected by parameters "Dirichlet", "Mixed", "Relation", "Short" are now never used (parameters will be ignored). Use of these algorithms sometimes resulted in incorrect answers. Reported by J. Klueners.

·Magma now uses the LLL algorithm of Nguyen and Stehle (L^2) for many number field calculations, replacing the usage of KANT-based LLL and MLLL methods. In particular, an infinite loop when taking the LLL of an order with large denominator (thus causing underflow in double-precision) has been eliminated.

·A bug has been fixed concerning precision of the real and complex images of elements (or bases of orders). The complexity of the change of basis transformation by which the element is defined is now taken into account. The bug made certain computations impossible, including the class group of some fields of moderate or large degree.

·Bugs in expanding power product representations have been fixed.

Polytopes

·A potential bug in MinkowskiDecomposition has been fixed. This could incorrectly result in claiming that a higher-dimensional lattice simplex was indecomposable.

Real Numbers

·The MinimalPolynomial intrinsic has been changed to always return a polynomial with positive leading coefficient. A crash (memory corruption) with polynomials of degree 1 was also fixed.

·The deprecated intrinsics LinearRelation and PowerRelation of real or complex numbers now only use the "LLL" option, and ignore the "Hastad" option in all cases. The latter was quite buggy and never achieved as good as results in any event. The newer intrinsics to use (present for many versions by now) are IntegerRelation and MinimalPolynomial.

Relations

·Several crashes have been fixed when creating relations of items that are not group elements.

Transcendental Functions

·An internal issue with the norm of complex number with differing real and imaginary relative precisions has been patched. However, for some intrinsics such as the Polylog, the user must still some exercise caution in the arguments they pass to the function.