Change log for Magma V2.14-16 (Released 10/9/2008)

Associative Algebras

·Equality of ideals of orders of associative algebras over the rational field has been fixed.

Coding Theory

·A crash in IsLinear has been fixed. Reported by M. Grassl.

Diophantine Equations

·A crash in solving Thue equations has been fixed. Reported by E. Gonzalez-Jimenez.

Elliptic Curves

·Fixed a bug in isogenies that would cause crashes or invalid answers when trying to get preimages of a point defined over an extension of the field used to define the isogeny.

Galois Theory

·A bug in MSumPolynomial has been fixed. For certain input Magma internal errors could have been triggered. Reported by J. KlŸners.

·A problem in SolveByRadicals that would induce a runtime error due to some non-optimal prime has been fixed.

·A problem in the computation of Galois groups of reducible linear polynomials has been fixed.

Groups

·A crash in the permutation group EARNS routine (called by several other routines, including SylowSubgroup) has been fixed. Bug reported by Florian MÃ¶ller.

·A hang in order computation for matrix groups defined over number fields has been fixed.

·A bug in construction of subgroups of matrix groups has been corrected. Bug reported by Eamonn O'Brien (as a Centralizer call).

·Some missing files used by ClassicalMaximals have been added. Bug reported by Eamonn O'Brien.

Local Fields

·A bug in SplittingField for polynomials over p-adic fields was fixed. In certain circumstances the field returned was too small, in particular the unramified part could have been too small. Reported and fixed by T. Dokchitser.

·IsIrreducible for polynomials over local rings and fields and series rings and fields and extensions of has been corrected.

·An internal function checking polynomials for squarefreeness was using a wrong test. As a result, MinimalPolyomial would in certain cases return wrong results. Reported by Ch. Greve.

·The function implementing DefiningPolynomial for towers of local rings was wrong, resulting in either reducible polynomials or polynomials of wrong degree in certain examples. Reported by Ch. Greve.

·There have been several bug fixes to factorization of polynomials over local rings.

·Norm and trace computations in ramified extensions where the precision is not divisible by the ramification degree wrongly returned results with too high precision. Reported by N. Bruin.

Modules over Dedekind Domains

·Pseudo matricies over the integers or a polynomial ring are now printed consistent with other Magma matrices.

·For certain pairs of modules over Dedekind domains, a bug in the code for elementary divisors would result in runtime errors. Discovered by S. Glasby.

Number Fields

·A bug in norm eqautions for number fields of degree 2 has been fixed. During the translation to a conic a wrong sign was used. Reported by M. Kirschmer.

·The intrinsic SUnitAction could, on illegal input, enter an infinite loop that would eventually run out of memory. This has been fixed by introducing more strict argument checks, in particular it is now verified that the set of ideals is closed under the action induced by the map. Problem reported by J. Voight.

·A rare case in AutomorphismGroup for absolutely normal fields would cause internal errors in certain cases.

Polynomial Rings

·A crash in polynomial quotient rings has been fixed. Reported by D. Alexander.

·A memory leak in polynomial quotient rings has been fixed.

·A bug in polynomial factorization over the integers has been fixed (coming out of CentralIdempotents). Reported by G. Wiese.

·A bug in polynomial factorization over finite fields with non-standard extensions has been fixed. Reported by M. Zieve.

Quadratic Fields

·A problem in the map returned from the class group computation would cause soem elements in the abstract abeian group to be internally non-normalized resulting in strange behaviour.

·Denominators of ideals in quadratic fields were ignored when computing generators for principal ideals via quadratic forms.

Quaternion Algebras

·Missing parentheses in printing elements have been fixed. Reported by M. Zieve.

·Attempted creation of orders of quaternion algebras which are not really orders has been fixed to check for non orders sooner.

Schemes

·A bug in checks on creation of maps between schemes has been fixed. Reported by J. Cremona.

Sparse Matrices

·Checks have been inserted for incompatible operations on sparse matrices. Reported by M. Grassl.

System

·A buffer overflow in the line editor code was fixed: certain files read using iload could trigger internal errors. Reported by M. Kida.