Change log for Magma V2.21-11 (Released 12/3/2016)

Commutative Algebra

·A crash in Groebner basis computation of algebraic number fields of degree 1 has been fixed.

Elliptic Curve Pairings

·A problem with ReducedTatePairing has been fixed. Reported by B. Allombert.

Elliptic Curves

·An incorrect answer with Order of a torsion point over a number field has been fixed. The error was that the p-power torsion was not being bounded correctly in some cases. Reported by E. Gonzalez Jimenez.

Function Fields

·The application of the Completion mapping and use of Expand have been fixed for non-simple relative extensions.

·UnderlyingRing can now be applied to extensions of infinite degree.

·The CoveringStructure of two sets of places is now a group of divisors which all places in those sets can be coerced into.

·Automorphisms has been fixed for non-simple extensions.

·A crash involving factorization of a chain of function fields (coming from BaseChange for hyperelliptic curves) has been fixed. Reported by M. Stoll.

Groups

·An error in applying CayleyGraph to a group of type GrpFP has been fixed. Bug reported by Miles Reid.

·Incorrect printing of certain values in character tables has been fixed. The bug afflicted printing of non-integer values in a cyclotomic field of degree 2, where the magnitude of the coefficients exceeded 230. Printing of individual characters and character values was not in error. Bug reported by Eamonn O'Brien.

Lattices

·The InnerProductMatrix of a lattice over a real field is now of the correct degree.

·AutomorphismsGroup has been fixed when Bacher polynomials are used.

·ClosestVectors has been fixed in a case where the inner product matrix has large entries.

·BKZ now works for matrices whose rows are dependent. Reported by M. Kudo.

Lie Theory

·A crash caused by incorrect input to LieRepresentationDecomposition has been fixed. The crash has become a runtime error. Bug reported by Markus Grassl.

Number Fields

·Internal errors with the message "assertion order_basis_real_inv(ord) failed" can no longer occur. (This occurred where a lower bound is obtained on the eigenvalues of a real matrix. Now, appropriate precision is used for this; previously, no attempt was made to do so. This likely meant that the bound obtained was sometimes garbage; it is not known whether this was likely to cause incorrect results to be returned to the user.)

·A major problem (existing for several years) has been fixed, where calls to Completion or LocalRing would corrupt existing local rings. Reported by M. Stoll.

·A segfault which could occur during calls to various routines has been fixed. Reported by M. Stoll.

·Significant improvements have been made to conic solving. (As a consequence, descent methods are now effective for certain elliptic curves.)

·The CoveringStructure of two sets of places is now a group of divisors which all places in those sets can be coerced into.

·ChineseRemainderTheorem taking an ideal, a sequence of infinite places, an element and a sequence of signs has been fixed when the element given is in the ideal. Reported by M. Kirschmer.