Change log for Magma V2.25-9 (Released 4/3/2021)

Class Field Theory

·A crash in HeckeCharacterGroup due to equal but non identical orders has been fixed. Reported by M. Kida.

Elliptic and Hyperelliptic Curves

·A crash in EllipticCurveSearch due to insufficient precision has been fixed. Reported by A. Brumer. Fixed by J. Cremona.

·A problem with various descent routines has been fixed, ultimately due to insufficient precision being used, with an inexact zero then being tested for squareness. Reported by J. Rouse.

·A change in recent releases of Magma which caused large computations undertaken by EllipticCurveSearch to hang has been fixed.

·A problem when the user specifies insufficient precision for hyperelliptic curve intrinsics such as CanonicalHeight and ReducedBasis has been fixed. Reported by M. Stoll.

·An error in Minzlaff's code when computing the zeta function (ZetaFunction) of a superelliptic curve over Fpn for n > 2 has been reported and fixed by A. Best.

Galois Theory

·The roots returned by GaloisSplittingField when given a polynomial over a number field were sometimes wrong. This has been fixed.

Groebner Bases

·The function GroebnerBasis when applied to an ideal or set/sequence of polynomials now has a second return value D which gives the sequence of degrees encountered in each step of the F4 algorithm (whether computing the easy GB before a conversion, or a direct F4 computation), when that is non-trivial. The function EasyIdeal similarly now has a second return value D giving the sequence of degrees encountered when computing the easy basis (the third return value is now the isomorphism map which used to be the second return value). Feature requested by F. Sauer and R. Minko.

·A crash in computing Groebner bases over the field GF(2k) for k = 2,3,4 has been fixed. Reported by D. Craven.

·A crash in computing primary decomposition over algebraically closed fields has been fixed. Reported by F. Sauer.

Group Theory

·TameGenus is a new package produced by P.A. Brooksbank, J. Maglione, and J.B. Wilson. It provides the basis for polynomial time algorithms for computing automorphism groups and deciding isomorphism for "tame genus" p-groups: these include d-generator groups of order p(d + 2), exponent p, and class 2. The HB documentation will be available in the next release.

·A correction have been made to the Atlas database of representations for quasisimple groups. Representation number 24 for the group 2J2d2 has been replaced by the correct representation.

Integer Ring

·A rare crash in ECPP (coming from IsPrime) has been fixed. Reported by J. Gimble.

Lie Algebras

·The closure algorithm for the computation of subalgebras of Lie algebras has been greatly improved, particularly in the case of large sparse algebras in characteristic zero. Issue reported and problem input supplied by R. Zeier.

Multilinear Algebra

·An upgrade of the package for multilinear algebra to the version released August, 2020 has been installed. Changes have been made to improve performance and to fix some bugs. The package was created and is maintained by P. A. Brooksbank, J. Maglione and J. B. Wilson. Updated HB documentation will be available in the next release.

Polynomial Rings

·A crash in multivariate polynomial GCD over finite fields has been fixed. Reported by L. Kay Jin.

·Some automatic coercions are now handled properly with chains of mixed univariate/polynomial rings. Issue reported by M. Zieve.

Representation Theory

·A crash in IsIsomorphic for G-modules over finite fields has been fixed. Reported by D. Holt.

·The IsIsomorphic algorithm for G-modules over finite fields has been improved, so that the initial tests for non-isomorphism are much stronger, fixing slow behaviour for certain inputs. Behaviour reported by D. Benson.

·A crash in intrinsic IrreducibleModules when applied to a KG-module, where K is the rationals, has been fixed. Reported by U Thiel.

·A crash in intrinsic Constituents when applied to a KG-module, where K is a cyclotomic field, has been fixed. Reported by U Thiel.

Sparse Matrices

·The efficiency of the function Submatrix(S, I, J where S is a sparse matrix and I,J are index sequences has been greatly improved. Issue reported by J. Gibson.

System

·Fixed a possible crash during Detach if the package file had multiple intrinsics with the same signature. Reported by T. Keller.

·Some miscellaneous crashes when more than 2^30 handles were in use have been fixed.

Thue Equations

·A crash in the intrinsic Solutions when solving certain Thue equations has been fixed. Reported by A. Gherga.

Vector Spaces

·The *:= operator has been improved for vector space elements. Issue reported by M. Grassl.