Change log for Magma V2.27-6 (Released 11/11/2022)

Algebraic Number Fields

·A fix has been made to the computation of GCDs of elements of quotients of orders. Reported by D. Yasaki.

·The default algorithm to compute the class group of number fields does not now use the initial sieving phase by default; to force this on, one should give the parameter Al := "Sieve" to functions ClassGroup, ClassNumber, etc.

Complex Field

·Some bugs in the computation of complex roots of polynomials where the roots were very close to each other have been fixed. Reported by J. Voight and E. Costa.

Function Fields

·The GeometricGaloisGroup computation now performs more checks on the values at which the input polynomial is specialised. Reported by D. Krumm.

Group Algebras

·The error message has been made more informative in the case that coercion of a sequence into a group algebra A fails (if the vector representation is not used in A). Issue reported by H. Johnston.

Group Theory

·The maximal subgroups of permutation and matrix groups are now cached after being computed.

Integer Ring

·A message dumped by ECPP has been suppressed.

Matrices

·Matrix multiplication over a class of finite fields GF(p^e) where p > 7, e is composite and pe > 220 has been improved (including parallelisation). Issue reported by C. Rito.

·Matrix multiplication over GF(p) for medium-sized p has been improved in the AVX2 executable.

·A bug in the algorithm for computing the Hermite Normal Form of a certain type of sparse integer matrix has been fixed. Reported by H. Johnston.

Modular Curves

·Fixed a possible crash in ModularDegree that was introduced in V2.26-6.

Multivariate Polynomials

·The input type to NewtonPolygon has been generalised to RngMPolEltGL.

·The input type to CoefficientNumerator and CoefficientDenominator has been generalised to GenMPolBElt.

Rational Field

·New function HJContinuedFraction(r) which takes a rational x and returns the sequence of partial quotients of the Hirzebruch-Jung continued fraction expansion of x. Related new function HJContinuedFractionValue(C) which takes such an expansion and returns the corresponding rational number.

Schemes

·A crash in Dimension for schemes over non-fields has been fixed. Reported by N. Katz.