Change log for Magma V2.26-7 (Released 24/9/2021)

Affine Algebras

·The functions VectorSpace, Dimension, MatrixAlgebra and Algebra applied to an affine algebra Q = I/J have been fixed to include the case where I is a proper ideal. The same is now true for quotients of free algebras. Issue reported by G. Brown.

·A crash in Image for homomorphisms between modules defined over affine algebras has been fixed. Reported by J. Gibson.

Arithmetic Geometry

·A hang in polynomial factorisation arising when testing isomorphism of hyperelliptic curves has been fixed. Reported by A. Sutherland.

·A bug in the Tuitman algorithm for computing zeta functions related to precision has been fixed. Reported by M. Kyng.

·A number of optimisations have been made to parts of the Tuitman algorithm for computing zeta functions which substantially improve performance in many cases.

Coding Theory

·The intrinsic StandardForm now works for codes defined over prime-powered residue rings, not just Z4.

Commutative Algebra

·A hang in polynomial factorisation arising from isomorphism testing of hyperelliptic curves has been fixed. Reported by A. Sutherland.

·A crash in version of the F4 algorithm that uses the sparse monomial representation when there are more than 255 variables has been fixed. Reported by M. Bardi.

·A crash in Dimension for ideals with a grading containing zeros has been fixed. Reported by M. Reid.

Complex Field

·An inaccuracy in root finding over complex fields arising from computing reduced modules of hyperelliptic curves has been fixed. Reported by M. Stoll and A. Sutherland.

Galois Theory

·A precision has been increased when computing GaloisGroups of polynomials over characteristic 0 rational function fields to improve the accuracy of results. Reported by G. McGuire.

Graphs and Digraphs

·The quo operator for graphs and digraphs has been extended to return the quotient map as the 4-th return value. The domain of this map is the vertex set of the original graph, the codomain is the vertex set of the quotient graph. Preimages are supported, returning some vertex of the original graph that maps to the given vertex of the quotient. Request of J. Gibson.

Group Representations

·A bug where the characters of an abelian group could be re-ordered by the SaveCharacterTable mechanism has been fixed. Bug reported by U. Thiel.

·A TestGModule intrinsic has been added. This takes a ModGrp as input, and checks that the group representation defined by the module is valid. This is done by computing a presentation for the group and then checking that each relator evaluates to the identity.

·References to a development intrinsic AHomANF were accidentally included in previous releases, causing errors when certain intrinsics were listed. This has been fixed. Reported by E. Costa.

Group Theory

·A crash in pQuotient when certain internal structures become too large has been fixed. Now an error is raised rather than having a crash. Reported by M. Vaughan-Lee.

·Part of the word relation handling machinery has been modified so as to work with relations of length larger than two million instead of raising an internal error. Reported by M. Vaughan-Lee.

·A bug in the intrinsic meet for matrix groups that caused certain instances to run very slowly has been fixed. Reported by E. O'Brien.

·A crash caused when constructing a subgroup of a group automorphism group (type GrpAuto) has been fixed. Crash reported by D. Roe.

·Group homomorphisms for the automorphism group type have been extended to handle a sequence of group elements when defining the domain in the map constructor. Example provided by D. Roe.

·The automorphism group of a finite nilpotent group is now computed using an algorithm specific to nilpotent groups thereby bypassing the use of the error-prone intrinsic AutomorphismGroupSolubleGroup. Reported by D. Roe.

Magma Programming Language

·An attempt to define a new signature for '[]', Explode, or Sprintf now raises an error instead of crashing. Reported by E. Costa and T. Keller.

Mappings

·Error messages which may arise from some preimage computations for rule maps have been improved.

Number Fields

·A bug when inverting elements of low-degree number fields where the defining polynomial has large integer coefficients has been fixed. Reported by R. Rathbun.

·The computation of first roots of elements of number fields is now handled as a trivial case. Reported by R. Zomorrodian.

·The test for a number field being a subfield of another (intrinsic IsSubfield) no longer involves computing a maximal order. Reported by M. Grassl.

·The test for a two number fields being isomorphic (intrinsic IsIsomorphic no longer involves computing a maximal order. Reported by M. Grassl.

·The prefactorisation of the discriminant when computing a MaximalOrder has been improved.

·An improvement has been made when UsePowerProduct is true when computing PicardGroup. Further, the expansion of large powers is avoided.

·A check is made to ensure that the unit rank is at most 10 when calling intrinsic ExceptionalUnits. Reported by D. Lorenzini.