--- title: "Magma V2.16-8 Patch Notes" canonical: "https://docs.magma-maths.org/patchnotes/2.16-8.html" source: "https://docs.magma-maths.org/patchnotes/2.16-8.md" --- # Magma V2.16-8 Patch Notes ## Algebraic Curves - A bug in `CartierRepresentation` with a multiplicity argument has been fixed. Reported by A. Elkin. ## Brandt Modules - For `HeckeOperator` at a ramified prime, an infinite loop occurred with the `ComputeGrams` option. This case is disallowed. Reported by K. Buzzard. ## Characters of Groups - A bug causing a crash has been fixed in the [`SchurIndex`](../RepresentationTheory/CharactersOfFiniteGroups/schur-index.md#function-schurindex-algchtrelt) function. ## Coding Theory - The dimension of quantum codes over extensions of degree larger than two was incorrectly calculated. This has been fixed; the dimension of a quantum code is now returned as a rational. Reported by M. Grassl. - The computation of the MacWilliams transform (of a weight distribution) has been mildly sped up. - The intrinsic [`NumberOfWords`](../CodingTheory/AdditiveCodes/structural.md#function-numberofwords-code-rngintelt) as applied to a linear code will now use the weight distribution where this is expected to be faster. (In practice, when the dual is small.) ## Coherent Sheaves - A bug in the computation of the maximal module of a sheaf (accessed by, eg, [`FullModule`](../AlgebraicGeometry/Sheaves/accessors.md#function-fullmodule-shfcoh)) has been fixed. Reported by E. Rains. ## Cryptography - Fixed a bug in the hexadecimal digit conversion used by `SHA1`, which would cause incorrect results whenever the input contained alphabetic characters. (i.e., a–f or A–F.) Reported by F. Hess. ## Elliptic Curves - Fixed a minor bug with Hints in 4-descent, to simply re-call the function when the x-coordinates are not distinct. An example with SetSeed(1) would be for [`FourDescent(x^4 - 2*x^3 + 7*x^2 + 6*x + 9)`](../ArithmeticGeometry/EllipticCurvesOverQAndNumberFields/mordell-weil.md#function-fourdescent-crvhyp) at p = 3. ## Finite Fields - A bug in [`CommonOverfield`](../BasicRings/FiniteFields/creation.md#function-commonoverfield-fldfin-fldfin) has been fixed. Reported by E. Thomé. ## Galois Groups - A fix has been made to `GaloisGroup` for a function field of characteristic p. The problem may have only occurred for small p. Reported by F. Möller. - A fix has been made to `GaloisGroup` for a function field of characteristic 2. Reported by F. Möller. - A problem with a wrong bound in [`GaloisSubfieldTower`](../GlobalFields/GaloisGroupsAndAutomorphisms/galois.md#function-galoissubfieldtower-galoisdata-grpperm) has been fixed. In same (very rare) cases where the bound was actually sharp the reconstruction failed. Reported by M. Watkins. ## Groups - The simple group recognition code for Sp4 in characteristic 2, SU3, and SU4 has been revised by Peter Brooksbank, fixing a number of bugs. - A bug giving an infinite loop in the `Simplify` command for finitely presented groups has been fixed. Bug reported by S. Humphries. - A bug causing a crash in `LowIndexSubgroups` has been fixed. Fixed by Derek Holt. - A bug in [`ClassicalMaximals`](../FiniteGroups/AlmostSimpleGroups/properties-lie-groups.md#function-classicalmaximals-monstgelt-rngintelt-rngintelt) has been fixed. There was a missing maximal subgroup of U(5,2) (missing group isomorphic to L(2,11)). Fixed by D. Holt. - Bugs in the standard form functions [`UnitaryForm`](../FiniteGroups/AlmostSimpleGroups/group-recognition.md#function-unitaryform-grpmat) and `QuadraticForm` have been fixed. There were problems producing standard forms of odd degree. Fixed by D. Holt. - The function `IsHomomorphism` for matrix groups is described in the manual but was not implemented. It is now implemented. Reported by A. Munemasa. - A bug in the `MaximalSubgroups` code for families PSp(4,q), PSU(3,q), and PSU(4,q) has been rectified. The bug caused an infinite loop, but no incorrect results were returned. F. by Derek Holt. - The quotient group constructor G/N has been extended to return the quotient group and, when two return values are assigned, the corresponding epimorphism. - A spurious line in the printing of a subgroup lattice has been removed. Also the order of printing has been reversed, so the whole group, and then maximal subgroups, come at the top. ## Hilbert modular forms - A failure in [`HilbertCuspForms`](../ModularArithmeticGeometry/HilbertModularForms/creation.md#function-hilbertcuspforms-fldnum-rngordidl-seqenum) over `NumberField(x^2-2869)` has been fixed. Reported by J. Bryk. ## Lattices - A bug in the computation of the inverse of the quotient map of a lattice by a sublattice has been fixed. Bug reported by N. Scheithauer. ## Lists - Indexing a list by a sequence now works for ranged sequences as well. ## Local Fields - (Trivial) code to access the Frobenius of a local field has been added. Reported by A. Elkin. - New code to obtain the Verschiebung of a local field has been added. Requested by A. Elkin. ## Matrices - When creating a matrix by coercion of a sequence into the parent structure, the sequence is now allowed to be a sequence of sequences. ## Number Fields - Fixed a bug in `IsPrincipal` for fractional ideals in non-maximal orders. In this case sometime principality would not get recognized or wrong generators could be returned. Reported by M. Kirschmer and J. Klüners. - A problem in the code for the norm computation of elements in product representation could sometimes produce inconsistent results. - A problem in the prime decomposition code would sometimes use special methods for Kummer extensions when not appropriate, resulting in ideals that are wrongly labelled prime. - Added a function to obtain ring class fields from non-maximal orders. - Fixed the code for Hilbert90 which would occasionally generate errors for correct input. Also, the result would frequently lie in a different ring from the input. - The code for computing the gcd of a sequence of algebraic numbers had difficulties with short lists and lists containing too many zero elements. In this case a runtime error would be triggered. - The function [`UnitGroupAsSubgroup`](../GlobalFields/NumberFieldsAndOrders/unit-group.md#function-unitgroupassubgroup-rngord) was trying to use a variable before assigning it, resulting in runtime errors. Reported by J. Klüners. ## Polynomial Rings - A crash when computing the cardinality of a module over a residue ring has been fixed. Reported by M. Grassl. - A crash when computing the roots of a polynomial over a local ring which it could not be coerced into has been fixed. - A crash when calling multivariate GCD over several different finite fields has been fixed. Reported by T. Fisher. ## Quaternion Algebras - LeftIdealClasses now return left ideals not right ideals. Reported by K. Buzzard. - Several bugs in `MaximalOrder` and `HilbertSymbol` for quaternion algebras have been fixed. Reported by J. Sisling, S. Donnelly. - Enumerate also works for quaternion orders and ideals over Z. ## Schemes - Various changes have been made to [`PointSearch`](../AlgebraicGeometry/Schemes/anfs.md#function-pointsearch-sch-fldrat-rngintelt). The first is to allow the user to avoid singularity checks via a flag. The second is a bug fix for umbilical points that could cause some small points to be missed. This was reported by T. Fisher and N. Bruin. - A long-standing issue with `IsProjective`, `IsAffine`, and [`EmptySubscheme`](../AlgebraicGeometry/Schemes/schemes-creation.md#function-emptysubscheme-sch) in which incorrect answers could be returned in certain exceptional cases has been fixed. These intrinsics now take advantage of the toric geometry package when appropriate. ## Simplicial Complexes - A bug in the computation of the boundary maps of the chain complex of a simplicial complex has been fixed. Bug reported by S. Humphries. ## System - Fixed a bug that could occur under rare circumstances when package code called an eval which triggered the load of other package code.