Change log for Magma V2.16-6 (Released 24/2/2010)

Associative Algebras

·Equality of orders over polynomial rings has been fixed.

·Equality of ideals of orders of quaternion algebras over rings other than orders of number fields has been fixed.

·Conjugate of ideals of orders of quaternion algebras has been fixed.

·The comparison cmpeq is now available for quaternion orders as well as associative orders.

·RightIdealClasses for indefinite algebras has been fixed.

Boolean Polynomial Rings

·A problem in NormalForm for boolean polynomials has been fixed.

Coherent Sheaves

·A bug in the internal function re-expressing a module as one over its Noether Normalising ring has been fixed. This was causing crashes in a number of sheaf intrinsics. Reported by C. Quitte (for IsLocallyFree).

·Failure of sheaf intrinsic calls due to failure of module saturation (occurs when the sheaf has non-equidimensional support or the support is of dimension zero) now produces a proper error message. Reported by C. Quitte (for an IsIsomorphic crash).

Commutative Algebra

·A crash when computing a limited-degree Groebner basis over binary polynomials has been fixed.

Cones and Polyhedra

·Fixed a bug in subset.

·Fixed a bug when Pick's formula is used to compute the Volume of a polygon under certain conditions.

·Fixed a bug that can occasionally cause the return type of Points to change when a polytope is translated by an (integral) lattice vector.

·Improved image/preimage operations for maps of sets of cones and polyhedra.

·Improved mapping code for polytopes.

·Improved the implementation of Barvinok's algorithm.

·Improved the Fourier-Motzkin implementation.

·Improved SimplicialSubdivision.

·Tightened the bounding region searched by Points, BoundaryPoints, and InteriorPoints.

·Modified the Polyhedron constructor so that slicing by a hyperplane is more intuitive.

·Modified IsFakeWeightedProjectiveSpace and IsWeightedProjectiveSpace to also return the corresponding weights.

·Renamed AllConesOfCodimension to ConesOfCodimension.

·Renamed AllConesOfDimension to Cones.

·Renamed Ehrhart to EhrhartSeries.

·Renamed IsRegular to IsSmooth to better reflect the toric context.

·Added 'cone + point'.

·Added the Barvinok intrinsic to run Barvinok's algorithm on a sequence of integer points.

·Added the FourierMotzkin intrinsic.

·Added a new Polyhedron constructor for taking hyperplane slices through a given polyhedron.

·Added PolytopeOfWPS: this implements Conrads' techniques to quickly calculate a simplex whose spanning fan corresponds to the indicated weighted projective space.

·You can now calculate the integral lattice points contained a given hyperplane slice through a cone C using the Points intrinsic.

·The toric code over the finite field GF(q) associated to a polytope can be calculated using ToricCode.

·Added BoundingBox intrinsic.

·Added NonvanishingForm for polytopes.

·Now supports face enumeration via Faces, NumberOfFaces, and FaceIndices.

·Also supports edge enumeration via Edges, NumberOfEdges, and EdgeIndices.

·The face graph of a polyhedron can be calculated via Graph.

·Added fVector and fPolynomial.

·The lattice automorphism group of of a polytope can be calculated via AutomorphismGroup.

·Added FixedPoints to return the points in P fixed by a group acting on the underlying lattice.

·Added FixedSubspaceToPolyhedron to return the subspace (realised as a polyhedron) fixed by a group action on a toric lattice.

Finitely Presented Groups

·A bug in low index normal subgroups has been fixed. Reported by M. Conder.

Function Fields

·Using the sub operator in an infinite degree extension of function fields produced an internal error rather than a user error. This has been corrected. Reported by Thomas Preu.

·A memory fix has been made to Completion of a function field at a place when the completion map was deleted without being used. Reported by C. Quitte.

General Local Fields

·Fix to mapping of elements from the ramified representation of degree 1 extensions.

·Added RelativePrecision for elements of general local fields.

·Improved mapping to the ramified representation.

·Re-implementation of FixedField using invariants rather than matrix operations.

·Added Degree of a general local field over a given coefficient ring.

L-Series

·A typo with EulerFactor for a modular form has been corrected.

·Faster code from Anton Mellit has been added for symmetric powers and tensor products.

Lattice Database

·New code to support computations involving version 0.2 has been added. This corrects various problems arising with theta series having more than 256 terms.

Linear Codes over Finite Rings

·The intrinsic KernelZ2CodeZ4 has been improved.

Matrix Groups

·The package for infinite matrix groups implemented by Eamonn O'Brien and based on algorithms of Detinko and Flannery has been revised.

Number Fields

·A problem producing an internal error when powering certain ideals in number fields has been fixed.

Schemes

·A memory problem in Module that would cause internal errors later on has been fixed. Reported by Arsen Elkin.

·A crash in the computation of RationalPoints for schemes in the zero-dimensional projective ambient has been fixed.

Toric Geometry

·Fixed a bug in the general fan constructor.

·Fixed a bug when calculating the irrelevant decomposition using IrrelevantComponents or IrrelevantGenerators.

·Modified the data returned by WeightsOfFlip.

·Made Resolution deterministic and significantly faster.

·Renamed Hilbert to HilbertSeries.

·Renamed ProductFan to Fan.

·A new ToricVariety constructor allows the creation of a rank 2 toric variety using data of a torus quotient.

·Added a ToricVariety constructor that does not require the user to specify the quotient weights.

·Also added ToricVariety constructors to unify the creation of projective space, weighted projective space, and fake weighted projective space.

·Added IsSingular.

·Added Terminalisation and Canonicalisation.

·Added Degree to calculate the degree of the nef and big divisor D on its associated complete toric variety X.

Toric Lattices

·Fixed printing of 0-dimensional lattice points.

Valuation Rings

·A problem with non-uniqueness of remainders (leading to non-unique Groebner bases) has been fixed. Reported by C. Quitte.