Magma V2.16-6 Patch Notes

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.