--- title: "Magma V2.16-6 Patch Notes" canonical: "https://docs.magma-maths.org/patchnotes/2.16-6.html" source: "https://docs.magma-maths.org/patchnotes/2.16-6.md" --- # 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`](../MagmaLanguage/StatementsAndExpressions/boolean.md#operation-operation-cmpeq-any-any-boolelt) is now available for quaternion orders as well as associative orders. - [`RightIdealClasses`](../Algebras/QuaternionAlgebras/ideal-theory.md#function-rightidealclasses-algquatord) 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`](../AlgebraicGeometry/Sheaves/shf:preds.md#function-shf-loc-free)). - 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`](../AlgebraicGeometry/ToricVarieties/toric-fans.md#function-simplicialsubdivision-torfan). - Tightened the bounding region searched by `Points`, [`BoundaryPoints`](../Geometry/Polytopes/combinatorics.md#function-boundarypoints-torpol), and [`InteriorPoints`](../Geometry/Polytopes/combinatorics.md#function-interiorpoints-torpol). - Modified the `Polyhedron` constructor so that slicing by a hyperplane is more intuitive. - Modified [`IsFakeWeightedProjectiveSpace`](../AlgebraicGeometry/ToricVarieties/toric-varieties.md#function-isfakeweightedprojectivespace-torvar) and [`IsWeightedProjectiveSpace`](../AlgebraicGeometry/ToricVarieties/toric-varieties.md#function-isweightedprojectivespace-torvar) to also return the corresponding weights. - Renamed `AllConesOfCodimension` to [`ConesOfCodimension`](../AlgebraicGeometry/ToricVarieties/toric-fans.md#function-conesofcodimension-torfan-rngintelt). - Renamed `AllConesOfDimension` to [`Cones`](../AlgebraicGeometry/ToricVarieties/toric-fans.md#function-cones-torfan). - Renamed `Ehrhart` to [`EhrhartSeries`](../Geometry/Polytopes/combinatorics.md#function-ehrhartseries-torpol). - Renamed `IsRegular` to [`IsSmooth`](../AlgebraicGeometry/ToricVarieties/toric-cones-and-polyhedra.md#function-issmooth-torpol) 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`](../Geometry/Polytopes/polytopes-cones-polyhedra.md#function-polytopeofwps-rngintelt): 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`](../CodingTheory/AlgebraicGeometricCodes/decode-2.md#function-toriccode-torpol-rngintelt). - Added [`BoundingBox`](../Geometry/Polytopes/polytopes-cones-polyhedra.md#function-boundingbox-torpol) intrinsic. - Added `NonvanishingForm` for polytopes. - Now supports face enumeration via `Faces`, `NumberOfFaces`, and [`FaceIndices`](../Geometry/Polytopes/basic-combinatorics.md#function-faceindices-torpol-rngintelt). - Also supports edge enumeration via `Edges`, `NumberOfEdges`, and `EdgeIndices`. - The face graph of a polyhedron can be calculated via `Graph`. - Added [`fVector`](../Geometry/Polytopes/basic-combinatorics.md#function-fvector-torcon) 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`](../Geometry/Polytopes/polytopes-cones-polyhedra.md#function-fixedsubspacetopolyhedron-grpmat) 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`](../CodingTheory/LinearCodesOverZ4/z4-invar.md#function-kernelz2codez4-codelinrng) 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`](../AlgebraicGeometry/ToricVarieties/cox-rings.md#function-irrelevantcomponents-rngcox) or [`IrrelevantGenerators`](../AlgebraicGeometry/ToricVarieties/cox-rings.md#function-irrelevantgenerators-rngcox). - Modified the data returned by [`WeightsOfFlip`](../AlgebraicGeometry/ToricVarieties/toric-geometry.md#function-weightsofflip-torvar-rngintelt). - 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.