This metaticket collects tickets related to manifolds in Sage 9.3 or higher. For the initial implementation of manifolds in Sage up to version 9.2, see the metaticket 1: #18528.

The works listed here result from the SageManifolds project, developed by the following authors.

Generic

• Add a bit of typing to manifold code #29775: Add a bit of typing to manifold code (merged in Sage 9.6.beta7)
• Metaticket - SageManifolds Code Improvement Discussion #30139: Metaticket about manifold code improvement
• Replace __eq__ by _richcmp_ for manifolds #30116: Replace __eq__ by _richcmp_ for manifolds
• Unicode operators for sage.manifolds #30473: Unicode operators for sage.manifolds (merged in Sage 9.4.beta5)
• Delete Deprecated Features #30554: Metaticket: Deprecated features
• Add Examples to Manifolds Catalog #30189: Metaticket: Add examples to manifold catalog
• Add Folder for Manifold Examples #30799: Add folder for manifold examples (merged in Sage 9.3.beta0)
• Add more typing information to manifold package #31006: Add more typing information to manifold package (merged in Sage 9.6.rc0)
• fix some typos in manifolds/ #31202: Fix some typos in src/sage/manifolds/ (merged in Sage 9.3.beta9)
• Forgetful Functors for Manifold Objects #31241; Forgetful functors for manifold objects
• Remove Python 2 compatibility from manifolds #31704: Remove Python 2 compatibility from manifolds (merged in Sage 9.4.beta2)
• Restructure manifold module #32274: Restructure manifold module
• Fix a few documentation issues in manifolds #32457: Fix a few documentation issues in manifolds (merged in Sage 9.5.beta2)
• sage.tensor, sage.manifolds: __copy__, __deepcopy__ methods for all classes that define "copy" methods #32476: __copy__, __deepcopy__ methods for all classes that define copy methods
• Invoke manifolds with structure more conveniently #33001: Invoke manifolds with structure more conveniently (merged in Sage 9.6.beta3)
• Some performance improvements in the manifolds code #33110: Some performance improvements in the manifolds code (merged in Sage 9.6.beta2)
• sage.manifolds, sage.tensor: Fix spelling errors #33539: sage.manifolds, sage.tensor: Fix spelling errors (merged in Sage 9.6.beta7)
• Fix docstring markup in sage/manifolds #34158: Fix docstring markup in sage/manifolds (merged in Sage 9.7.beta7)
• sage.manifolds, sage.tensor: Remove imports from sage.arith.all, sage.rings.all #34428: sage.manifolds, sage.tensor: Remove imports from sage.arith.all, sage.rings.all (merged in Sage 9.7.rc0)
• modernize super in manifolds/ #34532: modernize super() in sage.manifolds (merged in Sage 9.8.beta1)

Algebraic part

• Enhance symmetry handling for tensors #28813: Enhance symmetry handling for tensors
• extension of admissible indices conventions for tensors with indices #29099: Extension of admissible indices conventions for tensors with indices
• Matrix and Components should have a sparse iterator #29619: Sparse iterator for tensor components (merged in Sage 9.8.beta0)
• Compacting the display of tensor product #29820: Compacting the display of tensor product
• Parallelization of Wedge Product #29796: Parallelization of wedge product
• sage.tensor.modules: Add SymPowerFreeModule #30095: sage.tensor.modules: Add SymPowerFreeModule
• sage.tensor.modules: Add backends using TensorFlow Core, PyTorch, SymPy #30096: sage.tensor.modules: Add backends using TensorFlow Core and PyTorch:
• Add category FreeModules (without distinguished basis) #30164: Add category FreeModules (without distinguished basis)
• Trivial coercion Modules(QQ)(FiniteRankFreeModule(QQ, 3)) fails #30174: Trivial coercion Modules(QQ)(FiniteRankFreeModule(QQ, 3)) fails (merged in Sage 9.3.beta8)
• Submodules of TensorFreeModule defined by the symmetries of a Components object #30229: Submodules of TensorFreeModule defined by the symmetries of a Components object (merged in Sage 9.8.beta0)
• Add construction methods to FiniteRankFreeModule, CombinatorialFreeModule and Cartesian products #30235: Add construction methods to FiniteRankFreeModule, CombinatorialFreeModule and Cartesian products (merged in Sage 9.7.rc0)
• New implementation class FiniteRankDualFreeModule #30241: New implementation class FiniteRankDualFreeModule (merged in Sage 9.8.beta0)
• Make ExtPowerFreeModule a quotient of TensorFreeModule #30242: Make ExtPowerFreeModule a quotient of TensorFreeModule
• FreeModuleAutomorphism should not inherit from FreeModuleTensor #30245: FreeModuleAutomorphism should not inherit from FreeModuleTensor
• Use _matmul_ operator (@) for matrix multiplication, map composition, tensor contraction #30244: Use _matmul_ operator (@)
• Phased permutation groups #30276: Phased permutation groups
• sage.tensor.modules.free_module_basis: Make Basis_abstract a subclass of AbstractFamily #30300: Make Basis_abstract a subclass of AbstractFamily (merged in Sage 9.7.rc0)
• Arithmetic on tensor module elements, manifold objects: Always Return a Copy #30302: Arithmetic on tensor module elements, manifold objects: always return a copy
• Refactor Components into parent & element #30307: Refactor Components into parent & element
• Tensor Product Method for FiniteRankFreeModule #31276: Tensor product method for FiniteRankFreeModule (merged in Sage 9.7.rc0)
• _sympy_ methods for tensor component classes #31946: _sympy_ methods for tensor component classes
• Meta-ticket: Efficient numerical computations with tensor trains #31991: Metaticket: Efficient numerical computations with tensor trains
• FiniteRankFreeModuleMorphism: Add method SVD (singular value decomposition) #31992: FiniteRankFreeModuleMorphism: Add method SVD (singular value decomposition)
• Tensor canonicalization #32028: Tensor canonicalization
• Action of a sympy TensorSymmetry #32029: Action of a SymPy TensorSymmetry
• Graphical representations of tensors #32034: Graphical representations of tensors
• Generate non-redundant indices of tensors with symmetries efficiently #32318: Generate non-redundant indices of tensors with symmetries efficiently (merged in Sage 9.5.beta1)
• Bug in multiple tensor contractions with scalar result #32355: Bug in multiple tensor contractions with scalar result (merged in Sage 9.5.beta1)
• Remove unnecessary uses of symbolic functions in sage.tensor.modules #32415: Remove unnecessary uses of symbolic functions in sage.tensor.modules (merged in Sage 9.5.beta1)
• sage.tensor.modules: remove dependency on sage.manifolds #32708: sage.tensor.modules: remove dependency on sage.manifolds (merged in Sage 9.5.beta5)
• sage.tensor.modules: make doctests involving SR optional #32712: sage.tensor.modules: make doctests involving SR optional (merged in Sage 9.5.beta5)
• Bad handling of tensor names in unary negation operator #33938: Bad handling of tensor names in unary negation operator
• Common base class for FiniteRankFreeModule and TensorFreeModule #34424: Common base class for FiniteRankFreeModule and TensorFreeModule (merged in Sage 9.7.rc0)
• TensorFreeModule.isomorphism_with_fixed_basis #34427: TensorFreeModule.isomorphism_with_fixed_basis (merged in Sage 9.8.beta0)
• Put tensor modules of FiniteRankFreeModule in Modules().TensorProducts() #34448: Put tensor modules of FiniteRankFreeModule in Modules().TensorProducts() (merged in Sage 9.8.beta1)
• sage.tensor: Canonicalize sym, antisym #34451: sage.tensor: Canonicalize sym, antisym (merged in Sage 9.8.beta0)
• Allow for tensor product of a FiniteRankFreeModule dual #34471: Allow for tensor product of a FiniteRankFreeModule dual
• Make FiniteRankFreeModule.tensor_module(0, 1) return the dual #34474: Make FiniteRankFreeModule.tensor_module(0, 1) return the dual (merged in Sage 9.8.beta0)
• FiniteRankFreeModule.tensor_from_comp: Deprecate #34482: FiniteRankFreeModule.tensor_from_comp: Deprecate
• Quotient modules of TensorFreeModule, TensorFreeSubmodule #34483: Quotient modules of TensorFreeModule, TensorFreeSubmodule
• Add method tensor_factor_index_maps to tensor products #34485: Add method tensor_factor_index_maps to tensor products
• Construction for tensor submodules with prescribed symmetries #34499: Construction for tensor submodules with prescribed symmetries
• Construction for FiniteRankDualFreeModule #34605: Construction for FiniteRankDualFreeModule
• Method dual_pairing for modules in sage.tensor #34621: Method dual_pairing for modules in sage.tensor
• Slight documentation update for modules built upon a FiniteRankFreeModule #34792: Slight documentation update for modules built upon a FiniteRankFreeModule (merged in Sage 9.8.beta5)

Topological manifolds

• Improve simplifications in calculus on manifolds #24151: Improve simplifications in calculus on manifolds
• Make simplifications in SymPy calculus on manifolds rely on SymPy only #24290: Make simplifications in SymPy calculus on manifolds rely on SymPy only
• Manifolds with boundary #30080: Manifolds with boundary
• symbolic ring, coercion, restriction: compatible? #30232: Coercion/conversion SR to ScalarFieldAlgebra
• Immutability of chart functions #30310: Immutability of chart functions (merged in Sage 9.3.beta9)
• Immutability of Scalar Fields II #30311: Immutability of scalar fields II (merged in Sage 9.4.beta0)
• Stronger Categories for Manifold Examples: Connectedness #31243: Stronger categories for manifold examples: connectedness (merged in Sage 9.3.beta7)
• product of manifolds #31371: Product of manifolds
• copy_from for scalar fields #31654: Equip scalar fields with copy_from method (merged in Sage 9.4.beta1)
• Make open subsets of immersed/embedded submanifolds immersed/embedded submanifolds #31674: Make open subsets of immersed/embedded submanifolds immersed/embedded submanifolds (merged in Sage 9.4.beta1)
• Open subsets of arbitrary subsets of manifolds #31677: Open subsets of arbitrary subsets of manifolds (merged in Sage 9.4.beta1)
• ContinuousMap.image: if map is an isomorphism and domain_subset is open, create a submanifold #31685: ContinuousMap.image: if map is an isomorphism and domain_subset is open, create a submanifold
• Sheaves on manifolds #31703: Sheaves on manifolds
• Manifold: Change some methods to generators #31720: Manifold: Change some methods to generators
• Chart.subchart_poset, superchart_poset, Manifold.chart_poset #31771: Chart.subchart_poset, superchart_poset, Manifold.chart_poset
• Pass name and latex_name to copy method in set_restriction #31854: Pass name and latex_name to copy method in set_restriction (merged in Sage 9.4.beta3)
• Refine category of ScalarField #31883: Refine category of ScalarField (merged in Sage 9.4.beta4)
• Refine categories of Chart objects, add method codomain #31894: Refine categories of Chart objects, add method codomain
• Chart: Implement pickling via __getstate__/__setstate__ #31901: Chart: Implement pickling via __getstate__/__setstate__
• The inverse of the inverse should be self in CoordChange #31923: The inverse of the inverse should be self in CoordChange (merged in Sage 9.4.beta4)
• Eliminate direct use of the Chart._domain attribute #32009: Eliminate direct use of the Chart._domain attribute (merged in Sage 9.4.beta6)
• Chart: Add init argument coord_restrictions, deprecate method add_restrictions #32102: Chart: Add init argument coord_restrictions, deprecate method add_restrictions (merged in Sage 9.4.beta6)
• Bug in Chart.__init__ regarding the determination of top charts #32112: Bug in Chart.__init__ regarding the determination of top charts (merged in Sage 9.4.beta6)
• Chart._parse_coordinates #32116: Chart._parse_coordinates (merged in Sage 9.4.beta6)
• Chart-wise assumptions #32120: Chart-wise assumptions
• Bad determination of the coordinate range when restricting charts to subdomains #32929: Bad determination of the coordinate range when restricting charts to subdomains (merged in Sage 9.5.beta8)
• Lazy transition maps #33225: Lazy transition maps
• Bug in ExpressionNice with composite variables #33399: Bug in ExpressionNice with composite variables (merged in Sage 9.6.beta4)
• Manifold.options.omit_function_arguments ineffective for arguments not in alphabetic order #33957: Manifold.options.omit_function_arguments ineffective for arguments not in alphabetic order (merged in Sage 9.7.beta4)
• Fix wrong link in the documentation of topological submanifolds #34565: Fix wrong link in the documentation of topological submanifolds (merged in Sage 9.8.beta1)

Manifold subsets

• Meta-ticket: Families, posets, complexes of manifold subsets #31740 Meta-ticket: Families, posets, complexes of manifold subsets
• declare_union yields wrong results #30263: declare_union yields wrong results
• Topological closure of manifold subsets, methods ManifoldSubset.closure, is_closed, declare_closed #31644: Topological closure of manifold subsets, methods ManifoldSubset.closure, is_closed, declare_closed (merged in Sage 9.4.beta4)
• Images of continuous maps and embedded submanifolds as manifold subsets #31653: Images of continuous maps and embedded submanifolds as manifold subsets (merged in Sage 9.4.beta1)
• Plotting subsets of real manifolds #31675: Plotting subsets of real manifolds
• Poset of manifold subsets #31680: Poset of manifold subsets (merged in Sage 9.4.beta3)
• manifolds: Add _test_... methods that check invariants of subset relations #31682: Add _test_... methods that check invariants of subset relations
• ManifoldSubset: Change some methods to generators #31718: ManifoldSubset: Change some methods to generators (merged in Sage 9.4.beta3)

Differentiable manifolds

• Automorphism fields: remove SR enforcement when computing the inverse #28629: Automorphism fields: remove SR enforcement when computing the inverse
• Manifolds: Vector Valued Forms #28640: Vector-valued forms:
• Bug in parallelized computations involving symbolic functions #27492: Bug in parallelized computations involving symbolic functions
• Inheritance Structure: Tensor Fields -> Vec. Bdl. Sections #29234: Inheritance structure: tensor fields as sections of vector bundles
• New Algorithm for Characteristic Classes #29581: New algorithm for characteristic classes (merged in Sage 9.5.beta3)
• Characteristic Classes: Sequences #30211: Characteristic classes: sequences (merged in Sage 9.4.beta0)
• Meta-ticket: Immutability for manifold objects #30261: Immutability for manifold objects
• Mixed Forms: set_comp, comp #30272: Mixed forms: set_comp, comp (merged in Sage 9.4.beta6)
• Immutability of Bundle Connections #30284: Immutability of bundle connections (merged in Sage 9.3.rc0)
• sage.manifolds: Connect to Pymanopt #30495: sage.manifolds: Connect to Pymanopt
• Tensor Arithmetics on Minimal Amount of Domains #30714: Tensor arithmetics on minimal amount of domains
• Covariant Derivatives along smooth Maps #30781: Covariant derivatives along smooth maps
• Subintervals of OpenInterval and UniqueRepresentation #30830: Subintervals of OpenInterval and UniqueRepresentation (merged in Sage 9.3.beta2)
• Connect RealSet to sage.manifolds #30832: Connect RealSet to sage.manifolds (merged in Sage 9.4.beta4)
• Documentation of Item Assignment Behavior for Bundle Connections #31215: Documentation of item assignment behavior for bundle connections (merged in Sage 9.3.beta7)
• Grassmann Manifolds #31249: Grassmann manifolds
• Follow Up: Mutability of Sections and Tensor Fields #31255: Follow up: Mutability of sections and tensor fields (merged in Sage 9.3.beta7)
• Remove deprecated form input for bundle connections #31273: Remove deprecated form input for bundle connections (merged in Sage 9.3.beta7)
• Method subs() ineffective on tensor fields #31316: Method subs() ineffective on tensor fields
• Make self-diffeomorphisms default #31323: Make self-diffeomorphisms default (merged in Sage 9.3.beta9)
• Circle doesn't have an orientation #31324: Circle doesn't have an orientation
• Add method tangent_vector to differentiable manifolds #31609: Add method tangent_vector() to differentiable manifolds (merged in Sage 9.4.beta1)
• Follow-up: provide 3-sphere with additional features #31617: Provide 3-sphere with additional features
• Simplify VectorField.__call__ #31633: Simplify VectorField.__call__ (merged in Sage 9.4.beta1)
• Slight speed-up in copy method #31658: Speeding-up copy method for tensor fields (merged in Sage 9.4.beta1)
• DifferentiableManifold.open_subset: update vector frames and change of frames #31678: DifferentiableManifold.open_subset: update vector frames and change of frames
• Turn mixed form algebra into de Rham complex #31691: Turn mixed form algebra into de Rham complex (and add de Rham cohomology) (merged in Sage 9.4.beta1)
• Refactor display behavior of mixed forms #31692: Refactor display behavior of mixed forms (merged in Sage 9.4.beta1)
• Immutability for mixed forms #31706: Immutability for mixed forms (merged in Sage 9.4.beta6)
• Mixed form name bug for pullback bundle #31784: Mixed form name bug for pullback bundle (merged in Sage 9.4.beta2)
• Replace OpenInterval, RealLine instances by instances of a subclass of DifferentiableManifold+RealSet #31878: Replace OpenInterval, RealLine instances by instances of a subclass of DifferentiableManifold + RealSet
• Pullback silently fails in some cases with multiple charts #31904: Pullback silently fails in some cases with multiple charts (merged in Sage 9.4.beta4)
• remove deprecated diff. forms #32313: Remove deprecated differential forms (merged in Sage 9.5.beta1)
• Turn De Rham Cohomology into Algebra #32270: Turn de Rham cohomology into algebra (merged in Sage 9.5.beta1)
• Allow for coordinate changes in curve plots #32578: Allow for coordinate changes in curve plots (merged in Sage 9.5.beta4)
• Natural bundles: local data (and orientations) #32974: Natural bundles: local data (and orientations)
• Add example of projective space to manifold catalog #33221: Add projective space to manifold catalog (merged in Sage 9.6.beta1)
• Add examples of tangent vector fields to curves to plot documentation #33711: Add examples of tangent vector fields to curves to plot documentation
• Issue with set_name for interior products with zero result #33780: Issue with set_name for interior products with zero result (merged in Sage 9.6.rc4)
• Total space of vector bundles #34173: Total space of vector bundles
• VectorFieldModule: Faster fast path for tensor_module, exterior_power, dual_exterior_power #34486: VectorFieldModule: Faster fast path for tensor_module, exterior_power, dual_exterior_power (merged in Sage 9.8.beta1)
• New implementation class VectorFieldDualFreeModule #34501: New implementation class VectorFieldDualFreeModule (merged in Sage 9.8.beta1)
• VectorFieldModule, TensorFieldModule, DiffFormModule: Add methods tensor_product, tensor_power, update category of TensorFieldModule #34589: VectorFieldModule, TensorFieldModule, DiffFormModule: Add methods tensor_product, tensor_power (merged in Sage 9.8.beta4)

Pseudo-Riemannian manifolds

• Enter the components of a metric while declaring #25457: Declaring a metric along with its components
• Energy momentum tensor, Einstein tensor and Einstein space-time #25500: Energy momentum tensor, Einstein tensor and Einstein space-time
• Add Spheres smoothly embedded in Euclidean Space to Manifold Catalog #30804: Add standard sphere to manifold catalog (merged in Sage 9.3.beta2)
• More Flexible Coordinate Treatment for EuclideanSpace #30824: More flexible coordinate treatment for EuclideanSpace
• Use ambient metric by default in hodge_dual #31322: Use ambient metric by default in hodge_dual (merged in Sage 9.3.beta9)
• Manifold of piecewise linear functions with k marked breakpoints #31707: Manifold of piecewise linear functions with k marked breakpoints
• Euclidean 3-space: offer several flavours of spherical coordinates #31747: Add spherical coordinates with equator-based latitude
• manifolds.Sphere: Add barycentric coordinates of spherical triangles / Whitney forms #31777: manifolds.Sphere: Add barycentric coordinates of spherical triangles / Whitney forms
• Improve handling of metrics on pseudo-Riemannian submanifolds #31781: Improve handling of metrics on pseudo-Riemannian submanifolds (merged in Sage 9.5.beta0)
• Add support for tangent_vector_eval_at for geodesics on manifolds integrated over multiple charts #31813: Add support for tangent_vector_eval_at for geodesics on manifolds integrated over multiple charts
• Move examples from sage.geometry.riemannian_manifolds to sage.manifolds #32228: Move examples from sage.geometry.riemannian_manifolds to sage.manifolds
• Sphere: improve handling of default charts #32953: Sphere: improve handling of default charts (merged in Sage 9.6.beta3)

Poisson manifolds

• Add symplectic structures #30362: Add symplectic structures (merged in Sage 9.6.beta0)

Complex and almost complex manifolds

• Implementation of Almost-Complex structures for manifolds through Hodge structures #18786: almost complex structures through Hodge structures

CC: @tscrim @mkoeppe @mjungmath @honglizhaobob

Component: manifolds

Keywords: tensor, differential geometry

Author: see ticket description

Issue created by migration from https://trac.sagemath.org/ticket/30525