SageManifolds metaticket 2

[Eric Gourgoulhon]

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

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

Algebraic part

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

Topological manifolds

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

Manifold subsets

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

Differentiable manifolds

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

Pseudo-Riemannian manifolds

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

Poisson manifolds

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

Complex and almost complex manifolds

• #18786: almost complex structures through Hodge structures