specified AbstractFrameBundle, etc

chakravala · Jul 26, 2024 · d2189c4 · d2189c4
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diff --git a/Project.toml b/Project.toml
@@ -1,7 +1,7 @@
 name = "Cartan"
 uuid = "e24af43f-9fd5-4672-9264-a75f3ae40eb2"
 authors = ["Michael Reed"]
-version = "0.2.0"
+version = "0.3.0"
 
 [deps]
 Requires = "ae029012-a4dd-5104-9daa-d747884805df"
@@ -12,7 +12,7 @@ LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 [compat]
 julia = "1"
 Requires = "1"
-Grassmann = "0.8"
+Grassmann = "0.8, 0.9"
 
 [extras]
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

diff --git a/README.md b/README.md
@@ -12,35 +12,42 @@
 [![Gitter](https://badges.gitter.im/Grassmann-jl/community.svg)](https://gitter.im/Grassmann-jl/community?utm_source=badge&utm_medium=badge&utm_campaign=pr-badge)
 [![Build status](https://ci.appveyor.com/api/projects/status/klhdg493nvs0oi7h?svg=true)](https://ci.appveyor.com/project/chakravala/cartan-jl)
 
-Provides `TensorField{B,F,N} <: GlobalFiber{LocalTensor{B,F},N}` implementation for both a local `ProductSpace` topology and the simplicial mesh topologies imported with [Grassmann.jl](https://github.com/chakravala/Grassmann.jl).
+Provides `TensorField{B,F,N} <: GlobalFiber{LocalTensor{B,F},N}` implementation for both a local `ProductSpace` and general `ImmersedTopology` specifications on any `AbstractFrameBundle` expressed with [Grassmann.jl](https://github.com/chakravala/Grassmann.jl) algebra.
 Many of these modular methods can work on input meshes or product topologies of any dimension, although there are some methods which are specialized.
 Building on this, `Cartan` provides an algebra for any `GlobalSection` and associated bundles on a manifold, such as general `Connection` and `CovariantDerivative` operators in terms of `Grassmann` elements.
 Utility package for differential geometry and tensor calculus intended for packages such as [Adapode.jl](https://github.com/chakravala/Adapode.jl).
 
 The `Cartan` package is intended to standardize the composition of various methods and functors applied to specialized categories transformed with a unified representation over a product topology, especially having fibers of the `Grassmann` algebra.
-Initial topologies include `ProductSpace` types and implicitly simplicial manifolds.
+Initial topologies include `ProductSpace` types and in general the `ImmersedTopology`.
 ```
-RealRegion{V, T} where {V, T<:Real} (alias for ProductSpace{V, T, N, N, S} where {V, T<:Real, N, S<:AbstractArray{T, 1}})
-Interval (alias for ProductSpace{V, T, 1, 1} where {V, T})
+Positions{P, G} where {P<:Chain, G} (alias for AbstractArray{<:Coordinate{P, G}, 1} where {P<:Chain, G})
+Interval{P, G} where {P<:AbstractReal, G} (alias for AbstractArray{<:Coordinate{P, G}, 1} where {P<:Union{Real, Single{V, G, B, <:Real} where {V, G, B}, Chain{V, G, <:Real, 1} where {V, G}}, G})
+IntervalRange (alias for GridFrameBundle{P, G, 1, PA, GA} where {P<:Real, G, PA<:AbstractRange, GA})
 Rectangle (alias for ProductSpace{V, T, 2, 2} where {V, T})
 Hyperrectangle (alias for ProductSpace{V, T, 3, 3} where {V, T})
+RealRegion{V, T} where {V, T<:Real} (alias for ProductSpace{V, T, N, N, S} where {V, T<:Real, N, S<:AbstractArray{T, 1}})
+RealSpace{N, P, G} where {N, P<:(Chain{V, 1, <:Real} where V), G} (alias for AbstractArray{<:Coordinate{P, G}, N} where {N, P<:(Chain{V, 1, <:Real} where V), G})
+AlignedRegion{N, P, G, PA, GA} where {N, P<:Chain, G<:InducedMetric, PA<:(ProductSpace{V, <:Real, N, N, <:AbstractRange} where V), GA<:Global} (alias for GridFrameBundle{P, G, N, PA, GA} where {N, P<:Chain, G<:InducedMetric, PA<:(ProductSpace{V, <:Real, N, N, <:AbstractRange} where V), GA<:Global})
+AlignedSpace{N} where N (alias for GridFrameBundle{P, G, N, PA, GA} where {N, P<:Chain, G<:InducedMetric, PA<:(ProductSpace{V, <:Real, N, N, <:AbstractRange} where V), GA})
+GridFrameBundle{P,G,N,PA<:AbstractArray{P,N},GA<:AbstractArray{G,N}} <: AbstractFrameBundle{Coordinate{P,G},N}
+SimplexFrameBundle{P,G,PA<:AbstractVector{P},GA<:AbstractVector{G},TA<:ImmersedTopology} <: AbstractFrameBundle{Coordinate{P,G},1}
+FacetFrameBundle{P,G,PA,GA,TA<:ImmersedTopology} <: AbstractFrameBundle{Coordinate{P,G},1}
+AbstractFrameBundle{Coordinate{B,F},N} where {B,F,N}
 ```
 Visualizing `TensorField` reperesentations can be standardized in combination with [Makie.jl](https://github.com/MakieOrg/Makie.jl) or [UnicodePlots.jl](https://github.com/JuliaPlots/UnicodePlots.jl).
 
 Due to the versatility of the `TensorField` type instances, it's possible to disambiguate them into these type alias specifications with associated methods:
 ```Julia
-MeshFunction (alias for TensorField{B, F, 1, BA} where {B, F<:AbstractReal, BA<:ChainBundle})
-ElementFunction (alias for TensorField{B, F, 1, PA} where {B, F<:AbstractReal, PA<:(AbstractVector)})
-IntervalMap (alias for TensorField{B, F, 1, PA} where {B, F, PA<:(AbstractArray{<:Union{Real, Single{V, G, B, <:Real} where {V, G, B}, Chain{V, G, <:Real, 1} where {V, G}}, 1})})
-RectangleMap (alias for TensorField{B, F, 2, BA} where {B, F, BA<:(ProductSpace{V, T, 2, 2} where {V, T})})
-HyperrectangleMap (alias for TensorField{B, F, 3, PA} where {B, F, PA<:(ProductSpace{V, T, 3, 3} where {V, T})})
-ParametricMap (alias for TensorField{B, F, N, PA} where {B, F, N, PA<:(ProductSpace{V, T, N, N, S} where {V, T<:Real, N, S<:AbstractArray{T, 1}})})
-RealFunction (alias for TensorField{B, F, 1, PA} where {B, F<:AbstractReal, PA<:(AbstractVector{<:AbstractReal})})
-PlaneCurve (alias for TensorField{B, F, 1, PA} where {B, F<:(Chain{V, G, Q, 2} where {V, G, Q}), PA<:(AbstractVector{<:AbstractReal})})
-SpaceCurve (alias for TensorField{B, F, 1, PA} where {B, F<:(Chain{V, G, Q, 3} where {V, G, Q}), PA<:(AbstractVector{<:AbstractReal})})
-SurfaceGrid (alias for TensorField{B, F, 2, PA} where {B, F<:AbstractReal, PA<:(AbstractMatrix)})
-VolumeGrid (alias for TensorField{B, F, 3, PA} where {B, F<:AbstractReal, PA<:(AbstractArray{P, 3} where P)})
-ScalarGrid (alias for TensorField{B, F, N, PA} where {B, F<:AbstractReal, N, PA<:AbstractArray})
+ScalarMap (alias for TensorField{B, F, 1, BA} where {B, F<:AbstractReal, BA<:SimplexFrameBundle})
+IntervalMap (alias for TensorField{B, F, 1, P} where {B, F, P<:(AbstractArray{<:Coordinate{P, G}, 1} where {P<:Union{Real, Single{V, G, B, <:Real} where {V, G, B}, Chain{V, G, <:Real, 1} where {V, G}}, G})})
+RectangleMap (alias for TensorField{B, F, 2, P} where {B, F, P<:(AbstractMatrix{<:Coordinate{P, G}} where {P<:(Chain{V, 1, <:Real} where V), G})})
+HyperrectangleMap (alias for TensorField{B, F, 3, P} where {B, F, P<:(AbstractArray{<:Coordinate{P, G}, 3} where {P<:(Chain{V, 1, <:Real} where V), G})})
+ParametricMap (alias for TensorField{B, F, N, P} where {B, F, N, P<:(AbstractArray{<:Coordinate{P, G}, N} where {N, P<:(Chain{V, 1, <:Real} where V), G})})RealFunction (alias for TensorField{B, F, 1, PA} where {B, F<:AbstractReal, PA<:(AbstractVector{<:AbstractReal})})
+PlaneCurve (alias for ParametricMap (alias for TensorField{B, F, N, P} where {B, F, N, P<:(AbstractArray{<:Coordinate{P, G}, N} where {N, P<:(Chain{V, 1, <:Real} where V), G})}))
+SpaceCurve (alias for TensorField{B, F, 1, P} where {B, F<:(Chain{V, G, Q, 3} where {V, G, Q}), P<:(AbstractVector{<:Coordinate{P, G}} where {P<:AbstractReal, G})})
+SurfaceGrid (alias for TensorField{B, F, 2, P} where {B, F<:AbstractReal, P<:(AbstractMatrix{<:Coordinate{P, G}} where {P<:(Chain{V, 1, <:Real} where V), G})})
+VolumeGrid (alias for TensorField{B, F, 3, P} where {B, F<:AbstractReal, P<:(AbstractArray{<:Coordinate{P, G}, 3} where {P<:(Chain{V, 1, <:Real} where V), G})})
+ScalarGrid (alias for TensorField{B, F, N, P} where {B, F<:AbstractReal, N, P<:(AbstractArray{<:Coordinate{P, G}, N} where {P<:(Chain{V, 1, <:Real} where V), G})})
 GlobalFrame{B, N, N} where {B<:(LocalFiber{P, <:TensorNested} where P), N, N} (alias for Cartan.GlobalSection{B, N, N1, BA, FA} where {B<:(LocalFiber{P, <:TensorNested} where P), N, N1, BA, FA<:AbstractArray{N, N1}})
 DiagonalField (alias for TensorField{B, F} where {B, F<:DiagonalOperator})
 EndomorphismField (alias for TensorField{B, F} where {B, F<:(TensorOperator{V, V, T} where {V, T<:(TensorAlgebra{V, <:TensorAlgebra{V}})})})