Some more documentation progress

docs/LocalPreferences.toml

@@ -0,0 +1,2 @@
+[SUNRepresentations]
+display_mode = "dimension"

docs/make.jl

@@ -7,14 +7,18 @@ using DocumenterInterLinks
 
 links = InterLinks(
     "MatrixAlgebraKit" => "https://quantumkithub.github.io/MatrixAlgebraKit.jl/stable/",
-    "TensorOperations" => "https://quantumkithub.github.io/TensorOperations.jl/stable/"
+    "TensorOperations" => "https://quantumkithub.github.io/TensorOperations.jl/stable/",
+    "TensorKitSectors" => "https://quantumkithub.github.io/TensorKitSectors.jl/dev/"
 )
 
 pages = [
     "Home" => "index.md",
     "Manual" => [
         "man/intro.md", "man/tutorial.md",
-        "man/spaces.md", "man/sectors.md", "man/tensors.md",
+        "man/spaces.md", "man/symmetries.md",
+        "man/sectors.md", "man/gradedspaces.md",
+        "man/fusiontrees.md", "man/tensors.md",
+        "man/tensormanipulations.md",
     ],
     "Library" => [
         "lib/sectors.md", "lib/fusiontrees.md",

docs/src/index.md

@@ -8,34 +8,23 @@ CurrentModule = TensorKit
 
 ## Package summary
 
-TensorKit.jl aims to be a generic package for working with tensors as they appear throughout
-the physical sciences. TensorKit implements a parametric type [`Tensor`](@ref) (which is
-actually a specific case of the type [`TensorMap`](@ref)) and defines for these types a
-number of vector space operations (scalar multiplication, addition, norms and inner
-products), index operations (permutations) and linear algebra operations (multiplication,
-factorizations). Finally, tensor contractions can be performed using the `@tensor` macro
-from [TensorOperations.jl](https://github.com/QuantumKitHub/TensorOperations.jl).
-
-Currently, most effort is oriented towards tensors as they appear in the context of quantum
-many-body physics and in particular the field of tensor networks. Such tensors often have
-large dimensions and take on a specific structure when symmetries are present. By employing
-concepts from category theory, we can represent and manipulate tensors with a large
-variety of symmetries, including abelian and non-abelian symmetries, fermionic statistics,
-as well as generalized (a.k.a. non-invertible or anyonic) symmetries.
-
-At the same time, TensorKit.jl focusses on computational efficiency and performance. The
-underlying storage of a tensor's data can be any `DenseArray`. When the data is stored
-in main memory (corresponding to `Array`), multiple CPUs can be leveraged as many
-operations come with multithreaded implementations, either by distributing the different
-blocks in case of a structured tensor (i.e. with symmetries) or by using multithreading
-provided by the package [Strided.jl](https://github.com/Jutho/Strided.jl). Support for 
-storing and manipulating tensors on NVidia and AMD GPUs is currently being developed,
-whereas support for distributed arrays is planned for the future.
+TensorKit.jl aims to be a generic package for working with tensors as they appear throughout the physical sciences.
+TensorKit implements a parametric type [`Tensor`](@ref) (which is actually a specific case of the type [`TensorMap`](@ref)) and defines for these types a number of vector space operations (scalar multiplication, addition, norms and inner products), index operations (permutations) and linear algebra operations (multiplication, factorizations).
+Finally, tensor contractions can be performed using the `@tensor` macro from [TensorOperations.jl](https://github.com/QuantumKitHub/TensorOperations.jl).
+
+Currently, most effort is oriented towards tensors as they appear in the context of quantum many-body physics and in particular the field of tensor networks.
+Such tensors often have large dimensions and take on a specific structure when symmetries are present.
+By employing concepts from category theory, we can represent and manipulate tensors with a large variety of symmetries, including abelian and non-abelian symmetries, fermionic statistics, as well as generalized (a.k.a. non-invertible or anyonic) symmetries.
+
+At the same time, TensorKit.jl focusses on computational efficiency and performance.
+The underlying storage of a tensor's data can be any `DenseArray`.
+When the data is stored in main memory (corresponding to `Array`), multiple CPUs can be leveraged as many operations come with multithreaded implementations, either by distributing the different blocks in case of a structured tensor (i.e. with symmetries) or by using multithreading provided by the package [Strided.jl](https://github.com/Jutho/Strided.jl).
+Support for storing and manipulating tensors on Nvidia and AMD GPUs is currently being developed, whereas support for distributed arrays is planned for the future.
 
 ## Contents of the manual
 
 ```@contents
-Pages = ["man/intro.md", "man/spaces.md", "man/sectors.md", "man/tensors.md"]
+Pages = ["man/intro.md", "man/spaces.md", "man/symmetries.md", "man/sectors.md", "man/gradedspaces.md", "man/fusiontrees.md", "man/tensors.md", "man/tensormanipulations.md"]
 Depth = 2
 ```
 

docs/src/lib/fusiontrees.md

@@ -31,8 +31,7 @@ braid(f::FusionTree{I,N}, levels::NTuple{N,Int}, p::NTuple{N,Int}) where {I<:Sec
 permute(f::FusionTree{I,N}, p::NTuple{N,Int}) where {I<:Sector,N}
 ```
 
-These can be composed to implement elementary manipulations of fusion-splitting tree pairs,
-according to the following methods
+These can be composed to implement elementary manipulations of fusion-splitting tree pairs, according to the following methods
 
 ```julia
 # TODO: add documentation for the following methods
@@ -44,9 +43,8 @@ TensorKit.cycleclockwise
 TensorKit.cycleanticlockwise
 ```
 
-Finally, these are used to define large manipulations of fusion-splitting tree pairs, which
-are then used in the index manipulation of `AbstractTensorMap` objects. The following methods
-defined on fusion splitting tree pairs have an associated definition for tensors.
+Finally, these are used to define large manipulations of fusion-splitting tree pairs, which are then used in the index manipulation of `AbstractTensorMap` objects.
+The following methods defined on fusion splitting tree pairs have an associated definition for tensors.
 ```@docs
 repartition(::FusionTree{I,N₁}, ::FusionTree{I,N₂}, ::Int) where {I<:Sector,N₁,N₂}
 transpose(::FusionTree{I}, ::FusionTree{I}, ::IndexTuple{N₁}, ::IndexTuple{N₂}) where {I<:Sector,N₁,N₂}

docs/src/lib/sectors.md

@@ -35,10 +35,7 @@ TimeReversed
 ProductSector
 ```
 
-Several more concrete sector types can be found in other packages such as
-[SUNRepresentations.jl](https://github.com/QuantumKitHub/SUNRepresentations.jl),
-[CategoryData.jl](https://github.com/QuantumKitHub/CategoryData.jl),
-[QWignerSymbols.jl](https://github.com/lkdvos/QWignerSymbols.jl), ...:
+Several more concrete sector types can be found in other packages such as [SUNRepresentations.jl](https://github.com/QuantumKitHub/SUNRepresentations.jl), [CategoryData.jl](https://github.com/QuantumKitHub/CategoryData.jl), [QWignerSymbols.jl](https://github.com/lkdvos/QWignerSymbols.jl), ...:
 
 Some of these types are parameterized by a type parameter that represents a group.
 We therefore also provide a number of types to represent groups:
@@ -54,17 +51,15 @@ TensorKitSectors.Dihedral
 TensorKitSectors.ProductGroup
 ```
 
-The following types are used to characterise different properties of the different types
-of sectors:
+The following types are used to characterize different properties of the different types of sectors:
 
 ```@docs
 FusionStyle
 BraidingStyle
 UnitStyle
 ```
 
-Finally, the following auxiliary types are defined to facilitate the implementation
-of some of the methods on sectors:
+Finally, the following auxiliary types are defined to facilitate the implementation of some of the methods on sectors:
 
 ```@docs
 TensorKitSectors.SectorValues
@@ -73,8 +68,7 @@ TensorKitSectors.SectorProductIterator
 
 ## Useful constants
 
-The following constants are defined to facilitate obtaining the type associated
-with the group elements or the irreducible representations of a given group:
+The following constants are defined to facilitate obtaining the type associated with the group elements or the irreducible representations of a given group:
 
 ```@docs
 Irrep
@@ -83,8 +77,7 @@ GroupElement
 
 ## Methods for characterizing and manipulating `Sector` objects
 
-The following methods can be used to obtain properties such as topological data
-of sector objects, or to manipulate them or create related sectors:
+The following methods can be used to obtain properties such as topological data of sector objects, or to manipulate them or create related sectors:
 
 ```@docs
 unit
@@ -107,8 +100,7 @@ TensorKitSectors.sectorscalartype
 deligneproduct(::Sector, ::Sector)
 ```
 
-We have also the following methods that are specific to certain types of sectors
-and serve as accessors to their fields:
+We have also the following methods that are specific to certain types of sectors and serve as accessors to their fields:
 
 ```@docs
 charge
@@ -121,8 +113,14 @@ Furthermore, we also have one specific method acting on groups, represented as t
 ×
 ```
 
-Because we sometimes want to customize the string representation of our sector types,
-we also have the following method:
+Mapping between sectors and linear indices is only used for sectors `I` for which `Base.IteratorSize(values(I)) == HasLength()`.
+In that case, we map an index `i` to a sector `c` via `c = getindex(values(I), i)`, and provide an inverse mapping
+
+```@docs
+TensorKitSectors.findindex
+```
+
+Because we sometimes want to customize the string representation of our sector types, we also have the following method:
 
 ```@docs
 TensorKitSectors.type_repr
@@ -133,4 +131,3 @@ Finally, we provide functionality to compile all revelant methods for a sector:
 ```@docs
 TensorKitSectors.precompile_sector
 ```
-

docs/src/lib/spaces.md

@@ -21,25 +21,22 @@ ProductSpace
 HomSpace
 ```
 
-together with the following specific type for encoding the inner product structure of
-a space:
+together with the following specific type for encoding the inner product structure of a space:
 
 ```@docs
 InnerProductStyle
 ```
 
 ## Useful constants
 
-The following constants are defined to easily create the concrete type of `GradedSpace`
-associated with a given type of sector.
+The following constants are defined to easily create the concrete type of `GradedSpace` associated with a given type of sector.
 
 ```@docs
 Vect
 Rep
 ```
 
-In this respect, there are also a number of type aliases for the `GradedSpace` types
-associated with the most common sectors, namely
+In this respect, there are also a number of type aliases for the `GradedSpace` types associated with the most common sectors, namely
 
 ```julia
 const ZNSpace{N} = Vect[ZNIrrep{N}]
@@ -110,16 +107,15 @@ isepimorphic
 isisomorphic
 ```
 
-Inserting trivial space factors or removing such factors for `ProductSpace` instances
-can be done with the following methods.
+Inserting trivial space factors or removing such factors for `ProductSpace` instances can be done with the following methods.
+
 ```@docs
 insertleftunit(::ProductSpace, ::Val{i}) where {i}
 insertrightunit(::ProductSpace, ::Val{i}) where {i}
 removeunit(::ProductSpace, ::Val{i}) where {i}
 ```
 
-There are also specific methods for `HomSpace` instances, that are used in determining
-the resuling `HomSpace` after applying certain tensor operations.
+There are also specific methods for `HomSpace` instances, that are used in determining the resulting `HomSpace` after applying certain tensor operations.
 
 ```@docs
 flip(W::HomSpace{S}, I) where {S}