Elementary Differentials as LaTeXString (#140)

* Added function that returns the elementary differentials as latexstrings

* Now using \prime instead of '

* Implemented requested changes

* Update LaTeXStrings version in Project.toml

Co-authored-by: Hendrik Ranocha <ranocha@users.noreply.github.com>

* Update docstrings for elementary_differential in src/RootedTrees.jl

Co-authored-by: Hendrik Ranocha <ranocha@users.noreply.github.com>

* Update test/Project.toml

Co-authored-by: Hendrik Ranocha <ranocha@users.noreply.github.com>

* Added whitespace after comma. Changed that for the tests, too. Added picture of rendered LaTeXStrings to docs

* Changes by formatter

---------

Co-authored-by: Hendrik Ranocha <ranocha@users.noreply.github.com>

Author: pw0lf

Project.toml

@@ -1,9 +1,10 @@
 name = "RootedTrees"
 uuid = "47965b36-3f3e-11e9-0dcf-4570dfd42a8c"
 authors = ["Hendrik Ranocha <mail@ranocha.de> and contributors"]
-version = "2.19.2"
+version = "2.20.0"
 
 [deps]
+LaTeXStrings = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
 Latexify = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Preferences = "21216c6a-2e73-6563-6e65-726566657250"
@@ -17,6 +18,7 @@ Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
 PlotsExt = "Plots"
 
 [compat]
+LaTeXStrings = "1"
 Latexify = "0.15, 0.16"
 LinearAlgebra = "1"
 Plots = "1"

docs/make.jl

@@ -18,7 +18,8 @@ DocMeta.setdocmeta!(RootedTrees,
 # as necessary
 open(joinpath(@__DIR__, "src", "license.md"), "w") do io
     # Point to source license file
-    println(io, """
+    println(io,
+            """
     ```@meta
     EditURL = "https://github.com/SciML/RootedTrees.jl/blob/main/LICENSE.md"
     ```
@@ -34,7 +35,8 @@ end
 
 open(joinpath(@__DIR__, "src", "contributing.md"), "w") do io
     # Point to source license file
-    println(io, """
+    println(io,
+            """
     ```@meta
     EditURL = "https://github.com/SciML/RootedTrees.jl/blob/main/CONTRIBUTING.md"
     ```

docs/src/tutorials/basics.md

@@ -73,6 +73,17 @@ savefig("basics_tree.png"); nothing # hide
 
 ![](basics_tree.png)
 
+To get the elementary differential, corresponding to a `RootedTree`, as a [`LaTeXString`](https://github.com/JuliaStrings/LaTeXStrings.jl), you can use [`elementary_differential`](@ref).
+
+```@example basics
+for t in RootedTreeIterator(4)
+    println(elementary_differential(t))
+end
+```
+In LaTeX this results in the following output:
+
+![latex-elementary_differentials](https://user-images.githubusercontent.com/125130707/282897199-4967fe07-a370-4d64-b671-84f578a52391.png)
+
 
 ## Number of trees
 

src/RootedTrees.jl

@@ -4,6 +4,8 @@ module RootedTrees
 
 using LinearAlgebra: dot
 
+using LaTeXStrings: latexstring
+
 using Latexify: Latexify
 using Preferences: @set_preferences!, @load_preference
 using RecipesBase: RecipesBase
@@ -15,7 +17,7 @@ end
 export RootedTree, rootedtree, rootedtree!, RootedTreeIterator,
        ColoredRootedTree, BicoloredRootedTree, BicoloredRootedTreeIterator
 
-export butcher_representation
+export butcher_representation, elementary_differential
 
 export α, β, γ, density, σ, symmetry, order, root_color
 
@@ -25,7 +27,8 @@ export count_trees
 
 export subtrees, SubtreeIterator
 
-export partition_forest, PartitionForestIterator,
+export partition_forest,
+       PartitionForestIterator,
        partition_skeleton,
        all_partitions, PartitionIterator
 
@@ -1009,8 +1012,10 @@ end
 
 Base.IteratorSize(::Type{<:PartitionIterator}) = Base.HasLength()
 Base.length(partitions::PartitionIterator) = 2^length(partitions.edge_set)
-function Base.eltype(::Type{PartitionIterator{TreeInput, TreeOutput}}) where {TreeInput,
-                                                                              TreeOutput}
+function Base.eltype(::Type{
+                            PartitionIterator{TreeInput, TreeOutput}
+                            }) where {TreeInput,
+                                      TreeOutput}
     Tuple{PartitionForestIterator{TreeOutput}, TreeOutput}
 end
 
@@ -1053,10 +1058,13 @@ end
 end
 
 # necessary for simple and convenient use since the iterates may be modified
-function Base.collect(partitions::PartitionIterator{TreeInput, TreeOutput}) where {
-                                                                                   TreeInput,
-                                                                                   TreeOutput
-                                                                                   }
+function Base.collect(partitions::PartitionIterator{
+                                                    TreeInput,
+                                                    TreeOutput
+                                                    }) where {
+                                                              TreeInput,
+                                                              TreeOutput
+                                                              }
     iterates = Vector{Tuple{Vector{TreeOutput}, TreeOutput}}()
     sizehint!(iterates, length(partitions))
     for (forest, skeleton) in partitions
@@ -1413,6 +1421,42 @@ function butcher_representation(t::RootedTree, normalize::Bool = true)
     return result
 end
 
+"""
+    elementary_differential(t::RootedTree)
+
+Returns the elementary differential as a `LaTeXString`
+from the package [LaTeXStrings.jl](https://github.com/JuliaStrings/LaTeXStrings.jl).
+
+"""
+function elementary_differential(t::RootedTree)
+    return latexstring(rec_elementary_differential(t))
+end
+
+# Function used to go recursively through the RootedTree 
+# to generate the elementary differential of the tree.
+function rec_elementary_differential(t::RootedTree)
+    subtree_strings = String[]
+    for subtree in SubtreeIterator(t)
+        push!(subtree_strings, rec_elementary_differential(subtree))
+    end
+    k = length(subtree_strings)
+    if k == 0 # Special-Case: No Subtree
+        return "f"
+    elseif k == 1 # Special-Case: Just 1 Subtree. No () needed
+        return "f^{\\prime}" * subtree_strings[1]
+    end
+    if k in (2, 3) # For first, second and third derivative \prime is used. For the rest just the number of the derivative
+        el_diff = "f^{$("\\prime"^k)}("
+    else
+        el_diff = "f^{($(k))}("
+    end
+    for s in subtree_strings[1:(end - 1)]
+        el_diff *= s * ", "
+    end
+    el_diff *= subtree_strings[end] * ")"
+    return el_diff
+end
+
 include("colored_trees.jl")
 include("latexify.jl")
 include("plot_recipes.jl")

test/Project.toml

@@ -1,12 +1,14 @@
 [deps]
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
+LaTeXStrings = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
 Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 UnicodePlots = "b8865327-cd53-5732-bb35-84acbb429228"
 
 [compat]
 Aqua = "0.8"
+LaTeXStrings = "1"
 Plots = "1"
 StaticArrays = "1.3"
 UnicodePlots = "2, 3"

test/runtests.jl

@@ -7,6 +7,8 @@ using RootedTrees.Latexify: latexify
 using Plots: Plots, plot
 Plots.unicodeplots()
 
+using LaTeXStrings: @L_str
+
 using Aqua: Aqua
 
 @testset "RootedTrees" begin
@@ -301,6 +303,7 @@ using Aqua: Aqua
             @test isempty(RootedTrees.subtrees(t1))
             @test butcher_representation(empty(t1)) == "∅"
             @test RootedTrees.latexify(empty(t1)) == "\\varnothing"
+            @test elementary_differential(t1) == L"$f$"
 
             @inferred order(t1)
             @inferred σ(t1)
@@ -321,6 +324,7 @@ using Aqua: Aqua
             @test RootedTrees.latexify(t2) == latex_string
             @test latexify(t2) == latex_string
             @test RootedTrees.subtrees(t2) == [rootedtree([2])]
+            @test elementary_differential(t2) == L"$f^{\prime}f$"
 
             t3 = rootedtree([1, 2, 2])
             @test order(t3) == 3
@@ -334,6 +338,7 @@ using Aqua: Aqua
             @test RootedTrees.latexify(t3) == latex_string
             @test latexify(t3) == latex_string
             @test RootedTrees.subtrees(t3) == [rootedtree([2]), rootedtree([2])]
+            @test elementary_differential(t3) == L"$f^{\prime\prime}(f, f)$"
 
             t4 = rootedtree([1, 2, 3])
             @test order(t4) == 3
@@ -347,6 +352,7 @@ using Aqua: Aqua
             @test RootedTrees.latexify(t4) == latex_string
             @test latexify(t4) == latex_string
             @test RootedTrees.subtrees(t4) == [rootedtree([2, 3])]
+            @test elementary_differential(t4) == L"$f^{\prime}f^{\prime}f$"
 
             t5 = rootedtree([1, 2, 2, 2])
             @test order(t5) == 4
@@ -358,6 +364,7 @@ using Aqua: Aqua
             @test butcher_representation(t5) == "[τ³]"
             @test RootedTrees.subtrees(t5) ==
                   [rootedtree([2]), rootedtree([2]), rootedtree([2])]
+            @test elementary_differential(t5) == L"$f^{\prime\prime\prime}(f, f, f)$"
 
             t6 = rootedtree([1, 2, 2, 3])
             @inferred RootedTrees.subtrees(t6)
@@ -369,6 +376,7 @@ using Aqua: Aqua
             @test t6 == t2 ∘ t2 == t4 ∘ t1
             @test butcher_representation(t6) == "[[τ]τ]"
             @test RootedTrees.subtrees(t6) == [rootedtree([2, 3]), rootedtree([2])]
+            @test elementary_differential(t6) == L"$f^{\prime\prime}(f^{\prime}f, f)$"
 
             t7 = rootedtree([1, 2, 3, 3])
             @test order(t7) == 4
@@ -377,6 +385,7 @@ using Aqua: Aqua
             @test β(t7) == α(t7) * γ(t7)
             @test t7 == t1 ∘ t3
             @test butcher_representation(t7) == "[[τ²]]"
+            @test elementary_differential(t7) == L"$f^{\prime}f^{\prime\prime}(f, f)$"
 
             t8 = rootedtree([1, 2, 3, 4])
             @test order(t8) == 4
@@ -385,6 +394,7 @@ using Aqua: Aqua
             @test α(t8) == 1
             @test t8 == t1 ∘ t4
             @test butcher_representation(t8) == "[[[τ]]]"
+            @test elementary_differential(t8) == L"$f^{\prime}f^{\prime}f^{\prime}f$"
 
             t9 = rootedtree([1, 2, 2, 2, 2])
             @test order(t9) == 5
@@ -394,6 +404,7 @@ using Aqua: Aqua
             @test β(t9) == α(t9) * γ(t9)
             @test t9 == t5 ∘ t1
             @test butcher_representation(t9) == "[τ⁴]"
+            @test elementary_differential(t9) == L"$f^{(4)}(f, f, f, f)$"
 
             t10 = rootedtree([1, 2, 2, 2, 3])
             @test order(t10) == 5
@@ -403,6 +414,8 @@ using Aqua: Aqua
             @test β(t10) == α(t10) * γ(t10)
             @test t10 == t3 ∘ t2 == t6 ∘ t1
             @test butcher_representation(t10) == "[[τ]τ²]"
+            @test elementary_differential(t10) ==
+                  L"$f^{\prime\prime\prime}(f^{\prime}f, f, f)$"
 
             t11 = rootedtree([1, 2, 2, 3, 3])
             @test order(t11) == 5
@@ -411,6 +424,8 @@ using Aqua: Aqua
             @test α(t11) == 4
             @test t11 == t2 ∘ t3 == t7 ∘ t1
             @test butcher_representation(t11) == "[[τ²]τ]"
+            @test elementary_differential(t11) ==
+                  L"$f^{\prime\prime}(f^{\prime\prime}(f, f), f)$"
 
             t12 = rootedtree([1, 2, 2, 3, 4])
             @test order(t12) == 5
@@ -420,6 +435,8 @@ using Aqua: Aqua
             @test β(t12) == α(t12) * γ(t12)
             @test t12 == t2 ∘ t4 == t8 ∘ t1
             @test butcher_representation(t12) == "[[[τ]]τ]"
+            @test elementary_differential(t12) ==
+                  L"$f^{\prime\prime}(f^{\prime}f^{\prime}f, f)$"
 
             t13 = rootedtree([1, 2, 3, 2, 3])
             @test order(t13) == 5
@@ -429,6 +446,8 @@ using Aqua: Aqua
             @test β(t13) == α(t13) * γ(t13)
             @test t13 == t4 ∘ t2
             @test butcher_representation(t13) == "[[τ][τ]]"
+            @test elementary_differential(t13) ==
+                  L"$f^{\prime\prime}(f^{\prime}f, f^{\prime}f)$"
 
             t14 = rootedtree([1, 2, 3, 3, 3])
             @test order(t14) == 5
@@ -438,6 +457,8 @@ using Aqua: Aqua
             @test β(t14) == α(t14) * γ(t14)
             @test t14 == t1 ∘ t5
             @test butcher_representation(t14) == "[[τ³]]"
+            @test elementary_differential(t14) ==
+                  L"$f^{\prime}f^{\prime\prime\prime}(f, f, f)$"
 
             t15 = rootedtree([1, 2, 3, 3, 4])
             @test order(t15) == 5
@@ -447,6 +468,8 @@ using Aqua: Aqua
             @test β(t15) == α(t15) * γ(t15)
             @test t15 == t1 ∘ t6
             @test butcher_representation(t15) == "[[[τ]τ]]"
+            @test elementary_differential(t15) ==
+                  L"$f^{\prime}f^{\prime\prime}(f^{\prime}f, f)$"
 
             t16 = rootedtree([1, 2, 3, 4, 4])
             @test order(t16) == 5
@@ -456,6 +479,8 @@ using Aqua: Aqua
             @test β(t16) == α(t16) * γ(t16)
             @test t16 == t1 ∘ t7
             @test butcher_representation(t16) == "[[[τ²]]]"
+            @test elementary_differential(t16) ==
+                  L"$f^{\prime}f^{\prime}f^{\prime\prime}(f, f)$"
 
             t17 = rootedtree([1, 2, 3, 4, 5])
             @test order(t17) == 5
@@ -465,6 +490,8 @@ using Aqua: Aqua
             @test β(t17) == α(t17) * γ(t17)
             @test t17 == t1 ∘ t8
             @test butcher_representation(t17) == "[[[[τ]]]]"
+            @test elementary_differential(t17) ==
+                  L"$f^{\prime}f^{\prime}f^{\prime}f^{\prime}f$"
 
             # test non-canonical representation
             level_sequence = [1, 2, 3, 2, 3, 4, 2, 3, 2, 3, 4, 5, 6, 2, 3, 4]