Added feature that generates the elementary weight of a rooted tree as a latexstring

Project.toml

@@ -1,7 +1,7 @@
 name = "RootedTrees"
 uuid = "47965b36-3f3e-11e9-0dcf-4570dfd42a8c"
 authors = ["Hendrik Ranocha <[email protected]> and contributors"]
-version = "2.20.0"
+version = "2.21.0"
 
 [deps]
 LaTeXStrings = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"

docs/src/tutorials/basics.md

@@ -73,17 +73,27 @@ 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).
+To get the elementary differential, corresponding to a `RootedTree`, as a [`LaTeXString`](https://github.com/JuliaStrings/LaTeXStrings.jl), you can use [`elementary_differential_latexstring`](@ref).
 
 ```@example basics
 for t in RootedTreeIterator(4)
-    println(elementary_differential(t))
+    println(elementary_differential_latexstring(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)
 
+Similarly, to get the elementary weight, corresponding to a `RootedTree`, as a [`LaTeXString`](https://github.com/JuliaStrings/LaTeXStrings.jl), you can use [`elementary_weight_latexstring`](@ref).
+
+```@example basics
+for t in RootedTreeIterator(4)
+    println(elementary_weight_latexstring(t))
+end
+```
+
+![latex elemenary weights](https://private-user-images.githubusercontent.com/125130707/298310491-8a035faf-fd1a-4fc0-92be-c3387eb53177.png?jwt=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJnaXRodWIuY29tIiwiYXVkIjoicmF3LmdpdGh1YnVzZXJjb250ZW50LmNvbSIsImtleSI6ImtleTUiLCJleHAiOjE3MDYxNjY1ODAsIm5iZiI6MTcwNjE2NjI4MCwicGF0aCI6Ii8xMjUxMzA3MDcvMjk4MzEwNDkxLThhMDM1ZmFmLWZkMWEtNGZjMC05MmJlLWMzMzg3ZWI1MzE3Ny5wbmc_WC1BbXotQWxnb3JpdGhtPUFXUzQtSE1BQy1TSEEyNTYmWC1BbXotQ3JlZGVudGlhbD1BS0lBVkNPRFlMU0E1M1BRSzRaQSUyRjIwMjQwMTI1JTJGdXMtZWFzdC0xJTJGczMlMkZhd3M0X3JlcXVlc3QmWC1BbXotRGF0ZT0yMDI0MDEyNVQwNzA0NDBaJlgtQW16LUV4cGlyZXM9MzAwJlgtQW16LVNpZ25hdHVyZT1kYzQyYjM0MWY0MDU5YWZlYzBmODA4MjFiZGIxN2E3YjhkYTdmZDNkYTU5NmI5OTEwNWFiZjg0OGZjNDg1MzZhJlgtQW16LVNpZ25lZEhlYWRlcnM9aG9zdCZhY3Rvcl9pZD0wJmtleV9pZD0wJnJlcG9faWQ9MCJ9.GB-PigOlQqenzgruzWg19qslzM6RXeX4xWwCNreOvNY)
+
 
 ## Number of trees
 

src/RootedTrees.jl

@@ -17,7 +17,8 @@ end
 export RootedTree, rootedtree, rootedtree!, RootedTreeIterator,
        ColoredRootedTree, BicoloredRootedTree, BicoloredRootedTreeIterator
 
-export butcher_representation, elementary_differential
+export butcher_representation, elementary_differential_latexstring,
+       elementary_weight_latexstring
 
 export α, β, γ, density, σ, symmetry, order, root_color
 
@@ -1417,14 +1418,16 @@ function butcher_representation(t::RootedTree, normalize::Bool = true)
     return result
 end
 
+@deprecate elementary_differential(t::RootedTree) elementary_differential_latexstring(t)
+
 """
-    elementary_differential(t::RootedTree)
+    elementary_differential_latexstring(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)
+function elementary_differential_latexstring(t::RootedTree)
     return latexstring(rec_elementary_differential(t))
 end
 
@@ -1453,6 +1456,85 @@ function rec_elementary_differential(t::RootedTree)
     return el_diff
 end
 
+"""
+    elementary_weight_latexstring(t::RootedTree)
+
+Returns the elementary_weight as a `LaTeXString`
+from the package [LaTeXStrings.jl](https://github.com/JuliaStrings/LaTeXStrings.jl).
+"""
+function elementary_weight_latexstring(t::RootedTree)
+    # Creating the alphabet for the indices
+    a = collect('d':'z') # all letters except of a,b and c
+    p = order(t)
+    n = ceil(Int, p / 23)
+    alphabet = String[]
+    # if the tree could need more than the 23 available letters, the letter get a number as a suffix
+    if n == 1
+        alphabet = [string(letter) for letter in a]
+    else
+        for i in 1:n
+            alphabet = vcat(alphabet, [letter * string(i) for letter in a])
+        end
+    end
+
+    substrings = String[]
+    first_index = splice!(alphabet, 1)
+    indices = [first_index]
+
+    substring, idx, _ = elm_weights_rec!(t, first_index, alphabet) # Call the recursive function
+    indices = vcat(indices, idx)
+    push!(substrings, substring)
+
+    pushfirst!(substrings, "\\sum_{$(join(indices,", "))}b_{$(first_index)}")
+    return latexstring(join(substrings))
+end
+
+# Function used to go recursively through the RootedTree 
+# to generate the elementary weight of the tree.
+function elm_weights_rec!(t::RootedTree, last_index, a)
+    alphabet = copy(a)
+    # leaf-node
+    if length(t.level_sequence) == 1 && t.level_sequence[1] != 1
+        return "c_{$(last_index)}", [], alphabet
+    else
+        substrings = String[]
+        indices = String[]
+        if t.level_sequence[1] != 1 # Specialcase: Complete Tree
+            push!(substrings, "a_{$(last_index),$(alphabet[1])}")
+            index = splice!(alphabet, 1)
+            push!(indices, index)
+        else
+            index = last_index
+        end
+        # counting identical trees
+        prev_tree = 0
+        tree_count = 1
+        for subtree in SubtreeIterator(t)
+            if subtree == prev_tree
+                tree_count += 1
+                continue
+                # When reaching the last one of identical trees, the substring gets the number of trees as an exponent
+            elseif tree_count > 1
+                substrings[end] = "($(substrings[end]))^{$tree_count}"
+            end
+            prev_tree = copy(subtree)
+            tree_count = 1
+            substring, idx, alphabet = elm_weights_rec!(subtree, index, alphabet)
+            indices = vcat(indices, idx)
+            push!(substrings, substring)
+        end
+        # Specialcase: The identical trees were the last ones 
+        if tree_count > 1
+            if length(prev_tree.level_sequence) == 1
+                substrings[end] = "$(substrings[end])^{$tree_count}"
+            else
+                substrings[end] = "($(substrings[end]))^{$tree_count}"
+            end
+        end
+        return join(substrings), indices, alphabet
+    end
+end
+
 include("colored_trees.jl")
 include("latexify.jl")
 include("plot_recipes.jl")

test/runtests.jl

@@ -303,7 +303,8 @@ using Aqua: Aqua
             @test isempty(RootedTrees.subtrees(t1))
             @test butcher_representation(empty(t1)) == "∅"
             @test RootedTrees.latexify(empty(t1)) == "\\varnothing"
-            @test elementary_differential(t1) == L"$f$"
+            @test elementary_differential_latexstring(t1) == L"$f$"
+            @test elementary_weight_latexstring(t1) == L"$\sum_{d}b_{d}$"
 
             @inferred order(t1)
             @inferred σ(t1)
@@ -324,7 +325,8 @@ 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"$f^{\prime}f$"
+            @test elementary_differential_latexstring(t2) == L"$f^{\prime}f$"
+            @test elementary_weight_latexstring(t2) == L"$\sum_{d}b_{d}c_{d}$"
 
             t3 = rootedtree([1, 2, 2])
             @test order(t3) == 3
@@ -338,7 +340,8 @@ 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"$f^{\prime\prime}(f, f)$"
+            @test elementary_differential_latexstring(t3) == L"$f^{\prime\prime}(f, f)$"
+            @test elementary_weight_latexstring(t3) == L"$\sum_{d}b_{d}c_{d}^{2}$"
 
             t4 = rootedtree([1, 2, 3])
             @test order(t4) == 3
@@ -352,7 +355,8 @@ 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"$f^{\prime}f^{\prime}f$"
+            @test elementary_differential_latexstring(t4) == L"$f^{\prime}f^{\prime}f$"
+            @test elementary_weight_latexstring(t4) == L"$\sum_{d, e}b_{d}a_{d,e}c_{e}$"
 
             t5 = rootedtree([1, 2, 2, 2])
             @test order(t5) == 4
@@ -364,7 +368,9 @@ using Aqua: Aqua
             @test butcher_representation(t5) == "[τ³]"
             @test RootedTrees.subtrees(t5) ==
                   [rootedtree([2]), rootedtree([2]), rootedtree([2])]
-            @test elementary_differential(t5) == L"$f^{\prime\prime\prime}(f, f, f)$"
+            @test elementary_differential_latexstring(t5) ==
+                  L"$f^{\prime\prime\prime}(f, f, f)$"
+            @test elementary_weight_latexstring(t5) == L"$\sum_{d}b_{d}c_{d}^{3}$"
 
             t6 = rootedtree([1, 2, 2, 3])
             @inferred RootedTrees.subtrees(t6)
@@ -376,7 +382,10 @@ 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"$f^{\prime\prime}(f^{\prime}f, f)$"
+            @test elementary_differential_latexstring(t6) ==
+                  L"$f^{\prime\prime}(f^{\prime}f, f)$"
+            @test elementary_weight_latexstring(t6) ==
+                  L"$\sum_{d, e}b_{d}a_{d,e}c_{e}c_{d}$"
 
             t7 = rootedtree([1, 2, 3, 3])
             @test order(t7) == 4
@@ -385,7 +394,9 @@ using Aqua: Aqua
             @test β(t7) == α(t7) * γ(t7)
             @test t7 == t1 ∘ t3
             @test butcher_representation(t7) == "[[τ²]]"
-            @test elementary_differential(t7) == L"$f^{\prime}f^{\prime\prime}(f, f)$"
+            @test elementary_differential_latexstring(t7) ==
+                  L"$f^{\prime}f^{\prime\prime}(f, f)$"
+            @test elementary_weight_latexstring(t7) == L"$\sum_{d, e}b_{d}a_{d,e}c_{e}^{2}$"
 
             t8 = rootedtree([1, 2, 3, 4])
             @test order(t8) == 4
@@ -394,7 +405,10 @@ using Aqua: Aqua
             @test α(t8) == 1
             @test t8 == t1 ∘ t4
             @test butcher_representation(t8) == "[[[τ]]]"
-            @test elementary_differential(t8) == L"$f^{\prime}f^{\prime}f^{\prime}f$"
+            @test elementary_differential_latexstring(t8) ==
+                  L"$f^{\prime}f^{\prime}f^{\prime}f$"
+            @test elementary_weight_latexstring(t8) ==
+                  L"$\sum_{d, e, f}b_{d}a_{d,e}a_{e,f}c_{f}$"
 
             t9 = rootedtree([1, 2, 2, 2, 2])
             @test order(t9) == 5
@@ -404,7 +418,8 @@ using Aqua: Aqua
             @test β(t9) == α(t9) * γ(t9)
             @test t9 == t5 ∘ t1
             @test butcher_representation(t9) == "[τ⁴]"
-            @test elementary_differential(t9) == L"$f^{(4)}(f, f, f, f)$"
+            @test elementary_differential_latexstring(t9) == L"$f^{(4)}(f, f, f, f)$"
+            @test elementary_weight_latexstring(t9) == L"$\sum_{d}b_{d}c_{d}^{4}$"
 
             t10 = rootedtree([1, 2, 2, 2, 3])
             @test order(t10) == 5
@@ -414,8 +429,10 @@ 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) ==
+            @test elementary_differential_latexstring(t10) ==
                   L"$f^{\prime\prime\prime}(f^{\prime}f, f, f)$"
+            @test elementary_weight_latexstring(t10) ==
+                  L"$\sum_{d, e}b_{d}a_{d,e}c_{e}c_{d}^{2}$"
 
             t11 = rootedtree([1, 2, 2, 3, 3])
             @test order(t11) == 5
@@ -424,8 +441,10 @@ using Aqua: Aqua
             @test α(t11) == 4
             @test t11 == t2 ∘ t3 == t7 ∘ t1
             @test butcher_representation(t11) == "[[τ²]τ]"
-            @test elementary_differential(t11) ==
+            @test elementary_differential_latexstring(t11) ==
                   L"$f^{\prime\prime}(f^{\prime\prime}(f, f), f)$"
+            @test elementary_weight_latexstring(t11) ==
+                  L"$\sum_{d, e}b_{d}a_{d,e}c_{e}^{2}c_{d}$"
 
             t12 = rootedtree([1, 2, 2, 3, 4])
             @test order(t12) == 5
@@ -435,8 +454,10 @@ 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) ==
+            @test elementary_differential_latexstring(t12) ==
                   L"$f^{\prime\prime}(f^{\prime}f^{\prime}f, f)$"
+            @test elementary_weight_latexstring(t12) ==
+                  L"$\sum_{d, e, f}b_{d}a_{d,e}a_{e,f}c_{f}c_{d}$"
 
             t13 = rootedtree([1, 2, 3, 2, 3])
             @test order(t13) == 5
@@ -446,8 +467,10 @@ using Aqua: Aqua
             @test β(t13) == α(t13) * γ(t13)
             @test t13 == t4 ∘ t2
             @test butcher_representation(t13) == "[[τ][τ]]"
-            @test elementary_differential(t13) ==
+            @test elementary_differential_latexstring(t13) ==
                   L"$f^{\prime\prime}(f^{\prime}f, f^{\prime}f)$"
+            @test elementary_weight_latexstring(t13) ==
+                  L"$\sum_{d, e}b_{d}(a_{d,e}c_{e})^{2}$"
 
             t14 = rootedtree([1, 2, 3, 3, 3])
             @test order(t14) == 5
@@ -457,8 +480,10 @@ using Aqua: Aqua
             @test β(t14) == α(t14) * γ(t14)
             @test t14 == t1 ∘ t5
             @test butcher_representation(t14) == "[[τ³]]"
-            @test elementary_differential(t14) ==
+            @test elementary_differential_latexstring(t14) ==
                   L"$f^{\prime}f^{\prime\prime\prime}(f, f, f)$"
+            @test elementary_weight_latexstring(t14) ==
+                  L"$\sum_{d, e}b_{d}a_{d,e}c_{e}^{3}$"
 
             t15 = rootedtree([1, 2, 3, 3, 4])
             @test order(t15) == 5
@@ -468,8 +493,10 @@ using Aqua: Aqua
             @test β(t15) == α(t15) * γ(t15)
             @test t15 == t1 ∘ t6
             @test butcher_representation(t15) == "[[[τ]τ]]"
-            @test elementary_differential(t15) ==
+            @test elementary_differential_latexstring(t15) ==
                   L"$f^{\prime}f^{\prime\prime}(f^{\prime}f, f)$"
+            @test elementary_weight_latexstring(t15) ==
+                  L"$\sum_{d, e, f}b_{d}a_{d,e}a_{e,f}c_{f}c_{e}$"
 
             t16 = rootedtree([1, 2, 3, 4, 4])
             @test order(t16) == 5
@@ -479,8 +506,10 @@ using Aqua: Aqua
             @test β(t16) == α(t16) * γ(t16)
             @test t16 == t1 ∘ t7
             @test butcher_representation(t16) == "[[[τ²]]]"
-            @test elementary_differential(t16) ==
+            @test elementary_differential_latexstring(t16) ==
                   L"$f^{\prime}f^{\prime}f^{\prime\prime}(f, f)$"
+            @test elementary_weight_latexstring(t16) ==
+                  L"$\sum_{d, e, f}b_{d}a_{d,e}a_{e,f}c_{f}^{2}$"
 
             t17 = rootedtree([1, 2, 3, 4, 5])
             @test order(t17) == 5
@@ -490,8 +519,20 @@ using Aqua: Aqua
             @test β(t17) == α(t17) * γ(t17)
             @test t17 == t1 ∘ t8
             @test butcher_representation(t17) == "[[[[τ]]]]"
-            @test elementary_differential(t17) ==
+            @test elementary_differential_latexstring(t17) ==
                   L"$f^{\prime}f^{\prime}f^{\prime}f^{\prime}f$"
+            @test elementary_weight_latexstring(t17) ==
+                  L"$\sum_{d, e, f, g}b_{d}a_{d,e}a_{e,f}a_{f,g}c_{g}$"
+
+            # test elementary_weight_latexstring which needs more than 23 indices
+
+            t18 = rootedtree(collect(1:25))
+            @test elementary_weight_latexstring(t18) ==
+                  L"$\sum_{d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, d2}b_{d1}a_{d1,e1}a_{e1,f1}a_{f1,g1}a_{g1,h1}a_{h1,i1}a_{i1,j1}a_{j1,k1}a_{k1,l1}a_{l1,m1}a_{m1,n1}a_{n1,o1}a_{o1,p1}a_{p1,q1}a_{q1,r1}a_{r1,s1}a_{s1,t1}a_{t1,u1}a_{u1,v1}a_{v1,w1}a_{w1,x1}a_{x1,y1}a_{y1,z1}a_{z1,d2}c_{d2}$"
+
+            t19 = rootedtree([1, 2, 2, 3, 2, 3])
+            @test elementary_weight_latexstring(t19) ==
+                  L"$\sum_{d, e}b_{d}(a_{d,e}c_{e})^{2}c_{d}$"
 
             # test non-canonical representation
             level_sequence = [1, 2, 3, 2, 3, 4, 2, 3, 2, 3, 4, 5, 6, 2, 3, 4]