Add Bourbaki tables

Project.toml

@@ -9,6 +9,7 @@ LRUCache = "8ac3fa9e-de4c-5943-b1dc-09c6b5f20637"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
 Preferences = "21216c6a-2e73-6563-6e65-726566657250"
+PrettyTables = "08abe8d2-0d0c-5749-adfa-8a2ac140af0d"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 
 [compat]
@@ -19,6 +20,7 @@ LRUCache = "1.6"
 LinearAlgebra = "1"
 PrecompileTools = "1"
 Preferences = "1"
+PrettyTables = "2.3.2"
 StaticArrays = "1"
 Test = "1"
 julia = "1.9"

docs/src/roots.md

@@ -222,6 +222,39 @@ dual_coxeter_number
 degrees_fundamental_invariants
 ```
 
+## Bourbaki tables
+
+`bourbaki_table` collects the root-system data appearing in Bourbaki's finite-type
+plates into one programmatic object. It uses intrinsic simple-root coordinates rather
+than a separate Euclidean realization for each Dynkin family.
+
+```jldoctest roots
+julia> table = bourbaki_table(TypeA{2});
+
+julia> table.exponents
+2-element Vector{Int64}:
+ 1
+ 2
+
+julia> table.root_lattice_quotient
+1-element Vector{Int64}:
+ 3
+
+julia> table.opposition_involution
+2-element StaticArraysCore.SVector{2, Int64} with indices SOneTo(2):
+ 2
+ 1
+```
+
+Display the table itself to see a Unicode plate rendered with PrettyTables.jl: the
+Dynkin diagram, all positive roots and coroots, fundamental weights, Coxeter and
+lattice invariants, Weyl-group data, and finite and affine Cartan matrices.
+
+```@docs
+BourbakiTable
+bourbaki_table
+```
+
 ## Examples
 
 ### A2