From 746ac41432e0c9194f2ab50f5675fe258f4ecdec Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Lars=20G=C3=B6ttgens?= <lars.goettgens@rwth-aachen.de>
Date: Tue, 20 Aug 2024 15:00:54 +0200
Subject: [PATCH] Move `dim_of_simple_module` to the root system

---
 .../LieAlgebras/src/LieAlgebraModule.jl       | 15 ++----
 experimental/LieAlgebras/src/LieAlgebras.jl   |  1 +
 experimental/LieAlgebras/src/RootSystem.jl    | 50 +++++++++++++++++++
 .../LieAlgebras/test/LieAlgebraModule-test.jl |  4 +-
 4 files changed, 57 insertions(+), 13 deletions(-)

diff --git a/experimental/LieAlgebras/src/LieAlgebraModule.jl b/experimental/LieAlgebras/src/LieAlgebraModule.jl
index d1e01ba54740..6aa80ec27a2b 100644
--- a/experimental/LieAlgebras/src/LieAlgebraModule.jl
+++ b/experimental/LieAlgebras/src/LieAlgebraModule.jl
@@ -1429,7 +1429,8 @@ end
 @doc raw"""
     dim_of_simple_module([T = Int], L::LieAlgebra{C}, hw::Vector{<:IntegerUnion}) -> T
 
-Computes the dimension of the simple module of the Lie algebra `L` with highest weight `hw`.
+Compute the dimension of the simple module of the Lie algebra `L` with highest weight `hw`
+ using Weyl's dimension formula.
 The return value is of type `T`.
 
 # Example
@@ -1441,19 +1442,11 @@ julia> dim_of_simple_module(L, [1, 1, 1])
 ```
 """
 function dim_of_simple_module(T::Type, L::LieAlgebra, hw::Vector{<:IntegerUnion})
-  @req is_dominant_weight(hw) "Not a dominant weight."
   if has_root_system(L)
     R = root_system(L)
-    rho = weyl_vector(R)
-    hw_rho = WeightLatticeElem(R, hw) + rho
-    num = one(ZZ)
-    den = one(ZZ)
-    for alpha in positive_roots(R)
-      num *= ZZ(dot(hw_rho, alpha))
-      den *= ZZ(dot(rho, alpha))
-    end
-    return T(div(num, den))
+    return dim_of_simple_module(T, R, hw)
   else # TODO: remove branch once root system detection is implemented
+    @req is_dominant_weight(hw) "Not a dominant weight."
     return T(
       GAPWrap.DimensionOfHighestWeightModule(
         codomain(Oscar.iso_oscar_gap(L)), GAP.Obj(hw; recursive=true)
diff --git a/experimental/LieAlgebras/src/LieAlgebras.jl b/experimental/LieAlgebras/src/LieAlgebras.jl
index 1fa023704c07..e5c62c46891b 100644
--- a/experimental/LieAlgebras/src/LieAlgebras.jl
+++ b/experimental/LieAlgebras/src/LieAlgebras.jl
@@ -56,6 +56,7 @@ import ..Oscar:
   inv,
   is_abelian,
   is_finite,
+  is_integral,
   is_isomorphism,
   is_nilpotent,
   is_perfect,
diff --git a/experimental/LieAlgebras/src/RootSystem.jl b/experimental/LieAlgebras/src/RootSystem.jl
index 20c8b732bfe9..d428004793eb 100644
--- a/experimental/LieAlgebras/src/RootSystem.jl
+++ b/experimental/LieAlgebras/src/RootSystem.jl
@@ -883,6 +883,10 @@ function is_dominant(w::WeightLatticeElem)
   return all(>=(0), coefficients(w))
 end
 
+function is_integral(w::WeightLatticeElem)
+  return all(is_integer, coefficients(w))
+end
+
 @doc raw"""
     reflect(w::WeightLatticeElem, s::Int) -> WeightLatticeElem
     
@@ -906,6 +910,9 @@ function root_system(w::WeightLatticeElem)
   return w.root_system
 end
 
+###############################################################################
+# more functions
+
 function dot(r::RootSpaceElem, w::WeightLatticeElem)
   @req root_system(r) === root_system(w) "parent root system mismatch"
 
@@ -920,6 +927,49 @@ function dot(w::WeightLatticeElem, r::RootSpaceElem)
   return dot(r, w)
 end
 
+@doc raw"""
+    dim_of_simple_module([T = Int], R::RootSystem, hw::WeightLatticeElem -> T
+    dim_of_simple_module([T = Int], R::RootSystem, hw::Vector{<:IntegerUnion}) -> T
+
+Compute the dimension of the simple module of the Lie algebra defined by the root system `R`
+with highest weight `hw` using Weyl's dimension formula.
+The return value is of type `T`.
+
+# Example
+```jldoctest
+julia> R = root_system(:B, 2);
+
+julia> dim_of_simple_module(R, [1, 0])
+5
+```
+"""
+function dim_of_simple_module(T::Type, R::RootSystem, hw::WeightLatticeElem)
+  @req root_system(hw) === R "parent root system mismatch"
+  @req is_dominant(hw) "not a dominant weight"
+  @req is_integral(hw) "not an integral weight"
+  rho = weyl_vector(R)
+  hw_rho = hw + rho
+  num = one(ZZ)
+  den = one(ZZ)
+  for alpha in positive_roots(R)
+    num *= ZZ(dot(hw_rho, alpha))
+    den *= ZZ(dot(rho, alpha))
+  end
+  return T(div(num, den))
+end
+
+function dim_of_simple_module(T::Type, R::RootSystem, hw::Vector{<:IntegerUnion})
+  return dim_of_simple_module(T, R, WeightLatticeElem(R, hw))
+end
+
+function dim_of_simple_module(R::RootSystem, hw::Vector{<:IntegerUnion})
+  return dim_of_simple_module(Int, R, hw)
+end
+
+function dim_of_simple_module(R::RootSystem, hw::WeightLatticeElem)
+  return dim_of_simple_module(Int, R, hw)
+end
+
 ###############################################################################
 # internal helpers
 
diff --git a/experimental/LieAlgebras/test/LieAlgebraModule-test.jl b/experimental/LieAlgebras/test/LieAlgebraModule-test.jl
index 433eae1e592c..f96aa25a4510 100644
--- a/experimental/LieAlgebras/test/LieAlgebraModule-test.jl
+++ b/experimental/LieAlgebras/test/LieAlgebraModule-test.jl
@@ -719,9 +719,9 @@
       @test dim == 393513120
     end
 
-    let L = lie_algebra(QQ, :B, 7)
+    let R = root_system(:B, 7)
       dim = @inferred dim_of_simple_module(
-        ZZRingElem, L, [7, 2, 5, 1, 0, 2, 6]
+        ZZRingElem, R, [7, 2, 5, 1, 0, 2, 6]
       )
       @test dim isa ZZRingElem
       @test dim == 307689492858882008424585750