Move dim_of_simple_module to the root system

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)

experimental/LieAlgebras/src/LieAlgebras.jl

@@ -56,6 +56,7 @@ import ..Oscar:
   inv,
   is_abelian,
   is_finite,
+  is_integral,
   is_isomorphism,
   is_nilpotent,
   is_perfect,

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
 

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