Fix basis_lie_demazure which wouldn't finish for some inputs

experimental/BasisLieHighestWeight/src/BasisLieHighestWeight.jl

@@ -54,6 +54,8 @@ export basis_lie_highest_weight_string
 export basis_lie_demazure
 export basis_lie_demazure_ffl
 export basis_lie_demazure_lusztig
+export basis_lie_demazure_nz
+export basis_lie_demazure_string
 
 end
 
@@ -75,3 +77,5 @@ export basis_lie_highest_weight_string
 export basis_lie_demazure
 export basis_lie_demazure_ffl
 export basis_lie_demazure_lusztig
+export basis_lie_demazure_nz
+export basis_lie_demazure_string

experimental/BasisLieHighestWeight/src/MainAlgorithm.jl

@@ -308,7 +308,19 @@ function add_new_monomials!(
       zero_coordinates,
     ),
   )
-  isempty(poss_mon_in_weightspace) && error("The input seems to be invalid.")
+  if isempty(poss_mon_in_weightspace)
+    if V isa SimpleModuleData
+      error(
+        "The input seems to be invalid. Not enough monomials for weightspace $(highest_weight(V) - weight_w) in module with highest weight $(highest_weight(V))"
+      )
+    elseif V isa DemazureModuleData
+      error(
+        "The input seems to be invalid. Not enough monomials for weightspace $((highest_weight(V) - weight_w) * weyl_group_elem(V)) in module with extremal weight $(highest_weight(V) * weyl_group_elem(V))"
+      )
+    else
+      error("unreachable")
+    end
+  end
   poss_mon_in_weightspace = sort(poss_mon_in_weightspace; order=monomial_ordering)
 
   # check which monomials should get added to the basis

experimental/BasisLieHighestWeight/src/UserFunctions.jl

@@ -696,6 +696,54 @@ function basis_lie_demazure_lusztig(
   return basis_lie_highest_weight_compute(V, operators, monomial_ordering)
 end
 
+@doc raw"""
+    basis_lie_demazure_string(type::Symbol, rank::Int, highest_weight::Vector{Int}, weyl_group_elem::Vector{Int}, reduced_expression::Vector{Int})
+
+Compute a monomial basis for the demazure module with extremal weight
+`highest_weight * weyl_group_elem` (in terms of the fundamental weights $\omega_i$),
+for a simple Lie algebra of type `type_rank`.
+
+Let $\omega_0 = s_{i_1} \cdots s_{i_N}$ be a reduced expression of the longest element in the Weyl group of $L$
+given as indices $[i_1, \dots, i_N]$ in `reduced_expression`.
+Then the birational sequence used consists of $\alpha_{i_1}, \dots, \alpha_{i_N}$.
+
+The monomial ordering is fixed to `neglex` (negative lexicographic order).
+
+# Examples
+```jldoctest
+julia> basis_lie_demazure_string(:B, 3, [1,1,1],[1,2], [3,2,3,2,1,2,3,2,1])
+Monomial basis of a Demazure module
+  of extremal weight [1, 1, 1] * s1 * s2
+  of dimension 5
+  with monomial ordering neglex([x1, x2, x3, x4, x5, x6, x7, x8, x9])
+over Lie algebra of type B3
+  where the used birational sequence consists of the following roots (given as coefficients w.r.t. alpha_i):
+    [0, 0, 1]
+    [0, 1, 0]
+    [0, 0, 1]
+    [0, 1, 0]
+    [1, 0, 0]
+    [0, 1, 0]
+    [0, 0, 1]
+    [0, 1, 0]
+    [1, 0, 0]
+  and the basis was generated by Minkowski sums of the bases of the following Demazure modules:
+    [1, 0, 0] * s1 * s2
+    [0, 1, 0] * s1 * s2
+    [0, 0, 1] * s1 * s2
+```
+"""
+function basis_lie_demazure_string(
+  type::Symbol, rank::Int, highest_weight::Vector{Int}, weyl_group_elem::Vector{Int},
+  reduced_expression::Vector{Int},
+)
+  monomial_ordering = :neglex
+  L = lie_algebra(QQ, type, rank)
+  V = DemazureModuleData(L, highest_weight, weyl_group_elem)
+  operators = demazurify_operators(V, operators_by_index(L, reduced_expression))
+  return basis_lie_highest_weight_compute(V, operators, monomial_ordering)
+end
+
 @doc raw"""
     basis_lie_demazure_ffl(type::Symbol, rank::Int, highest_weight::Vector{Int}, weyl_group_elem::Vector{Int})
 
@@ -742,3 +790,51 @@ function basis_lie_demazure_ffl(
   # simple roots at the right end speed up the program very much
   return basis_lie_highest_weight_compute(V, operators, monomial_ordering)
 end
+
+@doc raw"""
+    basis_lie_demazure_nz(type::Symbol, rank::Int, highest_weight::Vector{Int}, weyl_group_elem::Vector{Int}, reduced_expression::Vector{Int})
+
+Compute a monomial basis for the demazure module with extremal weight
+`highest_weight * weyl_group_elem` (in terms of the fundamental weights $\omega_i$),
+for a simple Lie algebra of type `type_rank`.
+
+Let $\omega_0 = s_{i_1} \cdots s_{i_N}$ be a reduced expression of the longest element in the Weyl group of $L$
+given as indices $[i_1, \dots, i_N]$ in `reduced_expression`.
+Then the birational sequence used consists of $\alpha_{i_1}, \dots, \alpha_{i_N}$.
+
+The monomial ordering is fixed to `degrevlex` (degree reverse lexicographic order).     
+
+# Examples
+```jldoctest
+julia> basis_lie_demazure_nz(:B, 3, [1,1,1],[1,2], [3,2,3,2,1,2,3,2,1])
+Monomial basis of a Demazure module
+  of extremal weight [1, 1, 1] * s1 * s2
+  of dimension 5
+  with monomial ordering degrevlex([x1, x2, x3, x4, x5, x6, x7, x8, x9])
+over Lie algebra of type B3
+  where the used birational sequence consists of the following roots (given as coefficients w.r.t. alpha_i):
+    [0, 0, 1]
+    [0, 1, 0]
+    [0, 0, 1]
+    [0, 1, 0]
+    [1, 0, 0]
+    [0, 1, 0]
+    [0, 0, 1]
+    [0, 1, 0]
+    [1, 0, 0]
+  and the basis was generated by Minkowski sums of the bases of the following Demazure modules:
+    [1, 0, 0] * s1 * s2
+    [0, 1, 0] * s1 * s2
+    [0, 0, 1] * s1 * s2
+```
+"""
+function basis_lie_demazure_nz(
+  type::Symbol, rank::Int, highest_weight::Vector{Int}, weyl_group_elem::Vector{Int},
+  reduced_expression::Vector{Int},
+)
+  monomial_ordering = :degrevlex
+  L = lie_algebra(QQ, type, rank)
+  V = DemazureModuleData(L, highest_weight, weyl_group_elem)
+  operators = demazurify_operators(V, operators_by_index(L, reduced_expression))
+  return basis_lie_highest_weight_compute(V, operators, monomial_ordering)
+end

experimental/BasisLieHighestWeight/src/WeylPolytope.jl

@@ -65,7 +65,7 @@ function compute_zero_coordinates(
     if !isdisjoint(
       non_zeros, findall(!iszero, coefficients(operator_as_root(bir_sequence, c)))
     )
-      union!(non_zeros, findall(<(0), coefficients(operator_as_weight(bir_sequence, c))))
+      union!(non_zeros, findall(!=(0), coefficients(operator_as_weight(bir_sequence, c))))
     else
       push!(zero_coordinates, c)
     end