some cleanup, still need docs and tests

oscar-system · Dec 4, 2024 · fa57b77 · fa57b77
1 parent b990e1a
commit fa57b77
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diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl
@@ -9,7 +9,6 @@ export contracted_partial_shift_graph
 export exterior_shift
 export face_size
 export generic_unipotent_matrix
-export partial_ext_shift_lv
 export partial_shift_graph
 export partial_shift_graph_vertices
 export rothe_matrix

diff --git a/experimental/AlgebraicShifting/src/PartialShift.jl b/experimental/AlgebraicShifting/src/PartialShift.jl
@@ -316,59 +316,46 @@ julia> L = exterior_shift(GF(2), K, w)
 Abstract simplicial complex of dimension 2 on 6 vertices
 ```
 """
-function exterior_shift(F::Field, K::ComplexOrHypergraph, p::PermGroupElem)
+function exterior_shift(F::Field, K::ComplexOrHypergraph,
+                        p::PermGroupElem; las_vegas::Bool=false)
   n = n_vertices(K)
   @req n == degree(parent(p)) "number of vertices - 1 should equal the rank of the root system"
-  return exterior_shift(K, rothe_matrix(F, p))
+  las_vegas && return exterior_shift_lv(F, K, p)
+  return exterior_shift(K, rothe_matrix(F, p);)
 end
 
-function exterior_shift(F::Field, K::ComplexOrHypergraph, w::WeylGroupElem)
+function exterior_shift(F::Field, K::ComplexOrHypergraph, w::WeylGroupElem; kw...)
   n = n_vertices(K)
   phi = isomorphism(PermGroup, parent(w))
-  return exterior_shift(F, K, phi(w))
+  return exterior_shift(F, K, phi(w); kw)
 end
 
-function exterior_shift(F::Field, K::ComplexOrHypergraph)
+function exterior_shift(F::Field, K::ComplexOrHypergraph; kw...)
   n = n_vertices(K)
   W = weyl_group(:A, n - 1)
   return exterior_shift(F, K, longest_element(W))
 end
 
-exterior_shift(K::ComplexOrHypergraph) = exterior_shift(QQ, K)
+exterior_shift(K::ComplexOrHypergraph; kw...) = exterior_shift(QQ, K; kw)
 
 ################################################################################
 # Las Vegas Partial Shifting
 
-# returns a random invertible matrices of the given sample size
-function random_invertible_matrices(n::Int; range::Int = 100, sample_size::Int=100, F::Field=QQ)
-  n_samples = 0
-  samples = Set{MatElem}()
-  n_non_inv = 0
-  while (n_samples < sample_size)
-    a = matrix(F, round.(Integer, range .* rand(n,n)) .- range // 2)
-    if iszero(det(a))
-      n_non_inv += 1
-      continue
-    end
-    push!(samples, a)
-    n_samples = length(samples)
-  end
-  # @info "probability of non invertible matrix" n_non_inv / (n_non_inv + sample_size)
-  return collect(samples)
-end
-
-function random_unipotent_matrix(F::Field, n::Int)
+function random_rothe_matrix(F::Field, p::PermGroupElem)
   char = characteristic(F)
   range = char == 0 ? 100 : char
-  upper_triangular_matrix(
-    reduce(vcat, [
-      [F(1); F.(round.(Integer, range .* rand(i)) .- (range // 2))] for i in reverse(0:n-1)
-        ]))
+  u = identity_matrix(F, n)
+  n = degree(parent(p))
+  for (i, j) in inversions(p)
+    u[i, j] = F.(round.(Integer, range .* rand(i)) .- (range // 2)) 
+  end
+
+  return u * permutation_matrix(F, p)
 end
 
 function random_shift(F::Field, K::ComplexOrHypergraph, p::PermGroupElem;)
   n = n_vertices(K)
-  exterior_shift(K, random_unipotent_matrix(F, n) * permutation_matrix(F, p))
+  exterior_shift(K, random_rothe_matrix(F, p))
 end
 
 random_shift(K::ComplexOrHypergraph, p::PermGroupElem) = random_shift(QQ, K, p)
@@ -377,7 +364,7 @@ random_shift(K::ComplexOrHypergraph, p::PermGroupElem) = random_shift(QQ, K, p)
 function check_shifted(F::Field,
                        src::UniformHypergraph,
                        dst::UniformHypergraph,
-                       w::WeylGroupElem,)
+                       p::PermGroupElem)
   dst_faces = faces(dst)
   if length(dst_faces) == 1
     max_face = dst_faces[1]
@@ -390,7 +377,7 @@ function check_shifted(F::Field,
   nCk = sort(subsets(n, k))
   max_face_index = findfirst(x -> x == max_face, nCk)
   cols = nCk[1:max_face_index - 1]
-  r = rothe_matrix(F, w)
+  r = rothe_matrix(F, p)
 
   if max_face_index > num_rows 
     M = compound_matrix(r, src)[collect(1:num_rows), collect(1:length(cols))]
@@ -403,29 +390,26 @@ end
 function check_shifted(F::Field, 
                        src::SimplicialComplex,
                        dst::SimplicialComplex,
-                       w::WeylGroupElem)
+                       p::PermGroupElem)
   n = n_vertices(src)
   f_vec = f_vector(src)
   k = length(f_vec)
 
   while k > 1
     uhg_src = uniform_hypergraph(complex_faces(src, k - 1), n)
     uhg_dst = uniform_hypergraph(complex_faces(dst, k - 1), n)
-    !check_shifted(F, uhg_src, uhg_dst, w) && return false
+    !check_shifted(F, uhg_src, uhg_dst, p) && return false
     k -= 1
   end
   return true
 end
 
-function partial_ext_shift_lv(F::Field, K::ComplexOrHypergraph, w::WeylGroupElem)
+function exterior_shift_lv(F::Field, K::ComplexOrHypergraph, p::PermGroupElem)
   sample_size = characteristic(F) == 0 ? 10 : 100
-  W = parent(w)
-  phi = isomorphism(PermGroup, W)
-
-  shift = partialsort!([random_shift(F, K, phi(w)) for _ in 1:sample_size], 1;
+  shift = partialsort!([random_shift(F, K, p) for _ in 1:sample_size], 1;
                       lt=isless_lex)
-  check_shifted(F, K, shift, w) && return shift
-  return nothing # partial_ext_shift_lv(F, w, K)
+  check_shifted(F, K, shift, p) && return shift
+  return nothing 
 end
 
 ###############################################################################