use stored OD values for factor groups

docs/src/Groups/group_characters.md

@@ -209,6 +209,7 @@ symplectic_components(characters::Vector{GAPGroupClassFunction}, n::Int)
 ```@docs
 class_multiplication_coefficient
 known_class_fusion
+known_class_fusions
 order(tbl::GAPGroupCharacterTable)
 possible_class_fusions
 approximate_class_fusion

experimental/OrthogonalDiscriminants/src/data.jl

@@ -95,10 +95,11 @@
 function orthogonal_discriminants(tbl::Oscar.GAPGroupCharacterTable)
   p = characteristic(tbl)
   if p == 0
-    id = identifier(tbl)
+    ordtbl = tbl
   else
-    id = identifier(ordinary_table(tbl))
+    ordtbl = ordinary_table(tbl)
   end
+  id = identifier(ordtbl)
   res = fill("", number_conjugacy_classes(tbl))
   if haskey(OD_simple_names, id)
     simp = OD_simple_names[id]
@@ -112,13 +113,76 @@
           res[l[2]] = l[4]
         end
         return res
+      else
+#TODO: compute the reductions mod p (not dividing the group order)
+      end
+    end
+  else
+    # Perhaps a factor of `tbl` belongs to the database.
+    facttbl = nothing
+    for r in known_class_fusions(ordtbl)
+      if 1 < length(class_positions_of_kernel(r[2]))
+        id = r[1]
+        if haskey(OD_simple_names, id)
+          simp = OD_simple_names[id]
+          data = OD_data[simp]
+          if haskey(data, id)
+            data = data[id]
+            facttbl = character_table(id)
+            if haskey(data, string(p))
+              if p != 0
+                facttbl = mod(facttbl, p)
+              end
+              facttbl != nothing && break
+            end
+          end
+        end
+      end
+    end
+    if facttbl != nothing
+      # Set the known values for the factor.
+      mp = [findfirst(is_equal(restrict(x, tbl)), tbl) for x in facttbl]
+      data = data[string(p)]
+      for l in data
+        res[mp[l[2]]] = l[4]
+      end
+      # Set values for faithful characters if applicable.
+      perf = (count(chi -> degree(chi) == 1, tbl) == 1)
+      if perf && order(tbl) == 2*order(facttbl) && p != 2
+        # deal with the faithful characters of a perfect central extension 2.G,
+        # the image of the spinor norm is trivial
+        for i in 1:length(tbl)
+          chi = tbl[i]
+          deg = degree(chi)
+          ind = indicator(chi)
+          if ind == 1 && length(class_positions_of_kernel(chi)) == 1
+            if mod(deg, 4) == 0
+              if p == 0
+                res[i] = "1"
+              else
+                res[i] = "O+"
+              end
+            elseif mod(deg, 2) == 0
+              if p == 0
+                res[i] = "-1"
+              else
+                # Check whether -1 is a square in the character field.
+                if mod(p-1, 4) == 0 || mod(degree(character_field(chi)[1]), 2) == 0
+                  res[i] = "O+"
+                else
+                  res[i] = "O-"
+                end
+              end
+            end
+          end
+        end
       end
     end
   end
 
-  # `tbl` is outside the scope of the database.
+  # Fill missing values.
   for i in 1:length(tbl)
-    if indicator(tbl[i]) == 1 && is_even(numerator(degree(tbl[i])))
+    if res[i] == "" && indicator(tbl[i]) == 1 && is_even(numerator(degree(tbl[i])))
       res[i] = "?"
     end
   end
@@ -480,7 +544,7 @@
             (!comment_matches(comment)) && (good_comment = false)
           elseif comment_matches isa String
             (!(comment_matches in comment)) && (good_comment = false)
-          elseif is_empty(intersect(comment, comment_matches ))
+          elseif is_empty(intersect(comment, comment_matches))
             good_comment = false
           end
         end

experimental/OrthogonalDiscriminants/test/data.jl

@@ -50,6 +50,13 @@ end
   end
 end
 
+@testset "orthogonal_discriminants for central extensions" begin
+  name = "2.L3(4)"
+  t = character_table(name)
+  @test orthogonal_discriminants(t) ==
+  ["","21","","","","","","","","105","","","1","1","1","1","-1","-1"]
+end
+
 using Documenter
 
 #

src/GAP/wrappers.jl

@@ -48,6 +48,7 @@ GAP.@wrap CoefficientsFamily(x::GapObj)::GapObj
 GAP.@wrap CoefficientsOfUnivariatePolynomial(x::GapObj)::GapObj
 GAP.@wrap CoeffsCyc(x::GAP.Obj, y::Int)::GapObj
 GAP.@wrap CollectionsFamily(x::GapObj)::GapObj
+GAP.@wrap ComputedClassFusions(x::GapObj)::GapObj
 GAP.@wrap ComputedPowerMaps(x::GapObj)::GapObj
 GAP.@wrap Conductor(x::Any)::GapInt
 GAP.@wrap ConjugacyClass(x::GapObj, y::GapObj)::GapObj

src/Groups/group_characters.jl

@@ -1601,6 +1601,19 @@ function known_class_fusion(subtbl::GAPGroupCharacterTable, tbl::GAPGroupCharact
     end
 end
 
+@doc raw"""
+    known_class_fusions(tbl::GAPGroupCharacterTable)
+
+Return the vector of pairs `(name, fus)` where `name` is the identifier of
+a character table
+and `fus` is the stored class fusion from `tbl` to this table,
+see [`known_class_fusion`](@ref).
+"""
+function known_class_fusions(tbl::GAPGroupCharacterTable)
+    return Tuple{String, Vector{Int64}}[(String(r.name), Vector{Int}(r.map))
+             for r in GAPWrap.ComputedClassFusions(GAPTable(tbl))]
+end
+
 
 #############################################################################
 ##

src/exports.jl

@@ -883,6 +883,7 @@ export kernel
 export klee_minty_cube
 export klein_bottle
 export known_class_fusion
+export known_class_fusions
 export koszul_complex
 export koszul_homology
 export koszul_matrix