Changing affordable_real and related tests

src/sa_basis.jl

@@ -1,22 +1,27 @@
 function affordable_real(
     irreducible_characters,
-    multiplicities = fill(1, length(irreducible_characters)),
+    multiplicities,
 )
     irr_real = similar(irreducible_characters, 0)
     mls_real = similar(multiplicities, 0)
     for (i, χ) in pairs(irreducible_characters)
         ι = Characters.frobenius_schur(χ)
-        if abs(ι) == 1 # real or quaternionic
-            @debug "real/quaternionic:" χ
+        if ι == 1 # real
+            @debug "real" χ
             push!(irr_real, χ)
             push!(mls_real, multiplicities[i])
-        else # complex one...
+        elseif ι == -1 # quaternionic
+            @debug "quaternionic" χ
+            @assert iseven(multiplicities[i]) "Multiplicities of quaternionic character must be even."
+            push!(irr_real, 2 * χ)
+            push!(mls_real, div(multiplicities[i], 2))
+        else # complex
             cχ = conj(χ)
             k = findfirst(==(cχ), irreducible_characters)
-            @assert k !== nothing
+            @assert k !== nothing "Conjugate character not found."
             @debug "complex" χ conj(χ) = irreducible_characters[k]
-            if k > i # ... we haven't already observed a conjugate of
-                @assert multiplicities[i] == multiplicities[k]
+            if k > i # we haven't already observed a conjugate
+                @assert multiplicities[i] == multiplicities[k] "Multiplicities of complex conjugates must be equal."
                 push!(irr_real, χ + cχ)
                 push!(mls_real, multiplicities[i])
             end

test/projections.jl

@@ -21,7 +21,7 @@ end
     G = PermGroup([perm"(1,2,3,4)"])
     chars = let irr = SymbolicWedderburn.irreducible_characters(G)
         if !all(isreal, irr)
-            irr, _ = SymbolicWedderburn.affordable_real(irr)
+            irr, _ = SymbolicWedderburn.affordable_real(irr,fill(1, length(irr)))
         end
         SymbolicWedderburn.Character{Float64}.(irr)
     end
@@ -64,3 +64,25 @@ end
         end
     end
 end
+
+@testset "affordable real all cases" begin
+    G = SmallPermGroups[24][3] # SL(2,3)
+    tbl = SymbolicWedderburn.CharacterTable(Rational{Int}, G)
+    chars = SymbolicWedderburn.irreducible_characters(tbl)
+
+    @test SymbolicWedderburn.degree.(chars)==[1, 1, 1, 2, 2, 2, 3]
+    @test all(χ -> isone(dot(χ, χ)), chars)
+    chars_fl = SymbolicWedderburn.Character{ComplexF64}.(chars)
+    @test SymbolicWedderburn.degree.(chars_fl)==[1, 1, 1, 2, 2, 2, 3]
+    @test all(χ -> isapprox(dot(χ, χ), 1), chars_fl)
+
+
+
+    charsR, _ = SymbolicWedderburn.affordable_real(chars,fill(2,length(chars)))
+    @test SymbolicWedderburn.degree.(charsR) == [1, 2, 4, 4, 3]
+    @test [dot(χ, χ) for χ in charsR] == [1, 2, 2, 4, 1]
+
+    charsR_fl = SymbolicWedderburn.Character{Float64}.(charsR)
+    @test all( [1, 2, 4, 4, 3] .== SymbolicWedderburn.degree.(charsR_fl),)
+    @test all( [1, 2, 2, 4, 1].≈[dot(χ, χ) for χ in charsR_fl],)
+end

test/sa_basis.jl

@@ -9,7 +9,7 @@
     @test all(isone ∘ SymbolicWedderburn.degree, chars_fl)
     @test all(χ -> isapprox(dot(χ, χ), 1), chars_fl)
 
-    charsR, _ = SymbolicWedderburn.affordable_real(chars)
+    charsR, _ = SymbolicWedderburn.affordable_real(chars,fill(1, length(chars)))
     @test SymbolicWedderburn.degree.(charsR) ==
           [dot(χ, χ) for χ in charsR] ==
           [1, 1, 2, 2, 2, 2]