Update projections.jl

adding a test for doubling the quaternionic characters

test/projections.jl

@@ -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