Add broken tests

test/perm_grp_algebra.jl

@@ -1,3 +1,6 @@
+using Test
+using PermutationGroups
+import StarAlgebras as SA
 @testset "POC: group algebra" begin
     G = PermGroup(perm"(1,2,3,4,5,6)", perm"(1,2)")
     g = Permutation(perm"(1,4,3,6)(2,5)", G)
@@ -17,7 +20,7 @@
     zcfs = SA.SparseCoefficients([one(G), h], [1, -1])
     xzcfs = SA.SparseCoefficients([one(G), g, h, g * h], [1, -1, -1, 1])
 
-    RG = SA.StarAlgebra(G, db)
+   RG = SA.StarAlgebra(G, db)
 
     x = SA.AlgebraElement(xcfs, RG)
     y = SA.AlgebraElement(ycfs, RG)
@@ -116,12 +119,27 @@
             SA.AlgebraElement(z, sbRG)
         end
 
-        dx = SA.AlgebraElement(SA.coeffs(x, basis(RG)), RG)
-        dy = SA.AlgebraElement(SA.coeffs(y, basis(RG)), RG)
-
-        @test dx + dy == SA.AlgebraElement(SA.coeffs(x + y, basis(RG)), RG)
-
-        @test dx * dy == SA.AlgebraElement(SA.coeffs(x * y, basis(RG)), RG)
+        dx = SA.AlgebraElement(SA.coeffs(x, SA.basis(RG)), RG)
+        dy = SA.AlgebraElement(SA.coeffs(y, SA.basis(RG)), RG)
+
+        @test dx + dy == SA.AlgebraElement(SA.coeffs(x + y, SA.basis(RG)), RG)
+
+        @test dx * dy == SA.AlgebraElement(SA.coeffs(x * y, SA.basis(RG)), RG)
+
+        a = SA.AlgebraElement([2], SA.StarAlgebra(G, SA.SubBasis([g], db)))
+        b = SA.AlgebraElement([-3], SA.StarAlgebra(G, SA.SubBasis([h], db)))
+        # `Base.+` assumes that using the basis of the first argument will suffice
+        # We should redefine `Base.:+(a::SubBasis, b::SubBasis)` to first
+        # convert `a` and `b` to their implicit basis equivalent and then
+        # do `+` and then convert the result back
+        # `MultivariateBases` defines an `implicit` function.
+        # Why not having an `explicit` as well ?
+        # My dream implementation would be
+        # Base.:+(a::SubBasis, b::SubBasis) = explicit(implicit(a) + implicit(b))
+        # so we just need to implement `implicit` and `explicit` 👼
+        @test_broken SA.explicit(SA.implicit(a)) == a
+        @test_broken SA.explicit(SA.implicit(b)) == b
+        @test_broken a + b == SA.explicit(SA.implicit(a) + SA.implicit(b))
+        @test_broken a * b == SA.explicit(SA.implicit(a) * SA.implicit(b))
     end
 end
-