def testMul_2x3(self):
        a   = ComplexM(2,3,
                [
                  [(3,2)  , (0,0)   , (5,-6) ],
                  [(1,0)  , (4,2)   , (0,1)  ],
                ]
            )
        b   = ComplexM(3,2,
                [
                  [(5,0)  , (2,-1)],
                  [(0,0)  , (4,5)],
                  [(7,-4) , (2,7)],
                ]
            )
        res = ComplexM(2,2,
                [
                  [(26,-52)  , (60,24)],
                  [(9,7)    , (1,29)],
                ]
            )

        self.assertEqual(a*b, res)
        self.assertNotEqual(b*a, a*b)

        self.assertIsNone(a.get_identity())
        self.assertIsNone(b.get_identity())
        self.assertIsNotNone(res.get_identity())

        x = Complex(4,-3.5)
        self.assertEqual(x * (a*b), (x*a) * b)
        self.assertEqual(x * (a*b), a * (x*b))

        self.assertEqual((a*b).transpose(), b.transpose() * a.transpose())
        self.assertEqual((a*b).adjoint(), b.adjoint() * a.adjoint())
        self.assertEqual((a*b).conjugate(), a.conjugate() * b.conjugate())
    def testMul_3x3(self):
        a   = ComplexM(3,3,
                [
                  [(3,2)  , (0,0)   , (5,-6) ],
                  [(1,0)  , (4,2)   , (0,1)  ],
                  [(4,-1) , (0,0)   , (4,0)  ],
                ]
            )
        b   = ComplexM(3,3,
                [
                  [(5,0)  , (2,-1)  , (6,-4) ],
                  [(0,0)  , (4,5)   , (2,0)  ],
                  [(7,-4) , (2,7)   , (0,0)  ],
                ]
            )
        res = ComplexM(3,3,
                [
                  [(26,-52)  , (60,24)  , (26,0) ],
                  [(9,7)    , (1,29)   , (14,0)  ],
                  [(48,-21) , (15,22)  , (20,-22)  ],
                ]
            )

        self.assertEqual(a*b, res)
        self.assertNotEqual(b*a, a*b)

        ident = a.get_identity()
        self.assertEqual(a, a*ident)
        self.assertEqual(b, b*ident)

        x = Complex(2,-1)
        self.assertEqual(x * (a*b), (x*a) * b)
        self.assertEqual(x * (a*b), a * (x*b))

        c = res
        self.assertEqual((a*b)*c, a*(b*c))
        self.assertEqual(a*(b+c), (a*b)+(a*c))
        self.assertEqual((a*b).transpose(), b.transpose() * a.transpose())
        self.assertEqual((a*b).adjoint(), b.adjoint() * a.adjoint())
        self.assertEqual((a*b).conjugate(), a.conjugate() * b.conjugate())