/// <summary>
        /// Tests a pair of expressions for identicality using the equality definitions defined in this class.
        /// </summary>
        /// <param name="E1">The first expression to test</param>
        /// <param name="E2">The second expression to test</param>
        public static bool TestIdenticality(Expression E1, Expression E2)
        {
            //Test for "null" arguments
            if ((E1 as object) == null && (E2 as object) == null) return true;
            if ((E1 as object) == null || (E2 as object) == null) return false;

            //To be identical, they must have the same type
            if (E1.GetType() != E2.GetType()) return false;

            //If E1 maps to E2
            if (E1.MapsTo(E2)) return true;

            //Fast tests amoungst operands
            if ((E1 is Irreducible) && (E2 is Irreducible)) return TestIdenticality_FastTests_Operands(E1, E2);

            //Test for identicality amoungst binary operations
            if (((E1 is Operation) && (E1 as Operation).Arity == 2) && ((E2 is Operation) && (E2 as Operation).Arity == 2)) return TestEquality(E1, E2, BinaryOperations);

            //If we couldn't determine that they are equal:
            return false;
        }
        /// <summary>
        /// Tests a pair of expressions for equality using the equality definitions defined in this class.
        /// </summary>
        /// <param name="E1">The first expression to test</param>
        /// <param name="E2">The second expression to test</param>
        public static bool TestEquality(Expression E1, Expression E2)
        {
            //Test for "null" arguments
            if ((E1 as object) == null && (E2 as object) == null) return true;
            if ((E1 as object) == null || (E2 as object) == null) return false;

            //If E1 maps to E2
            if (E1.MapsTo(E2)) return true;

            //Fast tests amoungst operands
            if ((E1 is Irreducible) && (E2 is Irreducible)) return TestEquality_FastTests_Operands(E1, E2);

            //Test for equality amoungst operands - OLD
            //if (((E1 is Irreducible) || (E1 is IntrinsicIrreducible)) && ((E2 is Irreducible) || (E2 is IntrinsicIrreducible))) return TestEquality(E1, E2, Operands);

            //Test for equality amoungst binary operations
            if (((E1 is Operation) && (E1 as Operation).Arity == 2) && ((E2 is Operation) && (E2 as Operation).Arity == 2)) if (TestEquality(E1, E2, BinaryOperations)) return true;

            //Test for equality via grouping operations
            //if (TestEquality(E1, E2, Groupings)) return true;

            //If we couldn't determine that they are equal:
            return false;
        }