コード例 #1
0
        /// <summary>
        /// The Reflexive Property states that for every real number x, x = x.
        /// </summary>
        /// <param name="equation"></param>
        /// <returns>True: Satisfy, False: Un-satisfy, null: </returns>
        private bool?Satisfy(Equation equation)
        {
            bool lhsNumeric = LogicSharp.IsNumeric(equation.Lhs);
            bool rhsNumeric = LogicSharp.IsNumeric(equation.Rhs);

            if (lhsNumeric && rhsNumeric)
            {
                return(equation.Lhs.Equals(equation.Rhs));
            }
            var leftVar  = equation.Lhs as Var;
            var rightVar = equation.Rhs as Var;

            if (leftVar != null && rightVar != null)
            {
                bool result = leftVar.Equals(rightVar);
                if (result)
                {
                    return(true);
                }
                return(null);
            }

            /*            var leftTerm  = equation.Lhs as Term;
             *          var rightTerm = equation.Rhs as Term;
             *          if (leftTerm != null && rightTerm != null)
             *          {
             *
             *              return leftTerm.Equals(rightTerm);
             *          }*/
            return(null);
        }
コード例 #2
0
        private static bool SatisfyCalcCondition(
            Func <Expression, Expression, BinaryExpression> func,
            object x, object y, out object output)
        {
            output = null;
            if (func.Method.Name.Equals("Divide"))
            {
                return(false);
            }

            if (LogicSharp.IsNumeric(x) && LogicSharp.IsNumeric(y))
            {
                double xDoubleVal;
                double yDoubleVal;
                bool   isXDouble = LogicSharp.IsDouble(x, out xDoubleVal);
                bool   isYDouble = LogicSharp.IsDouble(y, out yDoubleVal);
                if (isXDouble || isYDouble)
                {
                    var xExpr = Expression.Constant(xDoubleVal);
                    var yExpr = Expression.Constant(yDoubleVal);
                    var rExpr = func(xExpr, yExpr);
                    output = Expression.Lambda <Func <double> >(rExpr).Compile().Invoke();
                    int iResult;
                    if (LogicSharp.IsInt(output, out iResult))
                    {
                        output = iResult;
                        return(true);
                    }
                    return(true);
                }
            }
            return(false);
        }
コード例 #3
0
        public static bool IsQuadraticTerm(this Term term)
        {
            if (term == null)
            {
                return(false);
            }
            if (!term.ContainsVar())
            {
                return(false);
            }
            var cond1 = term.Op == Expression.Power;
            var lst   = term.Args as List <object>;

            if (lst == null || lst.Count != 2)
            {
                return(false);
            }
            var isNum = LogicSharp.IsNumeric(lst[1]);

            if (!isNum)
            {
                return(false);
            }
            double number;

            LogicSharp.IsDouble(lst[1], out number);
            var cond2 = number.Equals(2.0);

            return(cond1 && cond2);
        }
コード例 #4
0
        private static bool SatisfyGoalCondition(Equation eq)
        {
            var  lhs        = eq.Lhs;
            var  rhs        = eq.Rhs;
            bool rhsNumeral = LogicSharp.IsNumeric(rhs);

            return(Var.IsVar(lhs) && rhsNumeral);
        }
コード例 #5
0
        private static bool SatisfySymmetricCondition(object lhs, object rhs)
        {
            bool lhsNumeric = LogicSharp.IsNumeric(lhs);
            bool rhsNumeric = LogicSharp.IsNumeric(rhs);

            if (lhsNumeric && !rhsNumeric)
            {
                return(true);
            }
            return(false);
        }
コード例 #6
0
ファイル: Goal.cs プロジェクト: JakeCode11/CSharp.Logic
        public override bool Equals(object obj)
        {
            var eqGoal = obj as EqGoal;

            if (eqGoal != null)
            {
                if (Rhs == null)
                {
                    return(Lhs.Equals(eqGoal.Lhs));
                }

                bool isNum1 = LogicSharp.IsNumeric(Rhs);
                bool isNum2 = LogicSharp.IsNumeric(eqGoal.Rhs);
                bool result;
                if (isNum1 && isNum2)
                {
                    result = LogicSharp.NumericEqual(Rhs, eqGoal.Rhs);
                }
                else
                {
                    result = Rhs.Equals(eqGoal.Rhs);
                }
                return(Lhs.Equals(eqGoal.Lhs) && result);
            }

            var eq = obj as Equation;

            if (eq != null)
            {
                if (Rhs == null)
                {
                    return(Lhs.Equals(eq.Lhs));
                }
                bool isNum1 = LogicSharp.IsNumeric(Rhs);
                bool isNum2 = LogicSharp.IsNumeric(eq.Rhs);
                bool result;
                if (isNum1 && isNum2)
                {
                    result = LogicSharp.NumericEqual(Rhs, eq.Rhs);
                }
                else
                {
                    result = Rhs.Equals(eq.Rhs);
                }

                if (eq.Lhs == null)
                {
                    return(false);
                }
                return(Lhs.ToString().Equals(eq.Lhs.ToString()) && result);
            }

            return(false);
        }
コード例 #7
0
        /*
         * Move sqare root head to the rhs
         * E.g  x^2=4 -> x=4^(0.5)
         *
         */
        private static bool SatisfyTransitiveCondition2(object lhs, object rhs)
        {
            bool rhsNumeric = LogicSharp.IsNumeric(rhs);
            var  lhsTerm    = lhs as Term;

            if (lhsTerm != null)
            {
                if (lhsTerm.Op.Method.Name.Equals("Power") && rhsNumeric)
                {
                    return(true);
                }
            }
            return(false);
        }
コード例 #8
0
ファイル: Term.cs プロジェクト: JakeCode11/CSharp.Logic
        public override bool Equals(object obj)
        {
            if (obj is Term)
            {
                var term = obj as Term;
                if (!Op.Equals(term.Op))
                {
                    return(false);
                }

                var lst  = Args as List <object>;
                var lst1 = term.Args as List <object>;
                Debug.Assert(lst != null);
                Debug.Assert(lst1 != null);
                if (lst.Count != lst1.Count)
                {
                    return(false);
                }

                for (int i = 0; i < lst.Count; i++)
                {
                    var curr1 = lst[i];
                    var curr2 = lst1[i];

                    bool isNum1 = LogicSharp.IsNumeric(curr1);
                    bool isNum2 = LogicSharp.IsNumeric(curr2);
                    bool result;
                    if (isNum1 && isNum2)
                    {
                        result = LogicSharp.NumericEqual(curr1, curr2);
                    }
                    else
                    {
                        if (curr1 == null || curr2 == null)
                        {
                            return(false);
                        }
                        result = curr1.Equals(curr2);
                    }
                    if (!result)
                    {
                        return(false);
                    }
                }
                return(true);
                //return !lst.Where((t, i) => !t.Equals(lst1[i])).Any();
            }
            return(false);
        }
コード例 #9
0
        /*
         * E.g -1*x=2
         */
        private static bool SatisfyTransitiveCondition3(object lhs, object rhs)
        {
            return(false);

            bool rhsNumeric = LogicSharp.IsNumeric(rhs);

            if (!rhsNumeric)
            {
                return(false);
            }

            var lhsTerm = lhs as Term;

            if (lhsTerm == null)
            {
                return(false);
            }
            if (!lhsTerm.Op.Method.Name.Equals("Multiply"))
            {
                return(false);
            }
            var lst = lhsTerm.Args as List <object>;

            Debug.Assert(lst != null);
            foreach (var temp in lst)
            {
                bool isNumber = LogicSharp.IsNumeric(temp);
                if (isNumber)
                {
                    return(true);
                }
                var term = temp as Term;
                if (term != null && !term.ContainsVar())
                {
                    return(true);
                }
            }
            return(false);
        }
コード例 #10
0
        private static bool SatisfyTransitiveCondition5(
            object lhs, object rhs, out object newLhs, out object newRhs)
        {
            newLhs = null;
            newRhs = null;
            var lhsTerm = lhs as Term;

            if (lhsTerm != null && lhsTerm.Op.Method.Name.Equals("Divide"))
            {
                var lst = lhsTerm.Args as List <object>;
                Debug.Assert(lst != null);
                Debug.Assert(lst.Count == 2);
                bool denomIsNum = LogicSharp.IsNumeric(lst[1]);
                if (denomIsNum)
                {
                    newLhs = lst[0];
                    newRhs = new Term(Expression.Multiply, new List <object> {
                        lst[1], rhs
                    });
                    return(true);
                }
            }
            var rhsTerm = rhs as Term;

            if (rhsTerm != null && rhsTerm.Op.Method.Name.Equals("Divide"))
            {
                var  lst        = rhsTerm.Args as List <object>;
                bool denomIsNum = LogicSharp.IsNumeric(lst[1]);
                if (denomIsNum)
                {
                    newLhs = new Term(Expression.Multiply, new List <object> {
                        lst[1], lhs
                    });
                    newRhs = lst[0];
                    return(true);
                }
            }
            return(false);
        }
コード例 #11
0
        /*
         * E.g 2/y=4, x/2=4
         */
        private static bool SatisfyTransitiveCondition4(object lhs, object rhs)
        {
            bool rhsNumeric = LogicSharp.IsNumeric(rhs);

            if (!rhsNumeric)
            {
                return(false);
            }

            var lhsTerm = lhs as Term;

            if (lhsTerm == null)
            {
                return(false);
            }
            if (!lhsTerm.Op.Method.Name.Equals("Divide"))
            {
                return(false);
            }
            var lst = lhsTerm.Args as List <object>;

            Debug.Assert(lst != null);
            if (lst.Count != 2)
            {
                return(false);
            }
            foreach (var temp in lst)
            {
                bool isNumber = LogicSharp.IsNumeric(temp);
                if (isNumber)
                {
                    return(true);
                }
            }
            return(false);
        }
コード例 #12
0
ファイル: Term.cs プロジェクト: JakeCode11/CSharp.Logic
        public override string ToString()
        {
            var builder = new StringBuilder();

            var tuple = Args as Tuple <object, object>;

            if (tuple != null)
            {
                #region Tuple Format
                builder.Append('(');

                var lTerm = tuple.Item1;
                var rTerm = tuple.Item2;

                builder.Append(lTerm);

                if (Op.Method.Name.Equals("Add"))
                {
                    builder.Append('+');
                }
                else if (Op.Method.Name.Equals("Substract"))
                {
                    builder.Append('-');
                }
                else if (Op.Method.Name.Equals("Multiply"))
                {
                    builder.Append('*');
                }
                else if (Op.Method.Name.Equals("Divide"))
                {
                    builder.Append('/');
                }

                builder.Append(rTerm.ToString());
                builder.Append(')');
                #endregion
            }

            var lst = Args as List <object>;
            if (lst != null)
            {
                for (int i = 0; i < lst.Count; i++)
                {
                    var  variable  = lst[i] as Var;
                    bool number    = LogicSharp.IsNumeric(lst[i]);
                    var  localTerm = lst[i] as Term;

                    #region Var
                    if (variable != null)
                    {
                        if (Op.Method.Name.Equals("Add"))
                        {
                            if (i != 0)
                            {
                                builder.Append("+");
                            }
                        }

                        if (Op.Method.Name.Equals("Power"))
                        {
                            if (i != 0)
                            {
                                builder.Append("^");
                            }
                        }
                        builder.Append(variable);
                    }
                    #endregion

                    #region Numerics
                    if (number)
                    {
                        if (Op.Method.Name.Equals("Add"))
                        {
                            if (i != 0)
                            {
                                double dnum;
                                bool   result = LogicSharp.IsDouble(lst[i], out dnum);
                                if (dnum < 0.0)
                                {
                                    builder.Append("-");
                                    double absNum = Math.Abs(dnum);
                                    builder.Append(absNum);
                                }
                                else
                                {
                                    builder.Append("+");
                                    builder.Append(lst[i].ToString());
                                }
                            }
                            else
                            {
                                builder.Append(lst[i].ToString());
                            }
                        }
                        else if (Op.Method.Name.Equals("Multiply"))
                        {
                            double dnum;
                            LogicSharp.IsDouble(lst[i], out dnum);
                            double absNum = Math.Abs(dnum) - 1.0;
                            if (absNum > 0.0001)
                            {
                                builder.Append(lst[i]);
                            }
                            else
                            {
                                if (dnum < 0.0d)
                                {
                                    builder.Append("-");
                                }
                            }
                        }
                        else if (Op.Method.Name.Equals("Divide"))
                        {
                            if (i != 0)
                            {
                                builder.Append("/");
                                builder.Append(lst[i].ToString());
                            }
                            else
                            {
                                builder.Append(lst[i].ToString());
                            }
                        }
                        else if (Op.Method.Name.Equals("Power"))
                        {
                            if (i != 0)
                            {
                                builder.Append("^");
                            }
                            builder.Append(lst[i].ToString());
                        }
                    }
                    #endregion

                    #region Term
                    if (localTerm != null)
                    {
                        //precatch
                        if (Op.Method.Name.Equals("Add"))
                        {
                            if (i != 0)
                            {
                                bool result = localTerm.InvertOp();
                                if (!result)
                                {
                                    builder.Append("+");
                                }

                                /*else
                                 * {
                                 *  builder.Append("-");
                                 * }*/
                            }
                            builder.Append(localTerm.ToString());
                        }

                        if (Op.Method.Name.Equals("Multiply") ||
                            Op.Method.Name.Equals("Power")
                            )
                        {
                            bool needBrace = false;
                            needBrace = localTerm.NeedBracket();
                            if (needBrace)
                            {
                                builder.Append("(");
                                builder.Append(localTerm.ToString());
                                builder.Append(")");
                            }
                            else
                            {
                                builder.Append(localTerm.ToString());
                            }
                        }

                        if (Op.Method.Name.Equals("Divide"))
                        {
                            if (i != 0)
                            {
                                builder.Append("/");
                            }
                            bool needBrace = false;
                            needBrace = localTerm.NeedBracket();
                            if (needBrace)
                            {
                                builder.Append("(");
                                builder.Append(localTerm.ToString());
                                builder.Append(")");
                            }
                            else
                            {
                                builder.Append(localTerm.ToString());
                            }
                        }
                    }
                    #endregion
                }
            }

            return(builder.ToString());
        }
コード例 #13
0
        private static bool SatisfyAssociativeCondition(Term inTerm,
                                                        object obj1, object obj2, out object output1, out object output2)
        {
            output1 = null;
            output2 = null;
            if (inTerm.Op.Method.Name.Equals("Add"))
            {
                var term1 = obj1 as Term;
                var term2 = obj2 as Term;

                if (term1 != null && term2 != null)
                {
                    if (term1.Op.Method.Name.Equals("Add") &&
                        term2.Op.Method.Name.Equals("Add"))
                    {
                        var term1Args = term1.Args as List <object>;
                        var term2Args = term2.Args as List <object>;

                        if (term1Args != null && term2Args != null)
                        {
                            var term1Arg2 = term1Args[1];
                            var term2Arg2 = term2Args[1];
                            if (LogicSharp.IsNumeric(term1Arg2) &&
                                LogicSharp.IsNumeric(term2Arg2))
                            {
                                output1 = new Term(Expression.Add, new List <object> {
                                    term1Args[0], term2Args[0]
                                });
                                output2 = new Term(Expression.Add, new List <object> {
                                    term1Arg2, term2Arg2
                                });
                                return(true);
                            }
                        }
                    }

/*                    if (term1.Op.Method.Name.Equals("Add") && term2.Op.Method.Name.Equals("Multiply"))
 *                  {
 *                      var lst = term1.Args as List<object>;
 *                      object obj = lst[lst.Count-1];
 *                      if (LogicSharp.IsNumeric(obj) || NotSpecialVariables(obj))
 *                      {
 *                          var newLst = new List<object>();
 *                          for (var i = 0; i < lst.Count - 1; i++)
 *                          {
 *                              newLst.Add(lst[i]);
 *                          }
 *                          output1 = newLst.Count == 1 ? newLst[0] : new Term(Expression.Add, newLst);
 *                          output2 = new Term(Expression.Add, new List<object>() { obj, obj2 });
 *                          return true;
 *                      }
 *                  }*/
                    if (term1.Op.Method.Name.Equals("Multiply") && term2.Op.Method.Name.Equals("Add"))
                    {
                        var    lst = term2.Args as List <object>;
                        object obj = lst[lst.Count - 1];
                        if (LogicSharp.IsNumeric(obj) || NotSpecialVariables(obj))
                        {
                            var newLst = new List <object>();
                            for (var i = 0; i < lst.Count - 1; i++)
                            {
                                newLst.Add(lst[i]);
                            }
                            newLst.Insert(0, obj1);
                            output1 = new Term(Expression.Add, newLst);
                            output2 = obj;
                            return(true);
                        }
                    }
                }

                if (term1 != null && term2 == null)
                {
                    if (!term1.Op.Method.Name.Equals("Add"))
                    {
                        return(false);
                    }
                    var lst = term1.Args as List <object>;
                    Debug.Assert(lst != null);
                    object obj = lst[lst.Count - 1];
                    if (LogicSharp.IsNumeric(obj) || NotSpecialVariables(obj))
                    {
                        var newLst = new List <object>();
                        for (var i = 0; i < lst.Count - 1; i++)
                        {
                            newLst.Add(lst[i]);
                        }
                        output1 = newLst.Count == 1 ? newLst[0] : new Term(Expression.Add, newLst);
                        output2 = new Term(Expression.Add, new List <object>()
                        {
                            obj, obj2
                        });
                        return(true);
                    }
                    return(false);
                }
            }
            else if (inTerm.Op.Method.Name.Equals("Multiply"))
            {
                var term1 = obj1 as Term;
                var term2 = obj2 as Term;
                if (term1 == null && term2 != null)
                {
                    if (term2.Op.Method.Name.Equals("Multiply"))
                    {
                        var lst = term2.Args as List <object>;
                        Debug.Assert(lst != null);
                        object obj = lst[0];
                        if (LogicSharp.IsNumeric(obj) || NotSpecialVariables(obj))
                        {
                            output1 = new Term(Expression.Multiply, new List <object>()
                            {
                                obj1, obj
                            });
                            var newLst = new List <object>();
                            for (var i = 1; i < lst.Count; i++)
                            {
                                newLst.Add(lst[i]);
                            }
                            output2 = newLst.Count == 1 ? newLst[0] : new Term(Expression.Multiply, newLst);
                            return(true);
                        }
                    }
                }
            }
            return(false);
        }
コード例 #14
0
        //commutative law
        private static bool SatisfyCommutativeCondition(Term inTerm, object obj1, object obj2)
        {
            if (inTerm.Op.Method.Name.Equals("Add"))
            {
                //e.g 3+x => x+3
                if (LogicSharp.IsNumeric(obj1))
                {
                    var variable = obj2 as Var;
                    if (variable != null)
                    {
                        return(true);
                    }
                    var term = obj2 as Term;
                    if (term != null && term.ContainsVar())
                    {
                        return(true);
                    }
                }

                //e.g (1+1)+(x+1)=>(x+1)+(1+1)
                var term1 = obj1 as Term;
                if (term1 != null && !term1.ContainsVar())
                {
                    var variable = obj2 as Var;
                    if (variable != null)
                    {
                        return(true);
                    }

                    var term = obj2 as Term;
                    if (term != null && term.ContainsVar())
                    {
                        return(true);
                    }
                }

                var variable11 = obj1 as Var;
                var term2      = obj2 as Term;

                if (variable11 != null && term2.QuadraticTerm())
                {
                    return(true);
                }

                //(2*y)+(2*x) -> (2*x)+(2*y)
                // x + x^2    -> x^2 + x
                if (term1 != null && term2 != null)
                {
                    var term1Lst = term1.Args as List <object>;
                    Debug.Assert(term1Lst != null);
                    var term1Var = term1Lst[1] as Var;

                    var term2Lst = term2.Args as List <object>;
                    Debug.Assert(term2Lst != null);
                    var term2Var = term2Lst[1] as Var;
                    if (term1Var != null && term2Var != null)
                    {
                        bool condition1 = term1Var.ToString().Equals("Y") ||
                                          term1Var.ToString().Equals("y");
                        bool condition2 = term2Var.ToString().Equals("X") ||
                                          term2Var.ToString().Equals("x");
                        if (condition1 && condition2)
                        {
                            return(true);
                        }
                    }
                    if (!term1.QuadraticTerm() && term2.QuadraticTerm())
                    {
                        return(true);
                    }
                }
            }
            else if (inTerm.Op.Method.Name.Equals("Multiply"))
            {
                var term1 = obj1 as Term;
                var term2 = obj2 as Term;

                /*                if (term1 != null && term2 == null)
                 *              {
                 *                  return true;
                 *              }*/

                //e.g x*3 -> 3*x
                //e.g 3*x*3 -> x*3*3
                if (LogicSharp.IsNumeric(obj2))
                {
                    var variable = obj1 as Var;
                    if (variable != null)
                    {
                        return(true);
                    }
                    var term = obj1 as Term;
                    if (term != null && term.ContainsVar())
                    {
                        return(true);
                    }
                }
            }
            return(false);
        }
コード例 #15
0
        /// <summary>
        /// if x = y and y = z, then x = z
        /// if x = y, then x + a = y + a
        /// if x^2 = y^2, then x = y
        /// if x = y, then ax = ay
        /// ax = ay -> x=y
        /// </summary>
        /// <param name="goal"></param>
        /// <param name="gGoal"></param>
        /// <returns></returns>
        public static object ApplyTransitive(this Equation currentEq, Equation rootEq, bool withEqRule,
                                             bool lineCheck = false)
        {
            Equation localEq = currentEq;
            object   lhs     = currentEq.Lhs;
            object   rhs     = currentEq.Rhs;

            if (!withEqRule)
            {
                return(localEq);
            }

            //Power Inverse
            if (SatisfyTransitiveCondition2(lhs, rhs))
            {
                #region Condition2

                var cloneEq  = currentEq.Clone();
                var cloneEq2 = currentEq.Clone();

                var lhsTerm = cloneEq.Lhs as Term;
                Debug.Assert(lhsTerm != null);
                var cloneLst = lhsTerm.Args as List <object>;
                Debug.Assert(cloneLst != null);
                cloneEq.Lhs = cloneLst[0];
                cloneEq.Rhs = new Term(Expression.Power, new List <object>()
                {
                    cloneEq.Rhs, 0.5
                });

                var lhsTerm2 = cloneEq2.Lhs as Term;
                Debug.Assert(lhsTerm2 != null);
                var cloneLst2 = lhsTerm2.Args as List <object>;
                Debug.Assert(cloneLst2 != null);
                cloneEq2.Lhs = cloneLst2[0];
                var internal1 = new Term(Expression.Power, new List <object>()
                {
                    cloneEq2.Rhs, 0.5
                });
                cloneEq2.Rhs = new Term(Expression.Multiply, new List <object>()
                {
                    -1, internal1
                });

                string rule        = EquationsRule.Rule(EquationsRule.EquationRuleType.Transitive);
                string appliedRule = EquationsRule.Rule(
                    EquationsRule.EquationRuleType.Transitive,
                    localEq, null);
                string KC = EquationsRule.RuleConcept(EquationsRule.EquationRuleType.Transitive);
                var    ts = new TraceStep(localEq, cloneEq, KC, rule, appliedRule);
                rootEq._innerLoop.Add(ts);
                //localEq = cloneEq;

                var lst = new List <Equation>();
                lst.Add(cloneEq);
                lst.Add(cloneEq2);
                return(lst);

                #endregion
            }

            if (!lineCheck)
            {
                //Add Inverse
                if (SatifyTransitiveCondition0(lhs, rhs))
                {
                    #region condition0

                    var cloneEq = currentEq.Clone();

                    var rhsTerm = new Term(Expression.Add, new List <object>()
                    {
                        cloneEq.Rhs
                    });

                    var lhsTerm = cloneEq.Lhs as Term;
                    Debug.Assert(lhsTerm != null);

                    var lst = lhsTerm.Args as List <object>;
                    Debug.Assert(lst != null);

                    for (int i = 0; i < lst.Count; i++)
                    {
                        var  temp     = lst[i];
                        bool isNumber = LogicSharp.IsNumeric(temp);
                        if (isNumber)
                        {
                            var inverseRhs = new Term(Expression.Multiply, new List <object>()
                            {
                                -1, temp
                            });
                            lst.Remove(temp);
                            var rhsArgLst = rhsTerm.Args as List <object>;
                            Debug.Assert(rhsArgLst != null);
                            rhsArgLst.Add(inverseRhs);
                            break;
                        }

                        var term = temp as Term;
                        if (term != null && !term.ContainsVar())
                        {
                            var inverseRhs = new Term(Expression.Multiply, new List <object>()
                            {
                                -1, temp
                            });
                            lst.Remove(i);
                            var rhsArgLst = rhsTerm.Args as List <object>;
                            Debug.Assert(rhsArgLst != null);
                            rhsArgLst.Add(inverseRhs);
                            break;
                        }
                    }

                    cloneEq.Rhs = rhsTerm;
                    if (lst.Count == 1)
                    {
                        cloneEq.Lhs = lst[0];
                    }

                    string rule        = EquationsRule.Rule(EquationsRule.EquationRuleType.Transitive);
                    string appliedRule = EquationsRule.Rule(
                        EquationsRule.EquationRuleType.Transitive,
                        localEq, null);

                    string KC = EquationsRule.RuleConcept(EquationsRule.EquationRuleType.Transitive);

                    var traceStep = new TraceStep(localEq, cloneEq, KC, rule, appliedRule);
                    rootEq._innerLoop.Add(traceStep);
                    localEq = cloneEq;
                    return(localEq);

                    #endregion
                }
            }
            else
            {
                if (SatisfyTransitiveCondition1(lhs, rhs))
                {
                    #region Condition1
                    var cloneEq = currentEq.Clone();


                    var inverseRhs = new Term(Expression.Multiply, new List <object>()
                    {
                        -1, rhs
                    });
                    var lhsTerm = cloneEq.Lhs as Term;
                    if (lhsTerm != null)
                    {
                        var cloneLst = lhsTerm.Args as List <object>;
                        Debug.Assert(cloneLst != null);
                        if (lhsTerm.Op.Method.Name.Equals("Add"))
                        {
                            cloneLst.Add(inverseRhs);
                        }
                        else
                        {
                            cloneEq.Lhs = new Term(Expression.Add, new List <object>()
                            {
                                lhs, inverseRhs
                            });
                        }
                    }
                    else
                    {
                        cloneEq.Lhs = new Term(Expression.Add, new List <object>()
                        {
                            lhs, inverseRhs
                        });
                    }
                    cloneEq.Rhs = 0;
                    string rule        = EquationsRule.Rule(EquationsRule.EquationRuleType.Transitive);
                    string appliedRule = EquationsRule.Rule(
                        EquationsRule.EquationRuleType.Transitive,
                        localEq, null);

                    string KC = EquationsRule.RuleConcept(EquationsRule.EquationRuleType.Transitive);

                    var traceStep = new TraceStep(localEq, cloneEq, KC, rule, appliedRule);
                    rootEq._innerLoop.Add(traceStep);
                    localEq = cloneEq;
                    #endregion
                }
            }

            //Mutliply Inverse
            if (SatisfyTransitiveCondition3(lhs, rhs))
            {
                #region condition3

                var cloneEq = currentEq.Clone();

                var rhsTerm = new Term(Expression.Multiply, new List <object>()
                {
                    cloneEq.Rhs
                });

                var lhsTerm = cloneEq.Lhs as Term;
                Debug.Assert(lhsTerm != null);

                var lst = lhsTerm.Args as List <object>;
                Debug.Assert(lst != null);

                for (int i = 0; i < lst.Count; i++)
                {
                    var  temp     = lst[i];
                    bool isNumber = LogicSharp.IsNumeric(temp);
                    if (isNumber)
                    {
                        var inverseRhs = new Term(Expression.Divide, new List <object>()
                        {
                            1, temp
                        });
                        lst.Remove(temp);
                        var rhsArgLst = rhsTerm.Args as List <object>;
                        Debug.Assert(rhsArgLst != null);
                        rhsArgLst.Add(inverseRhs);
                        break;
                    }

                    var term = temp as Term;
                    if (term != null && !term.ContainsVar())
                    {
                        var inverseRhs = new Term(Expression.Divide, new List <object>()
                        {
                            1, temp
                        });
                        lst.Remove(i);
                        var rhsArgLst = rhsTerm.Args as List <object>;
                        Debug.Assert(rhsArgLst != null);
                        rhsArgLst.Add(inverseRhs);
                        break;
                    }
                }

                cloneEq.Rhs = rhsTerm;
                if (lst.Count == 1)
                {
                    cloneEq.Lhs = lst[0];
                }

                string rule        = EquationsRule.Rule(EquationsRule.EquationRuleType.Transitive);
                string appliedRule = EquationsRule.Rule(
                    EquationsRule.EquationRuleType.Transitive,
                    localEq, null);

                string KC = EquationsRule.RuleConcept(EquationsRule.EquationRuleType.Transitive);

                var traceStep = new TraceStep(localEq, cloneEq, KC, rule, appliedRule);
                rootEq._innerLoop.Add(traceStep);
                localEq = cloneEq;
                return(localEq);

                #endregion
            }

            //Divide Inverse
            if (SatisfyTransitiveCondition4(lhs, rhs))
            {
                #region condition4
                var cloneEq = currentEq.Clone();

                var lhsTerm = cloneEq.Lhs as Term;
                Debug.Assert(lhsTerm != null);

                var lst = lhsTerm.Args as List <object>;
                Debug.Assert(lst != null);
                Debug.Assert(lst.Count == 2);

                bool numerator   = LogicSharp.IsNumeric(lst[0]);
                bool deNumerator = LogicSharp.IsNumeric(lst[1]);

                if (deNumerator)
                {
                    var rhsTerm = new Term(Expression.Multiply, new List <object>()
                    {
                        lst[1], cloneEq.Rhs
                    });
                    var newEq = new Equation(lst[0], rhsTerm);

                    string rule        = EquationsRule.Rule(EquationsRule.EquationRuleType.Transitive);
                    string appliedRule = EquationsRule.Rule(
                        EquationsRule.EquationRuleType.Transitive,
                        localEq, newEq);

                    string KC = EquationsRule.RuleConcept(EquationsRule.EquationRuleType.Transitive);

                    var traceStep = new TraceStep(localEq, newEq, KC, rule, appliedRule);
                    rootEq._innerLoop.Add(traceStep);
                    localEq = newEq;
                    return(localEq);
                }


                if (numerator)
                {
                    var rhsTerm = new Term(Expression.Divide, new List <object>()
                    {
                        lst[0], cloneEq.Rhs
                    });
                    var    newEq       = new Equation(lst[1], rhsTerm);
                    string rule        = EquationsRule.Rule(EquationsRule.EquationRuleType.Transitive);
                    string appliedRule = EquationsRule.Rule(
                        EquationsRule.EquationRuleType.Transitive,
                        localEq, newEq);

                    string KC = EquationsRule.RuleConcept(EquationsRule.EquationRuleType.Transitive);

                    var traceStep = new TraceStep(localEq, newEq, KC, rule, appliedRule);
                    rootEq._innerLoop.Add(traceStep);
                    localEq = newEq;
                    return(localEq);
                }

                #endregion
            }

            return(localEq);
        }