public void TestForComparation()
{
Variable x = new Variable("x");
var c1 = x + x;
var c2 = x + x;
Assert.AreEqual(c1.GetHashCode(), c2.GetHashCode());
}
public void TestForSimplification()
{
Variable x = new Variable("x");
Expression s1 = SMath.Exp(SMath.Ln(x));
Assert.AreEqual(s1.Simplify(), x);
Expression s2 = SMath.Ln(SMath.Exp(x));
Assert.AreEqual(s2.Simplify(), x);
Expression s3 = SMath.Sqrt((SMath.Exp(SMath.Ln(x)) - x) ^ 10);
Assert.AreEqual(s3.Simplify(), Constant.Zero);
Expression s4 = (x ^ 6) / (x ^ 4);
Assert.AreEqual(s4.Simplify(), x ^ 2);
Expression s5 = (x ^ 6) * (x ^ 9);
Assert.AreEqual(s5.Simplify(), x ^ 15);
Expression s6 = (Constant.One ^ 6) ^ 2;
Assert.AreEqual(s6.Simplify(), Constant.One);
}
public void TestForDerivation()
{
Variable x = new Variable("x");
Variable y = new Variable("y");
Expression e = SMath.Exp(x + y);
Expression dx = e.Derivate(x).Simplify();
Assert.AreEqual(dx, e);
Expression dy = e.Derivate(y).Simplify();
Assert.AreEqual(dy, e);
Expression dxy = e.Derivate(x).Derivate(y).Simplify();
Assert.AreEqual(dxy, e);
Expression xdy = x.Derivate(y).Simplify();
Assert.AreEqual(xdy, Constant.Zero);
Expression ydx = y.Derivate(x).Simplify();
Assert.AreEqual(ydx, Constant.Zero);
Expression d1 = (x * y).Derivate(x).Simplify();
Assert.AreEqual(d1, y);
Expression d2 = (x * y).Derivate(y).Simplify();
Assert.AreEqual(d2, x);
Expression d3 = (x + y).Derivate(x).Simplify();
Assert.AreEqual(d3, Constant.One);
Expression d4 = (x + y).Derivate(y).Simplify();
Assert.AreEqual(d4, Constant.One);
Expression d5 = (1 / x).Derivate(x).Simplify();
Assert.AreEqual(d5, -(1 / x ^ 2));
}
static Expression LaplaceTransform(Expression expr, Variable t, Variable s)
{
return 0;
}
static double NSolve(Expression f, Variable v, double v0 = 0, double eps = 1e-6)
{
double vn1 = v0;
Expression phi = v - f / f.Derivate(v).Simplify();
v.Value = vn1;
do
{
vn1 = phi.Process();
v.Value = vn1;
} while (Math.Abs(f.Process()) > eps);
return vn1;
}
static double NIntegrate(Expression f, Variable v, double a, double b, double eps = 1e-2)
{
double res = 0;
Expression df = f.Derivate(v).Simplify();
v.Value = a;
for (double pv = a, cv = a + eps, step = eps;
cv < b + step / 2;
v.Value = cv, step = eps / (1 + Math.Abs(df.Process())), pv = cv, cv += step)
{
v.Value = (pv + cv) / 2;
res += step * f.Process();
}
return res;
}
public override Expression Derivate(Variable dv)
{
return Constant.Zero;
}
static Expression Solve(Expression left, Expression right, Variable v)
{
left = left.Simplify();
right = right.Simplify();
Console.WriteLine("\t{0} = {1} // {2} == {3}", left, right, left.GetType().Name, right.GetType().Name);
if (!left.IsDependOf(v)) throw new Exception("Can't solve equation. No dependencies of variable '" + v.Name + "'.");
if (left is Symbolic.Operators.Scalar.Add)
{
Expression ll = Left(left);
Expression lr = Right(left);
if (lr.IsDependOf(v)) return Solve(lr, right - ll, v);
else return Solve(ll, right - lr, v);
}
else if (left is Symbolic.Operators.Scalar.Sub)
{
Expression ll = Left(left);
Expression lr = Right(left);
if (lr.IsDependOf(v)) return Solve(-lr, right - ll, v);
else return Solve(ll, right + lr, v);
}
else if (left is Symbolic.Operators.Scalar.Div)
{
Expression ll = Left(left);
Expression lr = Right(left);
if (lr.IsDependOf(v)) return Solve(lr, ll / right, v);
else return Solve(ll, right * lr, v);
}
else if (left is Symbolic.Operators.Scalar.Mul)
{
Expression ll = Left(left);
Expression lr = Right(left);
if (lr.IsDependOf(v)) return Solve(lr, right / ll, v);
else return Solve(ll, right / lr, v);
}
else if (left is Symbolic.Operators.Scalar.Pow)
{
Expression ll = Left(left);
Expression lr = Right(left);
if (lr.IsDependOf(v)) return Solve(lr, SMath.Log(right, ll), v);
else return Solve(ll, right ^ (1 / lr), v);
}
else if (left is Symbolic.Functions.Sqrt)
{
Expression ll = (left as Symbolic.Functions.Sqrt).Args[0];
return Solve(ll, right ^ 2, v);
}
else if (left is Symbolic.Functions.Sin)
{
Expression ll = (left as Symbolic.Functions.Sin).Args[0];
return Solve(ll, SMath.ArcSin(right), v);
}
else if (left is Symbolic.Functions.Cos)
{
Expression ll = (left as Symbolic.Functions.Cos).Args[0];
return Solve(ll, SMath.ArcCos(right), v);
}
else if (left is Symbolic.Functions.Tan)
{
Expression ll = (left as Symbolic.Functions.Tan).Args[0];
return Solve(ll, SMath.ArcTan(right), v);
}
else if (left is Symbolic.Functions.ArcSin)
{
Expression ll = (left as Symbolic.Functions.ArcSin).Args[0];
return Solve(ll, SMath.Sin(right), v);
}
else if (left is Symbolic.Functions.ArcCos)
{
Expression ll = (left as Symbolic.Functions.ArcCos).Args[0];
return Solve(ll, SMath.Cos(right), v);
}
else if (left is Symbolic.Functions.ArcTan)
{
Expression ll = (left as Symbolic.Functions.ArcTan).Args[0];
return Solve(ll, SMath.Tan(right), v);
}
else if (left is Symbolic.Functions.Exp)
{
Expression ll = (left as Symbolic.Functions.Exp).Args[0];
return Solve(ll, SMath.Ln(right), v);
}
else if (left is Symbolic.Functions.Ln)
{
Expression ll = (left as Symbolic.Functions.Ln).Args[0];
return Solve(ll, SMath.Exp(right), v);
}
else if (left is Variable && left.IsDependOf(v)) return right;
else throw new Exception("Can't solve equation. Unknown equation type.");
}
public override Expression Derivate(Variable dv)
{
throw new NotImplementedException();
}
public override Expression Replace(Variable v, Expression expr)
{
return this;
}
static Expression Laplace(Expression expr, Variable x, Variable y, Variable z)
{
return expr.Derivate(x, 2).Simplify() + expr.Derivate(y, 2).Simplify() + expr.Derivate(z, 2).Simplify();
}
static Expression TableIntegral(Expression expr, Variable v)
{
if (expr is Constant)
{
if (expr == Constant.Zero) return Constant.One;
else return expr * v;
}
//else if (expr is Symbolic.Functions.Sin) ;
else throw new NotImplementedException();
}
public override bool IsDependOf(Variable var)
{
throw new NotImplementedException();
}
public override Expression Replace(Variable v, Expression expr)
{
if (this == v) return expr;
else return this;
}
public override bool IsDependOf(Variable var)
{
return var.Name == this.Name;
}
public override Expression Derivate(Variable dv)
{
if (dv.Name == this.Name) return Constant.One;
else return Constant.Zero;
}
public new Vector Replace(Variable v, Expression expr)
{
throw new NotImplementedException();
}
static Expression Integrate(Expression expr, Variable v)
{
if (IsAddOp(expr))
{
var l = Left(expr);
var r = Right(expr);
if (expr is Symbolic.Operators.Scalar.Add) return Integrate(l, v) + Integrate(r, v);
else return Integrate(l, v) - Integrate(r, v);
}
else if (expr is Symbolic.Operators.Scalar.Mul)
{
if (!Left(expr).IsDependOf(v)) return Left(expr) * Integrate(Right(expr), v);
else if (!Right(expr).IsDependOf(v)) return Right(expr) * Integrate(Left(expr), v);
else throw new NotImplementedException(); //Partial integration
}
else return TableIntegral(expr, v);
}
public override bool IsDependOf(Variable var)
{
return false;
}
public static void Main(string[] args)
{
var x = new Variable("x");
var y = new Variable("y");
var z = new Variable("z");
var u = new Variable("u");
var f = x ^ x;
Console.WriteLine(f);
Console.WriteLine(f.Derivate(x));
Console.ReadKey();
}
public override Expression Derivate(Variable dv)
{
return this;
}
