protected override Expression VisitBinary(Binary B)
{
Expression L = Visit(B.Left);
Expression R = Visit(B.Right);
// Evaluate substitution operators.
if (B is Substitute)
{
return(Visit(L.Substitute(Set.MembersOf(R).Cast <Arrow>())));
}
Real?LR = AsReal(L);
Real?RR = AsReal(R);
// Evaluate relational operators on constants.
if (LR != null && RR != null)
{
switch (B.Operator)
{
case Operator.Equal: return(Constant.New(LR.Value == RR.Value));
case Operator.NotEqual: return(Constant.New(LR.Value != RR.Value));
case Operator.Less: return(Constant.New(LR.Value < RR.Value));
case Operator.Greater: return(Constant.New(LR.Value <= RR.Value));
case Operator.LessEqual: return(Constant.New(LR.Value > RR.Value));
case Operator.GreaterEqual: return(Constant.New(LR.Value >= RR.Value));
case Operator.ApproxEqual: return(Constant.New(
LR.Value == RR.Value ||
Real.Abs(LR.Value - RR.Value) < 1e-12 * Real.Max(Real.Abs(LR.Value), Real.Abs(RR.Value))));
}
}
// Evaluate boolean operators if possible.
switch (B.Operator)
{
case Operator.And:
if (IsFalse(LR) || IsFalse(RR))
{
return(Constant.New(false));
}
else if (IsTrue(LR) && IsTrue(RR))
{
return(Constant.New(true));
}
break;
case Operator.Or:
if (IsTrue(LR) || IsTrue(RR))
{
return(Constant.New(true));
}
else if (IsFalse(LR) && IsFalse(RR))
{
return(Constant.New(false));
}
break;
case Operator.Equal:
case Operator.ApproxEqual:
if (L.Equals(R))
{
return(Constant.New(true));
}
break;
case Operator.NotEqual:
if (L.Equals(R))
{
return(Constant.New(false));
}
break;
}
return(Binary.New(B.Operator, L, R));
}
/// <summary>
/// Solve a differential equation or system of differential equations f for functions y[t], with initial conditions y^(n)[0] = y0.
/// </summary>
/// <param name="f">Equation or set of equations to solve.</param>
/// <param name="y">Functions to solve for.</param>
/// <param name="y0">Values for y^(n)[0].</param>
/// <param name="t">Independent variable.</param>
/// <returns>Expression or set of expressions for y.</returns>
public static Expression DSolve(Expression f, Expression y, Expression y0, Expression t)
{
IEnumerable <Expression> result = Set.MembersOf(f).Cast <Equal>().DSolve(Set.MembersOf(y), Set.MembersOf(y0).Cast <Arrow>(), t);
return((f is Set || result.Count() != 1) ? Set.New(result) : result.Single());
}
public static bool DependsOn(this IEnumerable <Expression> f, Expression x)
{
return(DependsOn(f, Set.MembersOf(x)));
}
public static Expression NSolve(Expression f, Expression x)
{
IEnumerable <Expression> result = Set.MembersOf(f).Cast <Equal>().NSolve(Set.MembersOf(x).Cast <Arrow>());
return((f is Set || result.Count() != 1) ? Set.New(result) : result.Single());
}
/// <summary>
/// Check if f is a function of x.
/// </summary>
/// <param name="f"></param>
/// <param name="x"></param>
/// <returns>true if f is a function of x.</returns>
public static bool DependsOn(this Expression f, Expression x)
{
return(DependsOn(f, Set.MembersOf(x)));
}
