static void Main(string[] args)
{
// 3 * (y + x)
var e1 =
new Mult(
new Const(3),
new Plus(
new Var("y"),
new Var("x")
)
);
// 3 * y + x
var e2 =
new Plus(
new Mult(
new Const(3),
new Var("y")
),
new Var("x")
);
Console.WriteLine(e1); // (3 * (y + x))
Console.WriteLine(e2); // ((3 * y) + x)
var env = new Dictionary <string, int>
{
{ "x", 2 },
{ "y", 4 }
};
Console.WriteLine(e1.Eval(env)); // 18
Console.WriteLine(e2.Eval(env)); // 14
// x^2 + xy + y^3
var e3 =
new Plus(
new Mult(
new Var("x"),
new Var("x")
),
new Plus(
new Mult(
new Var("x"),
new Var("y")
),
new Mult(
new Var("y"),
new Mult(
new Var("y"),
new Var("y")
)
)
)
);
Console.WriteLine(e3); // ((x * x) + ((x * y) + (y * (y * y))))
var e3x = e3.Deriv("x");
var e3y = e3.Deriv("y");
Console.WriteLine(e3x); // (((1 * x) + (x * 1)) + (((1 * y) + (x * 0)) + ((0 * (y * y)) + (y * ((0 * y) + (y * 0))))))
Console.WriteLine(e3y); // (((0 * x) + (x * 0)) + (((0 * y) + (x * 1)) + ((1 * (y * y)) + (y * ((1 * y) + (y * 1))))))
// Compute slope at point (1, 1)
env = new Dictionary <string, int>
{
{ "x", 1 },
{ "y", 1 }
};
Console.WriteLine(e3x.Eval(env)); // 3
Console.WriteLine(e3y.Eval(env)); // 4
// For recursive descent, because slope in y direction is steeper,
// we'd move in that direction. Then redo the calculation and move
// accordingly until slope becomes zero and we've reached the flat
// part.
}