private void binaryOperationsToolStripMenuItem_Click(object sender, EventArgs e)
{
PrintLine("P E R F O R M I N G B I N A R Y O P E R A T I O N E Q U A L I T Y T E S T S");
PrintLine("-----------------------------------------------------------------------------------");
try
{
var s1 = new Sum(x, y);
var s12 = new Sum(x, y);
var s2 = new Sum(x, 2);
var s3 = new Sum(y, x);
var d1 = new Difference(x, y);
var d12 = new Difference(x, y);
var d2 = new Difference(x, 2);
var d3 = new Difference(y, x);
var p1 = new Product(x, y);
var p12 = new Product(x, y);
var p2 = new Product(x, 2);
var p3 = new Product(y, x);
var q1 = new Quotient(x, y);
var q12 = new Quotient(x, y);
var q2 = new Quotient(x, 2);
var q3 = new Quotient(y, x);
PrintLine("BASIC IDENTITY TESTS:");
PrintLine("(x + y) = (x + y) => " + (s1 == s12).ToString(), Color.Blue);
PrintLine("(x + y) = (y + x) => " + (s1 == s3).ToString(), Color.Blue);
PrintLine("(x + y) = (x + 2) => " + (s1 == s2).ToString(), Color.Blue);
PrintLine("(x - y) = (x - y) => " + (d1 == d12).ToString(), Color.Blue);
PrintLine("(x - y) = (y - x) => " + (d1 == d3).ToString(), Color.Blue);
PrintLine("(x - y) = (x - 2) => " + (d1 == d2).ToString(), Color.Blue);
PrintLine("(x * y) = (x * y) => " + (p1 == p12).ToString(), Color.Blue);
PrintLine("(x * y) = (y * x) => " + (p1 == p3).ToString(), Color.Blue);
PrintLine("(x * y) = (x * 2) => " + (p1 == p2).ToString(), Color.Blue);
PrintLine("(x / y) = (x / y) => " + (q1 == q12).ToString(), Color.Blue);
PrintLine("(x / y) = (y / x) => " + (q1 == q3).ToString(), Color.Blue);
PrintLine("(x / y) = (x / 2) => " + (q1 == q2).ToString(), Color.Blue);
var sr1 = new Sum(s1, z);
var sr12 = new Sum(s1, z);
var sr2 = new Sum(z, s1);
var sr21 = new Sum(new Sum(z, y), x);
var szc = new Sum(z, C);
var sr3 = new Sum(s1, szc);
var sr32 = new Sum(s1, szc);
var scz = new Sum(C, z);
var sr4 = new Sum(scz, s1);
var dr1 = new Difference(d1, z);
var dr12 = new Difference(d1, z);
var dr2 = new Difference(z, d1);
var dr21 = new Difference(new Difference(z, y), x);
var dzc = new Difference(z, C);
var dr3 = new Difference(d1, dzc);
var dr32 = new Difference(d1, dzc);
var dcz = new Difference(C, z);
var dr4 = new Difference(dcz, d1);
var pr1 = new Product(p1, z);
var pr12 = new Product(p1, z);
var pr2 = new Product(z, p1);
var pr21 = new Product(new Product(z, y), x);
var pzc = new Product(z, C);
var pr3 = new Product(p1, pzc);
var pr32 = new Product(p1, pzc);
var pcz = new Product(C, z);
var pr4 = new Product(pcz, p1);
var qr1 = new Quotient(q1, z);
var qr12 = new Quotient(q1, z);
var qr2 = new Quotient(z, q1);
var qr21 = new Quotient(new Quotient(z, y), x);
var qzc = new Quotient(z, C);
var qr3 = new Quotient(q1, qzc);
var qr32 = new Quotient(q1, qzc);
var qcz = new Quotient(C, z);
var qr4 = new Quotient(qcz, q1);
PrintLine("RECURSIVE IDENTITY TESTS:");
PrintLine("((x + y) + z) = ((x + y) + z) => " + (sr1 == sr12).ToString(), Color.Blue);
PrintLine("((x + y) + z) = (x + (y + z)) => " + (sr1 == sr2).ToString(), Color.Blue);
PrintLine("((x + y) + z) = ((z + y) + x) => " + (sr1 == sr21).ToString(), Color.Blue);
PrintLine("((x + y) + (z + C)) = ((x + y) + (z + C)) => " + (sr3 == sr32).ToString(), Color.Blue);
PrintLine("((x + y) + (z + C)) = ((C + z) + (x + y)) => " + (sr3 == sr4).ToString(), Color.Blue);
PrintLine("((x - y) - z) = ((x - y) - z) => " + (dr1 == dr12).ToString(), Color.Blue);
PrintLine("((x - y) - z) = (x - (y - z)) => " + (dr1 == dr2).ToString(), Color.Blue);
PrintLine("((x - y) - z) = ((z - y) - x) => " + (dr1 == dr21).ToString(), Color.Blue);
PrintLine("((x - y) - (z - C)) = ((x - y) - (z - C)) => " + (dr3 == dr32).ToString(), Color.Blue);
PrintLine("((x - y) - (z - C)) = ((C - z) - (x - y)) => " + (dr3 == dr4).ToString(), Color.Blue);
PrintLine("((x * y) * z) = ((x * y) * z) => " + (pr1 == pr12).ToString(), Color.Blue);
PrintLine("((x * y) * z) = (x * (y * z)) => " + (pr1 == pr2).ToString(), Color.Blue);
PrintLine("((x * y) * z) = ((z * y) * x) => " + (pr1 == pr21).ToString(), Color.Blue);
PrintLine("((x * y) * (z * C)) = ((x * y) * (z * C)) => " + (pr3 == pr32).ToString(), Color.Blue);
PrintLine("((x * y) * (z * C)) = ((C * z) * (x * y)) => " + (pr3 == pr4).ToString(), Color.Blue);
PrintLine("((x / y) / z) = ((x / y) / z) => " + (qr1 == qr12).ToString(), Color.Blue);
PrintLine("((x / y) / z) = (x / (y / z)) => " + (qr1 == qr2).ToString(), Color.Blue);
PrintLine("((x / y) / z) = ((z / y) / x) => " + (qr1 == qr21).ToString(), Color.Blue);
PrintLine("((x / y) / (z / C)) = ((x / y) / (z / C)) => " + (qr3 == qr32).ToString(), Color.Blue);
PrintLine("((x / y) / (z / C)) = ((C / z) / (x / y)) => " + (qr3 == qr4).ToString(), Color.Blue);
PrintLine("SUCCESS", Color.Green);
}
catch (Exception ex)
{
PrintLine(ex.Message, Color.Red);
}
PrintLine();
}
/// <summary>
/// Computes the symbolic subtraction between two expressions.
/// </summary>
/// <param name="E1">The first expression</param>
/// <param name="E2">The second expression</param>
public static Expression Subtract(Expression E1, Expression E2)
{
var O = new Difference(E1, E2);
if (O.CanTransform()) return O.Apply(true);
else return O;
}