public static void Sample_Blue_Disc()
{
//this example shows how to use diophantine to solve problem
//Consider 15 Blue Discs and 6 Red Discs
//Chance to pick 2 Blue Discs at random is 1/2 (15/21 * 14/20)
//Find the first arrangement
//where chance to pick 2 Blue Discs at random is 1/2
//but total number of Discs > 10^12
//Question from http://projecteuler.net
//formula X/(X + Y) * (X - 1)/(X + Y - 1) = 1/2
//2 * X * (X - 1) = (X + Y) * (X + Y - 1)
//2 * X * (X - 1) - (X + Y) * (X + Y - 1) = 0
var solutions = Diophantine.Parse((x, y) => 2 * x * (x - 1) - (x + y) * (x + y - 1)).Solutions;
//show formula
Console.WriteLine("Solutions for X: {0}", solutions[0].FuncX1.Body);
Console.WriteLine("Solutions for Y: {0}", solutions[0].FuncY1.Body);
Console.WriteLine();
//show X0, Y0
Console.WriteLine("X: {0}", solutions[0].X0);
Console.WriteLine("Y: {0}", solutions[0].Y0);
Console.WriteLine();
//show results
Console.WriteLine(solutions[0].First(s => s.X + s.Y > 1000000000000));
}
public static void ComplexHyperbolic2()
{
//this example shows how to solve hyperbolic formula aXX + bXY + cYY + dX + eY + f = 0
//3XX + 14XY + 6YY - 17X - 23Y - 505 = 0
var solutions = Diophantine.Parse((x, y) => 3 * x * x + 14 * x * y + 6 * y * y - 17 * x - 23 * y - 505).Solutions;
//show formula
Console.WriteLine("Solutions for X: {0}", solutions[0].FuncX1.Body);
Console.WriteLine("Solutions for Y: {0}", solutions[0].FuncY1.Body);
Console.WriteLine();
//show X0 and Y0
foreach (var solution in solutions)
{
Console.WriteLine("X: {0}", solution.X0);
Console.WriteLine("Y: {0}", solution.Y0);
Console.WriteLine();
}
//show results
foreach (var solution in solutions)
{
solution.Take(3).ForEach(s =>
Console.WriteLine("3*{0}*{0} + 14*{0}*{1} + 6*{1}*{1} - 17*{0} - 23*{1} - 505 = {2}", s.X, s.Y, 3 * s.X * s.X + 14 * s.X * s.Y + 6 * s.Y * s.Y - 17 * s.X - 23 * s.Y - 505));
Console.WriteLine();
}
}
public static void ComplexHyperbolic()
{
//this example shows how to solve hyperbolic formula aXX + bXY + cYY + dX + eY + f = 0
//3XX + 13XY + 5YY - 11X - 7Y - 92 = 0
var solutions = Diophantine.Parse((x, y) => 3 * x * x + 13 * x * y + 5 * y * y - 11 * x - 7 * y - 92).Solutions;
//show formula
Console.WriteLine("Solutions for X: {0}", solutions[0].FuncX1.Body);
Console.WriteLine("Solutions for Y: {0}", solutions[0].FuncY1.Body);
Console.WriteLine();
//show X0 and Y0
foreach (var solution in solutions)
{
Console.WriteLine("X: {0}", solution.X0);
Console.WriteLine("Y: {0}", solution.Y0);
Console.WriteLine();
}
//show results
foreach (var solution in solutions)
{
solution.Take(3).ForEach(s =>
Console.WriteLine("3*{0}*{0} + 13*{0}*{1} + 5*{1}*{1} - 11*{0} - 7*{1} - 92 = {2}", s.X, s.Y, 3 * s.X * s.X + 13 * s.X * s.Y + 5 * s.Y * s.Y - 11 * s.X - 7 * s.Y - 92));
Console.WriteLine();
}
}
public static void Hyperbolic()
{
//this example shows how to solve hyperbolic formula aXX + bXY + cYY + f = 0
//18XX + 41XY + 19YY - 24 = 0
var solutions = Diophantine.Parse((x, y) => 18 * x * x + 41 * x * y + 19 * y * y - 24).Solutions;
//show formula
Console.WriteLine("Solutions for X: {0}", solutions[0].FuncX1.Body);
Console.WriteLine("Solutions for Y: {0}", solutions[0].FuncY1.Body);
Console.WriteLine();
//show X0 and Y0
foreach (var solution in solutions)
{
Console.WriteLine("X: {0}", solution.X0);
Console.WriteLine("Y: {0}", solution.Y0);
Console.WriteLine();
}
//show results
foreach (var solution in solutions)
{
solution.Take(3).ForEach(s =>
Console.WriteLine("18*{0}*{0} + 41*{0}*{1} + 19*{1}*{1} - 24 = {2}", s.X, s.Y, 18 * s.X * s.X + 41 * s.X * s.Y + 19 * s.Y * s.Y - 24));
Console.WriteLine();
}
}
public static void Elliptical()
{
//this example shows how to solve elliptical formula where b^2 - 4ac < 0
//42XX + 8XY + 15YY + 23X + 17Y - 4915 = 0
var solutions = Diophantine.Parse((x, y) => 42 * x * x + 8 * x * y + 15 * y * y + 23 * x + 17 * y - 4915).Solutions;
//show results
solutions.ForEach(s =>
Console.WriteLine("42*{0}*{0} + 8*{0}*{1} + 15*{1}*{1} + 23*{0} + 17*{1} - 4915 = {2}", s.X0, s.Y0, 42 * s.X0 * s.X0 + 8 * s.X0 * s.Y0 + 15 * s.Y0 * s.Y0 + 23 * s.X0 + 17 * s.Y0 - 4915));
}
public static void SimpleHyperbolic()
{
//this example shows how to solve simple hyperbolic formula bXY + dX + eY + f = 0
//2XY + 5X + 56Y + 7 = 0
var solutions = Diophantine.Parse((x, y) => 2 * x * y + 5 * x + 56 * y + 7).Solutions;
//show results
solutions.ForEach(s =>
Console.WriteLine("2*{0}*{1} + 5*{0} + 56*{1} + 7 = {2}", s.X0, s.Y0, 2 * s.X0 * s.Y0 + 5 * s.X0 + 56 * s.Y0 + 7));
}
public static void Create2()
{
//this example shows how to create Diophantine
//you can create Diophantine by Diophantine.Parse(formula)
//for example 2X + 4X - 54 = 0
var solutions = Diophantine.Parse((x, y) => 2 * x + 4 * x - 54).Solutions;
//show results
Console.WriteLine(solutions[0].X0);
}
public static void Create()
{
//this example shows how to create Diophantine
//you can create Diophantine by new Diophantine(a,b,c,d,e,f)
//where aXX + bXY + cYY + dX + eY + f = 0
//for example 5X + -25 = 0
var solutions = new Diophantine(0, 0, 0, 5, 0, -25).Solutions;
//show results
Console.WriteLine(solutions[0].X0);
}
public static void Linear()
{
//this example shows how to solve linear formula dX + eY + f = 0
//10X + 84Y + 16 = 0
var solutions = Diophantine.Parse((x, y) => 10 * x + 84 * y + 16).Solutions;
//show formula
Console.WriteLine("Solutions for X: {0}", solutions[0].FuncX1.Body);
Console.WriteLine("Solutions for Y: {0}", solutions[0].FuncY1.Body);
//show results
Console.WriteLine();
solutions[0].Take(10).ForEach(s =>
Console.WriteLine("10*{0} + 84*{1} + 16 = {2}", s.X, s.Y, 10 * s.X + 84 * s.Y + 16));
}
public static void Parabolic()
{
//this example shows how to solve parabolic formula where b^2 - 4ac = 0
//8XX - 24XY + 18YY + 5X + 7Y + 16 = 0
var solutions = Diophantine.Parse((x, y) => 8 * x * x - 24 * x * y + 18 * y * y + 5 * x + 7 * y + 16).Solutions;
//show formula
for (var i = 0; i < solutions.Count; i++)
{
Console.WriteLine("Solution {0}", i + 1);
Console.WriteLine("Solutions for X: {0}", solutions[i].FuncX1.Body);
Console.WriteLine("Solutions for Y: {0}", solutions[i].FuncY1.Body);
Console.WriteLine();
}
//show results
foreach (var solution in solutions)
{
solution.Take(5).ForEach(s =>
Console.WriteLine("8*{0}*{0} - 24*{0}*{1} + 18*{1}*{1} + 5*{0} + 7*{1} + 16 = {2}", s.X, s.Y, 8 * s.X * s.X - 24 * s.X * s.Y + 18 * s.Y * s.Y + 5 * s.X + 7 * s.Y + 16));
Console.WriteLine();
}
}