void parabolic(BigInteger a, BigInteger b, BigInteger c, BigInteger d, BigInteger e, BigInteger f)
{
var g = BigIntegerExt.Gcd(a, c);
c = (c / g).Abs().Sqrt();
if (b.Sign > 0 == a.Sign < 0)
{
c = -c;
}
a = (a / g).Abs().Sqrt();
var m = c * d - a * e;
if (m.IsZero)
{
var u = MathExt2.DeriveQuadratic(a * g, d, a * f, true);
if (u.Length > 0)
{
linearWithGcd(a, c, -u[0]);
if (u.Length > 1 && u[0] != u[1])
{
linearWithGcd(a, c, -u[1]);
}
}
}
else
{
parabolic2(a, -c, m, a * g, d, a * f);
}
}
void elliptical(BigInteger a, BigInteger b, BigInteger c, BigInteger d, BigInteger e, BigInteger f)
{
var m = 4 * a;
var i = m * c - b * b;
var j = m * e - 2 * b * d;
var k = m * f - d * d;
var n = MathExt2.DeriveQuadratic(i, j, k, false);
if (n.Length == 0)
{
return;
}
m = 2 * a;
for (var u = n[0]; u <= n[1]; u += BigInteger.One)
{
var v = -(i * u * u + j * u + k);
var w = v.Sqrt();
if (w * w == v)
{
var s = d + (b * u);
addStaticSolution((Rational)(w - s) / m, u);
addStaticSolution((Rational)(-w - s) / m, u);
}
}
}
public static void DeriveQuadratic()
{
//this example shows how to find integer solution for aXX + bX + c = 0
//example -2XX + X + 15
//use MathExt2.DeriveQuadratic(a,b,c) to derive quadratic formula
BigInteger[] xs = MathExt2.DeriveQuadratic(-2, 1, 15);
//Show results
Console.WriteLine(xs[0]);
Console.WriteLine();
//Recheck
Console.WriteLine("-2*{0}*{0} + {0} + 15 = {1}", xs[0], -2 * xs[0] * xs[0] + xs[0] + 15);
}