/// <summary>Initializes a new instance of the <see cref="Factored" /> class.</summary>
/// <param name="d">The <c>d</c> value.</param>
/// <param name="e">The <c>e</c> value.</param>
/// <param name="h">The <c>h</c> value.</param>
/// <param name="f">The <c>f</c> value.</param>
/// <param name="g">The <c>g</c> value.</param>
/// <exception cref="ArgumentException">
/// <paramref name="d" />, <paramref name="d" />, or <paramref name="d" /> is <value>0</value>; this is not a quadratic
/// equation.
/// </exception>
/// <exception cref="OverflowException">
/// The product of <paramref name="d" /> and the <see cref="Math2.Gcd(long, long)" /> of the <paramref name="e" />,
/// <paramref name="h" /> pair and the <paramref name="f" />, <paramref name="g" /> pair exceeds the bounds of a
/// <see cref="long" />.
/// </exception>
public Factored(long d, long e, long h, long f, long g)
{
if (d == 0L)
{
throw new ArgumentException(
string.Format(CultureInfo.CurrentCulture, Strings.Arg_ZeroNonQuadraticFormat, nameof(d)),
nameof(d));
}
if (e == 0L)
{
throw new ArgumentException(
string.Format(CultureInfo.CurrentCulture, Strings.Arg_ZeroNonQuadraticFormat, nameof(e)),
nameof(e));
}
if (f == 0L)
{
throw new ArgumentException(
string.Format(CultureInfo.CurrentCulture, Strings.Arg_ZeroNonQuadraticFormat, nameof(f)),
nameof(f));
}
var ehGcd = Math2.Gcd(e, h);
var fgGcd = Math2.Gcd(f, g);
checked
{
this.D = d * ehGcd * fgGcd;
}
this.E = e / ehGcd;
this.F = f / fgGcd;
this.G = g / fgGcd;
this.H = h / ehGcd;
}
/// <summary>Converts a quadratic equation from the <see cref="Standard" /> form into the <see cref="Factored" /> form.</summary>
/// <param name="standard">The equation to convert.</param>
/// <returns>
/// The equation in <see cref="Factored" /> form or <value>null</value> if the result would have non-integer values.
/// </returns>
public static Factored FromStandard(Standard standard)
{
if (standard == null)
{
throw new ArgumentNullException(nameof(standard));
}
var d = Math2.Gcd(standard.A, standard.B, standard.C);
var aPrime = standard.A / d;
var bPrime = standard.B / d;
var cPrime = standard.C / d;
if (cPrime == 0)
{
return(new Factored(d, 1, 0, aPrime, bPrime));
}
foreach (var cPrimeFactor in Math2.Factor(cPrime, true, true))
{
var g = cPrimeFactor.Item1;
var h = cPrimeFactor.Item2;
foreach (var aPrimeFactor in Math2.Factor(aPrime))
{
var e = aPrimeFactor.Item1;
var f = aPrimeFactor.Item2;
if ((e * g) + (f * h) == bPrime)
{
return(new Factored(d, e, h, f, g));
}
}
}
return(null);
}