public static RadicalSumRatio Add(
RadicalSumRatio left,
RadicalSumRatio right)
{
// n1 n2 (n1 * d2) + (n2 * d1)
// -- + -- = ---------------------
// d1 d2 d1 * d2
RadicalSum numerator =
(left.Numerator * right.Denominator)
+ (right.Numerator * left.Denominator);
RadicalSum denominator = left.Denominator * right.Denominator;
return(new RadicalSumRatio(numerator, denominator));
}
public RadicalSumRatio(RadicalSum numerator, RadicalSum denominator)
{
if (RadicalSum.Zero == denominator)
{
throw new ArgumentException("Denominator cannot be zero", nameof(denominator));
}
if (denominator < RadicalSum.Zero)
{
ToSimplestForm(-numerator, -denominator, out _numerator, out _denominator);
}
else
{
ToSimplestForm(numerator, denominator, out _numerator, out _denominator);
}
}
public static RadicalSumRatio Multiply(
RadicalSumRatio left,
RadicalSumRatio right)
{
// C1n C2n commonFactorLeft * C1n_reduced commonFactorRight * C2n_reduced
// R = R1 * R2 = --- * --- = ------------------------------ * -------------------------------
// C1d C2d C1d C2d
//
// commonFactor * c1n_reduced * c2n_reduced
// = ----------------------------------------
// c2d * c1d
//
// ci_reduced === ci / commonFactori
// commonFactor === commonFactorLeft * commonFactorRight;
// Simplest form puts all common factors in numerator
var commonFactorLeft = Utilities.GetCommonFactor(left.Numerator.Coefficients);
var commonFactorRight = Utilities.GetCommonFactor(right.Numerator.Coefficients);
var commonFactor = commonFactorLeft * commonFactorRight;
var c_left_n_reduced = left.Numerator / commonFactorLeft;
var c_right_n_reduced = right.Numerator / commonFactorRight;
var d_left = left.Denominator;
var d_right = right.Denominator;
if (c_left_n_reduced == d_right)
{
c_left_n_reduced = RadicalSum.One;
d_right = RadicalSum.One;
}
if (c_right_n_reduced == d_left)
{
c_right_n_reduced = RadicalSum.One;
d_left = RadicalSum.One;
}
RadicalSum numerator = commonFactor * c_left_n_reduced * c_right_n_reduced;
RadicalSum denominator = d_left * d_right;
var result = new RadicalSumRatio(numerator, denominator);
return(result);
}
private static void ToSimplestForm(
RadicalSum n_in,
RadicalSum d_in,
out RadicalSum n_out,
out RadicalSum d_out)
{
// First extract common factors from numerator and denominator:
// N = common_factor_n * (N/common_factor_n); n_reduced === N/common_factor_n
// D = common_factor_d * (D/common_factor_d); d_reduced === D/common_factor_d
Rational common_factor_n = Utilities.GetCommonFactor(n_in.Coefficients);
Rational common_factor_d = Utilities.GetCommonFactor(d_in.Coefficients);
var n_reduced = n_in * Rational.Invert(common_factor_n);
var d_reduced = d_in * Rational.Invert(common_factor_d);
// N common_factor_n * (N/common_factor_n) common_factor_n * n_reduced n_reduced
// C = - = ------------------------------------- = --------------------------- = common_factor * ---------
// D common_factor_d * (D/common_factor_d) common_factor_d * d_reduced d_reduced
//
// common_factor === common_factor_n / common_factor_d
var common_factor = common_factor_n / common_factor_d;
if (n_reduced == d_reduced)
{
n_out = common_factor * RadicalSum.One;
d_out = RadicalSum.One;
}
else if (d_reduced.Radicals.Length == 1)
{
n_out = common_factor * n_reduced / d_reduced.Radicals[0];
d_out = RadicalSum.One;
}
else
{
n_out = common_factor * n_reduced;
d_out = d_reduced;
}
}
public RadicalSumRatio(RadicalSum numerator)
: this(numerator, RadicalSum.One)
{
}
/// <summary>
/// Converts to a sum of radicals by multiplying the numerator by the multiplicative inverse of the denominator.
/// WARNING: Finding the inverse could take a very long time and consume considerable memory and CPU. Use with caution.
/// </summary>
/// <param name="left"></param>
/// <param name="right"></param>
/// <returns></returns>
public RadicalSum ToRadicalSum()
{
return(RadicalSum.GroupDivide(Numerator, Denominator));
}