public static FractionX operator *(FractionX a, FractionX b)
{
var c = new FractionX(a.Numberator * b.Numberator, a.Denominator * b.Denominator);
c.Simplify();
return(c);
}
//
//
public static FractionX operator +(FractionX a, FractionX b)
{
FractionX ret = new FractionX((IntX)(a.Numberator * b.Denominator
+ b.Numberator * a.Denominator),
a.Denominator * b.Denominator);
ret.Simplify();
return(new FractionX(ret.Numberator, ret.Denominator));
}
public PolynomialX Copy()
{
FractionX[] polynomial = new FractionX[Coefficients.Length];
for (int i = 0; i < polynomial.Length; i++)
{
polynomial[i] = Coefficients[i];
}
return(new PolynomialX(polynomial));
}
//public void Round(int decimalPlaces)
//{
// for (int i = 0; i < Width; i++)
// for (int j = 0; j < Height; j++)
// Elements[i, j] = Elements[i, j].Round(decimalPlaces);
//}
///// <summary>
///// Throws exception if not a square matrix.
///// </summary>
///// <returns></returns>
//public Polynomial FindCharacteristicPolynomial()
//{
// if (Width != Height)
// throw new Exception("Must be square matrix.");
// //Method can be found at: https://en.wikipedia.org/wiki/Faddeev%E2%80%93LeVerrier_algorithm
// FractionX[] c = new FractionX[Width + 1];
// c[0] = (FractionX)1;
// var I = DiagonalMatrixX.IdentityMatrixX(Width);
// var M = (MatrixX)I;
// for (int i = 1; i < c.Length; i++)
// {
// //Console.WriteLine();
// //Console.WriteLine(M);
// M = this * M;
// c[i] = -1.0 / i * M.Trace();
// //Console.WriteLine(M);
// //Console.WriteLine(c[i]);
// if (i + 1 < c.Length)
// M += c[i] * I;
// }
// Polynomial poly = new Polynomial(c.Length);
// for (int i = 0; i < c.Length; i++)
// poly[i] = c[c.Length - i - 1];
// return poly;
//}
FractionX Trace()
{
FractionX trace = (FractionX)0;
for (int i = 0; i < Width; i++)
{
trace += this[i, i];
}
return(trace);
}
public FractionX F(FractionX x)
{
FractionX result = (FractionX)0;
FractionX term = (FractionX)1;
for (int i = 0; i < Coefficients.Length; i++)
{
result += Coefficients[i] * term;
term *= x;
}
return(result);
}
public PolynomialX DivideOutRoot(FractionX root)
{
var copy = Copy();
PolynomialX result = new PolynomialX(Coefficients.Length - 1);
FractionX last = Coefficients[Coefficients.Length - 1];
result[result.Coefficients.Length - 1] = last;
for (int i = Coefficients.Length - 3; i >= 0; i--)
{
copy[i + 1] += root * last;
result[i] = last = copy[i + 1];
}
return(result);
}