AlgebraicLongDivision(RealPolynomial dividend, RealPolynomial divisor)
{
if (dividend.Degree < divisor.Degree)
{
throw new ArgumentException("dividendCoef degree is smaller than divisorCoef");
}
AllRealDivisionResult r = new AllRealDivisionResult();
var quotient = new double [dividend.Degree - divisor.Degree + 1];
var divRemain = new double[dividend.Degree + 1];
for (int i = 0; i < divRemain.Length; ++i)
{
divRemain[i] = dividend.C(i);
}
for (int i = 0; i < quotient.Length; ++i)
{
double q = divRemain[dividend.Degree - i]
/ divisor.C(divisor.Degree);
quotient[quotient.Length - 1 - i] = q;
for (int j = 0; j <= divisor.Degree; ++j)
{
divRemain[dividend.Degree - i - j] -=
q * divisor.C(divisor.Degree - j);
}
}
r.quotient = new RealPolynomial(quotient);
r.remainder = new RealRationalPolynomial(
new RealPolynomial(divRemain).RemoveLeadingZeros(),
divisor.RemoveLeadingZeros());
return(r);
}
public RealRationalPolynomial(RealPolynomial aNumer, RealPolynomial aDenom)
{
numer = new double[aNumer.Degree + 1];
denom = new double[aDenom.Degree + 1];
for (int i = 0; i < numer.Length; ++i)
{
numer[i] = aNumer.C(i);
}
for (int i = 0; i < denom.Length; ++i)
{
denom[i] = aDenom.C(i);
}
}
public static RealPolynomial Add(RealPolynomial l, RealPolynomial r)
{
int degree = (l.Degree < r.Degree) ? r.Degree : l.Degree;
var c = new double[degree + 1];
for (int i = 0; i <= degree; ++i)
{
c[i] = 0;
if (i <= l.Degree)
{
c[i] += l.C(i);
}
if (i <= r.Degree)
{
c[i] += r.C(i);
}
}
return(new RealPolynomial(c));
}
Mul(RealPolynomial lhs, RealPolynomial rhs)
{
// 1次 p 2次 = 3次
// 2次 p 2次 = 4次
// 2次 p 3次 = 5次
// (p^2+2x+3) * (4x+5)
var c = new double[lhs.Degree + rhs.Degree + 1];
// C#では、cの要素は0で初期化される。
for (int iL = 0; iL <= lhs.Degree; ++iL)
{
for (int iR = 0; iR <= rhs.Degree; ++iR)
{
c[iL + iR] += lhs.C(iL) * rhs.C(iR);
}
}
return(new RealPolynomial(c));
}