private static RealPolynomial FromDegree(int degree)
{
RealPolynomial rp = new RealPolynomial();
rp.cof = new double[degree + 1];
return(rp);
}
public void DivMod(RealPolynomial b, out RealPolynomial result, out RealPolynomial mod)
{
RealPolynomial numerator = Copy();
RealPolynomial denominator = b;
result = new RealPolynomial(0.0);
// numerator / denominator = result + remainder / denominator
int curdeg;
double curfac;
do
{
curdeg = numerator.Degree - denominator.Degree;
if (curdeg < 0)
{
break;
}
curfac = numerator[numerator.Degree] / denominator[denominator.Degree];
numerator -= (denominator.MultPower(curdeg, curfac));
result[curdeg] += curfac;
if (numerator.Degree == 0)
{
break;
}
} while (numerator.Degree >= denominator.Degree && numerator.Degree >= 0);
mod = numerator;
}
public RealPolynomial Copy()
{
RealPolynomial res = FromDegree(Degree);
for (int l = 0; l < cof.Length; l++)
{
res[l] = this[l];
}
return(res);
}
private RealPolynomial MultPower(int power, double m)
{
RealPolynomial newpoly = FromDegree(power + Degree + 1);
for (int idx = 0; idx < cof.Length; idx++)
{
newpoly[idx + power] = cof[idx] * m;
}
newpoly.Clean();
return(newpoly);
}
public static RealPolynomial FromRoots(params double[] roots)
{
if (roots.Length <= 0)
{
return(new RealPolynomial(0));
}
RealPolynomial res = new RealPolynomial(1, -roots[0]);
for (int l = 1; l < roots.Length; l++)
{
res = res * new RealPolynomial(1, -roots[l]);
}
return(res);
}
public SturmSequence(RealPolynomial p)
{
RealPolynomial f1 = p.Copy();
RealPolynomial f2 = f1.Derivative;
RealPolynomial f3;
polys.Add(f1);
polys.Add(f2);
while (f2.Degree > 0)
{
f3 = -(f1 % f2);
polys.Add(f3);
f1 = f2;
f2 = f3;
}
}
public static RealPolynomial operator *(RealPolynomial a, RealPolynomial b)
{
int alen = a.cof.Length;
int blen = b.cof.Length;
RealPolynomial res = FromDegree(alen + blen - 1);
for (int bi = 0; bi < blen; bi++)
{
for (int ai = 0; ai < alen; ai++)
{
res[ai + bi] += a.cof[ai] * b.cof[bi];
}
}
res.Clean();
return(res);
}
public RealPolynomial Pow(int power)
{
if (power < 0)
{
throw new ArgumentException("RealPolynomial.Pow can only use posetive powers");
}
else if (power == 1)
{
return(new RealPolynomial(1.0));
}
RealPolynomial result = Copy();
for (int l = 1; l < power; l++)
{
result *= this;
}
return(result);
}
