public HighOrderComplexRationalPolynomial(FirstOrderComplexRationalPolynomial uni)
{
int numerCount = 1;
if (1 == uni.NumerDegree())
{
numerCount = 2;
}
numer = new WWComplex[numerCount];
for (int i = 0; i < numerCount; ++i)
{
numer[i] = uni.N(i);
}
int denomCount = 1;
if (1 == uni.DenomDegree())
{
denomCount = 2;
}
denom = new WWComplex[denomCount];
for (int i = 0; i < denomCount; ++i)
{
denom[i] = uni.D(i);
}
}
Mul(FirstOrderComplexRationalPolynomial lhs, FirstOrderComplexRationalPolynomial rhs)
{
// 分子の項 p 分子の項
var n2 = WWComplex.Mul(lhs.N(1), rhs.N(1));
var n1 = WWComplex.Add(WWComplex.Mul(lhs.N(1), rhs.N(0)),
WWComplex.Mul(lhs.N(0), rhs.N(1)));
var n0 = WWComplex.Mul(lhs.N(0), rhs.N(0));
// 分母の項 p 分母の項
var d2 = WWComplex.Mul(lhs.D(1), rhs.D(1));
var d1 = WWComplex.Add(WWComplex.Mul(lhs.D(1), rhs.D(0)),
WWComplex.Mul(lhs.D(0), rhs.D(1)));
var d0 = WWComplex.Mul(lhs.D(0), rhs.D(0));
return(new SecondOrderComplexRationalPolynomial(n2, n1, n0, d2, d1, d0));
}
Add(FirstOrderComplexRationalPolynomial L, FirstOrderComplexRationalPolynomial R)
{
/* nL nR
* p+2 p+4
* ─── + ────
* p+1 p+3
* dL dR
*
* nL dR nR dL
* 分子 = (p+2)(p+3) + (p+4)(p+1) = (p^2+5x+6) + (p^2+5x+4) = 2x^2+10x+10
* 分子の次数 = 2
*
* dL dR
* 分母 = (p+1)(p+3) = p^2 + (1+3)p + 1*3
* 分母の次数 = 2
*/
// 分子の項
var n2 = WWComplex.Add(
WWComplex.Mul(L.N(1), R.D(1)),
WWComplex.Mul(R.N(1), L.D(1)));
var n1 = WWComplex.Add(
WWComplex.Add(WWComplex.Mul(L.N(0), R.D(1)),
WWComplex.Mul(L.N(1), R.D(0))),
WWComplex.Add(WWComplex.Mul(R.N(0), L.D(1)),
WWComplex.Mul(R.N(1), L.D(0))));
var n0 = WWComplex.Add(
WWComplex.Mul(L.N(0), R.D(0)),
WWComplex.Mul(R.N(0), L.D(0)));
// 分母の項
var d2 = WWComplex.Mul(L.D(1), R.D(1));
var d1 = WWComplex.Add(WWComplex.Mul(L.D(0), R.D(1)),
WWComplex.Mul(L.D(1), R.D(0)));
var d0 = WWComplex.Mul(L.D(0), R.D(0));
return(new SecondOrderComplexRationalPolynomial(n2, n1, n0, d2, d1, d0));
}
MulComplexConjugatePair(FirstOrderComplexRationalPolynomial p0)
{
if (p0.NumerDegree() != 1 || p0.DenomDegree() != 1)
{
throw new ArgumentException("p0");
}
var n0 = p0.NumerCoeffs();
var d0 = p0.DenomCoeffs();
// n1, d1 : 共役の多項式の係数
var n1 = new WWComplex[2];
for (int i = 0; i < 2; ++i)
{
n1[i] = n0[i].ComplexConjugate();
}
var d1 = new WWComplex[2];
for (int i = 0; i < 2; ++i)
{
d1[i] = d0[i].ComplexConjugate();
}
var n = new double[3];
n[0] = WWComplex.Mul(n0[0], n1[0]).real;
n[1] = WWComplex.Add(WWComplex.Mul(n0[0], n1[1]), WWComplex.Mul(n0[1], n1[0])).real;
n[2] = WWComplex.Mul(n0[1], n1[1]).real;
var d = new double[3];
d[0] = WWComplex.Mul(d0[0], d1[0]).real;
d[1] = WWComplex.Add(WWComplex.Mul(d0[0], d1[1]), WWComplex.Mul(d0[1], d1[0])).real;
d[2] = WWComplex.Mul(d0[1], d1[1]).real;
return(new RealRationalPolynomial(n, d));
}
Add(HighOrderComplexRationalPolynomial lhs, FirstOrderComplexRationalPolynomial rhs)
{
/* nL nR
* p^2+2x+2 p+4
* ───────── + ────
* p^2+ p+1 p+3
* dL dR
*
* dL dR
* 分母 = (p^2+p+1) (p+3)
* 分母の次数 = degree(dL) + degree(dR) + 1
*
* nL dR nR dL
* 分子 = (p^2+2x+2)(p+3) + (p+4)(p^2+p+1)
* 分子の次数 = degree(nL) + degree(dR) + 1 か degree(nR) * degree(dL) + 1の大きいほう
*/
ComplexPolynomial denomL;
{
var d = new WWComplex[lhs.DenomDegree() + 1];
for (int i = 0; i <= lhs.DenomDegree(); ++i)
{
d[i] = lhs.D(i);
}
denomL = new ComplexPolynomial(d);
}
ComplexPolynomial numerL;
{
var n = new WWComplex[lhs.NumerDegree() + 1];
for (int i = 0; i <= lhs.NumerDegree(); ++i)
{
n[i] = lhs.N(i);
}
numerL = new ComplexPolynomial(n);
}
// 分母の項
ComplexPolynomial denomResult;
{
var denomX = new ComplexPolynomial(new WWComplex[0]);
if (1 == rhs.DenomDegree())
{
denomX = ComplexPolynomial.MultiplyC(ComplexPolynomial.MultiplyX(denomL), rhs.D(1));
}
var denomC = ComplexPolynomial.MultiplyC(denomL, rhs.D(0));
denomResult = ComplexPolynomial.Add(denomX, denomC);
}
// 分子の項
ComplexPolynomial numerResult;
{
ComplexPolynomial numer0;
{
var numerX0 = new ComplexPolynomial(new WWComplex[0]);
if (1 == rhs.DenomDegree())
{
numerX0 = ComplexPolynomial.MultiplyC(ComplexPolynomial.MultiplyX(numerL), rhs.D(1));
}
var numerC0 = ComplexPolynomial.MultiplyC(numerL, rhs.D(0));
numer0 = ComplexPolynomial.Add(numerX0, numerC0);
}
ComplexPolynomial numer1;
{
var numerX1 = new ComplexPolynomial(new WWComplex[0]);
if (1 == rhs.NumerDegree())
{
numerX1 = ComplexPolynomial.MultiplyC(ComplexPolynomial.MultiplyX(denomL), rhs.N(1));
}
var numerC1 = ComplexPolynomial.MultiplyC(denomL, rhs.N(0));
numer1 = ComplexPolynomial.Add(numerX1, numerC1);
}
numerResult = ComplexPolynomial.Add(numer0, numer1);
}
return(new HighOrderComplexRationalPolynomial(numerResult.ToArray(), denomResult.ToArray()));
}
