Reduction(WWComplex [] aNumerCoeffList, WWComplex [] aDenomRootList)
{
var rv = new PolynomialAndRationalPolynomial();
rv.coeffList = new WWComplex[0];
rv.numerCoeffList = new WWComplex[aNumerCoeffList.Length];
Array.Copy(aNumerCoeffList, rv.numerCoeffList, aNumerCoeffList.Length);
rv.denomRootList = new WWComplex[aDenomRootList.Length];
Array.Copy(aDenomRootList, rv.denomRootList, aDenomRootList.Length);
if (rv.numerCoeffList.Length - 1 < rv.denomRootList.Length)
{
// 既に分子の多項式の次数が分母の多項式の次数よりも低い。
return(rv);
}
// 分母の根のリスト⇒分母の多項式の係数のリストに変換。
var denomCoeffList = RootListToCoeffList(aDenomRootList, new WWComplex(1, 0));
var quotient = new List <WWComplex>();
while (denomCoeffList.Length <= rv.numerCoeffList.Length)
{
// denomの最も次数が高い項の係数がcdn、numerの最も次数が高い項の係数がcnnとすると
// denomiCoeffListを-cnn/cdn * s^(numerの次数-denomの次数)倍してnumerCoeffListと足し合わせてnumerの次数を1下げる。
// このときrv.coeffListにc == cnn/cdnを足す。
var c = WWComplex.Div(rv.numerCoeffList[rv.numerCoeffList.Length - 1],
denomCoeffList[denomCoeffList.Length - 1]);
quotient.Insert(0, c);
var denomMulX = new ComplexPolynomial(denomCoeffList);
while (denomMulX.Degree + 1 < rv.numerCoeffList.Length)
{
denomMulX = ComplexPolynomial.MultiplyX(denomMulX);
}
denomMulX = ComplexPolynomial.MultiplyC(denomMulX, WWComplex.Mul(c, -1));
// ここで引き算することで分子の多項式の次数が1減る。
int expectedOrder = rv.numerCoeffList.Length - 2;
rv.numerCoeffList = ComplexPolynomial.TrimPolynomialOrder(
ComplexPolynomial.Add(denomMulX, new ComplexPolynomial(rv.numerCoeffList)),
expectedOrder).ToArray();
// 引き算によって一挙に2以上次数が減った場合coeffListに0を足す。
int actualOrder = rv.numerCoeffList.Length - 1;
for (int i = 0; i < expectedOrder - actualOrder; ++i)
{
quotient.Insert(0, WWComplex.Zero());
}
}
rv.coeffList = quotient.ToArray();
return(rv);
}
RootListToCoeffList(WWComplex [] b, WWComplex c)
{
var coeff = new List <WWComplex>();
if (b.Length == 0)
{
// 定数項のみ。(?)
coeff.Add(c);
return(coeff.ToArray());
}
var b2 = new List <WWComplex>();
foreach (var i in b)
{
b2.Add(i);
}
// (p-b[0])
coeff.Add(WWComplex.Mul(b2[0], -1));
coeff.Add(WWComplex.Unity());
b2.RemoveAt(0);
WWComplex[] coeffArray = coeff.ToArray();
while (0 < b2.Count)
{
// 多項式に(p-b[k])を掛ける。
var s1 = ComplexPolynomial.MultiplyX(new ComplexPolynomial(coeffArray));
var s0 = ComplexPolynomial.MultiplyC(new ComplexPolynomial(coeffArray),
WWComplex.Mul(b2[0], -1));
coeffArray = ComplexPolynomial.Add(s1, s0).ToArray();
b2.RemoveAt(0);
}
return(ComplexPolynomial.MultiplyC(new ComplexPolynomial(coeffArray), c).ToArray());
}
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()));
}