/// <summary>
/// Получение разложения из строки
/// </summary>
/// <param name="s">Строка</param>
/// <returns>Разложение</returns>
public static FactoredPolynomial Parse(string s)
{
Regex rg = new Regex(@"(^\d+)|(\(.+?\))(\^(\d+))?");
MatchCollection ms = rg.Matches(s);
FactoredPolynomial fp = new FactoredPolynomial();
if (s == "")
{
}
foreach (Match m in ms)
{
Polynomial p;
int d;
if (m.Groups[1].Value == "")
{
p = Polynomial.Parse(m.Groups[2].Value);
d = m.Groups[3].Value == "" ? 1 : int.Parse(m.Groups[4].Value);
}
else
{
p = Polynomial.Parse(m.Groups[1].Value);
d = 0;
}
fp.AddFactor(p, d);
}
return(fp);
}
/// <summary>
/// Добавление разложения полиномов
/// </summary>
/// <param name="p">Полином</param>
public void AddFactors(FactoredPolynomial p)
{
for (int i = 0; i < p.Length; i++)
{
this[i].AddRange(p[i]);
}
}
/// <summary>
/// Разложение полинома в бесквадратную форму
/// </summary>
/// <param name="f">Полином</param>
/// <returns>Бесквадратное разложение полинома</returns>
private FactoredPolynomial SquareFreeFactor(Polynomial f)
{
FactoredPolynomial F = new FactoredPolynomial();
int i = 1;
Polynomial df = Derivative(f);
if (df.ToString() == "0")
{
F = PowP(SquareFreeFactor(GetPRoot(f)));
}
else
{
Polynomial g = GCD(f, df);
Polynomial h = DividePolynomials(f, g);
while (h.ToString() != "1")
{
Polynomial hs = GCD(h, g);
Polynomial l = DividePolynomials(h, hs);
F.AddFactor(l, i);
i++;
h = hs;
g = DividePolynomials(g, hs);
}
if (g.ToString() != "1")
{
g = GetPRoot(g);
F.AddFactors(PowP(SquareFreeFactor(g)));
}
}
return(F);
}
/// <summary>
/// Разложение полинома на простые множители
/// </summary>
/// <param name="f">Полином</param>
/// <param name="fp">Разложение в бесквадратную форму</param>
/// <returns>Разложение даннного полинома</returns>
public FactoredPolynomial Factor(Polynomial f, out FactoredPolynomial fp)
{
if (f.Degree < 2)
{
FactoredPolynomial sfp = new FactoredPolynomial();
sfp.AddFactor(f, 1);
fp = sfp;
return(sfp);
}
Polynomial divisor;
Polynomial f2 = MadeMonic(f, out divisor);
fp = SquareFreeFactor(f2);
FactoredPolynomial res = new FactoredPolynomial();
for (int i = 1; i < fp.Length; i++)
{
for (int j = 0; j < fp[i].Count; j++)
{
res[i].AddRange(Berlekamp(fp[i][j]));
}
}
res[0].Add(divisor);
return(res);
}
public TestInfo(FactoredPolynomial basep, Polynomial baseOpened, FactoredPolynomial factored, Polynomial factoredOpened, FactoredPolynomial squareFree, bool result, bool check)
{
BaseP = basep;
BaseOpened = baseOpened;
Factored = factored;
FactoredOpened = factoredOpened;
SquareFree = squareFree;
Succes = result;
FactorizationIdentity = BaseP == Factored;
Check = check;
}
public TestInfo Run(FactoredPolynomial c, bool check = false)
{
Polynomial controlp = OpenBraces(c);
if (controlp.Degree == 0)
{
return(Run());
}
string ps = controlp.ToString();
Polynomial parsedP = Polynomial.Parse(ps);
FactoredPolynomial SquareFree;
FactoredPolynomial factoredP = _f.Factor(parsedP, out SquareFree);
Polynomial res = OpenBraces(factoredP);
TestInfo inf = new TestInfo(c, controlp, factoredP, res, SquareFree, res == controlp, check);
return(inf);
}
public FactoredPolynomial GenFactoredP()
{
FactoredPolynomial fp = new FactoredPolynomial();
int d = 0;
while (d < _n - 1)
{
Polynomial p = _simpleFactors[_gen.Next(_simpleFactors.Count)];
int k = _gen.Next(1, 4);
while (p.Degree > MAX_FACTOR_DEGREE || !p.Monic || d + p.Degree * k > _n - 1)
{
k = _gen.Next(1, 4);
p = _simpleFactors[_gen.Next(_simpleFactors.Count)];
}
d += p.Degree * k;
fp.AddFactor(p, k);
}
return(fp);
}
public Polynomial OpenBraces(FactoredPolynomial p)
{
if (p.ToString() == "0")
{
return(new Polynomial(0));
}
Polynomial po = new Polynomial(1);
for (int i = 0; i < p.Length; i++)
{
for (int j = 0; j < p[i].Count; j++)
{
for (int k = 0; k < i || (i == 0 && k == 0); k++)
{
po = _f.Multiply(po, p[i][j]);
}
}
}
return(po);
}
/// <summary>
/// Возведение разложенного полинома в степень p
/// </summary>
/// <param name="p">Разложение полинома</param>
/// <returns>Разложение в степени p</returns>
public FactoredPolynomial PowP(FactoredPolynomial p)
{
p.Pow(P);
return(p);
}
