/// <summary>
/// Наибольший общий делитель 3 и более полиномов
/// </summary>
/// <param name="polynoms"> Список полиномов </param>
/// <returns></returns>
public static Polynom GetGCD(params Polynom[] polynoms)
{
Polynom h = new Polynom();
List <Polynom> sortedByDescending = polynoms.OrderBy(p => p.Degree).ToList();
for (int i = sortedByDescending.Count - 2; i >= 0; i--)
{
sortedByDescending[i] = GetGCD(sortedByDescending[i], sortedByDescending[i + 1]);
sortedByDescending.RemoveAt(i + 1);
}
return(sortedByDescending.First());
}
/// <summary>
/// Упростить рациональную функцию
/// </summary>
/// <param name="divisionResult"></param>
/// <returns></returns>
public Function Simplify(out List <Monom> divisionResult)
{
divisionResult = new List <Monom>();
if (numerator.LT.CompareTo(denominator.LT) >= 0) //сравниваем степени числителя и знаменателя
{
var reminder = new Polynom();
Polynom.DividePolynoms(numerator, denominator, out divisionResult, out reminder);
return(new RationalFunction(reminder, denominator));
}
else
{
return(new RationalFunction(numerator, denominator));
}
}
/// <summary>
/// Деление полиномов с остатком
/// </summary>
/// <param name="f"> Делимое </param>
/// <param name="g"> Делитель </param>
/// <param name="q"> Частное </param>
/// <param name="r"> Остаток </param>
public static void DividePolynoms(Polynom f, Polynom g, out List <Monom> q, out Polynom r)
{
q = new List <Monom>();
r = (Polynom)f.Clone();
while (r.Degree >= g.Degree)
{
if (!r.IsNull && Monom.CanDivide(r.LT, g.LT))
{
Monom divLT = r.LT / g.LT;
q.Add(divLT);
var temp = g * (divLT);
r = r - temp;
r = LexOrder.CreateOrderedPolynom(r);
r = r.SimplifyPolynom();
}
else
{
break;
}
}
}
/// <summary>
/// Перестановка мономов в полиноме
/// </summary>
/// <param name="poly"> Анализируемый полином </param>
/// <returns> Готовый полином </returns>
public static Polynom CreateOrderedPolynom(Polynom poly)
{
Polynom tempPolynom = poly, orderedPolynom;
Dictionary <Monom, int> monomRepeats = tempPolynom.monoms.ToDictionary(m => m, m => 1);
foreach (Monom t in tempPolynom.monoms)
{
foreach (Monom t1 in tempPolynom.monoms)
{
if (t.CompareTo(t1) > 0)
{
monomRepeats[t]++;
}
}
}
monomRepeats = monomRepeats.OrderByDescending(pair => pair.Value).ToDictionary(pair => pair.Key, pair => pair.Value);
//Составим упорядоченный полином
orderedPolynom = new Polynom(monomRepeats.Keys.ToList());
return(orderedPolynom.SimplifyPolynom());
}
/// <summary>
/// Наибольший общий делитель 2-х полиномов
/// </summary>
/// <param name="f"> Полином </param>
/// <param name="g"> Полином </param>
/// <returns> НОД - полином </returns>
public static Polynom GetGCD(Polynom f, Polynom g)
{
Polynom h = f.Degree > g.Degree ? (Polynom)f.Clone() : (Polynom)g.Clone();
Polynom s = f.Degree < g.Degree ? (Polynom)f.Clone() : (Polynom)g.Clone();
while (!s.IsNull)
{
if (h.Degree >= s.Degree)
{
Polynom rem = new Polynom();
List <Monom> q = new List <Monom>();
DividePolynoms(h, s, out q, out rem);
h = s;
s = rem;
}
else
{
break;
}
}
return(h);
}
public RationalFunction(Polynom num, Polynom denom)
{
numerator = num;
denominator = denom;
}