/// <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);
}
/// <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;
}
}
}