/// <summary>
/// S-полином
/// </summary>
/// <param name="a"> Полином </param>
/// <param name="b"> Полином </param>
/// <returns></returns>
public static Polynom S_polynom(Polynom a, Polynom b)
{
var lcm = Monom.GetLCM(a.LT, b.LT);
var sp = a * (lcm / a.LT) - b * (lcm / b.LT);
return(sp);
}
/// <summary>
/// Упрощение
/// </summary>
/// <returns> Упрощенный полином </returns>
public Polynom SimplifyPolynom()
{
List <int> nullCoefs = new List <int>();
for (int i = 0; i < monoms.Count; i++)
{
//найдем нулевые коэффициенты
if (monoms[i].Coef == 0)
{
monoms.RemoveAt(i);
//nullCoefs.Add(i);
i--;
}
}
for (int i = 0; i < monoms.Count; i++)
{
for (int j = i + 1; j < monoms.Count; j++)
{
if (Monom.AreEqual(monoms[i], monoms[j]))
{
monoms[i] = monoms[i] + monoms[j];
monoms.RemoveAt(j);
}
}
}
return(new Polynom(monoms));
}
/// <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;
}
}
}