/// <summary>
/// Остаток от деления. С возвратом целой части
/// </summary>
/// <param name="a">Делимое</param>
/// <param name="b">Делитель</param>
/// <param name="_div">Целая цасть</param>
/// <returns>Остаток</returns>
public static Polynom Remainder(Polynom a, Polynom b, out Polynom _div)
{
if (a.Degree < b.Degree)
{
_div = null;
return(a);
}
List <Monom> div = new List <Monom>(); // целая часть
while (a.Degree >= b.Degree)
{
BigInteger current_deg = a.Degree - b.Degree;
Monom c = new Monom(current_deg, 1); // целая часть от деления
BigInteger currentInt = a.coefficients[0].Coefficient * Extension.Inverse(b.coefficients[0].Coefficient, b.Fp);
c.MultiplyInt(currentInt);
div.Add(c);
Polynom temp = new Polynom(new List <Monom> {
c
}, a.Fp);
a -= temp * b;
a.NormPolynom();
}
_div = new Polynom(div, a.Fp);
return(a);
}
/// <summary>
/// Умножение монома на моном
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <returns></returns>
public static Monom operator *(Monom a, Monom b)
{
Monom c = new Monom();
c.Coefficient = a.Coefficient * b.Coefficient;
c.Degree = a.Degree + b.Degree;
return(c);
}
/// <summary>
/// Разность полиномов
/// </summary>
/// <param name="a">Уменьшаемое</param>
/// <param name="b">Вычитаемое</param>
/// <returns></returns>
public static Polynom operator -(Polynom a, Polynom b)
{
a.NormPolynom();
b.NormPolynom();
List <Monom> c = new List <Monom>();
int curnta = 0; // Текущий элемент в полиноме а
int curntb = 0; // Текущий элемент в полиноме b
while (curnta < a.coefficients.Count && curntb < b.coefficients.Count)
{
if (a.coefficients[curnta].Degree < b.coefficients[curntb].Degree)
{
c.Add(Monom.Negate(b.coefficients[curntb]));
curntb++;
}
else if (a.coefficients[curnta].Degree > b.coefficients[curntb].Degree)
{
c.Add(a.coefficients[curnta]);
curnta++;
}
else
{
c.Add(a.coefficients[curnta].SubNumber(b.coefficients[curntb].Coefficient));
curnta++;
curntb++;
}
}
if (curnta == a.coefficients.Count)
{
while (curntb < b.coefficients.Count)
{
c.Add(Monom.Negate(b.coefficients[curntb]));
curntb++;
}
}
else if (curntb == b.coefficients.Count)
{
while (curnta < a.coefficients.Count)
{
c.Add(a.coefficients[curnta]);
curnta++;
}
}
return(new Polynom(c, a.Fp));
}
/// <summary>
/// Изменяет знак коэффициента
/// </summary>
/// <returns></returns>
static public Monom Negate(Monom a)
{
return(new Monom(a.Degree, BigInteger.Negate(a.Coefficient)));
}