public static Polynomial Rem(Polynomial firstArg, Polynomial secondArg)
{
var firstDeg = firstArg.Deg;
var secondDeg = secondArg.Deg;
var newDeg = firstDeg - secondDeg;
var result = new ulong[newDeg + 1];
var reminder = (ulong[])firstArg._coefficients.Clone();
var mod = secondArg._mod;
ulong firstLc;
ulong secondLc = secondArg[secondDeg];
for (int i = 0; i <= newDeg; i++)
{
firstLc = reminder[firstDeg - i];
result[newDeg - i] = (firstLc * IntegerMath.Inverse(secondLc, mod)) % mod;
for (int j = 0; j <= secondDeg; j++)
{
reminder[firstDeg - secondDeg + j - i] =
(reminder[firstDeg - secondDeg + j - i] + (mod - (result[newDeg - i] * secondArg[j]) % mod)) % mod;
}
}
return(new Polynomial(reminder));
}
static ulong[] SlowInverseFt(ulong[] vector)
{
var size = vector.Length;
var res = new ulong[size];
ulong pow = (ulong)(Power / size);
ulong root_n = IntegerMath.ModPow(Root_1, pow, Mod);
ulong root_i = 1;
for (int i = 0; i < size; i++)
{
double temp = 0;
ulong root_j = 1;
for (int j = 0; j < size; j++)
{
temp = (temp + (vector[j] * root_j) % Mod) % Mod;
root_j = (root_j * root_i) % Mod;
}
res[i] = (ulong)(temp * IntegerMath.Inverse((ulong)size, Mod)) % Mod;
root_i = (root_i * root_n) % Mod;
}
return(res);
}
public static Polynomial Inverse(Polynomial polynomial, Polynomial mod, ulong fieldCharacteristic, out Polynomial gcd)
{
polynomial.SetMod(fieldCharacteristic);
mod.SetMod(fieldCharacteristic);
polynomial.Reduce();
mod.Reduce();
if (mod.Deg == -1 || polynomial.Deg == -1)
{
throw new InvalidOperationException("Обратный элемент не определен");
}
Polynomial bezoutCoefficient = new Polynomial(new ulong[] { 1 });
Polynomial nextBezoutCoefficient = new Polynomial();
gcd = polynomial % mod;
Polynomial reminder = mod;
Polynomial temp = new Polynomial();
Polynomial quotient;
gcd.SetMod(fieldCharacteristic);
gcd.Reduce();
bezoutCoefficient.SetMod(fieldCharacteristic);
bezoutCoefficient.Reduce();
nextBezoutCoefficient.SetMod(fieldCharacteristic);
nextBezoutCoefficient.Reduce();
while (reminder.Deg != -1)
{
temp = reminder;
quotient = gcd / reminder;
quotient.SetMod(fieldCharacteristic);
quotient.Reduce();
var qxr = quotient * reminder;
qxr.SetMod(fieldCharacteristic);
qxr.Reduce();
reminder = gcd - qxr;
reminder.SetMod(fieldCharacteristic);
reminder.Reduce();
gcd = temp;
temp = nextBezoutCoefficient;
var qxu = quotient * nextBezoutCoefficient;
qxu.SetMod(fieldCharacteristic);
qxu.Reduce();
nextBezoutCoefficient = bezoutCoefficient - qxu;
nextBezoutCoefficient.SetMod(fieldCharacteristic);
nextBezoutCoefficient.Reduce();
bezoutCoefficient = temp;
}
gcd = gcd % mod;
gcd.SetMod(fieldCharacteristic);
gcd.Reduce();
var c = gcd[0];
var inverse = IntegerMath.Inverse(c, fieldCharacteristic);
if (c != 1)
{
gcd = inverse * gcd;
gcd.SetMod(fieldCharacteristic);
gcd.Reduce();
}
if (gcd != new Polynomial(new ulong[] { 1 }))
{
throw new ArgumentException(string.Format("Обратный элемент к {0} не существует!", polynomial));
}
var res = (inverse * bezoutCoefficient) % mod;
res.SetMod(fieldCharacteristic);
res.Reduce();
return(res);
}
