public PolynomialOverFiniteField Mul(PolynomialOverFiniteField firstArg, PolynomialOverFiniteField secondArg)
{
int firstDeg = firstArg.Deg;
int secondDeg = secondArg.Deg;
if (firstDeg == -1 || secondDeg == -1)
{
return(new PolynomialOverFiniteField(new Polynomial[] { new Polynomial(new BigInteger[] { 0 }) }));
}
int maxdegree = firstDeg + secondDeg;
Polynomial[] result = new Polynomial[maxdegree + 1];
for (int i = 0; i <= firstDeg; i++)
{
for (int j = 0; j <= secondDeg; j++)
{
if (result[i + j] == null)
{
result[i + j] = new Polynomial(new BigInteger[] { 0 });
}
result[i + j] = _polynomialMath.Add(result[i + j], _polynomialMath.Mul(firstArg[i], secondArg[j]));
}
}
return(new PolynomialOverFiniteField(result, Mod, FieldChar));
}
public PolynomialOverFiniteField ModPow(PolynomialOverFiniteField polynomial, BigInteger power, PolynomialOverFiniteField mod)
{
if (power == 0)
{
return(new PolynomialOverFiniteField(new Polynomial[] { new Polynomial(new BigInteger[] { 1 }) }));
}
var res = new PolynomialOverFiniteField(new Polynomial[] { new Polynomial(new BigInteger[] { 1 }) });
var a = polynomial;
while (power != 0)
{
if (power % 2 != 0)
{
res = Rem(Mul(res, a), mod);
}
a = Rem(Mul(a, a), mod);
power >>= 1;
}
return(res);
}
public PolynomialOverFiniteField Add(PolynomialOverFiniteField firstArg, PolynomialOverFiniteField secondArg)
{
int firstDeg = firstArg.Deg;
int secondDeg = secondArg.Deg;
var maxDeg = Math.Max(firstDeg, secondDeg);
if (maxDeg == -1)
{
return(new PolynomialOverFiniteField(new Polynomial[] { new Polynomial(new BigInteger[1]) }));
}
var result = new Polynomial[maxDeg + 1];
if (firstDeg > secondDeg)
{
int i;
for (i = 0; i <= secondDeg; i++)
{
result[i] = _polynomialMath.Add(firstArg[i], secondArg[i]);
}
for (; i <= firstDeg; i++)
{
result[i] = firstArg[i];
}
}
else
{
int i;
for (i = 0; i <= firstDeg; i++)
{
result[i] = _polynomialMath.Add(firstArg[i], secondArg[i]);
}
for (; i <= secondDeg; i++)
{
result[i] = secondArg[i];
}
}
return(new PolynomialOverFiniteField(result, Mod, FieldChar));
}
public PolynomialOverFiniteField Div(PolynomialOverFiniteField firstArg, PolynomialOverFiniteField secondArg)
{
if (secondArg.Deg == -1)
{
throw new DivideByZeroException();
}
if (firstArg.Deg < secondArg.Deg)
{
return(new PolynomialOverFiniteField(new Polynomial[] { new Polynomial(new BigInteger[] { 0 }) }));
}
var firstDeg = firstArg.Deg;
var secondDeg = secondArg.Deg;
var newDeg = firstDeg - secondDeg;
var result = new Polynomial[newDeg + 1];
var reminder = (Polynomial[])firstArg.Coefficients.Clone();
Polynomial firstLc;
Polynomial secondLc = secondArg[secondDeg];
var inverse = new PolynomialInverse();
secondLc = inverse.Inverse(secondLc, Mod);
for (int i = 0; i <= newDeg; i++)
{
firstLc = reminder[firstDeg - i];
result[newDeg - i] = _polynomialMath.Mul(firstLc, secondLc);
for (int j = 0; j <= secondDeg; j++)
{
reminder[firstDeg - secondDeg + j - i] =
_polynomialMath.Sub(reminder[firstDeg - secondDeg + j - i], (_polynomialMath.Mul(result[newDeg - i], secondArg[j])));
}
}
return(new PolynomialOverFiniteField(result, Mod, FieldChar));
}
