public GFPoly AddOrSubtract(GFPoly other)
{
if (IsZero())
{
return(other);
}
if (other.IsZero())
{
return(this);
}
int[] smallCoefficients = Coefficients;
int[] largeCoefficients = other.Coefficients;
if (smallCoefficients.Length > largeCoefficients.Length)
{
(largeCoefficients, smallCoefficients) = (smallCoefficients, largeCoefficients);
}
int[] sumDiff = new int[largeCoefficients.Length];
int lenDiff = largeCoefficients.Length - smallCoefficients.Length;
Array.Copy(largeCoefficients, sumDiff, lenDiff);
for (int i = lenDiff; i < largeCoefficients.Length; i++)
{
sumDiff[i] = GaloisField.AddOrSubtract(smallCoefficients[i - lenDiff], largeCoefficients[i]);
}
return(new GFPoly(GaloisField, sumDiff));
}
public (GFPoly Quotient, GFPoly Remainder) Divide(GFPoly other)
{
GFPoly quotient = Zero(GaloisField);
GFPoly remainder = this;
int denomLeadTerm = other.GetCoefficient(other.Degree());
int inversDenomLeadTerm = GaloisField.Inverse(denomLeadTerm);
while (remainder.Degree() >= other.Degree() && !remainder.IsZero())
{
int degreeDiff = remainder.Degree() - other.Degree();
int scale = GaloisField.Multiply(remainder.GetCoefficient(remainder.Degree()), inversDenomLeadTerm);
GFPoly term = other.MultiplyByMonominal(degreeDiff, scale);
GFPoly itQuot = MonominalPoly(GaloisField, degreeDiff, scale);
quotient = quotient.AddOrSubtract(itQuot);
remainder = remainder.AddOrSubtract(term);
}
return(quotient, remainder);
}
public GFPoly Multiply(GFPoly other)
{
if (IsZero() || other.IsZero())
{
return(Zero(GaloisField));
}
int[] product = new int[Coefficients.Length + other.Coefficients.Length - 1];
for (int i = 0; i < Coefficients.Length; i++)
{
int ac = Coefficients[i];
for (int j = 0; j < other.Coefficients.Length; j++)
{
int bc = other.Coefficients[j];
product[i + j] = GaloisField.AddOrSubtract(product[i + j], GaloisField.Multiply(ac, bc));
}
}
return(new GFPoly(GaloisField, product));
}