/// <summary>
/// Multiply current Polynomial to anotherone.
/// </summary>
/// <returns>Result polynomial after multiply</returns>
internal Polynomial Multiply(Polynomial other)
{
if (Primitive != other.Primitive)
{
throw new ArgumentException("Polynomial cannot perform Multiply as they do not have same Primitive for GaloisField256");
}
if (IsMonomialZero || other.IsMonomialZero)
{
return(new Polynomial(GField, new int[] { 0 }));
}
int[] aCoefficients = Coefficients;
int aLength = aCoefficients.Length;
int[] bCoefficient = other.Coefficients;
int bLength = bCoefficient.Length;
int[] rCoefficients = new int[aLength + bLength - 1];
for (int aIndex = 0; aIndex < aLength; aIndex++)
{
int aCoeff = aCoefficients[aIndex];
for (int bIndex = 0; bIndex < bLength; bIndex++)
{
rCoefficients[aIndex + bIndex] =
GField.Addition(rCoefficients[aIndex + bIndex], GField.Product(aCoeff, bCoefficient[bIndex]));
}
}
return(new Polynomial(GField, rCoefficients));
}
/// <summary>
/// divide current polynomial by "other"
/// </summary>
/// <param name="other">The other.</param>
/// <returns>Result polynomial after divide</returns>
/// <remarks></remarks>
internal PolyDivideStruct Divide(Polynomial other)
{
if (Primitive != other.Primitive)
{
throw new ArgumentException(
"Polynomial can not perform Devide as they don't have same Primitive for GaloisField256");
}
if (other.isMonomialZero)
{
throw new ArgumentException("Can not devide by Polynomial Zero");
}
//this devide by other = a devide by b
int aLength = Coefficients.Length;
//We will make change to aCoefficient. It will return as remainder
var aCoefficients = new int[aLength];
Array.Copy(Coefficients, 0, aCoefficients, 0, aLength);
int bLength = other.Coefficients.Length;
if (aLength < bLength)
{
return(new PolyDivideStruct(new Polynomial(GField, new[] { 0 }), this));
}
else
{
//quotient coefficients
//qLastIndex = alength - blength qlength = qLastIndex + 1
var qCoefficients = new int[(aLength - bLength) + 1];
//Denominator
int otherLeadingTerm = other.GetCoefficient(other.Degree);
int inverseOtherLeadingTerm = GField.inverse(otherLeadingTerm);
for (int aIndex = 0; aIndex <= aLength - bLength; aIndex++)
{
if (aCoefficients[aIndex] != 0)
{
int aScalar = GField.Product(inverseOtherLeadingTerm, aCoefficients[aIndex]);
Polynomial term = other.MultiplyScalar(aScalar);
qCoefficients[aIndex] = aScalar;
int[] bCoefficient = term.Coefficients;
if (bCoefficient[0] != 0)
{
for (int bIndex = 0; bIndex < bLength; bIndex++)
{
aCoefficients[aIndex + bIndex] = GField.Subtraction(aCoefficients[aIndex + bIndex],
bCoefficient[bIndex]);
}
}
}
}
return(new PolyDivideStruct(new Polynomial(GField, qCoefficients),
new Polynomial(GField, aCoefficients)));
}
}
/// <summary>
/// Multiplay scalar to current polynomial
/// </summary>
/// <param name="scalar">The scalar.</param>
/// <returns>result of polynomial after multiply scalar</returns>
/// <remarks></remarks>
internal Polynomial MultiplyScalar(int scalar)
{
if (scalar == 0)
{
return(new Polynomial(GField, new[] { 0 }));
}
else if (scalar == 1)
{
return(this);
}
int length = Coefficients.Length;
var rCoefficient = new int[length];
for (int index = 0; index < length; index++)
{
rCoefficient[index] = GField.Product(Coefficients[index], scalar);
}
return(new Polynomial(GField, rCoefficient));
}