/// <summary>
/// Divides <c>this</c> by <c>b</c> and stores the result in a new PolynomialGF2n[2], quotient in result[0] and remainder in result[1]
/// </summary>
///
/// <param name="B">The divisor</param>
///
/// <returns>Retuens the quotient and remainder of <c>this</c> / <c>b</c></returns>
public GF2nPolynomial[] Divide(GF2nPolynomial B)
{
GF2nPolynomial[] result = new GF2nPolynomial[2];
GF2nPolynomial a = new GF2nPolynomial(this);
a.Shrink();
GF2nPolynomial shift;
GF2nElement factor;
int bDegree = B.Degree;
GF2nElement inv = (GF2nElement)B._coeff[bDegree].Invert();
if (a.Degree < bDegree)
{
result[0] = new GF2nPolynomial(this);
result[0].AssignZeroToElements();
result[0].Shrink();
result[1] = new GF2nPolynomial(this);
result[1].Shrink();
return(result);
}
result[0] = new GF2nPolynomial(this);
result[0].AssignZeroToElements();
int i = a.Degree - bDegree;
while (i >= 0)
{
factor = (GF2nElement)a._coeff[a.Degree].Multiply(inv);
shift = B.ScalarMultiply(factor);
shift.ShiftThisLeft(i);
a = a.Add(shift);
a.Shrink();
result[0]._coeff[i] = (GF2nElement)factor.Clone();
i = a.Degree - bDegree;
}
result[1] = a;
result[0].Shrink();
return(result);
}
/// <summary>
/// Computes the greatest common divisor of <c>this</c> and <c>g</c> and returns the result in a new PolynomialGF2n
/// </summary>
///
/// <param name="G">The GF2nPolynomial</param>
///
/// <returns>Returns gcd(<c>this</c>, <c>g</c>)</returns>
public GF2nPolynomial Gcd(GF2nPolynomial G)
{
GF2nPolynomial a = new GF2nPolynomial(this);
GF2nPolynomial b = new GF2nPolynomial(G);
a.Shrink();
b.Shrink();
GF2nPolynomial c;
GF2nPolynomial result;
GF2nElement alpha;
while (!b.IsZero())
{
c = a.Remainder(b);
a = b;
b = c;
}
alpha = a._coeff[a.Degree];
result = a.ScalarMultiply((GF2nElement)alpha.Invert());
return(result);
}
/// <summary>
/// Computes the greatest common divisor of <c>this</c> and <c>g</c> and returns the result in a new PolynomialGF2n
/// </summary>
///
/// <param name="G">The GF2nPolynomial</param>
///
/// <returns>Returns gcd(<c>this</c>, <c>g</c>)</returns>
public GF2nPolynomial Gcd(GF2nPolynomial G)
{
GF2nPolynomial a = new GF2nPolynomial(this);
GF2nPolynomial b = new GF2nPolynomial(G);
a.Shrink();
b.Shrink();
GF2nPolynomial c;
GF2nPolynomial result;
GF2nElement alpha;
while (!b.IsZero())
{
c = a.Remainder(b);
a = b;
b = c;
}
alpha = a._coeff[a.Degree];
result = a.ScalarMultiply((GF2nElement)alpha.Invert());
return result;
}
/// <summary>
/// Divides <c>this</c> by <c>b</c> and stores the result in a new PolynomialGF2n[2], quotient in result[0] and remainder in result[1]
/// </summary>
///
/// <param name="B">The divisor</param>
///
/// <returns>Retuens the quotient and remainder of <c>this</c> / <c>b</c></returns>
public GF2nPolynomial[] Divide(GF2nPolynomial B)
{
GF2nPolynomial[] result = new GF2nPolynomial[2];
GF2nPolynomial a = new GF2nPolynomial(this);
a.Shrink();
GF2nPolynomial shift;
GF2nElement factor;
int bDegree = B.Degree;
GF2nElement inv = (GF2nElement)B._coeff[bDegree].Invert();
if (a.Degree < bDegree)
{
result[0] = new GF2nPolynomial(this);
result[0].AssignZeroToElements();
result[0].Shrink();
result[1] = new GF2nPolynomial(this);
result[1].Shrink();
return result;
}
result[0] = new GF2nPolynomial(this);
result[0].AssignZeroToElements();
int i = a.Degree - bDegree;
while (i >= 0)
{
factor = (GF2nElement)a._coeff[a.Degree].Multiply(inv);
shift = B.ScalarMultiply(factor);
shift.ShiftThisLeft(i);
a = a.Add(shift);
a.Shrink();
result[0]._coeff[i] = (GF2nElement)factor.Clone();
i = a.Degree - bDegree;
}
result[1] = a;
result[0].Shrink();
return result;
}