public static PolynomialDouble GCD(PolynomialDouble polynomialLeft, PolynomialDouble polynomialRight)
{
PolynomialDouble A;
PolynomialDouble B;
if (polynomialLeft.Degree >= polynomialRight.Degree)
{
A = polynomialLeft.Clone();
B = polynomialRight.Clone();
}
else
{
A = polynomialRight.Clone();
B = polynomialLeft.Clone();
}
while (!B.IsZero())
{
var divisionResult = A / B;
A = B;
B = divisionResult.Mod;
}
return(A);
}
public static bool IsIrreducible(PolynomialDouble polynomial)
{
var result = ModularComposition(polynomial.Degree, polynomial);
if (result == new PolynomialDouble(1, 1.0))
{
return(true);
}
return(false);
}
public static MatrixInt Map(PolynomialDouble polynomial)
{
int[,] values = new int[1, polynomial.Degree];
for (int i = 0; i < polynomial.Degree; i++)
{
values[0, i] = (int)Math.Round(polynomial.Coefficients[i]);
}
var result = new MatrixInt(values);
return(result);
}
public static PolynomialExtendedGcdResult ExtendedGCD(PolynomialDouble polynomialLeft, PolynomialDouble polynomialRight)
{
PolynomialDouble A;
PolynomialDouble B;
PolynomialDouble X0 = new PolynomialDouble(new double[] { 1 });
PolynomialDouble X1 = new PolynomialDouble(new double[] { 0 });
PolynomialDouble Y0 = new PolynomialDouble(new double[] { 0 });
PolynomialDouble Y1 = new PolynomialDouble(new double[] { 1 });
if (polynomialLeft.Degree >= polynomialRight.Degree)
{
A = polynomialLeft.Clone();
B = polynomialRight.Clone();
}
else
{
A = polynomialRight.Clone();
B = polynomialLeft.Clone();
}
while (!B.IsZero())
{
var divisionResult = A / B;
A = B;
B = divisionResult.Mod;
var tempX = X0 - divisionResult.Result * X1;
X0 = X1;
X1 = tempX;
var tempY = Y0 - divisionResult.Result * Y1;
Y0 = Y1;
Y1 = tempY;
}
var result = new PolynomialExtendedGcdResult
{
Gcd = A,
S = X1,
T = Y0
};
return(result);
}
public static PolynomialDouble Map(MatrixInt matrix)
{
if (matrix.RowCount > 1)
{
throw new DimensionMismatchException("Base matrix for shoud consist of single row");
}
double[] values = new double[matrix.ColumnCount];
for (int i = 0; i < matrix.ColumnCount; i++)
{
values[i] = (double)matrix.Data[0, i];
}
var result = new PolynomialDouble(values);
return(result);
}
public static PolynomialDouble ModularComposition(int degree, PolynomialDouble polynomial)
{
if (degree == 0)
{
return(new PolynomialDouble(1, 1.0));
}
if (degree % 2 == 0)
{
var temp = ModularComposition(degree / 2, polynomial);
var anotherOne = new PolynomialDouble(temp.Degree + temp.Degree, 1.0);
return((anotherOne / polynomial).Mod);
}
else
{
var temp = ModularComposition(degree - 1, polynomial);
return((temp * temp / polynomial).Mod);
}
}
