/// <summary>
/// Method for calculatin (<paramref name="r"/>, <paramref name="s"/>) Hasse derivative value for bivariate polynomial <paramref name="polynomial"/> at point the (<paramref name="xValue"/>, <paramref name="yValue"/>)
/// </summary>
/// <param name="polynomial">Polynomial which Hasse derivative'll be calculated</param>
/// <param name="r">Hasse derivative order by x variable</param>
/// <param name="s">Hasse derivative order by y variable</param>
/// <param name="xValue">Value for x variable</param>
/// <param name="yValue">Value fro y variable</param>
/// <param name="combinationsCountCalculator">Combinations calculator contract implementation</param>
/// <param name="combinationsCache">Cache for storing calculated numbers of combinations</param>
/// <returns>Hasse derivative value</returns>
public static FieldElement CalculateHasseDerivative(this BiVariablePolynomial polynomial,
int r, int s, FieldElement xValue, FieldElement yValue,
ICombinationsCountCalculator combinationsCountCalculator, FieldElement[][] combinationsCache = null)
{
var field = polynomial.Field;
var derivativeValue = 0;
foreach (var coefficient in polynomial)
{
if (coefficient.Key.Item1 < r || coefficient.Key.Item2 < s)
{
continue;
}
var currentAddition = combinationsCountCalculator.Calculate(field, coefficient.Key.Item1, r, combinationsCache).Representation;
currentAddition = field.Multiply(currentAddition,
combinationsCountCalculator.Calculate(field, coefficient.Key.Item2, s, combinationsCache).Representation);
currentAddition = field.Multiply(currentAddition, coefficient.Value.Representation);
currentAddition = field.Multiply(currentAddition, field.Pow(xValue.Representation, coefficient.Key.Item1 - r));
currentAddition = field.Multiply(currentAddition, field.Pow(yValue.Representation, coefficient.Key.Item2 - s));
derivativeValue = field.Add(derivativeValue, currentAddition);
}
return(new FieldElement(field, derivativeValue));
}
/// <summary>
/// Constructor for creating interpolation polynomial builder based on Kotter's algorithm
/// </summary>
/// <param name="combinationsCountCalculator">Implementation of combinations count calculator contract</param>
public KotterAlgorithmBasedBuilder(ICombinationsCountCalculator combinationsCountCalculator)
{
if (combinationsCountCalculator == null)
{
throw new ArgumentNullException(nameof(combinationsCountCalculator));
}
_combinationsCountCalculator = combinationsCountCalculator;
_zeroMonomial = new Tuple <int, int>(0, 0);
}
/// <summary>
/// Constructor for creating instance of interpolation polynomial builder
/// </summary>
/// <param name="combinationsCountCalculator">Implementation of combinations count calculator contract</param>
/// <param name="linearSystemSolver">Implementation of linear systems solver contract</param>
public SimplePolynomialBuilder(ICombinationsCountCalculator combinationsCountCalculator, ILinearSystemSolver linearSystemSolver)
{
if (combinationsCountCalculator == null)
{
throw new ArgumentNullException(nameof(combinationsCountCalculator));
}
if (linearSystemSolver == null)
{
throw new ArgumentNullException(nameof(linearSystemSolver));
}
_combinationsCountCalculator = combinationsCountCalculator;
_linearSystemSolver = linearSystemSolver;
}
public BiVariablePolynomialTests()
{
_combinationsCountCalculator = new PascalsTriangleBasedCalcualtor();
}
