/// <summary>
/// Indexing property for obtain bivariate polynomial coefficient by variable power <paramref name="index"/>
/// </summary>
/// <param name="index">Variable power which coefficient is required</param>
/// <returns>Polynomial coefficient</returns>
public int this[int index]
{
get
{
if (index < 0 || index > Degree)
{
throw new IndexOutOfRangeException();
}
return(_coefficients[index]);
}
set
{
if (index < 0 || index > Degree)
{
throw new IndexOutOfRangeException();
}
if (Field.IsFieldElement(value) == false)
{
throw new ArgumentException(NameOfExtension.nameof(() => value));
}
_coefficients[index] = value;
}
}
/// <summary>
/// Method for finding irreducible polynomial degree <paramref name="degree"/> with coefficients from field with order <paramref name="fieldOrder"/>
/// </summary>
/// <param name="fieldOrder">Field order from which irreducible polynomials coefficients come</param>
/// <param name="degree">Irreducible polynomial degree</param>
/// <returns>Irreducible polynomial with specified properties</returns>
public GFPolynoms.Polynomial Find(int fieldOrder, int degree)
{
if (degree < 2)
{
throw new ArgumentException(NameOfExtension.nameof(() => degree));
}
var field = new PrimeOrderField(fieldOrder);
var possibleDivisors = new List <GFPolynoms.Polynomial>();
for (var i = 1; i *i <= degree; i++)
{
var templatePolynomial = GenerateTemplatePolynomial(field, i);
Generate(templatePolynomial, 0,
x =>
{
possibleDivisors.Add(new GFPolynoms.Polynomial(x));
return(false);
});
}
var result = GenerateTemplatePolynomial(field, degree);
Generate(result, 0, x => possibleDivisors.All(d => (x % d).IsZero == false));
return(result);
}
/// <summary>
/// Method for performing list decoding of Reed-Solomon code codeword
/// </summary>
/// <param name="n">Codeword length</param>
/// <param name="k">Information word length</param>
/// <param name="decodedCodeword">Recived codeword for decoding</param>
/// <param name="minCorrectValuesCount">Minimum number of valid values</param>
/// <returns>Decoding result</returns>
public Polynomial[] Decode(int n, int k, Tuple <FieldElement, FieldElement>[] decodedCodeword, int minCorrectValuesCount)
{
if (n <= 0)
{
throw new ArgumentException(NameOfExtension.nameof(() => n));
}
if (k <= 0 || k >= n)
{
throw new ArithmeticException(NameOfExtension.nameof(() => k));
}
if (minCorrectValuesCount <= 0 || minCorrectValuesCount * minCorrectValuesCount <= n * (k - 1))
{
throw new ArgumentException(NameOfExtension.nameof(() => minCorrectValuesCount) + " is to small");
}
if (decodedCodeword == null)
{
throw new ArgumentNullException(NameOfExtension.nameof(() => decodedCodeword));
}
if (decodedCodeword.Length != n)
{
throw new AggregateException(NameOfExtension.nameof(() => decodedCodeword));
}
var decrementedK = k - 1;
var temp = minCorrectValuesCount * minCorrectValuesCount - n * decrementedK;
var rootsMultiplicity = 1 + (int)Math.Floor((n * decrementedK + Math.Sqrt(n * n * decrementedK * decrementedK + 4d * temp)) / (2d * temp));
var maxWeightedDegree = rootsMultiplicity * minCorrectValuesCount - 1;
var interpolationPolynomial = _interpolationPolynomialBuilder.Build(new Tuple <int, int>(1, decrementedK), maxWeightedDegree,
decodedCodeword, rootsMultiplicity);
var possibleInformationPolynomials = _interpolationPolynomialFactorizator.Factorize(interpolationPolynomial, decrementedK);
return(SelectCorrectInformationPolynomials(possibleInformationPolynomials, decodedCodeword, minCorrectValuesCount));
}
/// <summary>
/// Method for bivariate interpolation polynomial building
/// </summary>
/// <param name="degreeWeight">Weight of bivariate monomials degree</param>
/// <param name="maxWeightedDegree">Maximum value of bivariate monomial degree</param>
/// <param name="roots">Roots of the interpolation polynomial</param>
/// <param name="rootsMultiplicity">Multiplicity of bivariate polynomial's roots</param>
/// <returns>Builded interpolation polynomial</returns>
public BiVariablePolynomial Build(
Tuple <int, int> degreeWeight,
int maxWeightedDegree,
Tuple <FieldElement, FieldElement>[] roots,
int rootsMultiplicity)
{
if (degreeWeight == null)
{
throw new ArgumentNullException(NameOfExtension.nameof(() => degreeWeight));
}
if (roots == null)
{
throw new ArgumentNullException(NameOfExtension.nameof(() => roots));
}
if (roots.Length == 0)
{
throw new ArgumentException(NameOfExtension.nameof(() => roots) + " is empty");
}
var field = roots[0].Item1.Field;
var variableIndexByMonomial = new Dictionary <Tuple <int, int>, int>();
var monomialByVariableIndex = new Dictionary <int, Tuple <int, int> >();
var equationsSystem = BuildEquationsSystem(field, degreeWeight,
maxWeightedDegree, maxWeightedDegree / degreeWeight.Item1, roots, rootsMultiplicity,
variableIndexByMonomial, monomialByVariableIndex);
var systemSolution = SolveEquationsSystem(field, variableIndexByMonomial.Count, equationsSystem);
return(ConstructInterpolationPolynomial(field, systemSolution, monomialByVariableIndex));
}
/// <summary>
/// Method for subtracting bivariate polynomial <paramref name="other"/> multiplied by <paramref name="b"/> from current bivariate polynomial
/// </summary>
/// <param name="b">Subtrahend multiplier</param>
/// <param name="other">Subtrahend</param>
public BiVariablePolynomial Subtract(FieldElement b, BiVariablePolynomial other)
{
if (Field.Equals(b.Field) == false)
{
throw new ArgumentException(NameOfExtension.nameof(() => b));
}
if (Field.Equals(other.Field) == false)
{
throw new ArgumentException(NameOfExtension.nameof(() => other));
}
if (b.Representation == 0)
{
return(this);
}
foreach (var otherCoefficient in other._coefficients)
{
FieldElement coeficientValue;
if (_coefficients.TryGetValue(otherCoefficient.Key, out coeficientValue) == false)
{
coeficientValue = Field.Zero();
_coefficients[otherCoefficient.Key] = coeficientValue;
}
coeficientValue.Subtract(b * otherCoefficient.Value);
if (coeficientValue.Representation == 0)
{
_coefficients.Remove(otherCoefficient.Key);
}
}
return(this);
}
/// <summary>
/// Method Calculating results of replacement bivariate polynomial <paramref name="polynomial"/> variable y by value <paramref name="yValue"/>
/// </summary>
/// <param name="polynomial">Modified polynomial</param>
/// <param name="yValue">Value for y variable</param>
/// <returns>Replacement results</returns>
public static Polynomial EvaluateY(this BiVariablePolynomial polynomial, FieldElement yValue)
{
if (polynomial == null)
{
throw new ArgumentNullException(NameOfExtension.nameof(() => polynomial));
}
if (yValue == null)
{
throw new ArgumentNullException(NameOfExtension.nameof(() => yValue));
}
if (polynomial.Field.Equals(yValue.Field) == false)
{
throw new AggregateException(NameOfExtension.nameof(() => yValue));
}
var field = polynomial.Field;
var resultCoefficients = new int[polynomial.MaxXDegree + 1];
foreach (var coefficient in polynomial)
{
resultCoefficients[coefficient.Key.Item1] = field.Add(resultCoefficients[coefficient.Key.Item1],
field.Multiply(coefficient.Value.Representation, field.Pow(yValue.Representation, coefficient.Key.Item2)));
}
return(new Polynomial(field, resultCoefficients));
}
/// <summary>
/// Converts source polynomial <paramref name="polynomial"/> to form p(x) = p_e(x^2)+x*p_o(x^2)
/// </summary>
/// <param name="polynomial">Polynomial for processing</param>
/// <returns>Pair (p_e(x), p_o(x))</returns>
public static Tuple <Polynomial, Polynomial> GetPolyphaseComponents(this Polynomial polynomial)
{
if (polynomial == null)
{
throw new ArgumentNullException(NameOfExtension.nameof(() => polynomial));
}
var evenDegreesCoefficients = new List <int>();
var oddDegreesCoefficients = new List <int>();
for (var i = 0; i <= polynomial.Degree; i++)
{
if (i % 2 == 0)
{
evenDegreesCoefficients.Add(polynomial[i]);
}
else
{
oddDegreesCoefficients.Add(polynomial[i]);
}
}
return(new Tuple <Polynomial, Polynomial>(new Polynomial(polynomial.Field, evenDegreesCoefficients.ToArray()),
new Polynomial(polynomial.Field, oddDegreesCoefficients.ToArray())));
}
/// <summary>
/// Constructor for creating field with order <paramref name="order"/> and irreducible polynomial <paramref name="irreduciblePolynomial"/>
/// </summary>
/// <param name="order">Field order</param>
/// <param name="irreduciblePolynomial">Field irreducible polynomial</param>
public PrimePowerOrderField(int order, GFPolynoms.Polynomial irreduciblePolynomial)
{
var analysisResult = AnalyzeOrder(order);
if (analysisResult.Count != 1)
{
throw new ArgumentException("Field order isn't a prime number power");
}
if (analysisResult.First().Value == 1)
{
throw new ArgumentException("Field order is a prime number");
}
if (irreduciblePolynomial == null)
{
throw new ArgumentNullException(NameOfExtension.nameof(() => irreduciblePolynomial));
}
if (irreduciblePolynomial.Field.Order != analysisResult.First().Key)
{
throw new ArgumentException("Irreducible polynomial isn't declared over properly field");
}
if (irreduciblePolynomial.Degree != analysisResult.First().Value)
{
throw new ArgumentException("Irreducible polynomial degree isn't correct");
}
if (Enumerable.Range(0, analysisResult.First().Key).Any(x => irreduciblePolynomial.Evaluate(x) == 0))
{
throw new ArgumentException(string.Format("Polynomial {0} isn't irreducible", irreduciblePolynomial));
}
Initialize(order, analysisResult.First().Key);
IrreduciblePolynomial = irreduciblePolynomial;
InitializeAdditionalStructures();
}
/// <summary>
/// Method for multiplying current polynomial by polynomial <paramref name="b"/>
/// </summary>
/// <param name="b">Factor</param>
public Polynomial Multiply(Polynomial b)
{
if (Field.Equals(b.Field) == false)
{
throw new ArgumentException(NameOfExtension.nameof(() => b));
}
if (Degree == 0 && _coefficients[0] == 0 || b.Degree == 0 && b[0] == 0)
{
_coefficients = new List <int> {
0
};
return(this);
}
var newCoefficients = new List <int>(Enumerable.Repeat(0, Degree + b.Degree + 1));
for (var i = 0; i <= Degree; i++)
{
for (var j = 0; j <= b.Degree; j++)
{
newCoefficients[i + j] = Field.Add(newCoefficients[i + j], Field.Multiply(_coefficients[i], b[j]));
}
}
_coefficients = newCoefficients;
return(Truncate());
}
/// <summary>
/// Method for shifting current polynomial by <paramref name="degreeDelta"/> positions to the right
/// </summary>
/// <param name="degreeDelta">Positions count for shifting</param>
public Polynomial RightShift(int degreeDelta)
{
if (degreeDelta < 0)
{
throw new ArgumentException(NameOfExtension.nameof(() => degreeDelta));
}
if (degreeDelta == 0 || Degree == 0 && _coefficients[0] == 0)
{
return(this);
}
var oldDegree = Degree;
Enlarge(oldDegree + degreeDelta);
for (var i = oldDegree; i >= 0; i--)
{
_coefficients[i + degreeDelta] = _coefficients[i];
if (i < degreeDelta)
{
_coefficients[i] = 0;
}
}
return(this);
}
/// <summary>
/// Constructor for initializing internal structures of the decoder
/// </summary>
/// <param name="rsStandardDecoder">Implementation of the Reed-Solomon code standard decoder</param>
/// <param name="linearSystemSolver">Implementation of the linear equations system solver</param>
public RsBasedDecoder(IStandardDecoder rsStandardDecoder, ILinearSystemSolver linearSystemSolver) : base(linearSystemSolver)
{
if (rsStandardDecoder == null)
{
throw new ArgumentNullException(NameOfExtension.nameof(() => rsStandardDecoder));
}
_rsStandardDecoder = rsStandardDecoder;
}
/// <summary>
/// Constructor for creation instance of decoder
/// </summary>
/// <param name="linearSystemSolver">Implementation of linear equations system solver contract</param>
public BerlekampWelchDecoder(ILinearSystemSolver linearSystemSolver)
{
if (linearSystemSolver == null)
{
throw new ArgumentNullException(NameOfExtension.nameof(() => linearSystemSolver));
}
_linearSystemSolver = linearSystemSolver;
}
/// <summary>
/// Constructor for initialization of internal objects
/// </summary>
/// <param name="linearSystemSolver">Implementation of the linear equations system solver</param>
protected FixedDistanceCodesDecoderBase(ILinearSystemSolver linearSystemSolver)
{
if (linearSystemSolver == null)
{
throw new ArgumentNullException(NameOfExtension.nameof(() => linearSystemSolver));
}
_linearSystemSolver = linearSystemSolver;
}
/// <summary>
/// Constructor for creation instance of the implementation of the wavelet code list decoding contract based on Guruswami–Sudan algorithm
/// </summary>
/// <param name="rsListDecoder">Implementation of the Reed-Solomon code list decoding contract</param>
/// <param name="linearSystemSolver">Implementation of the linear equations system solver</param>
public GsBasedDecoder(RsCodesTools.ListDecoder.IListDecoder rsListDecoder, ILinearSystemSolver linearSystemSolver) : base(linearSystemSolver)
{
if (rsListDecoder == null)
{
throw new ArgumentNullException(NameOfExtension.nameof(() => rsListDecoder));
}
_rsListDecoder = rsListDecoder;
}
/// <summary>
/// Constructor for creating bivariate monomials comparer with degree weights <paramref name="degreeWeight"/>
/// </summary>
/// <param name="degreeWeight">Weights of monomial variable's powers</param>
public BiVariableMonomialsComparer(Tuple <int, int> degreeWeight)
{
if (degreeWeight == null)
{
throw new ArgumentNullException(NameOfExtension.nameof(() => degreeWeight));
}
_degreeWeight = degreeWeight;
}
/// <summary>
/// Constructor for builder creation
/// </summary>
/// <param name="gcdFinder">Implementation of GCD algorithm contract</param>
public GcdBasedBuilder(IPolynomialsGcdFinder gcdFinder)
{
if (gcdFinder == null)
{
throw new ArgumentNullException(NameOfExtension.nameof(() => gcdFinder));
}
_gcdFinder = gcdFinder;
}
/// <summary>
/// Method for validation arguments of the algorithm
/// </summary>
/// <param name="a">First argument</param>
/// <param name="b">Second argument</param>
private static void ValidateArguments(Polynomial a, Polynomial b)
{
if (a == null)
{
throw new ArgumentNullException(NameOfExtension.nameof(() => a));
}
if (b == null)
{
throw new ArgumentNullException(NameOfExtension.nameof(() => b));
}
}
/// <summary>
/// Constructor for creating copy of the bivariate polynomial <paramref name="polynomial"/>
/// </summary>
/// <param name="polynomial">Copied bivariate polynomial</param>
public BiVariablePolynomial(BiVariablePolynomial polynomial)
{
if (polynomial == null)
{
throw new ArgumentNullException(NameOfExtension.nameof(() => polynomial));
}
Field = polynomial.Field;
_coefficients = polynomial._coefficients.ToDictionary(x => x.Key, x => new FieldElement(x.Value));
}
/// <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(NameOfExtension.nameof(() => combinationsCountCalculator));
}
_combinationsCountCalculator = combinationsCountCalculator;
_zeroMonomial = new Tuple <int, int>(0, 0);
}
/// <summary>
/// Method for finding irreducible polynomial degree <paramref name="degree"/> with coefficients from field with order <paramref name="fieldOrder"/>
/// </summary>
/// <param name="fieldOrder">Field order from which irreducible polynomials coefficients come</param>
/// <param name="degree">Irreducible polynomial degree</param>
/// <returns>Irreducible polynomial with specified properties</returns>
public GFPolynoms.Polynomial Find(int fieldOrder, int degree)
{
if (degree < 2)
{
throw new ArgumentException(NameOfExtension.nameof(() => degree));
}
var field = new PrimeOrderField(fieldOrder);
var result = GenerateTemplateGFPolynomial(field, degree);
return(result);
}
/// <summary>
/// Method for dividing field element <paramref name="a"/> by field element <paramref name="b"/>
/// </summary>
/// <param name="a">Dividend</param>
/// <param name="b">Divider</param>
/// <returns>Quotient</returns>
public int Divide(int a, int b)
{
ValidateArguments(a, b);
if (b == 0)
{
throw new ArgumentException(NameOfExtension.nameof(() => b));
}
return(a == 0
? 0
: ElementsByPowers[(PowersByElements[a] - PowersByElements[b] + Order - 1) % (Order - 1)]);
}
/// <summary>
/// Constructor for creation zero polynomial over field <paramref name="field"/>
/// </summary>
/// <param name="field">Field from which the coefficients of the polynomial</param>
public Polynomial(GaloisField field)
{
if (field == null)
{
throw new ArgumentNullException(NameOfExtension.nameof(() => field));
}
Field = field;
_coefficients = new List <int> {
0
};
}
/// <summary>
/// Method for subtracting polynomial <paramref name="b"/> from current
/// </summary>
/// <param name="b">Subtrahend</param>
public Polynomial Subtract(Polynomial b)
{
if (Field.Equals(b.Field) == false)
{
throw new ArgumentException(NameOfExtension.nameof(() => b));
}
Enlarge(b.Degree);
for (var i = 0; i <= b.Degree; i++)
{
_coefficients[i] = Field.Subtract(_coefficients[i], b[i]);
}
return(Truncate());
}
/// <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(NameOfExtension.nameof(() => combinationsCountCalculator));
}
if (linearSystemSolver == null)
{
throw new ArgumentNullException(NameOfExtension.nameof(() => linearSystemSolver));
}
_combinationsCountCalculator = combinationsCountCalculator;
_linearSystemSolver = linearSystemSolver;
}
/// <summary>
/// Constructor for creation implementation of contract of generating polynomials builder
/// </summary>
/// <param name="complementaryFiltersBuilder">Implementation of contract of complementary filters builder</param>
/// <param name="linearSystemSolver">Implementation of contract of linear equations system solver</param>
public LiftingSchemeBasedBuilder(IComplementaryFiltersBuilder complementaryFiltersBuilder, ILinearSystemSolver linearSystemSolver)
{
if (complementaryFiltersBuilder == null)
{
throw new ArgumentNullException(NameOfExtension.nameof(() => complementaryFiltersBuilder));
}
if (linearSystemSolver == null)
{
throw new ArgumentNullException(NameOfExtension.nameof(() => linearSystemSolver));
}
_complementaryFiltersBuilder = complementaryFiltersBuilder;
_linearSystemSolver = linearSystemSolver;
}
public DevisionResult(Polynomial quotient, Polynomial remainder)
{
if (quotient == null)
{
throw new ArgumentNullException(NameOfExtension.nameof(() => quotient));
}
if (remainder == null)
{
throw new ArgumentNullException(NameOfExtension.nameof(() => remainder));
}
Quotient = quotient;
Remainder = remainder;
}
/// <summary>
/// Constructor for creation
/// </summary>
/// <param name="interpolationPolynomialBuilder"></param>
/// <param name="interpolationPolynomialFactorizator"></param>
public GsDecoder(IInterpolationPolynomialBuilder interpolationPolynomialBuilder, IInterpolationPolynomialFactorizator interpolationPolynomialFactorizator)
{
if (interpolationPolynomialBuilder == null)
{
throw new ArgumentNullException(NameOfExtension.nameof(() => interpolationPolynomialBuilder));
}
if (interpolationPolynomialFactorizator == null)
{
throw new ArgumentNullException(NameOfExtension.nameof(() => interpolationPolynomialFactorizator));
}
_interpolationPolynomialBuilder = interpolationPolynomialBuilder;
_interpolationPolynomialFactorizator = interpolationPolynomialFactorizator;
}
/// <summary>
/// Constructor for creating oject with greates common divisor calculation results
/// </summary>
/// <param name="gcd">Greates common divisor</param>
/// <param name="quotients">Calculated quotients</param>
public GcdWithQuotients(Polynomial gcd, Polynomial[] quotients)
{
if (gcd == null)
{
throw new ArgumentNullException(NameOfExtension.nameof(() => gcd));
}
if (quotients == null)
{
throw new ArgumentNullException(NameOfExtension.nameof(() => quotients));
}
Gcd = gcd;
Quotients = quotients;
}
/// <summary>
/// Method for calculating polynomial value for variable value <paramref name="variableValue"/>
/// </summary>
/// <param name="variableValue">Variable value</param>
/// <returns>Polynomial value</returns>
public int Evaluate(int variableValue)
{
if (Field.IsFieldElement(variableValue) == false)
{
throw new ArgumentException(NameOfExtension.nameof(() => variableValue));
}
var result = 0;
for (var i = _coefficients.Count - 1; i >= 0; i--)
{
result = Field.Add(_coefficients[i], Field.Multiply(result, variableValue));
}
return(result);
}
/// <summary>
/// Creates polynomial p(x) = p_e(x^2)+x*p_o(x^2)
/// </summary>
/// <param name="evenComponent">p_e(x)</param>
/// <param name="oddComponent">p_o(x)</param>
/// <returns>Reconstructed polynomial</returns>
public static Polynomial CreateFormPolyphaseComponents(Polynomial evenComponent, Polynomial oddComponent)
{
if (evenComponent == null)
{
throw new ArgumentNullException(NameOfExtension.nameof(() => evenComponent));
}
if (oddComponent == null)
{
throw new ArgumentNullException(NameOfExtension.nameof(() => oddComponent));
}
if (evenComponent.Field.Equals(oddComponent.Field) == false)
{
throw new ArgumentException("Fields mismatch");
}
return(evenComponent.RaiseVariableDegree(2) + (oddComponent.RaiseVariableDegree(2) >> 1));
}