/// <summary>
/// Method for recursive search of bivariate polynomial's <paramref name="polynomial"/> factors with max degree <paramref name="maxFactorDegree"/>
/// </summary>
/// <param name="polynomial">Bivariate polynomial for factorization</param>
/// <param name="maxFactorDegree">Maximum degree of factor</param>
/// <param name="xSubstitution">Substitution for x variable</param>
/// <param name="ySubstitution">Substitution for y variable</param>
/// <param name="factors">Array of finded factors</param>
/// <param name="currentFactorCoefficients">Stack with current factor's coefficients</param>
private void Factorize(BiVariablePolynomial polynomial, int maxFactorDegree,
BiVariablePolynomial xSubstitution, BiVariablePolynomial ySubstitution,
ISet <Polynomial> factors, Stack <int> currentFactorCoefficients)
{
if (polynomial.EvaluateY(polynomial.Field.Zero()).IsZero)
{
factors.Add(new Polynomial(polynomial.Field, currentFactorCoefficients.Reverse().ToArray()));
}
if (currentFactorCoefficients.Count > maxFactorDegree)
{
return;
}
var roots = FindPolynomialRoots(polynomial.EvaluateX(polynomial.Field.Zero()));
foreach (var root in roots)
{
currentFactorCoefficients.Push(root.Representation);
ySubstitution[_zeroMonomial] = root;
Factorize(polynomial
.PerformVariablesSubstitution(xSubstitution, ySubstitution)
.DivideByMaxPossibleXDegree(), maxFactorDegree,
xSubstitution, ySubstitution,
factors, currentFactorCoefficients);
currentFactorCoefficients.Pop();
}
}
/// <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>
/// 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));
}
public void ShouldPerformFactorization(BiVariablePolynomial polynomial, int maxFactorDegree, Polynomial[] expectedFactors)
{
// When
var actualFactors = _factorizator.Factorize(polynomial, maxFactorDegree);
// Then
Assert.Equal(expectedFactors.Length, actualFactors.Length);
Assert.True(actualFactors.All(expectedFactors.Contains));
}
public void ShouldSetCoefficients(int coefficientValueRepresentation)
{
// Given
var polynomial = new BiVariablePolynomial(Gf5);
var monomial = new Tuple <int, int>(1, 1);
var coefficientValue = new FieldElement(Gf5, coefficientValueRepresentation);
// When
polynomial[monomial] = coefficientValue;
// Then
Assert.Equal(coefficientValue, polynomial[monomial]);
}
/// <summary>
/// Method for creation interpolation polynomial from linear system solution
/// </summary>
/// <param name="field">Finite field from which system coefficients were taken</param>
/// <param name="systemSolution">Solution of the linear equations system</param>
/// <param name="monomialByVariableIndex">Mapping from numbers to bivariate monomials</param>
/// <returns>Interpolation polynomial</returns>
private static BiVariablePolynomial ConstructInterpolationPolynomial(
GaloisField field,
SystemSolution systemSolution,
IReadOnlyDictionary <int, Tuple <int, int> > monomialByVariableIndex)
{
var interpolationPolynomial = new BiVariablePolynomial(field);
for (var i = 0; i < systemSolution.VariablesValues.Length; i++)
{
interpolationPolynomial[monomialByVariableIndex[i]] = systemSolution.VariablesValues[i];
}
if (interpolationPolynomial.IsZero)
{
throw new NonTrivialPolynomialNotFoundException();
}
return(interpolationPolynomial);
}
/// <summary>
/// Exponentiation of bivariate polynomial <paramref name="polynomial"/> to the degree <paramref name="degree"/>
/// </summary>
/// <param name="powersCache">Cache for storing Exponentiation results </param>
/// <param name="polynomial">Bivariate polynomial for exponentiation</param>
/// <param name="degree">Power for exponentiation</param>
private static BiVariablePolynomial Pow(IDictionary <int, BiVariablePolynomial> powersCache, BiVariablePolynomial polynomial, int degree)
{
BiVariablePolynomial result;
if (powersCache.TryGetValue(degree, out result) == false)
{
if (degree == 0)
{
result = new BiVariablePolynomial(polynomial.Field);
var pos = new Tuple <int, int>(0, 0);
result[pos] = polynomial.Field.One();
}
else
{
result = Pow(powersCache, polynomial, degree - 1) * polynomial;
}
powersCache[degree] = result;
}
return(result);
}
/// <summary>
/// Method for finding bivariate polynomial's <paramref name="interpolationPolynomial"/> factors with max degree <paramref name="maxFactorDegree"/>
/// </summary>
/// <param name="interpolationPolynomial">Bivariate polynomial for factorization</param>
/// <param name="maxFactorDegree">Maximum degree of factor</param>
/// <returns>Array of finded factors</returns>
public Polynomial[] Factorize(BiVariablePolynomial interpolationPolynomial, int maxFactorDegree)
{
var xSubstitution = new BiVariablePolynomial(interpolationPolynomial.Field)
{
[new Tuple <int, int>(1, 0)] = interpolationPolynomial.Field.One()
};
var ySubstitution = new BiVariablePolynomial(interpolationPolynomial.Field)
{
[new Tuple <int, int>(0, 0)] = interpolationPolynomial.Field.One(),
[new Tuple <int, int>(1, 1)] = interpolationPolynomial.Field.One()
};
var factors = new HashSet <Polynomial>();
var currentFactorCoefficients = new Stack <int>();
Factorize(interpolationPolynomial, maxFactorDegree,
xSubstitution, ySubstitution,
factors, currentFactorCoefficients);
return(factors.ToArray());
}
/// <summary>
/// Method for dividing bivariate polynomial <paramref name="polynomial"/> by variable x in maximum possible degree
/// </summary>
/// <param name="polynomial">Modified polynomial</param>
/// <returns>Dividing result</returns>
public static BiVariablePolynomial DivideByMaxPossibleXDegree(this BiVariablePolynomial polynomial)
{
if (polynomial == null)
{
throw new ArgumentNullException(NameOfExtension.nameof(() => polynomial));
}
var result = new BiVariablePolynomial(polynomial.Field);
if (polynomial.IsZero)
{
return(result);
}
var minXDegree = polynomial.Min(x => x.Key.Item1);
foreach (var coefficient in polynomial)
{
result[new Tuple <int, int>(coefficient.Key.Item1 - minXDegree, coefficient.Key.Item2)] = new FieldElement(coefficient.Value);
}
return(result);
}
/// <summary>
/// Method for calculating results of replacement bivariate polynomial <paramref name="polynomial"/> variable x by <paramref name="xSubstitution"/> and y by <paramref name="ySubstitution"/>
/// </summary>
/// <param name="polynomial">Modified polynomial</param>
/// <param name="xSubstitution">Substitution for x variable</param>
/// <param name="ySubstitution">Substitution for x variable</param>
/// <returns>Replacement results</returns>
public static BiVariablePolynomial PerformVariablesSubstitution(this BiVariablePolynomial polynomial,
BiVariablePolynomial xSubstitution, BiVariablePolynomial ySubstitution)
{
if (polynomial == null)
{
throw new ArgumentNullException(NameOfExtension.nameof(() => polynomial));
}
if (xSubstitution == null)
{
throw new ArgumentNullException(NameOfExtension.nameof(() => xSubstitution));
}
if (ySubstitution == null)
{
throw new ArgumentNullException(NameOfExtension.nameof(() => ySubstitution));
}
if (polynomial.Field.Equals(xSubstitution.Field) == false)
{
throw new ArithmeticException(NameOfExtension.nameof(() => xSubstitution));
}
if (polynomial.Field.Equals(ySubstitution.Field) == false)
{
throw new ArithmeticException(NameOfExtension.nameof(() => ySubstitution));
}
var result = new BiVariablePolynomial(polynomial.Field,
polynomial.CoefficientsCount * (Math.Max(xSubstitution.CoefficientsCount, ySubstitution.CoefficientsCount) + 1));
var xCache = new Dictionary <int, BiVariablePolynomial>(polynomial.CoefficientsCount);
var yCache = new Dictionary <int, BiVariablePolynomial>(polynomial.CoefficientsCount);
foreach (var coefficient in polynomial)
{
result.Add(coefficient.Value, Pow(xCache, xSubstitution, coefficient.Key.Item1)
* Pow(yCache, ySubstitution, coefficient.Key.Item2));
}
return(result);
}
/// <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(nameof(degreeWeight));
}
if (roots == null)
{
throw new ArgumentNullException(nameof(roots));
}
if (roots.Length == 0)
{
throw new ArgumentException($"{nameof(roots)} is empty");
}
var field = roots[0].Item1.Field;
var maxXDegree = maxWeightedDegree / degreeWeight.Item1;
var maxYDegree = maxWeightedDegree / degreeWeight.Item2;
var combinationsCache = new FieldElement[Math.Max(maxXDegree, maxYDegree) + 1][].MakeSquare();
var transformationMultiplier = new BiVariablePolynomial(field)
{
[new Tuple <int, int>(1, 0)] = field.One()
};
var monomialsComparer = new BiVariableMonomialsComparer(degreeWeight);
var buildingPolynomials = new BiVariablePolynomial[maxYDegree + 1];
var leadMonomials = new Tuple <int, int> [maxYDegree + 1];
for (var i = 0; i < buildingPolynomials.Length; i++)
{
var leadMonomial = new Tuple <int, int>(0, i);
buildingPolynomials[i] = new BiVariablePolynomial(field, (maxXDegree + 1) * (maxYDegree + 1))
{
[leadMonomial] = field.One()
};
leadMonomials[i] = leadMonomial;
}
foreach (var root in roots)
{
for (var r = 0; r < rootsMultiplicity; r++)
{
for (var s = 0; r + s < rootsMultiplicity; s++)
{
var anyCompatiblePolynomialFound = false;
var nonZeroDerivatives = new List <Tuple <int, FieldElement> >();
for (var i = 0; i < buildingPolynomials.Length; i++)
{
if (CalculateMonomialWeight(leadMonomials[i], degreeWeight) > maxWeightedDegree)
{
continue;
}
anyCompatiblePolynomialFound = true;
var hasseDerivative = buildingPolynomials[i].CalculateHasseDerivative(r, s, root.Item1, root.Item2,
_combinationsCountCalculator, combinationsCache);
if (hasseDerivative.Representation != 0)
{
nonZeroDerivatives.Add(new Tuple <int, FieldElement>(i, hasseDerivative));
}
}
if (anyCompatiblePolynomialFound == false)
{
throw new NonTrivialPolynomialNotFoundException();
}
if (nonZeroDerivatives.Count == 0)
{
continue;
}
var minimumIndex = FindMinimumIndexByLeadMonomial(nonZeroDerivatives,
i => leadMonomials[nonZeroDerivatives[i].Item1], monomialsComparer);
var minimumPolynomialIndex = nonZeroDerivatives[minimumIndex].Item1;
var minimumPolynomial = buildingPolynomials[minimumPolynomialIndex];
var minimumDerivative = nonZeroDerivatives[minimumIndex].Item2;
for (var i = 0; i < nonZeroDerivatives.Count; i++)
{
if (i != minimumIndex)
{
buildingPolynomials[nonZeroDerivatives[i].Item1]
.Subtract(nonZeroDerivatives[i].Item2.Divide(minimumDerivative), minimumPolynomial);
}
}
transformationMultiplier[_zeroMonomial] = FieldElement.InverseForAddition(root.Item1);
minimumPolynomial
.Multiply(minimumDerivative * transformationMultiplier);
leadMonomials[minimumPolynomialIndex] = new Tuple <int, int>(leadMonomials[minimumPolynomialIndex].Item1 + 1,
leadMonomials[minimumPolynomialIndex].Item2);
}
}
}
var resultPolynomialIndex = FindMinimumIndexByLeadMonomial(buildingPolynomials, i => leadMonomials[i], monomialsComparer);
if (CalculateMonomialWeight(leadMonomials[resultPolynomialIndex], degreeWeight) > maxWeightedDegree)
{
throw new NonTrivialPolynomialNotFoundException();
}
return(buildingPolynomials[resultPolynomialIndex]);
}
public void ShouldCalculateHasseDerivative(BiVariablePolynomial polynomial, int r, int s, FieldElement xValue, FieldElement yValue,
FieldElement expectedValue)
{
Assert.Equal(expectedValue, polynomial.CalculateHasseDerivative(r, s, xValue, yValue, _combinationsCountCalculator));
}
public void ShouldEvaluateY(BiVariablePolynomial polynomial, FieldElement yValue, Polynomial expectedResult)
{
Assert.Equal(expectedResult, polynomial.EvaluateY(yValue));
}
public void ShouldDivideByMaxPossibleXDegree(BiVariablePolynomial polynomial, BiVariablePolynomial expectedResult)
{
Assert.Equal(expectedResult, polynomial.DivideByMaxPossibleXDegree(), EqualityComparer <BiVariablePolynomial> .Default);
}
public void ShouldPerformVariablesSubstitution(BiVariablePolynomial polynomial,
BiVariablePolynomial xSubstitution, BiVariablePolynomial ySubstitution,
BiVariablePolynomial expectedResult)
{
Assert.Equal(expectedResult, polynomial.PerformVariablesSubstitution(xSubstitution, ySubstitution), EqualityComparer <BiVariablePolynomial> .Default);
}
public void ShouldMultiplyByFieldElement(BiVariablePolynomial a, FieldElement b, BiVariablePolynomial expectedResult)
{
Assert.Equal(expectedResult, a * b, EqualityComparer <BiVariablePolynomial> .Default);
}
public void ShouldMultiplyTwoPolynomials(BiVariablePolynomial a, BiVariablePolynomial b, BiVariablePolynomial expectedResult)
{
Assert.Equal(expectedResult, a * b, EqualityComparer <BiVariablePolynomial> .Default);
}
static BiVariablePolynomialTests()
{
Gf5 = new PrimeOrderField(5);
var polynomialForEvoluation = new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(1, 1)] = new FieldElement(Gf5, 2),
[new Tuple <int, int>(0, 1)] = new FieldElement(Gf5, 1),
[new Tuple <int, int>(2, 0)] = new FieldElement(Gf5, 1),
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 1),
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 4)
};
EvaluateTestsData = new[]
{
new object[] { polynomialForEvoluation, new FieldElement(Gf5, 1), new FieldElement(Gf5, 3), Gf5.Zero() },
new object[] { polynomialForEvoluation, new FieldElement(Gf5, 2), new FieldElement(Gf5, 4), Gf5.Zero() },
new object[] { polynomialForEvoluation, new FieldElement(Gf5, 3), new FieldElement(Gf5, 2), Gf5.Zero() },
new object[] { polynomialForEvoluation, new FieldElement(Gf5, 2), new FieldElement(Gf5, 3), Gf5.Zero() },
};
AddTestsData = new[]
{
new object[]
{
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 2),
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 3)
},
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 3),
[new Tuple <int, int>(0, 1)] = new FieldElement(Gf5, 4)
},
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 3),
[new Tuple <int, int>(0, 1)] = new FieldElement(Gf5, 4)
}
},
new object[]
{
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 2),
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 3),
[new Tuple <int, int>(0, 1)] = new FieldElement(Gf5, 4)
},
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 1)] = new FieldElement(Gf5, 4),
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 4),
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 4)
},
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 2),
[new Tuple <int, int>(0, 1)] = new FieldElement(Gf5, 3),
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 1)
}
}
};
SubtractTestsData = new[]
{
new object[]
{
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 2),
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 3)
},
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 3),
[new Tuple <int, int>(0, 1)] = new FieldElement(Gf5, 4)
},
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 4),
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 3),
[new Tuple <int, int>(0, 1)] = new FieldElement(Gf5, 1)
}
},
new object[]
{
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 2),
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 3),
[new Tuple <int, int>(0, 1)] = new FieldElement(Gf5, 4)
},
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 4),
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 4),
[new Tuple <int, int>(0, 1)] = new FieldElement(Gf5, 4)
},
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 3),
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 4)
}
}
};
MultiplyPolynomialsTestsData = new[]
{
new object[]
{
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 2),
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 3)
},
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 3),
[new Tuple <int, int>(0, 1)] = new FieldElement(Gf5, 4)
},
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 1),
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 4),
[new Tuple <int, int>(0, 1)] = new FieldElement(Gf5, 3),
[new Tuple <int, int>(1, 1)] = new FieldElement(Gf5, 2)
}
},
new object[]
{
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 2),
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 3),
[new Tuple <int, int>(0, 1)] = new FieldElement(Gf5, 4)
},
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 4),
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 1),
[new Tuple <int, int>(0, 1)] = new FieldElement(Gf5, 2)
},
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 3),
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 4),
[new Tuple <int, int>(2, 0)] = new FieldElement(Gf5, 3),
[new Tuple <int, int>(0, 2)] = new FieldElement(Gf5, 3)
}
},
new object[]
{
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 2),
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 3),
[new Tuple <int, int>(0, 1)] = new FieldElement(Gf5, 4)
},
new BiVariablePolynomial(Gf5),
new BiVariablePolynomial(Gf5)
}
};
var polynomialForMultiplication = new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 3),
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 2),
[new Tuple <int, int>(0, 1)] = new FieldElement(Gf5, 4),
[new Tuple <int, int>(1, 1)] = new FieldElement(Gf5, 1)
};
MultiplyByFieldElementTestsData = new[]
{
new object[] { polynomialForMultiplication, Gf5.Zero(), new BiVariablePolynomial(Gf5) },
new object[]
{
polynomialForMultiplication, new FieldElement(Gf5, 2),
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 1),
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 4),
[new Tuple <int, int>(0, 1)] = new FieldElement(Gf5, 3),
[new Tuple <int, int>(1, 1)] = new FieldElement(Gf5, 2)
}
}
};
SubstitutionTestsData = new[]
{
new object[]
{
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 1),
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 3),
[new Tuple <int, int>(0, 1)] = new FieldElement(Gf5, 2)
},
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 1)
},
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 3),
[new Tuple <int, int>(1, 1)] = new FieldElement(Gf5, 1)
},
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 2),
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 3),
[new Tuple <int, int>(1, 1)] = new FieldElement(Gf5, 2)
}
},
new object[]
{
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 1),
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 2),
[new Tuple <int, int>(2, 0)] = new FieldElement(Gf5, 1),
[new Tuple <int, int>(0, 1)] = new FieldElement(Gf5, 3),
[new Tuple <int, int>(1, 1)] = new FieldElement(Gf5, 1)
},
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 1),
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 1)
},
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 2),
[new Tuple <int, int>(1, 1)] = new FieldElement(Gf5, 1)
},
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 2),
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 1),
[new Tuple <int, int>(2, 0)] = new FieldElement(Gf5, 1),
[new Tuple <int, int>(1, 1)] = new FieldElement(Gf5, 4),
[new Tuple <int, int>(2, 1)] = new FieldElement(Gf5, 1)
}
},
new object[]
{
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 1),
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 3),
[new Tuple <int, int>(0, 1)] = new FieldElement(Gf5, 2)
},
new BiVariablePolynomial(Gf5),
new BiVariablePolynomial(Gf5),
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 1)
}
}
};
DivideByXDegreeTestsData = new[]
{
new object[]
{
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 2),
[new Tuple <int, int>(2, 0)] = new FieldElement(Gf5, 1),
[new Tuple <int, int>(1, 1)] = new FieldElement(Gf5, 3)
},
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 2),
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 1),
[new Tuple <int, int>(0, 1)] = new FieldElement(Gf5, 3)
}
},
new object[]
{
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 2),
[new Tuple <int, int>(2, 0)] = new FieldElement(Gf5, 1),
[new Tuple <int, int>(0, 1)] = new FieldElement(Gf5, 3)
},
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 2),
[new Tuple <int, int>(2, 0)] = new FieldElement(Gf5, 1),
[new Tuple <int, int>(0, 1)] = new FieldElement(Gf5, 3)
}
},
new object[]
{
new BiVariablePolynomial(Gf5),
new BiVariablePolynomial(Gf5)
}
};
EvaluateXTestsData = new[]
{
new object[]
{
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 3),
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 2),
[new Tuple <int, int>(0, 1)] = new FieldElement(Gf5, 1)
},
new FieldElement(Gf5, 1),
new Polynomial(Gf5, 0, 1)
},
new object[]
{
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 3),
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 2),
[new Tuple <int, int>(1, 1)] = new FieldElement(Gf5, 1)
},
Gf5.Zero(),
new Polynomial(Gf5, 3)
},
new object[]
{
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 2),
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 3),
[new Tuple <int, int>(2, 0)] = new FieldElement(Gf5, 2),
[new Tuple <int, int>(0, 1)] = new FieldElement(Gf5, 1),
[new Tuple <int, int>(1, 1)] = new FieldElement(Gf5, 1),
[new Tuple <int, int>(0, 2)] = new FieldElement(Gf5, 1)
},
new FieldElement(Gf5, 3),
new Polynomial(Gf5, 4, 4, 1)
}
};
EvaluateYTestsData = new[]
{
new object[]
{
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 3),
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 1),
[new Tuple <int, int>(0, 1)] = new FieldElement(Gf5, 2)
},
new FieldElement(Gf5, 1),
new Polynomial(Gf5, 0, 1)
},
new object[]
{
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 3),
[new Tuple <int, int>(0, 1)] = new FieldElement(Gf5, 2),
[new Tuple <int, int>(1, 1)] = new FieldElement(Gf5, 1)
},
Gf5.Zero(),
new Polynomial(Gf5, 3)
},
new object[]
{
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 2),
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 3),
[new Tuple <int, int>(2, 0)] = new FieldElement(Gf5, 2),
[new Tuple <int, int>(0, 1)] = new FieldElement(Gf5, 1),
[new Tuple <int, int>(1, 1)] = new FieldElement(Gf5, 1),
[new Tuple <int, int>(0, 2)] = new FieldElement(Gf5, 1)
},
new FieldElement(Gf5, 2),
new Polynomial(Gf5, 3, 0, 2)
}
};
CalculateHasseDerivativeTestsData = new[]
{
new object[]
{
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 2),
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 2),
[new Tuple <int, int>(0, 1)] = new FieldElement(Gf5, 2),
[new Tuple <int, int>(2, 0)] = new FieldElement(Gf5, 1),
[new Tuple <int, int>(0, 2)] = new FieldElement(Gf5, 1)
},
1, 1, Gf5.One(), Gf5.One(),
Gf5.Zero()
},
new object[]
{
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 2),
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 2),
[new Tuple <int, int>(0, 1)] = new FieldElement(Gf5, 2),
[new Tuple <int, int>(2, 2)] = new FieldElement(Gf5, 1)
},
1, 1, Gf5.One(), Gf5.One(),
new FieldElement(Gf5, 4)
},
new object[]
{
new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(0, 0)] = new FieldElement(Gf5, 2),
[new Tuple <int, int>(1, 0)] = new FieldElement(Gf5, 2),
[new Tuple <int, int>(0, 1)] = new FieldElement(Gf5, 2),
[new Tuple <int, int>(2, 2)] = new FieldElement(Gf5, 1)
},
2, 1, Gf5.One(), Gf5.One(),
new FieldElement(Gf5, 2)
}
};
}
static BiVariablePolynomialTests()
{
Gf5 = new PrimeOrderField(5);
var polynomialForEvoluation = new BiVariablePolynomial(Gf5)
{
[new Tuple <int, int>(1, 1)] = Gf5.CreateElement(2),
[new Tuple <int, int>(0, 1)] = Gf5.One(),
[new Tuple <int, int>(2, 0)] = Gf5.One(),
[new Tuple <int, int>(1, 0)] = Gf5.One(),
[new Tuple <int, int>(0, 0)] = Gf5.CreateElement(4)
};
EvaluateTestsData
= new TheoryData <EvaluationTestCase>
{
new EvaluationTestCase
{
Polynomial = polynomialForEvoluation,
XValue = Gf5.One(),
YValue = Gf5.CreateElement(3),
Expected = Gf5.Zero()
},
new EvaluationTestCase
{
Polynomial = polynomialForEvoluation,
XValue = Gf5.CreateElement(2),
YValue = new FieldElement(Gf5, 4),
Expected = Gf5.Zero()
},
new EvaluationTestCase
{
Polynomial = polynomialForEvoluation,
XValue = Gf5.CreateElement(3),
YValue = Gf5.CreateElement(2),
Expected = Gf5.Zero()
},
new EvaluationTestCase
{
Polynomial = polynomialForEvoluation,
XValue = Gf5.CreateElement(2),
YValue = Gf5.CreateElement(3),
Expected = Gf5.Zero()
},
};
AddTestsData
= new TheoryData <BinaryOperationTestCase>
{
new BinaryOperationTestCase
{
FirstOperand = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(2),
[Tuple.Create(1, 0)] = Gf5.CreateElement(3)
},
SecondOperand = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(3),
[Tuple.Create(0, 1)] = Gf5.CreateElement(4)
},
Expected = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(1, 0)] = Gf5.CreateElement(3),
[Tuple.Create(0, 1)] = Gf5.CreateElement(4)
}
},
new BinaryOperationTestCase
{
FirstOperand = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(2),
[Tuple.Create(1, 0)] = Gf5.CreateElement(3),
[Tuple.Create(0, 1)] = Gf5.CreateElement(4)
},
SecondOperand = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 1)] = Gf5.CreateElement(4),
[Tuple.Create(0, 0)] = Gf5.CreateElement(4),
[Tuple.Create(1, 0)] = Gf5.CreateElement(4)
},
Expected = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(1, 0)] = Gf5.CreateElement(2),
[Tuple.Create(0, 1)] = Gf5.CreateElement(3),
[Tuple.Create(0, 0)] = Gf5.One()
}
}
};
SubtractTestsData
= new TheoryData <BinaryOperationTestCase>
{
new BinaryOperationTestCase
{
FirstOperand = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(2),
[Tuple.Create(1, 0)] = Gf5.CreateElement(3)
},
SecondOperand = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(3),
[Tuple.Create(0, 1)] = Gf5.CreateElement(4)
},
Expected = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(4),
[Tuple.Create(1, 0)] = Gf5.CreateElement(3),
[Tuple.Create(0, 1)] = Gf5.One()
}
},
new BinaryOperationTestCase
{
FirstOperand = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(2),
[Tuple.Create(1, 0)] = Gf5.CreateElement(3),
[Tuple.Create(0, 1)] = Gf5.CreateElement(4)
},
SecondOperand = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(4),
[Tuple.Create(1, 0)] = Gf5.CreateElement(4),
[Tuple.Create(0, 1)] = Gf5.CreateElement(4)
},
Expected = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(3),
[Tuple.Create(1, 0)] = Gf5.CreateElement(4)
}
}
};
MultiplyPolynomialsTestsData
= new TheoryData <BinaryOperationTestCase>
{
new BinaryOperationTestCase
{
FirstOperand = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(2),
[Tuple.Create(1, 0)] = Gf5.CreateElement(3)
},
SecondOperand = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(3),
[Tuple.Create(0, 1)] = Gf5.CreateElement(4)
},
Expected = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.One(),
[Tuple.Create(1, 0)] = Gf5.CreateElement(4),
[Tuple.Create(0, 1)] = Gf5.CreateElement(3),
[Tuple.Create(1, 1)] = Gf5.CreateElement(2)
}
},
new BinaryOperationTestCase
{
FirstOperand = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(2),
[Tuple.Create(1, 0)] = Gf5.CreateElement(3),
[Tuple.Create(0, 1)] = Gf5.CreateElement(4)
},
SecondOperand = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(4),
[Tuple.Create(1, 0)] = Gf5.One(),
[Tuple.Create(0, 1)] = Gf5.CreateElement(2)
},
Expected = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(3),
[Tuple.Create(1, 0)] = Gf5.CreateElement(4),
[Tuple.Create(2, 0)] = Gf5.CreateElement(3),
[Tuple.Create(0, 2)] = Gf5.CreateElement(3)
}
},
new BinaryOperationTestCase
{
FirstOperand = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(2),
[Tuple.Create(1, 0)] = Gf5.CreateElement(3),
[Tuple.Create(0, 1)] = Gf5.CreateElement(4)
},
SecondOperand = new BiVariablePolynomial(Gf5),
Expected = new BiVariablePolynomial(Gf5)
}
};
var polynomialForMultiplication
= new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(3),
[Tuple.Create(1, 0)] = Gf5.CreateElement(2),
[Tuple.Create(0, 1)] = Gf5.CreateElement(4),
[Tuple.Create(1, 1)] = Gf5.One()
};
MultiplyByFieldElementTestsData
= new TheoryData <MultiplicationByFieldElementTestCase>
{
new MultiplicationByFieldElementTestCase
{
Polynomial = polynomialForMultiplication,
Multiplier = Gf5.Zero(),
Expected = new BiVariablePolynomial(Gf5)
},
new MultiplicationByFieldElementTestCase
{
Polynomial = polynomialForMultiplication,
Multiplier = Gf5.CreateElement(2),
Expected = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.One(),
[Tuple.Create(1, 0)] = Gf5.CreateElement(4),
[Tuple.Create(0, 1)] = Gf5.CreateElement(3),
[Tuple.Create(1, 1)] = Gf5.CreateElement(2)
}
}
};
SubstitutionTestsData
= new TheoryData <SubstitutionTestCase>
{
new SubstitutionTestCase
{
Polynomial = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.One(),
[Tuple.Create(1, 0)] = Gf5.CreateElement(3),
[Tuple.Create(0, 1)] = Gf5.CreateElement(2)
},
XSubstitution = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(1, 0)] = Gf5.One()
},
YSubstitution = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(3),
[Tuple.Create(1, 1)] = Gf5.One()
},
Expected = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(2),
[Tuple.Create(1, 0)] = Gf5.CreateElement(3),
[Tuple.Create(1, 1)] = Gf5.CreateElement(2)
}
},
new SubstitutionTestCase
{
Polynomial = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.One(),
[Tuple.Create(1, 0)] = Gf5.CreateElement(2),
[Tuple.Create(2, 0)] = Gf5.One(),
[Tuple.Create(0, 1)] = Gf5.CreateElement(3),
[Tuple.Create(1, 1)] = Gf5.One()
},
XSubstitution = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.One(),
[Tuple.Create(1, 0)] = Gf5.One()
},
YSubstitution = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(2),
[Tuple.Create(1, 1)] = Gf5.One()
},
Expected = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(2),
[Tuple.Create(1, 0)] = Gf5.One(),
[Tuple.Create(2, 0)] = Gf5.One(),
[Tuple.Create(1, 1)] = Gf5.CreateElement(4),
[Tuple.Create(2, 1)] = Gf5.One()
}
},
new SubstitutionTestCase
{
Polynomial = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.One(),
[Tuple.Create(1, 0)] = Gf5.CreateElement(3),
[Tuple.Create(0, 1)] = Gf5.CreateElement(2)
},
XSubstitution = new BiVariablePolynomial(Gf5),
YSubstitution = new BiVariablePolynomial(Gf5),
Expected = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.One()
}
}
};
DivideByXDegreeTestsData
= new TheoryData <DivideByXDegreeTestCase>
{
new DivideByXDegreeTestCase
{
Polynomial = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(1, 0)] = Gf5.CreateElement(2),
[Tuple.Create(2, 0)] = Gf5.One(),
[Tuple.Create(1, 1)] = Gf5.CreateElement(3)
},
Expected = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(2),
[Tuple.Create(1, 0)] = Gf5.One(),
[Tuple.Create(0, 1)] = Gf5.CreateElement(3)
}
},
new DivideByXDegreeTestCase
{
Polynomial = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(1, 0)] = Gf5.CreateElement(2),
[Tuple.Create(2, 0)] = Gf5.One(),
[Tuple.Create(0, 1)] = Gf5.CreateElement(3)
},
Expected = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(1, 0)] = Gf5.CreateElement(2),
[Tuple.Create(2, 0)] = Gf5.One(),
[Tuple.Create(0, 1)] = Gf5.CreateElement(3)
}
},
new DivideByXDegreeTestCase
{
Polynomial = new BiVariablePolynomial(Gf5),
Expected = new BiVariablePolynomial(Gf5)
}
};
EvaluateXTestsData
= new TheoryData <PartialEvaluationTestCase>
{
new PartialEvaluationTestCase
{
Polynomial = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(3),
[Tuple.Create(1, 0)] = Gf5.CreateElement(2),
[Tuple.Create(0, 1)] = Gf5.One()
},
VariableValue = Gf5.One(),
Expected = new Polynomial(Gf5, 0, 1)
},
new PartialEvaluationTestCase
{
Polynomial = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(3),
[Tuple.Create(1, 0)] = Gf5.CreateElement(2),
[Tuple.Create(1, 1)] = Gf5.One()
},
VariableValue = Gf5.Zero(),
Expected = new Polynomial(Gf5, 3)
},
new PartialEvaluationTestCase
{
Polynomial = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(2),
[Tuple.Create(1, 0)] = Gf5.CreateElement(3),
[Tuple.Create(2, 0)] = Gf5.CreateElement(2),
[Tuple.Create(0, 1)] = Gf5.One(),
[Tuple.Create(1, 1)] = Gf5.One(),
[Tuple.Create(0, 2)] = Gf5.One()
},
VariableValue = Gf5.CreateElement(3),
Expected = new Polynomial(Gf5, 4, 4, 1)
}
};
EvaluateYTestsData
= new TheoryData <PartialEvaluationTestCase>
{
new PartialEvaluationTestCase
{
Polynomial = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(3),
[Tuple.Create(1, 0)] = Gf5.One(),
[Tuple.Create(0, 1)] = Gf5.CreateElement(2)
},
VariableValue = Gf5.One(),
Expected = new Polynomial(Gf5, 0, 1)
},
new PartialEvaluationTestCase
{
Polynomial = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(3),
[Tuple.Create(0, 1)] = Gf5.CreateElement(2),
[Tuple.Create(1, 1)] = Gf5.One()
},
VariableValue = Gf5.Zero(),
Expected = new Polynomial(Gf5, 3)
},
new PartialEvaluationTestCase
{
Polynomial = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(2),
[Tuple.Create(1, 0)] = Gf5.CreateElement(3),
[Tuple.Create(2, 0)] = Gf5.CreateElement(2),
[Tuple.Create(0, 1)] = Gf5.One(),
[Tuple.Create(1, 1)] = Gf5.One(),
[Tuple.Create(0, 2)] = Gf5.One()
},
VariableValue = Gf5.CreateElement(2),
Expected = new Polynomial(Gf5, 3, 0, 2)
}
};
HasseDerivativeCalculationTestsData
= new TheoryData <HasseDerivativeCalculationTestCase>
{
new HasseDerivativeCalculationTestCase
{
Polynomial = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(2),
[Tuple.Create(1, 0)] = Gf5.CreateElement(2),
[Tuple.Create(0, 1)] = Gf5.CreateElement(2),
[Tuple.Create(2, 0)] = Gf5.One(),
[Tuple.Create(0, 2)] = Gf5.One()
},
R = 1,
S = 1,
XValue = Gf5.One(),
YValue = Gf5.One(),
Expected = Gf5.Zero()
},
new HasseDerivativeCalculationTestCase
{
Polynomial = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(2),
[Tuple.Create(1, 0)] = Gf5.CreateElement(2),
[Tuple.Create(0, 1)] = Gf5.CreateElement(2),
[Tuple.Create(2, 2)] = Gf5.One()
},
R = 1,
S = 1,
XValue = Gf5.One(),
YValue = Gf5.One(),
Expected = new FieldElement(Gf5, 4)
},
new HasseDerivativeCalculationTestCase
{
Polynomial = new BiVariablePolynomial(Gf5)
{
[Tuple.Create(0, 0)] = Gf5.CreateElement(2),
[Tuple.Create(1, 0)] = Gf5.CreateElement(2),
[Tuple.Create(0, 1)] = Gf5.CreateElement(2),
[Tuple.Create(2, 2)] = Gf5.One()
},
R = 2,
S = 1,
XValue = Gf5.One(),
YValue = Gf5.One(),
Expected = Gf5.CreateElement(2)
}
};
}
