/// <summary>
/// Method for transforming linear system matrix into rectangular form and finding system solution
/// </summary>
/// <param name="field">Finite field from which system coefficients were taken</param>
/// <param name="variablesCount">Variables count</param>
/// <param name="equationsSystem">Linear system's representation</param>
/// <returns>Linear system's solution</returns>
private SystemSolution SolveEquationsSystem(
GaloisField field,
int variablesCount,
IReadOnlyList <List <Tuple <int, FieldElement> > > equationsSystem)
{
var linearSystemMatrix = new FieldElement[equationsSystem.Count, variablesCount];
var zeros = new FieldElement[equationsSystem.Count];
for (var i = 0; i < equationsSystem.Count; i++)
{
zeros[i] = field.Zero();
for (var j = 0; j < variablesCount; j++)
{
linearSystemMatrix[i, j] = field.Zero();
}
}
for (var i = 0; i < equationsSystem.Count; i++)
{
for (var j = 0; j < equationsSystem[i].Count; j++)
{
linearSystemMatrix[i, equationsSystem[i][j].Item1] = equationsSystem[i][j].Item2;
}
}
return(_linearSystemSolver.Solve(linearSystemMatrix, zeros));
}
/// <summary>
/// Method for calculating number of combinations from <paramref name="n"/> by <paramref name="k"/> over field <paramref name="field"/>
/// </summary>
/// <param name="field">Field over which combinations count'll calculated</param>
/// <param name="n">Total elements count</param>
/// <param name="k">Selected elements count</param>
/// <param name="combinationsCache">Cache for storing combinations count</param>
/// <returns>Combinations count</returns>
public FieldElement Calculate(GaloisField field, int n, int k, FieldElement[][] combinationsCache = null)
{
var combinationsCount = combinationsCache?[n][k];
if (combinationsCount == null)
{
if (k == 0 || n == k)
{
combinationsCount = field.One();
}
else
{
if (n < k)
{
combinationsCount = field.Zero();
}
else
{
combinationsCount = Calculate(field, n - 1, k - 1, combinationsCache)
+ Calculate(field, n - 1, k, combinationsCache);
}
}
if (combinationsCache != null && n < combinationsCache.Length && k < combinationsCache[n].Length)
{
combinationsCache[n][k] = combinationsCount;
}
}
return(combinationsCount);
}
private static IEnumerable <FieldElement[]> PlaceErrors(GaloisField field,
int codewordLength,
IReadOnlyList <int> errorsPositions,
IList <int> noiseValue,
int currentErrorPosition)
{
if (currentErrorPosition == errorsPositions.Count)
{
var additiveNoise = Enumerable.Repeat(field.Zero(), codewordLength).ToArray();
for (var i = 0; i < errorsPositions.Count; i++)
{
additiveNoise[errorsPositions[i]] = field.CreateElement(noiseValue[i]);
}
yield return(additiveNoise);
yield break;
}
for (var i = noiseValue[currentErrorPosition]; i < field.Order; i++)
{
noiseValue[currentErrorPosition] = i;
foreach (var additiveNoise in PlaceErrors(field, codewordLength, errorsPositions, noiseValue, currentErrorPosition + 1))
{
yield return(additiveNoise);
}
}
noiseValue[currentErrorPosition] = 1;
}
/// <summary>
/// Indexing property for obtain bivariate polynomial coefficient by <paramref name="monomial"/>
/// </summary>
/// <param name="monomial">Monomial which coefficient is required</param>
/// <returns>Bivariate polynomial coefficient</returns>
public FieldElement this[Tuple <int, int> monomial]
{
get
{
FieldElement coefficient;
if (_coefficients.TryGetValue(monomial, out coefficient) == false)
{
coefficient = Field.Zero();
}
return(coefficient);
}
set
{
if (Field.Equals(value.Field) == false)
{
throw new ArgumentException("Incorrect field");
}
if (value.Representation != 0)
{
_coefficients[monomial] = value;
}
else
{
_coefficients.Remove(monomial);
}
}
}
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)
}
};
}