/// <summary>
/// Aplica o método da factorização em corpos finitos ao polinómio simples.
/// </summary>
/// <param name="polynom">O polinómio simples.</param>
/// <param name="integerModule">O corpo responsável pelas operações sobre os coeficientes.</param>
/// <param name="polynomField">O corpo responsável pelo produto de polinómios.</param>
/// <param name="bachetBezoutAlgorithm">O objecto responsável pelo algoritmo de máximo divisor comum.</param>
/// <returns>A lista dos factores.</returns>
private FiniteFieldPolynomialFactorizationResult <CoeffType> Factorize(
UnivariatePolynomialNormalForm <CoeffType> polynom,
IModularField <CoeffType> integerModule,
UnivarPolynomEuclideanDomain <CoeffType> polynomField,
LagrangeAlgorithm <UnivariatePolynomialNormalForm <CoeffType> > bachetBezoutAlgorithm)
{
var result = new List <UnivariatePolynomialNormalForm <CoeffType> >();
var polynomialStack = new Stack <UnivariatePolynomialNormalForm <CoeffType> >();
var processedPols = this.Process(
polynom,
result,
integerModule,
polynomField,
bachetBezoutAlgorithm);
foreach (var processedPol in processedPols)
{
polynomialStack.Push(processedPol);
}
while (polynomialStack.Count > 0)
{
var topPolynomial = polynomialStack.Pop();
processedPols = this.Process(
topPolynomial,
result,
integerModule,
polynomField,
bachetBezoutAlgorithm);
foreach (var processedPol in processedPols)
{
polynomialStack.Push(processedPol);
}
}
for (int i = 0; i < result.Count; ++i)
{
var leadingMon = result[i].GetLeadingCoefficient(integerModule);
if (!integerModule.IsMultiplicativeUnity(leadingMon))
{
var invLeadingMon = integerModule.MultiplicativeInverse(leadingMon);
result[i] = result[i].ApplyFunction(
c => integerModule.Multiply(c, invLeadingMon),
integerModule);
}
}
var mainLeadingMon = polynom.GetLeadingCoefficient(integerModule);
return(new FiniteFieldPolynomialFactorizationResult <CoeffType>(
mainLeadingMon,
result,
polynom));
}
/// <summary>
/// Calcula o máximo divisor comum entre dois polinómios.
/// </summary>
/// <param name="first">O primeiro polinómio.</param>
/// <param name="second">O segundo polinómio.</param>
/// <param name="polynomDomain">O domínio responsável pelas operações sobre os polinómios.</param>
/// <param name="field">O corpo responsável pelas operações sobre os coeficientes.</param>
/// <returns>O máximo divisor comum.</returns>
private UnivariatePolynomialNormalForm <CoeffType> GreatCommonDivisor(
UnivariatePolynomialNormalForm <CoeffType> first,
UnivariatePolynomialNormalForm <CoeffType> second,
UnivarPolynomEuclideanDomain <CoeffType> polynomDomain,
IField <CoeffType> field
)
{
var result = MathFunctions.GreatCommonDivisor(first, second, polynomDomain);
var leadingCoeff = result.GetLeadingCoefficient(field);
result = result.Multiply(field.MultiplicativeInverse(leadingCoeff), field);
return(result);
}
/// <summary>
/// Determina o produto de todos os factores modulares.
/// </summary>
/// <param name="modularFactors">Os factores modulares.</param>
/// <param name="modularDomain">O domínio modular.</param>
/// <returns>O resultado do produto dos factores modulares.</returns>
private UnivariatePolynomialNormalForm <CoeffType> ComputeModularProduct(
List <UnivariatePolynomialNormalForm <CoeffType> > modularFactors,
UnivarPolynomEuclideanDomain <CoeffType> modularDomain)
{
if (modularFactors.Count > 0)
{
var result = modularFactors[0];
for (int i = 1; i < modularFactors.Count; ++i)
{
result = modularDomain.Multiply(result, modularFactors[i]);
}
return(result);
}
else
{
return(modularDomain.MultiplicativeUnity);
}
}
/// <summary>
/// Executa o algoritmo sobre o polinómio com coeficientes inteiros.
/// </summary>
/// <remarks>
/// O polinómio tem de ser livre de quadrados. Caso contrário, o resultado da aplicação do algoritmo
/// é imprevisível.
/// </remarks>
/// <param name="polymomial">O polinómio.</param>
/// <param name="modularField">O corpo modular.</param>
/// <returns>A factorização do polinómio.</returns>
public FiniteFieldPolynomialFactorizationResult <CoeffType> Run(
UnivariatePolynomialNormalForm <CoeffType> polymomial,
IModularField <CoeffType> modularField)
{
var fractionField = new FractionField <CoeffType>(this.integerNumber);
var polynomDomain = new UnivarPolynomEuclideanDomain <CoeffType>(
polymomial.VariableName,
modularField);
var bachetBezourAlg = new LagrangeAlgorithm <UnivariatePolynomialNormalForm <CoeffType> >(polynomDomain);
var polynomialField = new UnivarPolynomEuclideanDomain <CoeffType>(
polymomial.VariableName,
modularField);
var result = this.Factorize(
polymomial,
modularField,
polynomialField,
bachetBezourAlg);
return(result);
}
/// <summary>
/// Aplica o algoritmo de factorização livre de quadrados a um polinómio.
/// </summary>
/// <param name="data">O polinómio.</param>
/// <param name="field">O corpos responsável pelas operações sobre os coeficientes.</param>
/// <returns>O resultado da factorização livre de quadrados.</returns>
/// <exception cref="ArgumentNullException">Caso algum dos argumentos seja nulo.</exception>
public SquareFreeFactorizationResult <CoeffType, CoeffType> Run(
UnivariatePolynomialNormalForm <CoeffType> data,
IField <CoeffType> field)
{
if (field == null)
{
throw new ArgumentNullException("field");
}
else if (data == null)
{
throw new ArgumentNullException("data");
}
else
{
var independentCoeff = field.MultiplicativeUnity;
var result = new Dictionary <int, UnivariatePolynomialNormalForm <CoeffType> >();
var currentDegree = 1;
var polynomDomain = new UnivarPolynomEuclideanDomain <CoeffType>(data.VariableName, field);
var dataDerivative = data.GetPolynomialDerivative(field);
var gcd = this.GreatCommonDivisor(data, dataDerivative, polynomDomain, field);
if (polynomDomain.IsMultiplicativeUnity(gcd))
{
result.Add(currentDegree, data.Clone());
}
else
{
var polyCoffactor = polynomDomain.Quo(data, gcd);
var nextGcd = this.GreatCommonDivisor(gcd, polyCoffactor, polynomDomain, field);
var squareFreeFactor = polynomDomain.Quo(polyCoffactor, nextGcd);
polyCoffactor = gcd;
gcd = nextGcd;
if (squareFreeFactor.Degree > 0)
{
result.Add(currentDegree, squareFreeFactor);
}
else
{
var value = squareFreeFactor.GetAsValue(field);
if (!field.IsMultiplicativeUnity(value))
{
if (field.IsMultiplicativeUnity(independentCoeff))
{
independentCoeff = value;
}
else
{
independentCoeff = field.Multiply(independentCoeff, value);
}
}
}
++currentDegree;
while (gcd.Degree > 0)
{
polyCoffactor = polynomDomain.Quo(polyCoffactor, gcd);
nextGcd = this.GreatCommonDivisor(gcd, polyCoffactor, polynomDomain, field);
squareFreeFactor = polynomDomain.Quo(gcd, nextGcd);
gcd = nextGcd;
if (squareFreeFactor.Degree > 0)
{
result.Add(currentDegree, squareFreeFactor);
}
else
{
var value = squareFreeFactor.GetAsValue(field);
if (!field.IsMultiplicativeUnity(value))
{
if (field.IsMultiplicativeUnity(independentCoeff))
{
independentCoeff = value;
}
else
{
independentCoeff = field.Multiply(independentCoeff, value);
}
}
}
++currentDegree;
}
var cofactorValue = polyCoffactor.GetAsValue(field);
if (!field.IsMultiplicativeUnity(cofactorValue))
{
if (field.IsMultiplicativeUnity(independentCoeff))
{
independentCoeff = cofactorValue;
}
else
{
independentCoeff = field.Multiply(independentCoeff, cofactorValue);
}
}
}
return(new SquareFreeFactorizationResult <CoeffType, CoeffType>(
independentCoeff,
result));
}
}
/// <summary>
/// Processa o polinómio determinando os respectivos factores.
/// </summary>
/// <remarks>
/// Os factores constantes são ignorados, os factores lineares são anexados ao resultado e os factores
/// cujos graus são superiores são retornados para futuro processamento. Se o polinómio a ser processado
/// for irredutível, é adicionado ao resultado.
/// </remarks>
/// <param name="polynom">O polinómio a ser processado.</param>
/// <param name="result">O contentor dos factores sucessivamente processados.</param>
/// <param name="integerModule">O objecto responsável pelas operações sobre inteiros.</param>
/// <param name="polynomField">O objecto responsável pelas operações sobre os polinómios.</param>
/// <param name="inverseAlgorithm">O algoritmo inverso.</param>
/// <returns></returns>
List <UnivariatePolynomialNormalForm <CoeffType> > Process(
UnivariatePolynomialNormalForm <CoeffType> polynom,
List <UnivariatePolynomialNormalForm <CoeffType> > result,
IModularField <CoeffType> integerModule,
UnivarPolynomEuclideanDomain <CoeffType> polynomField,
LagrangeAlgorithm <UnivariatePolynomialNormalForm <CoeffType> > inverseAlgorithm)
{
var resultPol = new List <UnivariatePolynomialNormalForm <CoeffType> >();
if (polynom.Degree < 2)
{
result.Add(polynom);
}
else
{
var module = new ModularBachetBezoutField <UnivariatePolynomialNormalForm <CoeffType> >(
polynom,
inverseAlgorithm);
var degree = polynom.Degree;
var arrayMatrix = new ArrayMathMatrix <CoeffType>(degree, degree, integerModule.AdditiveUnity);
arrayMatrix[0, 0] = integerModule.AdditiveUnity;
var pol = new UnivariatePolynomialNormalForm <CoeffType>(
integerModule.MultiplicativeUnity,
1,
polynom.VariableName,
integerModule);
var integerModuleValue = this.integerNumber.ConvertToInt(integerModule.Module);
pol = MathFunctions.Power(pol, integerModuleValue, module);
foreach (var term in pol)
{
arrayMatrix[term.Key, 1] = term.Value;
}
var auxPol = pol;
for (int i = 2; i < degree; ++i)
{
auxPol = module.Multiply(auxPol, pol);
foreach (var term in auxPol)
{
arrayMatrix[term.Key, i] = term.Value;
}
}
for (int i = 1; i < degree; ++i)
{
var value = arrayMatrix[i, i];
value = integerModule.Add(
value,
integerModule.AdditiveInverse(integerModule.MultiplicativeUnity));
arrayMatrix[i, i] = value;
}
var emtpyMatrix = new ZeroMatrix <CoeffType>(degree, 1, integerModule);
var linearSystemSolution = this.linearSystemSolver.Run(arrayMatrix, emtpyMatrix);
var numberOfFactors = linearSystemSolution.VectorSpaceBasis.Count;
if (numberOfFactors < 2)
{
result.Add(polynom);
}
else
{
var hPol = default(UnivariatePolynomialNormalForm <CoeffType>);
var linearSystemCount = linearSystemSolution.VectorSpaceBasis.Count;
for (int i = 0; i < linearSystemCount; ++i)
{
var currentBaseSolution = linearSystemSolution.VectorSpaceBasis[i];
var rowsLength = currentBaseSolution.Length;
for (int j = 1; j < rowsLength; ++j)
{
if (!integerModule.IsAdditiveUnity(currentBaseSolution[j]))
{
hPol = this.GetPolynomial(currentBaseSolution, integerModule, polynom.VariableName);
j = rowsLength;
}
if (hPol != null)
{
j = rowsLength;
}
}
if (hPol != null)
{
i = linearSystemCount;
}
}
for (int i = 0, k = 0; k < numberOfFactors && i < integerModuleValue; ++i)
{
var converted = this.integerNumber.MapFrom(i);
var currentPol = MathFunctions.GreatCommonDivisor(
polynom,
hPol.Subtract(converted, integerModule),
polynomField);
var currentDegree = currentPol.Degree;
if (currentDegree == 1)
{
result.Add(currentPol);
++k;
}
else if (currentDegree > 1)
{
resultPol.Add(currentPol);
++k;
}
}
}
}
return(resultPol);
}
/// <summary>
/// Executa o algoritmo que permite obter uma factorização livre de quadrados.
/// </summary>
/// <param name="polynomial">O polinómio de entrada.</param>
/// <returns>A factorização livre de quadrados.</returns>
/// <exception cref="ArgumentNullException">
/// Se o argumento for nulo.
/// </exception>
public SquareFreeFactorizationResult <Fraction <CoeffType>, CoeffType> Run(
UnivariatePolynomialNormalForm <Fraction <CoeffType> > polynomial)
{
if (polynomial == null)
{
throw new ArgumentNullException("polynomial");
}
else
{
var independentCoeff = this.fractionField.MultiplicativeUnity;
var result = new Dictionary <int, UnivariatePolynomialNormalForm <CoeffType> >();
var currentDegree = 1;
var polynomDomain = new UnivarPolynomEuclideanDomain <Fraction <CoeffType> >(
polynomial.VariableName,
this.fractionField);
var lagAlg = new LagrangeAlgorithm <CoeffType>(this.integerNumber);
var dataDerivative = polynomial.GetPolynomialDerivative(this.fractionField);
var gcd = this.GreatCommonDivisor(polynomial, dataDerivative, polynomDomain);
if (gcd.Degree == 0)
{
var lcm = this.GetDenominatorLcm(polynomial, lagAlg);
if (this.integerNumber.IsMultiplicativeUnity(lcm))
{
var integerPol = this.GetIntegerPol(polynomial);
result.Add(currentDegree, integerPol);
}
else
{
independentCoeff = new Fraction <CoeffType>(
this.integerNumber.MultiplicativeUnity,
lcm,
this.integerNumber);
var multipliable = new Fraction <CoeffType>(
lcm,
this.integerNumber.MultiplicativeUnity,
this.integerNumber);
var multipliedPol = polynomial.Multiply(independentCoeff, this.fractionField);
var integerPol = this.GetIntegerPol(multipliedPol);
result.Add(currentDegree, integerPol);
}
}
else
{
var polyCoffactor = polynomDomain.Quo(polynomial, gcd);
var nextGcd = this.GreatCommonDivisor(gcd, polyCoffactor, polynomDomain);
var squareFreeFactor = polynomDomain.Quo(polyCoffactor, nextGcd);
polyCoffactor = gcd;
gcd = nextGcd;
if (squareFreeFactor.Degree > 0)
{
var lcm = this.GetDenominatorLcm(squareFreeFactor, lagAlg);
if (this.integerNumber.IsMultiplicativeUnity(lcm))
{
var integerPol = this.GetIntegerPol(squareFreeFactor);
result.Add(currentDegree, integerPol);
}
else if (this.fractionField.IsAdditiveUnity(independentCoeff))
{
independentCoeff = new Fraction <CoeffType>(
this.integerNumber.MultiplicativeUnity,
MathFunctions.Power(lcm, currentDegree, this.integerNumber),
this.integerNumber);
var multipliable = new Fraction <CoeffType>(
lcm,
this.integerNumber.MultiplicativeUnity,
this.integerNumber);
var multipliedPol = squareFreeFactor.Multiply(independentCoeff, this.fractionField);
var integerPol = this.GetIntegerPol(multipliedPol);
result.Add(currentDegree, integerPol);
}
else
{
var multiplicationCoeff = new Fraction <CoeffType>(
this.integerNumber.MultiplicativeUnity,
MathFunctions.Power(lcm, currentDegree, this.integerNumber),
this.integerNumber);
independentCoeff = this.fractionField.Multiply(independentCoeff, multiplicationCoeff);
var multipliable = new Fraction <CoeffType>(
lcm,
this.integerNumber.MultiplicativeUnity,
this.integerNumber);
var multipliedPol = squareFreeFactor.Multiply(independentCoeff, this.fractionField);
var integerPol = this.GetIntegerPol(multipliedPol);
result.Add(currentDegree, integerPol);
}
}
else
{
var value = squareFreeFactor.GetAsValue(this.fractionField);
if (!this.fractionField.IsMultiplicativeUnity(value))
{
if (this.fractionField.IsMultiplicativeUnity(independentCoeff))
{
independentCoeff = value;
}
else
{
independentCoeff = this.fractionField.Multiply(independentCoeff, value);
}
}
}
++currentDegree;
while (gcd.Degree > 0)
{
polyCoffactor = polynomDomain.Quo(polyCoffactor, gcd);
nextGcd = MathFunctions.GreatCommonDivisor(gcd, polyCoffactor, polynomDomain);
squareFreeFactor = polynomDomain.Quo(gcd, nextGcd);
gcd = nextGcd;
if (squareFreeFactor.Degree > 0)
{
var lcm = this.GetDenominatorLcm(squareFreeFactor, lagAlg);
if (this.integerNumber.IsMultiplicativeUnity(lcm))
{
var integerPol = this.GetIntegerPol(squareFreeFactor);
result.Add(currentDegree, integerPol);
}
else if (this.fractionField.IsAdditiveUnity(independentCoeff))
{
independentCoeff = new Fraction <CoeffType>(
this.integerNumber.MultiplicativeUnity,
MathFunctions.Power(lcm, currentDegree, this.integerNumber),
this.integerNumber);
var multipliable = new Fraction <CoeffType>(
lcm,
this.integerNumber.MultiplicativeUnity,
this.integerNumber);
var multipliedPol = squareFreeFactor.Multiply(independentCoeff, this.fractionField);
var integerPol = this.GetIntegerPol(multipliedPol);
result.Add(currentDegree, integerPol);
}
else
{
var multiplicationCoeff = new Fraction <CoeffType>(
this.integerNumber.MultiplicativeUnity,
MathFunctions.Power(lcm, currentDegree, this.integerNumber),
this.integerNumber);
independentCoeff = this.fractionField.Multiply(independentCoeff, multiplicationCoeff);
var multipliable = new Fraction <CoeffType>(
lcm,
this.integerNumber.MultiplicativeUnity,
this.integerNumber);
var multipliedPol = squareFreeFactor.Multiply(multipliable, this.fractionField);
var integerPol = this.GetIntegerPol(multipliedPol);
result.Add(currentDegree, integerPol);
}
}
else
{
var value = squareFreeFactor.GetAsValue(this.fractionField);
if (!this.fractionField.IsMultiplicativeUnity(value))
{
if (this.fractionField.IsMultiplicativeUnity(independentCoeff))
{
independentCoeff = value;
}
else
{
independentCoeff = this.fractionField.Multiply(independentCoeff, value);
}
}
}
++currentDegree;
}
var cofactorValue = polyCoffactor.GetAsValue(this.fractionField);
if (!this.fractionField.IsMultiplicativeUnity(cofactorValue))
{
if (this.fractionField.IsMultiplicativeUnity(independentCoeff))
{
independentCoeff = cofactorValue;
}
else
{
independentCoeff = this.fractionField.Multiply(independentCoeff, cofactorValue);
}
}
}
return(new SquareFreeFactorizationResult <Fraction <CoeffType>, CoeffType>(
independentCoeff,
result));
}
}
/// <summary>
/// Permite obter a lista de factores irredutíveis a partir de uma factorização módulo um número primo.
/// </summary>
/// <param name="liftedFactorization">A factorização módulo o número primo.</param>
/// <param name="testValue">
/// O valor de teste que depende do grau, da norma e do coeficiente principal do polinómio original.
/// </param>
/// <param name="combinationsNumber">O número máximo de combinações a testar.</param>
/// <returns>A lista de factores irredutíveis.</returns>
/// <exception cref="ArgumentNullException">Se a factorização ou o valor de teste forem nulos.</exception>
/// <exception cref="ArgumentException">Se não forem providenciadas quaisquer combinações.</exception>
public SearchFactorizationResult <CoeffType> Run(
MultiFactorLiftingResult <CoeffType> liftedFactorization,
CoeffType testValue,
int combinationsNumber)
{
if (liftedFactorization == null)
{
throw new ArgumentNullException("liftedFactorization");
}
else if (testValue == null)
{
throw new ArgumentNullException("testValue");
}
else if (combinationsNumber <= 0)
{
throw new ArgumentException("At least one combination is expected.");
}
else
{
var modularField = this.modularFieldFactory.CreateInstance(liftedFactorization.LiftingPrimePower);
var halfPrime = this.integerNumber.Quo(
liftedFactorization.LiftingPrimePower,
this.integerNumber.MapFrom(2));
var modularFactors = new List <UnivariatePolynomialNormalForm <CoeffType> >();
foreach (var liftedFactor in liftedFactorization.Factors)
{
if (liftedFactor.Degree != 0)
{
modularFactors.Add(liftedFactor.ApplyFunction(
c => this.GetSymmetricRemainder(c, liftedFactorization.LiftingPrimePower, halfPrime),
this.integerNumber));
}
}
var integerFactors = new List <UnivariatePolynomialNormalForm <CoeffType> >();
// Lida com os factores lineares
var i = 0;
var constantCoeff = this.integerNumber.MultiplicativeUnity;
while (i < modularFactors.Count)
{
var currentModularFactor = modularFactors[i];
var norm = this.GetPlynomialNorm(currentModularFactor);
if (this.integerNumber.Compare(norm, testValue) < 0)
{
integerFactors.Add(currentModularFactor);
modularFactors.RemoveAt(i);
}
else
{
++i;
}
}
var modularPolynomialDomain = new UnivarPolynomEuclideanDomain <CoeffType>(
liftedFactorization.Polynom.VariableName,
modularField);
this.ProcessRemainingPolynomials(
modularFactors,
integerFactors,
liftedFactorization.LiftingPrimePower,
halfPrime,
testValue,
combinationsNumber,
modularPolynomialDomain);
return(new SearchFactorizationResult <CoeffType>(
liftedFactorization.Polynom,
integerFactors,
modularFactors));
}
}
/// <summary>
/// Permite processar as restantes combinações.
/// </summary>
/// <param name="modularFactors">Os factores modulares.</param>
/// <param name="integerFactors">Os factores inteiros.</param>
/// <param name="primePower">A potência de um número primo que servirá de módulo.</param>
/// <param name="halfPrimePower">A metade da potência do número primo.</param>
/// <param name="testValue">O valor de teste.</param>
/// <param name="combinationsNumber">O número máximo de polinómios nas combinações.</param>
/// <param name="modularPolynomialDomain">O corpo responsável pelas operações modulares.</param>
private void ProcessRemainingPolynomials(
List <UnivariatePolynomialNormalForm <CoeffType> > modularFactors,
List <UnivariatePolynomialNormalForm <CoeffType> > integerFactors,
CoeffType primePower,
CoeffType halfPrimePower,
CoeffType testValue,
int combinationsNumber,
UnivarPolynomEuclideanDomain <CoeffType> modularPolynomialDomain)
{
if (combinationsNumber > 1 && modularFactors.Count > 1)
{
var modularProduct = default(UnivariatePolynomialNormalForm <CoeffType>);
var currentCombinationNumber = 2;
var productStack = new Stack <UnivariatePolynomialNormalForm <CoeffType> >();
productStack.Push(modularFactors[0]);
var pointers = new Stack <int>();
pointers.Push(0);
pointers.Push(1);
var state = 0;
while (state != -1)
{
if (state == 0)
{
if (pointers.Count == currentCombinationNumber)
{
var topPointer = pointers.Pop();
var topPol = productStack.Pop();
// Obtém o produto de todos os polinómios.
var currentPol = modularPolynomialDomain.Multiply(
topPol,
modularFactors[topPointer]);
currentPol = currentPol.ApplyFunction(
c => this.GetSymmetricRemainder(
c,
primePower,
halfPrimePower),
this.integerNumber);
// Compara as normas com o valor de teste
var firstNorm = this.GetPlynomialNorm(currentPol);
if (this.integerNumber.Compare(firstNorm, testValue) < 0)
{
if (modularProduct == null)
{
modularProduct = this.ComputeModularProduct(
modularFactors,
modularPolynomialDomain);
}
var coPol = modularPolynomialDomain.Quo(
modularProduct,
currentPol);
coPol = coPol.ApplyFunction(
c => this.GetSymmetricRemainder(
c,
primePower,
halfPrimePower),
this.integerNumber);
var secondNorm = this.GetPlynomialNorm(coPol);
var normProd = this.integerNumber.Multiply(firstNorm, secondNorm);
if (this.integerNumber.Compare(normProd, testValue) < 0)
{
integerFactors.Add(currentPol);
modularFactors.RemoveAt(topPointer);
while (pointers.Count > 0)
{
var removeIndex = pointers.Pop();
modularFactors.RemoveAt(removeIndex);
}
productStack.Clear();
if (modularFactors.Count < currentCombinationNumber)
{
state = -1;
}
else
{
productStack.Push(modularFactors[0]);
pointers.Push(0);
pointers.Push(1);
}
}
else
{
productStack.Push(topPol);
pointers.Push(topPointer);
state = 1;
}
}
else
{
productStack.Push(topPol);
pointers.Push(topPointer);
state = 1;
}
}
else
{
var topPointer = pointers.Pop();
var topPol = productStack.Pop();
var currentPol = modularPolynomialDomain.Multiply(
topPol,
modularFactors[topPointer]);
currentPol = currentPol.ApplyFunction(
c => this.GetSymmetricRemainder(
c,
primePower,
halfPrimePower),
this.integerNumber);
productStack.Push(topPol);
productStack.Push(currentPol);
pointers.Push(topPointer);
pointers.Push(topPointer + 1);
}
}
else if (state == 1)
{
var pointerLimit = modularFactors.Count - combinationsNumber + pointers.Count + 1;
if (pointers.Count > 1)
{
var topPointer = pointers.Pop();
++topPointer;
if (topPointer < pointerLimit)
{
pointers.Push(topPointer);
state = 0;
}
else
{
productStack.Pop();
}
}
else
{
var topPointer = pointers.Pop();
++topPointer;
if (topPointer < pointerLimit)
{
pointers.Push(topPointer);
productStack.Push(modularFactors[topPointer]);
pointers.Push(topPointer + 1);
}
else
{
++currentCombinationNumber;
if (currentCombinationNumber < combinationsNumber)
{
state = -1;
}
else if (modularFactors.Count < currentCombinationNumber)
{
state = -1;
}
else
{
pointers.Push(0);
pointers.Push(1);
productStack.Push(modularFactors[0]);
}
}
}
}
}
}
}