/// <summary>
/// Inicialia o estado do algoritmo caso seja aplicável.
/// </summary>
/// <param name="status">O estado a ser tratado.</param>
/// <param name="polynomialDomain">O domínio polinomial.</param>
/// <param name="modularField">O corpo modular.</param>
/// <returns>Verdadeiro caso se verifique alguma inicialização e falso caso contrário.</returns>
/// <exception cref="ArgumentNullException">Se o estado for nulo.</exception>
private bool Initialize(
LinearLiftingStatus <T> status,
IEuclidenDomain <UnivariatePolynomialNormalForm <T> > polynomialDomain,
IModularField <T> modularField)
{
var result = false;
if (status.NotInitialized)
{
var leadingCoeff = status.W1Factor.GetLeadingCoefficient(modularField);
if (modularField.IsMultiplicativeUnity(leadingCoeff))
{
result = true;
var domainAlg = new LagrangeAlgorithm <UnivariatePolynomialNormalForm <T> >(
polynomialDomain);
var domainResult = domainAlg.Run(status.U1Factor, status.W1Factor);
var invGcd = modularField.MultiplicativeInverse(
domainResult.GreatestCommonDivisor.GetAsValue(modularField));
status.SPol = domainResult.FirstFactor.Multiply(
invGcd,
modularField);
status.TPol = domainResult.SecondFactor.Multiply(
invGcd,
modularField);
status.UFactor = status.U1Factor;
status.WFactor = status.W1Factor;
modularField.Module = this.integerNumber.Multiply(modularField.Module, modularField.Module);
status.InitializedFactorizationModulus = modularField.Module;
var ePol = polynomialDomain.Multiply(status.UFactor, status.WFactor);
ePol = polynomialDomain.Add(
status.Polynom,
polynomialDomain.AdditiveInverse(ePol));
status.EPol = ePol;
status.NotInitialized = false;
}
else
{
throw new MathematicsException(
"The W factor in lifting algorithm must be a monic polynomial.");
}
}
return(result);
}
/// <summary>
/// Aplica o lema do levantamento para elevar a factorização módulo m um número superior m'.
/// </summary>
/// <remarks>
/// Não é realizada qualquer verificação da integridade dos dados associados aos parâmetros de entrada.
/// Caso estes não sejam iniciados convenientemente, os resultados obtidos poderão não estar correctos.
/// </remarks>
/// <param name="status">Contém os dados de entrada.</param>
/// <param name="iterationsNumber">O número de iterações.</param>
/// <returns>Verdadeiro caso seja executada alguma iteração e falso caso contrário.</returns>
/// <exception cref="ArgumentNullException">
/// Se os dados de entrada forem passados com um apontador nulo.
/// </exception>
public bool Run(
LinearLiftingStatus <T> status,
int iterationsNumber)
{
if (status == null)
{
throw new ArgumentNullException("status");
}
else if (iterationsNumber < 1)
{
return(false);
}
else
{
var modularField = this.modularFieldFactory.CreateInstance(status.InitializedFactorizationModulus);
var polynomialDomain = this.polynomialDomainFactory.CreateInstance(
status.Polynom.VariableName,
modularField);
var result = this.Initialize(status, polynomialDomain, modularField);
var k = 0;
if (!status.FoundSolution &&
k < iterationsNumber)
{
result = true;
do
{
var sigmaProd = polynomialDomain.Multiply(
status.SPol,
status.EPol);
var monicDivisionResult = this.GetMonicDivision(
sigmaProd,
status.WFactor,
modularField);
// Cálculo dos factores
var firstMultTemp = polynomialDomain.Multiply(status.TPol, status.EPol);
var secondMultTemp = polynomialDomain.Multiply(
monicDivisionResult.Quotient,
status.UFactor);
status.UFactor = polynomialDomain.Add(status.UFactor, firstMultTemp);
status.UFactor = polynomialDomain.Add(status.UFactor, secondMultTemp);
status.WFactor = polynomialDomain.Add(status.WFactor, monicDivisionResult.Remainder);
// Cálculo dos restantes parâmetros
firstMultTemp = polynomialDomain.Multiply(status.SPol, status.UFactor);
secondMultTemp = polynomialDomain.Multiply(status.TPol, status.WFactor);
var b = polynomialDomain.Add(firstMultTemp, secondMultTemp);
b = b.Add(
modularField.AdditiveInverse(modularField.MultiplicativeUnity),
modularField);
firstMultTemp = polynomialDomain.Multiply(b, status.SPol);
monicDivisionResult = this.GetMonicDivision(
firstMultTemp,
status.WFactor,
modularField);
status.SPol = polynomialDomain.Add(
status.SPol,
polynomialDomain.AdditiveInverse(monicDivisionResult.Remainder));
firstMultTemp = polynomialDomain.Multiply(status.TPol, b);
secondMultTemp = polynomialDomain.Multiply(status.UFactor, monicDivisionResult.Quotient);
firstMultTemp = polynomialDomain.Add(firstMultTemp, secondMultTemp);
status.TPol = polynomialDomain.Add(
status.TPol,
polynomialDomain.AdditiveInverse(firstMultTemp));
status.LiftedFactorizationModule = modularField.Module;
modularField.Module = this.integerNumber.Multiply(
modularField.Module,
modularField.Module);
status.InitializedFactorizationModulus = modularField.Module;
status.EPol = polynomialDomain.Add(
status.Polynom,
polynomialDomain.AdditiveInverse(polynomialDomain.Multiply(
status.UFactor,
status.WFactor)));
status.FoundSolution = polynomialDomain.IsAdditiveUnity(status.EPol);
++k;
} while (!status.FoundSolution &&
k < iterationsNumber);
}
return(result);
}
}
/// <summary>
/// Contrói a árvore de factores.
/// </summary>
/// <param name="multiFactorLiftingStatus">Contém a factorização que se pretende elevar.</param>
/// <param name="modularField">O corpo modular sobre o qual são efectuadas as operações.</param>
/// <returns>A árvore.</returns>
private Tree <LinearLiftingStatus <CoeffType> > MountFactorTree(
MultiFactorLiftingStatus <CoeffType> multiFactorLiftingStatus,
IModularField <CoeffType> modularField)
{
var tree = new Tree <LinearLiftingStatus <CoeffType> >();
var currentNodes = new List <TreeNode <LinearLiftingStatus <CoeffType> > >();
var factorEnumerator = multiFactorLiftingStatus.Factorization.Factors.GetEnumerator();
if (factorEnumerator.MoveNext())
{
var factor = factorEnumerator.Current;
if (!modularField.IsMultiplicativeUnity(multiFactorLiftingStatus.Factorization.IndependentCoeff))
{
factor = factor.Multiply(multiFactorLiftingStatus.Factorization.IndependentCoeff, modularField);
}
currentNodes.Add(new TreeNode <LinearLiftingStatus <CoeffType> >(
new LinearLiftingStatus <CoeffType>(factor, modularField.Module),
tree,
null));
while (factorEnumerator.MoveNext())
{
factor = factorEnumerator.Current;
currentNodes.Add(new TreeNode <LinearLiftingStatus <CoeffType> >(
new LinearLiftingStatus <CoeffType>(factor, modularField.Module),
tree,
null));
}
}
if (currentNodes.Count < 2)
{
return(null);
}
else
{
var temporaryNodes = new List <TreeNode <LinearLiftingStatus <CoeffType> > >();
var count = 0;
while (currentNodes.Count > 1)
{
temporaryNodes.Clear();
var i = 0;
while (i < currentNodes.Count)
{
var parentNode = default(TreeNode <LinearLiftingStatus <CoeffType> >);
var first = currentNodes[i];
++i;
if (i < currentNodes.Count)
{
var second = currentNodes[i];
var product = first.NodeObject.Polynom.Multiply(
second.NodeObject.Polynom,
modularField);
var liftingStatus = new LinearLiftingStatus <CoeffType>(
product,
first.NodeObject.Polynom,
second.NodeObject.Polynom,
modularField.Module);
parentNode = new TreeNode <LinearLiftingStatus <CoeffType> >(
liftingStatus,
tree,
null);
first.InternalParent = parentNode;
second.InternalParent = parentNode;
parentNode.Add(first);
parentNode.Add(second);
++i;
}
else
{
parentNode = first;
}
temporaryNodes.Add(parentNode);
}
var swap = currentNodes;
currentNodes = temporaryNodes;
temporaryNodes = swap;
++count;
}
var lastNode = currentNodes[0];
tree.InternalRootNode = lastNode;
return(tree);
}
}
