/// <summary>
/// Determina se o polinómio geral é uma unidade multiplicativa.
/// </summary>
/// <param name="value">O polinómio a ser analisado.</param>
/// <returns>Verdadeiro caso o polinómios seja uma unidade multiplicativa e falso caso contrário.</returns>
/// <exception cref="ArgumentNullException">Se o argumento for nulo.</exception>
public virtual bool IsMultiplicativeUnity(GeneralDegUnivarPolynomNormalForm <CoeffType, DegreeType> value)
{
if (value == null)
{
throw new ArgumentNullException("value");
}
else
{
return(value.IsUnity(this.ring));
}
}
/// <summary>
/// Retorna um código confuso para a instância.
/// </summary>
/// <param name="obj">A instância.</param>
/// <returns>
/// Um código confuso para a instância que pode ser usado em vários algoritmos habituais.
/// </returns>
public virtual int GetHashCode(GeneralDegUnivarPolynomNormalForm <CoeffType, DegreeType> obj)
{
if (obj == null)
{
return(0);
}
else
{
return(obj.GetHashCode());
}
}
/// <summary>
/// Obtém o grau do polinómio.
/// </summary>
/// <param name="value">O polinómio do qual se pretende obter o grau.</param>
/// <returns>O valor do grau.</returns>
/// <exception cref="ArgumentNullException">Se o argumento for nulo.</exception>
public uint Degree(GeneralDegUnivarPolynomNormalForm <CoeffType, DegreeType> value)
{
if (value == null)
{
throw new ArgumentNullException("value");
}
else
{
return((uint)(object)value.Degree);
}
}
/// <summary>
/// Determina o inverso aditivo de um polinómio geral.
/// </summary>
/// <param name="number">O polinómio.</param>
/// <returns>O inverso aditivo.</returns>
/// <exception cref="ArgumentNullException">Caso o argumento seja nulo.</exception>
public virtual GeneralDegUnivarPolynomNormalForm <CoeffType, DegreeType> AdditiveInverse(
GeneralDegUnivarPolynomNormalForm <CoeffType, DegreeType> number)
{
if (number == null)
{
throw new ArgumentNullException("number");
}
else
{
return(number.GetSymmetric(this.ring));
}
}
/// <summary>
/// Cria uma instância de objectos do tipo <see cref="GeneralDegUnivarPolynomEuclideanDomain{CoeffType, DegreeType}"/>.
/// </summary>
/// <param name="variableName">O nome da variável.</param>
/// <param name="field">O corpo responsável pelas operações sobre os coeficiente.</param>
/// <param name="integerNumber">O objecto que é responsável pelas operações sobre os graus.</param>
public GeneralDegUnivarPolynomEuclideanDomain(
string variableName,
IField <CoeffType> field,
IIntegerNumber <DegreeType> integerNumber)
: base(variableName, field, integerNumber)
{
this.field = field;
this.unit = new GeneralDegUnivarPolynomNormalForm <CoeffType, DegreeType>(
this.field.MultiplicativeUnity,
this.integerNumber.MultiplicativeUnity,
this.variableName,
this.field,
this.integerNumber);
}
/// <summary>
/// Calcula o produto de dois polinomio gerais.
/// </summary>
/// <param name="left">O primeiro polinómio geral a ser multiplicado.</param>
/// <param name="right">O segundo polinómio geral a ser multiplicado.</param>
/// <returns>O resultado do produto dos polinómios.</returns>
/// <exception cref="ArgumentNullException">
/// Se pelo menos um dos argumentos for nulo.
/// </exception>
public virtual GeneralDegUnivarPolynomNormalForm <CoeffType, DegreeType> Multiply(
GeneralDegUnivarPolynomNormalForm <CoeffType, DegreeType> left,
GeneralDegUnivarPolynomNormalForm <CoeffType, DegreeType> right)
{
if (left == null)
{
throw new ArgumentNullException("left");
}
else if (right == null)
{
throw new ArgumentNullException("right");
}
else
{
return(left.Multiply(right, this.ring));
}
}
/// <summary>
/// Determina quando dois números de precisão dupla são iguais.
/// </summary>
/// <param name="x">O primeiro polinómio geral a ser comparado.</param>
/// <param name="y">O segundo polinómio geral a ser comparado.</param>
/// <returns>
/// Verdadeiro caso ambos os objectos sejam iguais e falso no caso contrário.
/// </returns>
public virtual bool Equals(
GeneralDegUnivarPolynomNormalForm <CoeffType, DegreeType> x,
GeneralDegUnivarPolynomNormalForm <CoeffType, DegreeType> y)
{
if (x == null && y == null)
{
return(true);
}
else if (x == null)
{
return(false);
}
else if (y == null)
{
return(false);
}
else
{
return(x.Equals(y));
}
}
/// <summary>
/// Calcula a soma repetida de um polinómio.
/// </summary>
/// <param name="element">O polinómio a ser somado.</param>
/// <param name="times">O número de vezes que a soma é aplicada.</param>
/// <returns>O resultado da soma repetida.</returns>
/// <exception cref="ArgumentNullException">Se o argumento for nulo.</exception>
public virtual GeneralDegUnivarPolynomNormalForm <CoeffType, DegreeType> AddRepeated(
GeneralDegUnivarPolynomNormalForm <CoeffType, DegreeType> element,
int times)
{
if (element == null)
{
throw new ArgumentNullException("element");
}
else
{
var result = new GeneralDegUnivarPolynomNormalForm <CoeffType, DegreeType>(
this.variableName,
this.integerNumber);
foreach (var termsKvp in element)
{
result = result.Add(
this.ring.AddRepeated(termsKvp.Value, times),
termsKvp.Key, this.ring);
}
return(result);
}
}
/// <summary>
/// Obtém o quociente e o resto da divisão entre dois polinómios.
/// </summary>
/// <param name="dividend">O dividendo.</param>
/// <param name="divisor">O divisor.</param>
/// <returns>O quociente e o resto.</returns>
/// <exception cref="ArgumentNullException">Caso algum dos argumentos seja nulo.</exception>
/// <exception cref="ArgumentException">Se os polinómios contiverem variáveis cujos nomes são diferentes.</exception>
/// <exception cref="DivideByZeroException">Se o divisor for uma unidade aditiva.</exception>
public DomainResult <GeneralDegUnivarPolynomNormalForm <CoeffType, DegreeType> > GetQuotientAndRemainder(
GeneralDegUnivarPolynomNormalForm <CoeffType, DegreeType> dividend,
GeneralDegUnivarPolynomNormalForm <CoeffType, DegreeType> divisor)
{
if (dividend == null)
{
throw new ArgumentNullException("dividend");
}
else if (divisor == null)
{
throw new ArgumentNullException("divisor");
}
else if (divisor.VariableName != divisor.VariableName)
{
throw new ArgumentException("Polynomials must share the same variable name in order to be operated.");
}
else
{
if (this.IsAdditiveUnity(divisor))
{
throw new DivideByZeroException("Can't divide by the null polynomial.");
}
else if (this.IsAdditiveUnity(dividend))
{
return(new DomainResult <GeneralDegUnivarPolynomNormalForm <CoeffType, DegreeType> >(
this.AdditiveUnity,
this.AdditiveUnity));
}
else if (this.integerNumber.Compare(divisor.Degree, dividend.Degree) > 0)
{
return(new DomainResult <GeneralDegUnivarPolynomNormalForm <CoeffType, DegreeType> >(
new GeneralDegUnivarPolynomNormalForm <CoeffType, DegreeType>(
this.variableName,
this.integerNumber),
dividend));
}
else
{
var remainderSortedCoeffs = dividend.GetOrderedCoefficients(this.integerNumber);
var divisorSorteCoeffs = divisor.GetOrderedCoefficients(this.integerNumber);
var quotientCoeffs = new GeneralDegUnivarPolynomNormalForm <CoeffType, DegreeType>(
this.variableName,
this.integerNumber);
var remainderLeadingDegree = remainderSortedCoeffs.Keys[remainderSortedCoeffs.Keys.Count - 1];
var divisorLeadingDegree = divisorSorteCoeffs.Keys[divisorSorteCoeffs.Keys.Count - 1];
var inverseDivisorLeadingCoeff = this.field.MultiplicativeInverse(divisorSorteCoeffs[divisorLeadingDegree]);
while (this.integerNumber.Compare(remainderLeadingDegree, divisorLeadingDegree) >= 0 &&
remainderSortedCoeffs.Count > 0)
{
var remainderLeadingCoeff = remainderSortedCoeffs[remainderLeadingDegree];
var differenceDegree = this.integerNumber.Add(remainderLeadingDegree,
this.integerNumber.AdditiveInverse(divisorLeadingDegree));
var factor = this.field.Multiply(
remainderLeadingCoeff,
inverseDivisorLeadingCoeff);
quotientCoeffs = quotientCoeffs.Add(factor, differenceDegree, this.field);
remainderSortedCoeffs.Remove(remainderLeadingDegree);
for (int i = 0; i < divisorSorteCoeffs.Keys.Count - 1; ++i)
{
var currentDivisorDegree = divisorSorteCoeffs.Keys[i];
var currentCoeff = this.field.Multiply(
divisorSorteCoeffs[currentDivisorDegree],
factor);
currentDivisorDegree = this.integerNumber.Add(currentDivisorDegree, differenceDegree);
var addCoeff = default(CoeffType);
if (remainderSortedCoeffs.TryGetValue(currentDivisorDegree, out addCoeff))
{
addCoeff = this.field.Add(
addCoeff,
this.field.AdditiveInverse(currentCoeff));
if (this.field.IsAdditiveUnity(addCoeff))
{
remainderSortedCoeffs.Remove(currentDivisorDegree);
}
else
{
remainderSortedCoeffs[currentDivisorDegree] = addCoeff;
}
}
else
{
remainderSortedCoeffs.Add(
currentDivisorDegree,
this.field.AdditiveInverse(currentCoeff));
}
}
if (remainderSortedCoeffs.Count > 0)
{
remainderLeadingDegree = remainderSortedCoeffs.Keys[remainderSortedCoeffs.Keys.Count - 1];
}
else
{
remainderLeadingDegree = this.integerNumber.AdditiveUnity;
}
}
var remainder = new GeneralDegUnivarPolynomNormalForm <CoeffType, DegreeType>(
remainderSortedCoeffs,
this.variableName,
this.field,
this.integerNumber);
return(new DomainResult <GeneralDegUnivarPolynomNormalForm <CoeffType, DegreeType> >(
quotientCoeffs,
remainder));
}
}
}
