/// <summary>
/// Permite efectuar a leitura de um polinómio com coeficientes fraccionários a partir de texto.
/// </summary>
/// <remarks>
/// Se a leitura não for bem sucedida, é lançada uma excep~ção.
/// </remarks>
/// <param name="polynomial">O texto.</param>
/// <returns>O polinómio.</returns>
public UnivariatePolynomialNormalForm <Fraction <int> > Read(string polynomial)
{
var integerDomain = new IntegerDomain();
var fractionField = new FractionField <int>(integerDomain);
var integerParser = new IntegerParser <string>();
var fractionParser = new FieldDrivenExpressionParser <Fraction <int> >(
new SimpleElementFractionParser <int>(integerParser, integerDomain),
fractionField);
var conversion = new ElementFractionConversion <int>(integerDomain);
var polInputReader = new StringReader(polynomial);
var polSymbolReader = new StringSymbolReader(polInputReader, false);
var polParser = new UnivariatePolynomialReader <Fraction <int>, CharSymbolReader <string> >(
"x",
fractionParser,
fractionField);
var result = default(UnivariatePolynomialNormalForm <Fraction <int> >);
if (polParser.TryParsePolynomial(polSymbolReader, conversion, out result))
{
// O polinómio foi lido com sucesso.
return(result);
}
else
{
// Não é possível ler o polinómio.
throw new Exception("Can't read integer polynomial.");
}
}
public void GetQuotientAndRemainderTest()
{
var dividend = " x^3-1/3*x^2+ - -x/5-1/2";
var divisor = "x^2-x/2+1";
// Os objectos responsáveis pelas operações sobre os coeficientes.
var integerDomain = new IntegerDomain();
var integerParser = new IntegerParser <string>();
var conversion = new ElementFractionConversion <int>(integerDomain);
var fractionField = new FractionField <int>(integerDomain);
// A leitura dos polinómios.
var dividendPol = TestsHelper.ReadFractionalCoeffsUnivarPol <int, IntegerDomain>(
dividend,
integerDomain,
integerParser,
conversion,
"x");
var divisorPol = TestsHelper.ReadFractionalCoeffsUnivarPol <int, IntegerDomain>(
divisor,
integerDomain,
integerParser,
conversion,
"x");
var polynomialDomain = new UnivarPolynomEuclideanDomain <Fraction <int> >(
"x",
fractionField);
var result = polynomialDomain.GetQuotientAndRemainder(dividendPol, divisorPol);
var expected = divisorPol.Multiply(result.Quotient, fractionField);
expected = expected.Add(result.Remainder, fractionField);
Assert.AreEqual(expected, dividendPol);
}
public void RunTest_IntegerPolynomial()
{
var integerDomain = new IntegerDomain();
var fractionField = new FractionField <int>(integerDomain);
var integerParser = new IntegerParser <string>();
var conversion = new ElementToElementConversion <int>();
var fractionConversion = new ElementFractionConversion <int>(integerDomain);
string variableName = "x";
var univarPolDomain = new UnivarPolynomEuclideanDomain <Fraction <int> >(
variableName,
fractionField);
var lagAlg = new LagrangeAlgorithm <UnivariatePolynomialNormalForm <Fraction <int> > >(univarPolDomain);
var firstValue = TestsHelper.ReadFractionalCoeffsUnivarPol <int, IntegerDomain>(
"(x-1/2)*(x+1/3)",
integerDomain,
integerParser,
fractionConversion,
variableName);
var secondValue = TestsHelper.ReadFractionalCoeffsUnivarPol <int, IntegerDomain>(
"(x-1/2)*(x-1)",
integerDomain,
integerParser,
fractionConversion,
variableName);
var gcd = TestsHelper.ReadFractionalCoeffsUnivarPol <int, IntegerDomain>(
"x-1/2",
integerDomain,
integerParser,
fractionConversion,
variableName);
var result = lagAlg.Run(firstValue, secondValue);
var mainGcdCoeff = result.GreatestCommonDivisor.GetLeadingCoefficient(fractionField);
var monicGcd = result.GreatestCommonDivisor.Multiply(
fractionField.MultiplicativeInverse(mainGcdCoeff),
fractionField);
Assert.AreEqual(gcd, monicGcd);
var firstTermExpression = univarPolDomain.Multiply(result.FirstFactor, result.FirstItem);
var secondTermExpression = univarPolDomain.Multiply(result.SecondFactor, result.SecondItem);
var actualExpression = univarPolDomain.Add(firstTermExpression, secondTermExpression);
Assert.AreEqual(result.GreatestCommonDivisor, actualExpression);
actualExpression = univarPolDomain.Multiply(result.GreatestCommonDivisor, result.FirstCofactor);
Assert.AreEqual(result.FirstItem, actualExpression);
actualExpression = univarPolDomain.Multiply(result.GreatestCommonDivisor, result.SecondCofactor);
Assert.AreEqual(result.SecondItem, actualExpression);
}
public void GetRootPowerSumsTest_IntegerFraction()
{
// Representação dos polinómios.
var polynomText = "(x-3)*(x-2)^2*(x+1)^3";
var variableName = "x";
// Estabelece os domínios.
var integerDomain = new IntegerDomain();
// Estabelece o corpo responsável pelas operações sobre as fracções.
var fractionField = new FractionField <int>(integerDomain);
// Estabelece os conversores.
var integerToFractionConversion = new ElementFractionConversion <int>(integerDomain);
// Estabelece os leitores individuais.
var integerParser = new IntegerParser <string>();
// Estabelece o leitor de fracções.
var fractionParser = new ElementFractionParser <int>(integerParser, integerDomain);
// Estabelece os polinómios.
var integerPolynomial = TestsHelper.ReadUnivarPolynomial(
polynomText,
fractionField,
fractionParser,
integerToFractionConversion,
variableName);
var integerFractionExpectedVector = new ArrayVector <Fraction <int> >(6);
integerFractionExpectedVector[0] = new Fraction <int>(4, 1, integerDomain);
integerFractionExpectedVector[1] = new Fraction <int>(20, 1, integerDomain);
integerFractionExpectedVector[2] = new Fraction <int>(40, 1, integerDomain);
integerFractionExpectedVector[3] = new Fraction <int>(116, 1, integerDomain);
integerFractionExpectedVector[4] = new Fraction <int>(304, 1, integerDomain);
integerFractionExpectedVector[5] = new Fraction <int>(860, 1, integerDomain);
var integerFractionActualVector = integerPolynomial.GetRootPowerSums(
fractionField,
new SparseDictionaryMathVectorFactory <Fraction <int> >());
Assert.AreEqual(
integerFractionExpectedVector.Length,
integerFractionActualVector.Length,
"Vector lengths aren't equal.");
for (int i = 0; i < integerFractionActualVector.Length; ++i)
{
Assert.AreEqual(integerFractionExpectedVector[i], integerFractionActualVector[i]);
}
}
public void GetRootPowerSumsTest()
{
// Representação dos polinómios.
var polynomText = "(x-3)*(x-2)^2*(x+1)^3";
var variableName = "x";
// Estabelece os domínios.
var integerDomain = new IntegerDomain();
// Estabelece o corpo responsável pelas operações sobre as fracções.
var fractionField = new FractionField <int>(integerDomain);
// Estabelece os conversores.
var integerToFractionConversion = new ElementFractionConversion <int>(integerDomain);
// Estabelece os leitores individuais.
var integerParser = new IntegerParser <string>();
// Estabelece o leitor de fracções.
var fractionParser = new ElementFractionParser <int>(integerParser, integerDomain);
// Estabelece os polinómios.
var integerPolynomial = TestsHelper.ReadUnivarPolynomial(
polynomText,
fractionField,
fractionParser,
integerToFractionConversion,
variableName);
var number = 10;
var roots = new int[] { 3, 2, 2, -1, -1, -1 };
var powerRoots = new int[] { 3, 2, 2, -1, -1, -1 };
var integerFractionExpectedVector = new ArrayVector <Fraction <int> >(number);
// Primeiro cálculo
var sum = powerRoots[0];
for (int i = 1; i < powerRoots.Length; ++i)
{
sum += powerRoots[i];
}
integerFractionExpectedVector[0] = new Fraction <int>(sum, 1, integerDomain);
for (int i = 1; i < number; ++i)
{
for (int j = 0; j < roots.Length; ++j)
{
powerRoots[j] *= roots[j];
}
sum = powerRoots[0];
for (int j = 1; j < powerRoots.Length; ++j)
{
sum += powerRoots[j];
}
integerFractionExpectedVector[i] = new Fraction <int>(sum, 1, integerDomain);
}
var integerFractionActualVector = integerPolynomial.GetRootPowerSums(
number,
fractionField,
new SparseDictionaryMathVectorFactory <Fraction <int> >());
Assert.AreEqual(
integerFractionExpectedVector.Length,
integerFractionActualVector.Length,
"Vector lengths aren't equal.");
for (int i = 0; i < integerFractionActualVector.Length; ++i)
{
Assert.AreEqual(integerFractionExpectedVector[i], integerFractionActualVector[i]);
}
}
public void GetPolynomialDerivativeTest_IntegerFraction()
{
var polynomialText = "1/2*x^5+3/4*x^4-2/7*x^3+5/3*x^2+1/5*x+9";
var polynomialDerivativeText = "5/2*x^4+3*x^3-6/7*x^2+10/3*x+1/5";
var variableName = "x";
var integerDomain = new IntegerDomain();
var longDomain = new LongDomain();
var bigIntegerDomain = new BigIntegerDomain();
var integerParser = new IntegerParser <string>();
var longParser = new LongParser <string>();
var bigIntegerParser = new BigIntegerParser <string>();
var longConversion = new LongToIntegerConversion();
var bigIntegerConversion = new BigIntegerToIntegerConversion();
var integerFractionConversion = new ElementFractionConversion <int>(integerDomain);
var longfractionConversion = new OuterElementFractionConversion <int, long>(longConversion, longDomain);
var bigIntegerfractionConversion = new OuterElementFractionConversion <int, BigInteger>(bigIntegerConversion, bigIntegerDomain);
var integerFractionField = new FractionField <int>(integerDomain);
var longFractionField = new FractionField <long>(longDomain);
var bigIntegerFractionField = new FractionField <BigInteger>(bigIntegerDomain);
// Coeficientes inteiros
var integerPolynomial = TestsHelper.ReadFractionalCoeffsUnivarPol <int, IntegerDomain>(
polynomialText,
integerDomain,
integerParser,
integerFractionConversion,
variableName);
var integerPolynomialDerivative = TestsHelper.ReadFractionalCoeffsUnivarPol <int, IntegerDomain>(
polynomialDerivativeText,
integerDomain,
integerParser,
integerFractionConversion,
variableName);
var integerActualPolDerivative = integerPolynomial.GetPolynomialDerivative(integerFractionField);
Assert.AreEqual(integerPolynomialDerivative, integerActualPolDerivative);
// Coeficientes longos
var longPolynomial = TestsHelper.ReadFractionalCoeffsUnivarPol <long, LongDomain>(
polynomialText,
longDomain,
longParser,
longfractionConversion,
variableName);
var longPolynomialDerivative = TestsHelper.ReadFractionalCoeffsUnivarPol <long, LongDomain>(
polynomialDerivativeText,
longDomain,
longParser,
longfractionConversion,
variableName);
var longActualPolDerivative = longPolynomial.GetPolynomialDerivative(longFractionField);
Assert.AreEqual(longPolynomialDerivative, longActualPolDerivative);
var bigIntegerPolynomial = TestsHelper.ReadFractionalCoeffsUnivarPol <BigInteger, BigIntegerDomain>(
polynomialText,
bigIntegerDomain,
bigIntegerParser,
bigIntegerfractionConversion,
variableName);
var bigIntegerPolynomialDerivative = TestsHelper.ReadFractionalCoeffsUnivarPol <BigInteger, BigIntegerDomain>(
polynomialDerivativeText,
bigIntegerDomain,
bigIntegerParser,
bigIntegerfractionConversion,
variableName);
var bigIntegerActualPolDerivative = bigIntegerPolynomial.GetPolynomialDerivative(bigIntegerFractionField);
Assert.AreEqual(bigIntegerPolynomialDerivative, bigIntegerActualPolDerivative);
}
public BigIntegerFractionToIntConversion()
{
this.elementFractionConversion = new ElementFractionConversion <BigInteger>(
new BigIntegerDomain());
}
