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/* |
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/* |
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* Copyright (c) 2005 The University of Notre Dame. All Rights Reserved. |
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* |
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* The University of Notre Dame grants you ("Licensee") a |
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namespace oopse { |
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template<typename ElemType> ElemType pow(ElemType x, int N) { |
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template<typename ElemType> ElemType pow(ElemType x, int N) { |
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ElemType result(1); |
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for (int i = 0; i < N; ++i) { |
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result *= x; |
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result *= x; |
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} |
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return result; |
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} |
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} |
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/** |
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* @class Polynomial Polynomial.hpp "math/Polynomial.hpp" |
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* A generic Polynomial class |
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*/ |
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template<typename ElemType> |
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class Polynomial { |
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/** |
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* @class Polynomial Polynomial.hpp "math/Polynomial.hpp" |
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* A generic Polynomial class |
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*/ |
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template<typename ElemType> |
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class Polynomial { |
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public: |
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typedef int ExponentType; |
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typedef ElemType CoefficientType; |
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typedef std::map<ExponentType, CoefficientType> PolynomialPairMap; |
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typedef typename PolynomialPairMap::iterator iterator; |
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typedef typename PolynomialPairMap::const_iterator const_iterator; |
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/** |
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* Calculates the value of this Polynomial evaluated at the given x value. |
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* @return The value of this Polynomial evaluates at the given x value |
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* @param x the value of the independent variable for this Polynomial function |
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*/ |
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ElemType evaluate(const ElemType& x) { |
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ElemType result = ElemType(); |
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ExponentType exponent; |
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CoefficientType coefficient; |
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public: |
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typedef Polynomial<ElemType> PolynomialType; |
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typedef int ExponentType; |
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typedef ElemType CoefficientType; |
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typedef std::map<ExponentType, CoefficientType> PolynomialPairMap; |
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typedef typename PolynomialPairMap::iterator iterator; |
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typedef typename PolynomialPairMap::const_iterator const_iterator; |
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|
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Polynomial() {} |
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Polynomial(ElemType v) {setCoefficient(0, v);} |
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/** |
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* Calculates the value of this Polynomial evaluated at the given x value. |
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* @return The value of this Polynomial evaluates at the given x value |
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* @param x the value of the independent variable for this Polynomial function |
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*/ |
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ElemType evaluate(const ElemType& x) { |
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ElemType result = ElemType(); |
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ExponentType exponent; |
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CoefficientType coefficient; |
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for (iterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) { |
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exponent = i->first; |
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coefficient = i->second; |
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result += pow(x, exponent) * coefficient; |
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} |
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for (iterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) { |
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exponent = i->first; |
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coefficient = i->second; |
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result += pow(x, exponent) * coefficient; |
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} |
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return result; |
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} |
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return result; |
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} |
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/** |
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* Returns the first derivative of this polynomial. |
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* @return the first derivative of this polynomial |
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* @param x |
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*/ |
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ElemType evaluateDerivative(const ElemType& x) { |
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ElemType result = ElemType(); |
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ExponentType exponent; |
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CoefficientType coefficient; |
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/** |
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* Returns the first derivative of this polynomial. |
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* @return the first derivative of this polynomial |
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* @param x |
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*/ |
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ElemType evaluateDerivative(const ElemType& x) { |
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ElemType result = ElemType(); |
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ExponentType exponent; |
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CoefficientType coefficient; |
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for (iterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) { |
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exponent = i->first; |
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coefficient = i->second; |
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result += pow(x, exponent - 1) * coefficient * exponent; |
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} |
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for (iterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) { |
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exponent = i->first; |
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coefficient = i->second; |
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result += pow(x, exponent - 1) * coefficient * exponent; |
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} |
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return result; |
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} |
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return result; |
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} |
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/** |
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* Set the coefficent of the specified exponent, if the coefficient is already there, it |
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* will be overwritten. |
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* @param exponent exponent of a term in this Polynomial |
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* @param coefficient multiplier of a term in this Polynomial |
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*/ |
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/** |
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* Set the coefficent of the specified exponent, if the coefficient is already there, it |
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* will be overwritten. |
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* @param exponent exponent of a term in this Polynomial |
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* @param coefficient multiplier of a term in this Polynomial |
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*/ |
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void setCoefficient(int exponent, const ElemType& coefficient) { |
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polyPairMap_.insert(PolynomialPairMap::value_type(exponent, coefficient)); |
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} |
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void setCoefficient(int exponent, const ElemType& coefficient) { |
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polyPairMap_.insert(typename PolynomialPairMap::value_type(exponent, coefficient)); |
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} |
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/** |
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* Set the coefficent of the specified exponent. If the coefficient is already there, just add the |
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* new coefficient to the old one, otherwise, just call setCoefficent |
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* @param exponent exponent of a term in this Polynomial |
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* @param coefficient multiplier of a term in this Polynomial |
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*/ |
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/** |
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* Set the coefficent of the specified exponent. If the coefficient is already there, just add the |
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* new coefficient to the old one, otherwise, just call setCoefficent |
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* @param exponent exponent of a term in this Polynomial |
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* @param coefficient multiplier of a term in this Polynomial |
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*/ |
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void addCoefficient(int exponent, const ElemType& coefficient) { |
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iterator i = polyPairMap_.find(exponent); |
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void addCoefficient(int exponent, const ElemType& coefficient) { |
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iterator i = polyPairMap_.find(exponent); |
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if (i != end()) { |
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i->second += coefficient; |
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} else { |
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setCoefficient(exponent, coefficient); |
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} |
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} |
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if (i != end()) { |
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i->second += coefficient; |
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} else { |
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setCoefficient(exponent, coefficient); |
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} |
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} |
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/** |
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* Returns the coefficient associated with the given power for this Polynomial. |
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* @return the coefficient associated with the given power for this Polynomial |
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* @exponent exponent of any term in this Polynomial |
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*/ |
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ElemType getCoefficient(ExponentType exponent) { |
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iterator i = polyPairMap_.find(exponent); |
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/** |
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* Returns the coefficient associated with the given power for this Polynomial. |
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* @return the coefficient associated with the given power for this Polynomial |
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* @exponent exponent of any term in this Polynomial |
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*/ |
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ElemType getCoefficient(ExponentType exponent) { |
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iterator i = polyPairMap_.find(exponent); |
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if (i != end()) { |
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return i->second; |
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} else { |
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return ElemType(0); |
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} |
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} |
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if (i != end()) { |
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return i->second; |
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} else { |
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return ElemType(0); |
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} |
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} |
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iterator begin() { |
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return polyPairMap_.begin(); |
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} |
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iterator begin() { |
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return polyPairMap_.begin(); |
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} |
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const_iterator begin() const{ |
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return polyPairMap_.begin(); |
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} |
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iterator end() { |
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return polyPairMap_.end(); |
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} |
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const_iterator begin() const{ |
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return polyPairMap_.begin(); |
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} |
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iterator end() { |
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return polyPairMap_.end(); |
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} |
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const_iterator end() const{ |
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return polyPairMap_.end(); |
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} |
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const_iterator end() const{ |
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return polyPairMap_.end(); |
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} |
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iterator find(ExponentType exponent) { |
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return polyPairMap_.find(exponent); |
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} |
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iterator find(ExponentType exponent) { |
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return polyPairMap_.find(exponent); |
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} |
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size_t size() { |
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return polyPairMap_.size(); |
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size_t size() { |
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return polyPairMap_.size(); |
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} |
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PolynomialType& operator += (const PolynomialType& p) { |
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typename Polynomial<ElemType>::const_iterator i; |
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for (i = p.begin(); i != p.end(); ++i) { |
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this->addCoefficient(i->first, i->second); |
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} |
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return *this; |
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} |
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PolynomialType& operator -= (const PolynomialType& p) { |
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typename Polynomial<ElemType>::const_iterator i; |
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for (i = p.begin(); i != p.end(); ++i) { |
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this->addCoefficient(i->first, -i->second); |
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} |
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} |
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|
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PolynomialType& operator *= (const PolynomialType& p) { |
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typename Polynomial<ElemType>::const_iterator i; |
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typename Polynomial<ElemType>::const_iterator j; |
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|
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for (i = this->begin(); i !=this->end(); ++i) { |
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for (j = p.begin(); j !=p.end(); ++j) { |
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this->addCoefficient( i->first + j->first, i->second * j->second); |
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} |
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} |
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return *this; |
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} |
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private: |
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private: |
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PolynomialPairMap polyPairMap_; |
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}; |
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PolynomialPairMap polyPairMap_; |
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}; |
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/** |
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* Generates and returns the product of two given Polynomials. |
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* @return A Polynomial containing the product of the two given Polynomial parameters |
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*/ |
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template<typename ElemType> |
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Polynomial<ElemType> operator *(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) { |
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/** |
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* Generates and returns the product of two given Polynomials. |
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* @return A Polynomial containing the product of the two given Polynomial parameters |
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*/ |
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template<typename ElemType> |
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Polynomial<ElemType> operator *(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) { |
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typename Polynomial<ElemType>::const_iterator i; |
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typename Polynomial<ElemType>::const_iterator j; |
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Polynomial<ElemType> p; |
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for (i = p1.begin(); i !=p1.end(); ++i) { |
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for (j = p2.begin(); j !=p2.end(); ++j) { |
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p.addCoefficient( i->first + j->first, i->second * j->second); |
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} |
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for (j = p2.begin(); j !=p2.end(); ++j) { |
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p.addCoefficient( i->first + j->first, i->second * j->second); |
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} |
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} |
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return p; |
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} |
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} |
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/** |
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* Generates and returns the sum of two given Polynomials. |
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* @param p1 the first polynomial |
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* @param p2 the second polynomial |
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*/ |
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template<typename ElemType> |
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Polynomial<ElemType> operator +(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) { |
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template<typename ElemType> |
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Polynomial<ElemType> operator *(const Polynomial<ElemType>& p, const ElemType v) { |
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typename Polynomial<ElemType>::const_iterator i; |
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Polynomial<ElemType> result; |
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|
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for (i = p.begin(); i !=p.end(); ++i) { |
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result.addCoefficient( i->first , i->second * v); |
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} |
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return result; |
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} |
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|
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template<typename ElemType> |
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Polynomial<ElemType> operator *( const ElemType v, const Polynomial<ElemType>& p) { |
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typename Polynomial<ElemType>::const_iterator i; |
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Polynomial<ElemType> result; |
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|
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for (i = p.begin(); i !=p.end(); ++i) { |
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result.addCoefficient( i->first , i->second * v); |
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} |
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return result; |
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} |
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|
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/** |
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* Generates and returns the sum of two given Polynomials. |
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* @param p1 the first polynomial |
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* @param p2 the second polynomial |
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*/ |
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template<typename ElemType> |
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Polynomial<ElemType> operator +(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) { |
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Polynomial<ElemType> p(p1); |
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typename Polynomial<ElemType>::const_iterator i; |
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for (i = p2.begin(); i != p2.end(); ++i) { |
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p.addCoefficient(i->first, i->second); |
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p.addCoefficient(i->first, i->second); |
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} |
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return p; |
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|
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} |
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} |
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|
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/** |
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* Generates and returns the difference of two given Polynomials. |
293 |
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* @return |
294 |
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* @param p1 the first polynomial |
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* @param p2 the second polynomial |
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*/ |
297 |
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template<typename ElemType> |
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Polynomial<ElemType> operator -(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) { |
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/** |
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* Generates and returns the difference of two given Polynomials. |
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* @return |
294 |
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* @param p1 the first polynomial |
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* @param p2 the second polynomial |
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*/ |
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template<typename ElemType> |
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Polynomial<ElemType> operator -(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) { |
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Polynomial<ElemType> p(p1); |
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typename Polynomial<ElemType>::const_iterator i; |
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for (i = p2.begin(); i != p2.end(); ++i) { |
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p.addCoefficient(i->first, -i->second); |
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p.addCoefficient(i->first, -i->second); |
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} |
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return p; |
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|
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} |
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} |
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|
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/** |
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* Tests if two polynomial have the same exponents |
313 |
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* @return true if these all of the exponents in these Polynomial are identical |
314 |
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* @param p1 the first polynomial |
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* @param p2 the second polynomial |
316 |
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* @note this function does not compare the coefficient |
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*/ |
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template<typename ElemType> |
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bool equal(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) { |
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/** |
312 |
> |
* Tests if two polynomial have the same exponents |
313 |
> |
* @return true if these all of the exponents in these Polynomial are identical |
314 |
> |
* @param p1 the first polynomial |
315 |
> |
* @param p2 the second polynomial |
316 |
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* @note this function does not compare the coefficient |
317 |
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*/ |
318 |
> |
template<typename ElemType> |
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> |
bool equal(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) { |
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typename Polynomial<ElemType>::const_iterator i; |
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typename Polynomial<ElemType>::const_iterator j; |
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|
324 |
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if (p1.size() != p2.size() ) { |
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< |
return false; |
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return false; |
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} |
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for (i = p1.begin(), j = p2.begin(); i != p1.end() && j != p2.end(); ++i, ++j) { |
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< |
if (i->first != j->first) { |
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return false; |
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} |
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> |
if (i->first != j->first) { |
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return false; |
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} |
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} |
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return true; |
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} |
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> |
} |
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|
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typedef Polynomial<double> DoublePolynomial; |
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> |
typedef Polynomial<double> DoublePolynomial; |
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|
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} //end namespace oopse |
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#endif //MATH_POLYNOMIAL_HPP |