[7576857] | 1 | /* |
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| 2 | Copyright (C) 2015 |
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| 3 | Alejandro Mujica (amujica en cenditel.gob.ve) |
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| 4 | José Angel Contreras (jancontreras en cenditel.gob.ve) |
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| 5 | Antonio Araujo (aaraujo en cenditel.gob.ve) |
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| 6 | Pedro Buitrago (pbuitrago en cenditel.gob.ve) |
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| 7 | |
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| 8 | CENDITEL Fundación Centro Nacional de Desarrollo e Investigación en |
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| 9 | Tecnologías Libres |
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| 10 | |
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| 11 | Este programa es software libre; Usted puede usarlo bajo los términos de la |
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| 12 | licencia de software GPL versión 2.0 de la Free Software Foundation. |
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| 13 | |
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| 14 | Este programa se distribuye con la esperanza de que sea útil, pero SIN |
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| 15 | NINGUNA GARANTÍA; tampoco las implícitas garantías de MERCANTILIDAD o |
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| 16 | ADECUACIÓN A UN PROPÓSITO PARTICULAR. |
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| 17 | Consulte la licencia GPL para más detalles. Usted debe recibir una copia |
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| 18 | de la GPL junto con este programa; si no, escriba a la Free Software |
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| 19 | Foundation Inc. 51 Franklin Street,5 Piso, Boston, MA 02110-1301, USA. |
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| 20 | */ |
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| 21 | |
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| 22 | /* |
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| 23 | Este archivo contiene la definición e implementación de una plantilla de clase |
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| 24 | para representar polinomios. |
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| 25 | |
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| 26 | Creado por: Alejandro J. Mujica |
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| 27 | Fecha de creación: |
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| 28 | */ |
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| 29 | |
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| 30 | |
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| 31 | # ifndef POLYNOMIAL_H |
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| 32 | # define POLYNOMIAL_H |
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| 33 | |
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| 34 | # include <stdexcept> |
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| 35 | # include <sstream> |
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| 36 | # include <vector> |
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| 37 | # include <limits> |
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| 38 | |
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| 39 | # include<iostream> |
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| 40 | |
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| 41 | /** |
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| 42 | * Plantilla para representar polinomios de una variable. |
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| 43 | * |
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| 44 | * @tparam NumberT Tipo de dato para los coeficientes. |
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| 45 | * |
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| 46 | * @author Alejandro Mujica (amujica en cenditel punto gob punto ve). |
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| 47 | * @author José Angel Contreras (jancontreras en cenditel punto gob punto ve). |
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| 48 | */ |
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| 49 | template <typename NumberT = double> |
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| 50 | class Polynomial |
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| 51 | { |
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| 52 | public: |
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| 53 | /// Tipo de conjunto para el polinomio. |
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| 54 | using PolynomialType = std::vector<NumberT>; |
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| 55 | /// Tipo de número para el grado. |
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| 56 | using DegreeType = typename PolynomialType::size_type; |
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| 57 | /// Tipo de número para los coeficientes. |
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| 58 | using NumberType = typename PolynomialType::value_type; |
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| 59 | |
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| 60 | private: |
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| 61 | DegreeType deg; |
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| 62 | PolynomialType pol; |
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| 63 | |
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| 64 | public: |
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| 65 | /// Construcción de un polinomio dado un grado. |
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| 66 | Polynomial(const DegreeType & _deg = DegreeType(0)); |
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| 67 | |
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| 68 | /// Construcción por medio de una lista de inicialización. |
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| 69 | Polynomial(const std::initializer_list<NumberType> &); |
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| 70 | |
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| 71 | /// Constructor copia |
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| 72 | Polynomial(const Polynomial &); |
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| 73 | |
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| 74 | /// Constructor de movimiento (move semantic) |
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| 75 | Polynomial(Polynomial &&); |
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| 76 | |
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| 77 | /// Retorna el grado del polinomio. |
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| 78 | const DegreeType & degree() const |
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| 79 | { |
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| 80 | return deg; |
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| 81 | } |
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| 82 | |
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| 83 | /** |
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| 84 | * Retorna el coeficiente de la posición dada. |
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| 85 | * |
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| 86 | * @param exp Grado del coeficiente deseado. |
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| 87 | * @return Coeficiente de la posición dada. |
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| 88 | * @throw overflow_error si el exponente es mayor que el grado del polinomio. |
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| 89 | */ |
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| 90 | const NumberType & get_coefficient(const DegreeType & exp) const |
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| 91 | { |
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| 92 | if (exp > deg) |
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| 93 | throw std::overflow_error("exp is greater than polynomial degree"); |
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| 94 | |
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| 95 | return pol.at(deg - exp); |
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| 96 | } |
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| 97 | |
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| 98 | /** |
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| 99 | * Asigna valor al coeficiente de la posición dada. |
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| 100 | * |
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| 101 | * @param exp Grado del coeficiente deseado. |
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| 102 | * @param value Valor que se asignará al coeficiente. |
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| 103 | * @throw overflow_error si el exponente es mayor que el grado del polinomio. |
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| 104 | */ |
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| 105 | void set_coefficient(const DegreeType & exp, const NumberType & value) |
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| 106 | { |
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| 107 | if (exp > deg) |
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| 108 | throw std::overflow_error("exp is greater than polynomial degree"); |
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| 109 | |
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| 110 | pol.at(deg - exp) = value; |
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| 111 | } |
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| 112 | |
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| 113 | /// Determina si el polinomio es nulo. |
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| 114 | bool is_null() const; |
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| 115 | |
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| 116 | bool operator ! () const; |
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| 117 | |
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| 118 | Polynomial operator + (const Polynomial &); |
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| 119 | |
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| 120 | Polynomial & operator += (const Polynomial &); |
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| 121 | |
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| 122 | Polynomial operator - (const Polynomial &); |
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| 123 | |
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| 124 | Polynomial & operator -= (const Polynomial &); |
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| 125 | |
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| 126 | Polynomial operator * (const Polynomial &); |
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| 127 | |
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| 128 | Polynomial operator / (const Polynomial &); |
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| 129 | |
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| 130 | Polynomial operator % (const Polynomial &); |
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| 131 | |
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| 132 | Polynomial & operator = (const Polynomial &); |
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| 133 | |
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| 134 | Polynomial & operator = (Polynomial &&); |
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| 135 | |
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| 136 | bool operator == (const Polynomial &) const; |
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| 137 | |
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| 138 | bool operator != (const Polynomial &) const; |
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| 139 | |
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| 140 | /// Retorna una representación del polinomio en cadena. |
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| 141 | std::string to_string(const char & var = 'x'); |
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| 142 | }; |
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| 143 | |
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| 144 | /** |
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| 145 | * Constructor que funge de paramétrico y por omisión al mismo tiempo. |
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| 146 | * |
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| 147 | * @param _deg Grado del polinomio. Por omisión es 0. |
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| 148 | */ |
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| 149 | template <typename NumberT> |
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| 150 | Polynomial<NumberT>::Polynomial(const Polynomial::DegreeType & _deg) |
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| 151 | : deg(_deg), pol(deg + DegreeType(1), NumberType(0)) |
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| 152 | { |
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| 153 | // Empty |
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| 154 | } |
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| 155 | |
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| 156 | /** |
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| 157 | * Construye un polinomio dada una lista de inicialización. |
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| 158 | * |
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| 159 | * Para inicializar el polinomio se deben pasar los valores de los coeficientes |
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| 160 | * entre llaves y separados por coma (,). Debe escribirse el polinomio |
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| 161 | * completo. |
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| 162 | * |
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| 163 | * Por ejemplo, si se quiere construir el polinomio |
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| 164 | * @f$p(x) = x^5 + 2x^4 + 3x^3 + 4x^2 + 5x + 6;@f$ |
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| 165 | * la instanciación debe realizarse de la siguiente manera: |
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| 166 | * @code{.cpp}Polynomial<> p = { 1, 2, 3, 4, 5, 6 };@endcode |
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| 167 | * |
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| 168 | * @param l Lista de inicialización del polinomio. |
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| 169 | */ |
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| 170 | template <typename NumberT> |
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| 171 | Polynomial<NumberT>::Polynomial(const std::initializer_list<NumberType> & l) |
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| 172 | : deg(DegreeType(l.size()) - DegreeType(1)), pol(l) |
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| 173 | { |
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| 174 | // Empty |
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| 175 | } |
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| 176 | |
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| 177 | template <typename NumberT> |
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| 178 | Polynomial<NumberT>::Polynomial(const Polynomial & p) |
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| 179 | : deg(p.deg), pol(p.pol) |
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| 180 | { |
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| 181 | // Empty |
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| 182 | } |
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| 183 | |
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| 184 | template <typename NumberT> |
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| 185 | Polynomial<NumberT>::Polynomial(Polynomial && p) |
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| 186 | : deg(DegreeType(0)), pol(deg + DegreeType(1), NumberType(0)) |
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| 187 | { |
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| 188 | std::swap(deg, p.deg); |
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| 189 | std::swap(pol, p.pol); |
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| 190 | } |
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| 191 | |
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| 192 | |
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| 193 | /**. |
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| 194 | * Un polinomio es nulo si todos sus coeficientes son cero. |
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| 195 | * |
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| 196 | * @return <code>true</code> si el polinomio es nulo y <code>false</code> en |
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| 197 | * caso contrario. |
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| 198 | */ |
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| 199 | template <typename NumberT> |
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| 200 | bool Polynomial<NumberT>::is_null() const |
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| 201 | { |
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| 202 | for (const NumberType & c : pol) |
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| 203 | if (c != NumberType(0)) |
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| 204 | return false; |
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| 205 | return true; |
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| 206 | } |
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| 207 | |
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| 208 | template <typename NumberT> |
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| 209 | bool Polynomial<NumberT>::operator ! () const |
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| 210 | { |
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| 211 | return is_null(); |
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| 212 | } |
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| 213 | |
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| 214 | template <typename NumberT> |
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| 215 | Polynomial<NumberT> |
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| 216 | Polynomial<NumberT>::operator + (const Polynomial & p) |
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| 217 | { |
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| 218 | const DegreeType & min_degree = std::min(deg, p.deg); |
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| 219 | const DegreeType & max_degree = std::max(deg, p.deg); |
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| 220 | |
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| 221 | Polynomial ret(max_degree); |
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| 222 | |
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| 223 | for (DegreeType i = DegreeType(0); i <= min_degree; ++i) |
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| 224 | ret.set_coefficient(i, get_coefficient(i) + p.get_coefficient(i)); |
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| 225 | |
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| 226 | const Polynomial & max_degree_pol = deg > p.deg ? *this : p; |
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| 227 | |
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| 228 | for (DegreeType i = min_degree + DegreeType(1); i <= max_degree; ++i) |
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| 229 | ret.set_coefficient(i, max_degree_pol.get_coefficient(i)); |
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| 230 | |
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| 231 | return ret; |
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| 232 | } |
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| 233 | |
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| 234 | template <typename NumberT> |
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| 235 | Polynomial<NumberT> & |
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| 236 | Polynomial<NumberT>::operator += (const Polynomial & p) |
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| 237 | { |
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| 238 | *this = *this + p; |
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| 239 | return *this; |
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| 240 | } |
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| 241 | |
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| 242 | template <typename NumberT> |
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| 243 | Polynomial<NumberT> |
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| 244 | Polynomial<NumberT>::operator - (const Polynomial & p) |
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| 245 | { |
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| 246 | const DegreeType & min_degree = std::min(deg, p.deg); |
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| 247 | const DegreeType & max_degree = std::max(deg, p.deg); |
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| 248 | |
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| 249 | Polynomial ret(max_degree); |
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| 250 | |
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| 251 | for (DegreeType i = DegreeType(0); i <= min_degree; ++i) |
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| 252 | ret.set_coefficient(i, get_coefficient(i) - p.get_coefficient(i)); |
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| 253 | |
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| 254 | Polynomial & max_degree_pol = deg > p.deg ? *this : p; |
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| 255 | |
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| 256 | char sign = &max_degree_pol == this ? 1 : -1; |
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| 257 | |
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| 258 | for (DegreeType i = min_degree + DegreeType(1); i <= max_degree; ++i) |
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| 259 | ret.set_coefficient(i, sign * max_degree_pol.get_coefficient(i)); |
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| 260 | |
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| 261 | return ret; |
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| 262 | } |
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| 263 | |
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| 264 | template <typename NumberT> |
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| 265 | Polynomial<NumberT> & |
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| 266 | Polynomial<NumberT>::operator -= (const Polynomial & p) |
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| 267 | { |
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| 268 | *this = *this - p; |
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| 269 | return *this; |
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| 270 | } |
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| 271 | |
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| 272 | template <typename NumberT> |
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| 273 | Polynomial<NumberT> |
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| 274 | Polynomial<NumberT>::operator * (const Polynomial & p) |
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| 275 | { |
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| 276 | Polynomial ret(deg + p.deg); |
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| 277 | |
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| 278 | for (DegreeType i = DegreeType(0); i <= deg; ++i) |
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| 279 | for (DegreeType j = DegreeType(0); j < p.deg; ++j) |
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| 280 | ret.set_coefficient(i + j, |
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| 281 | ret.get_coefficient(i + j) + get_coefficient(i) * p.get_coefficient(j)); |
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| 282 | |
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| 283 | |
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| 284 | return ret; |
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| 285 | } |
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| 286 | |
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| 287 | template <typename NumberT> |
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| 288 | Polynomial<NumberT> |
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| 289 | Polynomial<NumberT>::operator / (const Polynomial & p) |
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| 290 | { |
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| 291 | if (p.is_null()) |
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| 292 | throw std::logic_error("Polynomial devision by 0"); |
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| 293 | |
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| 294 | if (p.deg > deg) |
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| 295 | return Polynomial(); |
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| 296 | |
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| 297 | Polynomial ret(deg - p.deg); |
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| 298 | |
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| 299 | NumberType inv = NumberType(0); |
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| 300 | |
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| 301 | if (p.deg > 0) |
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| 302 | { |
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| 303 | Polynomial tmp = *this; |
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| 304 | |
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| 305 | DegreeType last = p.deg; |
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| 306 | |
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| 307 | while (last > DegreeType(0) and p.get_coefficient(last) == NumberType(0)) |
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| 308 | --last; |
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| 309 | |
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| 310 | inv = NumberType(1) / p.get_coefficient(last); |
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| 311 | |
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| 312 | for (DegreeType i = tmp.deg; i >= p.deg; --i) |
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| 313 | { |
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| 314 | ret.set_coefficient(i - p.deg, tmp.get_coefficient(i) * inv); |
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| 315 | |
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| 316 | for (DegreeType j = DegreeType(0); j <= p.deg; ++j) |
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| 317 | tmp.set_coefficient(i - j, |
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| 318 | tmp.get_coefficient(i - j) - p.get_coefficient(p.deg - j) * |
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| 319 | ret.get_coefficient(i - p.deg)); |
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| 320 | } |
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| 321 | |
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| 322 | return ret; |
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| 323 | } |
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| 324 | |
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| 325 | DegreeType first = DegreeType(0); |
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| 326 | |
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| 327 | while (first <= p.deg and p.get_coefficient(first) == NumberType(0)) |
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| 328 | ++first; |
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| 329 | |
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| 330 | inv = NumberType(1) / p.get_coefficient(first); |
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| 331 | |
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| 332 | for (NumberType & c : ret.pol) |
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| 333 | c *= inv; |
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| 334 | |
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| 335 | return ret; |
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| 336 | } |
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| 337 | |
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| 338 | template <typename NumberT> |
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| 339 | Polynomial<NumberT> |
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| 340 | Polynomial<NumberT>::operator % (const Polynomial & p) |
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| 341 | { |
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| 342 | if (p.is_null()) |
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| 343 | throw std::logic_error("Polynomial denominator = 0"); |
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| 344 | |
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| 345 | if (p.deg == DegreeType(0)) |
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| 346 | return Polynomial(); |
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| 347 | |
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| 348 | Polynomial ret = *this; |
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| 349 | |
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| 350 | DegreeType last = p.deg; |
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| 351 | |
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| 352 | while (last > DegreeType(0) and p.get_coefficient(last) == NumberType(0)) |
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| 353 | --last; |
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| 354 | |
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| 355 | NumberType inv = NumberType(1) / p.get_coefficient(last); |
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| 356 | |
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| 357 | for (DegreeType i = ret.deg; i >= p.deg; --i) |
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| 358 | { |
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| 359 | NumberType q = ret.get_coefficient(i) * inv; |
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| 360 | |
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| 361 | for (DegreeType j = DegreeType(0); j <= p.deg; ++j) |
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| 362 | ret.set_coefficient(i - j, ret.get_coefficient(i - j) - |
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| 363 | p.get_coefficient(p.deg - j) * q); |
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| 364 | } |
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| 365 | |
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| 366 | while (ret.deg > DegreeType(0) and ret.get_coefficient(ret.deg) == NumberType(0)) |
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| 367 | --ret.deg; |
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| 368 | |
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| 369 | return ret; |
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| 370 | } |
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| 371 | |
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| 372 | template <typename NumberT> |
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| 373 | Polynomial<NumberT> & |
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| 374 | Polynomial<NumberT>::operator = (const Polynomial & p) |
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| 375 | { |
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| 376 | if (&p == this) |
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| 377 | return *this; |
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| 378 | |
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| 379 | deg = p.deg; |
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| 380 | pol = p.pol; |
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| 381 | |
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| 382 | return *this; |
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| 383 | } |
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| 384 | |
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| 385 | template <typename NumberT> |
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| 386 | Polynomial<NumberT> & |
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| 387 | Polynomial<NumberT>::operator = (Polynomial && p) |
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| 388 | { |
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| 389 | std::swap(deg, p.deg); |
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| 390 | std::swap(pol, p.pol); |
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| 391 | |
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| 392 | return *this; |
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| 393 | } |
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| 394 | |
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| 395 | template <typename NumberT> |
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| 396 | bool Polynomial<NumberT>::operator == (const Polynomial & p) const |
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| 397 | { |
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| 398 | if (deg != p.deg) |
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| 399 | return false; |
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| 400 | |
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| 401 | for (DegreeType i = DegreeType(0); i <= deg; ++i) |
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| 402 | if (pol.at(i) != p.pol.at(i)) |
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| 403 | return false; |
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| 404 | |
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| 405 | return true; |
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| 406 | } |
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| 407 | |
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| 408 | template <typename NumberT> |
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| 409 | bool Polynomial<NumberT>::operator != (const Polynomial & p) const |
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| 410 | { |
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| 411 | return not (*this == p); |
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| 412 | } |
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| 413 | |
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| 414 | template <typename NumberT> |
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| 415 | std::string Polynomial<NumberT>::to_string(const char & var) |
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| 416 | { |
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| 417 | std::stringstream sstr; |
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| 418 | |
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| 419 | if (deg > DegreeType(1)) |
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| 420 | for (DegreeType i = DegreeType(0); i < deg - DegreeType(1); ++i) |
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| 421 | sstr << pol.at(i) << var << '^' << deg - i << " + "; |
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| 422 | |
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| 423 | if (deg > DegreeType(0)) |
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| 424 | sstr << pol.at(deg - DegreeType(1)) << var << " + "; |
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| 425 | |
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| 426 | sstr << pol.at(deg); |
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| 427 | |
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| 428 | return sstr.str(); |
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| 429 | } |
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| 430 | |
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| 431 | # endif // POLYNOMIAL_H |
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| 432 | |
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