1 | /* -*- C++ -*- |
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2 | * |
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3 | * This file is a part of LEMON, a generic C++ optimization library |
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4 | * |
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5 | * Copyright (C) 2003-2007 |
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6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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8 | * |
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9 | * Permission to use, modify and distribute this software is granted |
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10 | * provided that this copyright notice appears in all copies. For |
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11 | * precise terms see the accompanying LICENSE file. |
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12 | * |
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13 | * This software is provided "AS IS" with no warranty of any kind, |
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14 | * express or implied, and with no claim as to its suitability for any |
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15 | * purpose. |
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16 | * |
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17 | */ |
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18 | |
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19 | #ifndef LEMON_BEZIER_H |
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20 | #define LEMON_BEZIER_H |
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21 | |
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22 | ///\ingroup misc |
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23 | ///\file |
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24 | ///\brief A simple class implementing polynomials. |
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25 | /// |
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26 | ///\author Alpar Juttner |
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27 | |
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28 | #include<vector> |
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29 | |
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30 | namespace lemon { |
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31 | |
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32 | /// \addtogroup misc |
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33 | /// @{ |
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34 | |
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35 | ///Simple polinomial class |
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36 | |
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37 | ///This class implements a polynomial where the coefficients are of |
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38 | ///type \c T. |
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39 | /// |
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40 | ///The coefficients are stored in an std::vector. |
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41 | template<class T> |
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42 | class Polynomial |
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43 | { |
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44 | std::vector<T> _coeff; |
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45 | public: |
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46 | ///Construct a polynomial of degree \c d. |
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47 | explicit Polynomial(int d=0) : _coeff(d+1) {} |
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48 | ///\e |
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49 | template<class U> Polynomial(const U &u) : _coeff(1,u) {} |
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50 | ///\e |
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51 | template<class U> Polynomial(const Polynomial<U> &u) : _coeff(u.deg()+1) |
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52 | { |
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53 | for(int i=0;i<int(_coeff.size());i++) _coeff[i]=u[i]; |
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54 | } |
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55 | ///Query the degree of the polynomial. |
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56 | |
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57 | ///Query the degree of the polynomial. |
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58 | ///\warning This number differs from real degree of the polinomial if |
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59 | ///the coefficient of highest degree is 0. |
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60 | int deg() const { return _coeff.size()-1; } |
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61 | ///Set the degree of the polynomial. |
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62 | |
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63 | ///Set the degree of the polynomial. In fact it resizes the |
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64 | ///coefficient vector. |
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65 | void deg(int d) { _coeff.resize(d+1);} |
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66 | |
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67 | ///Returns (as a reference) the coefficient of degree \c d. |
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68 | typename std::vector<T>::reference operator[](int d) { return _coeff[d]; } |
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69 | ///Returns (as a const reference) the coefficient of degree \c d. |
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70 | typename std::vector<T>::const_reference |
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71 | operator[](int d) const {return _coeff[d];} |
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72 | |
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73 | ///Substitute the value u into the polinomial. |
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74 | |
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75 | ///Substitute the value u into the polinomial. |
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76 | ///The calculation will be done using type \c R. |
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77 | ///The following examples shows the usage of the template parameter \c R. |
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78 | ///\code |
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79 | /// Polynomial<dim2::Point<double> > line(1); |
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80 | /// line[0]=dim2::Point<double>(12,25); |
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81 | /// line[1]=dim2::Point<double>(2,7); |
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82 | /// ... |
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83 | /// dim2::Point<double> d = line.subst<dim2::Point<double> >(23.2); |
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84 | ///\endcode |
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85 | /// |
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86 | ///\code |
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87 | /// Polynomial<double> p; |
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88 | /// Polynomial<double> q; |
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89 | /// ... |
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90 | /// Polynomial<double> s = p.subst<Polynomial<double> >(q); |
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91 | ///\endcode |
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92 | template<class R,class U> |
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93 | R subst(const U &u) const |
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94 | { |
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95 | typename std::vector<T>::const_reverse_iterator i=_coeff.rbegin(); |
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96 | R v=*i; |
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97 | for(++i;i!=_coeff.rend();++i) v=v*u+*i; |
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98 | return v; |
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99 | } |
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100 | ///Substitute the value u into the polinomial. |
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101 | |
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102 | ///Substitute the value u into the polinomial. |
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103 | ///The calculation will be done using type \c T |
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104 | ///(i.e. using the type of the coefficients.) |
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105 | template<class U> |
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106 | T operator()(const U &u) const |
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107 | { |
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108 | return subst<T>(u); |
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109 | } |
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110 | |
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111 | ///Derivate the polynomial (in place) |
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112 | Polynomial &derivateMyself() |
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113 | { |
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114 | for(int i=1;i<int(_coeff.size());i++) _coeff[i-1]=i*_coeff[i]; |
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115 | _coeff.pop_back(); |
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116 | return *this; |
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117 | } |
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118 | |
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119 | ///Return the derivate of the polynomial |
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120 | Polynomial derivate() const |
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121 | { |
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122 | Polynomial tmp(deg()-1); |
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123 | for(int i=1;i<int(_coeff.size());i++) tmp[i-1]=i*_coeff[i]; |
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124 | return tmp; |
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125 | } |
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126 | |
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127 | ///Integrate the polynomial (in place) |
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128 | Polynomial &integrateMyself() |
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129 | { |
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130 | _coeff.push_back(T()); |
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131 | for(int i=_coeff.size()-1;i>0;i--) _coeff[i]=_coeff[i-1]/i; |
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132 | _coeff[0]=0; |
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133 | return *this; |
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134 | } |
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135 | |
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136 | ///Return the integrate of the polynomial |
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137 | Polynomial integrate() const |
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138 | { |
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139 | Polynomial tmp(deg()+1); |
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140 | tmp[0]=0; |
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141 | for(int i=0;i<int(_coeff.size());i++) tmp[i+1]=_coeff[i]/(i+1); |
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142 | return tmp; |
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143 | } |
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144 | |
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145 | ///\e |
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146 | template<class U> |
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147 | Polynomial &operator+=(const Polynomial<U> &p) |
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148 | { |
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149 | if(p.deg()>deg()) _coeff.resize(p.deg()+1); |
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150 | for(int i=0;i<=int(std::min(deg(),p.deg()));i++) |
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151 | _coeff[i]+=p[i]; |
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152 | return *this; |
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153 | } |
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154 | ///\e |
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155 | template<class U> |
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156 | Polynomial &operator-=(const Polynomial<U> &p) |
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157 | { |
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158 | if(p.deg()>deg()) _coeff.resize(p.deg()+1); |
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159 | for(int i=0;i<=std::min(deg(),p.deg());i++) _coeff[i]-=p[i]; |
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160 | return *this; |
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161 | } |
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162 | ///\e |
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163 | template<class U> |
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164 | Polynomial &operator+=(const U &u) |
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165 | { |
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166 | _coeff[0]+=u; |
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167 | return *this; |
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168 | } |
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169 | ///\e |
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170 | template<class U> |
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171 | Polynomial &operator-=(const U &u) |
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172 | { |
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173 | _coeff[0]+=u; |
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174 | return *this; |
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175 | } |
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176 | ///\e |
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177 | template<class U> |
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178 | Polynomial &operator*=(const U &u) |
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179 | { |
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180 | for(typename std::vector<T>::iterator i=_coeff.begin();i!=_coeff.end();++i) |
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181 | *i*=u; |
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182 | return *this; |
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183 | } |
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184 | ///\e |
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185 | template<class U> |
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186 | Polynomial &operator/=(const U &u) |
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187 | { |
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188 | for(typename std::vector<T>::iterator i=_coeff.begin();i!=_coeff.end();++i) |
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189 | *i/=u; |
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190 | return *this; |
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191 | } |
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192 | |
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193 | }; |
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194 | |
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195 | ///Equality comparison |
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196 | |
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197 | ///\relates Polynomial |
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198 | ///\warning Two polynomials are defined to be unequal if their degrees differ, |
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199 | ///even if the non-zero coefficients are the same. |
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200 | template<class U,class V> |
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201 | bool operator==(const Polynomial<U> &u,const Polynomial<V> &v) |
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202 | { |
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203 | if(u.deg()!=v.deg()) return false; |
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204 | for(int i=0;i<=u.deg();i++) if(u[i]!=v[i]) return false; |
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205 | return true; |
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206 | } |
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207 | |
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208 | ///Non-equality comparison |
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209 | |
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210 | ///\relates Polynomial |
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211 | ///\warning Two polynomials are defined to be unequal if their degrees differ, |
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212 | ///even if the non-zero coefficients are the same. |
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213 | template<class U,class V> |
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214 | bool operator!=(const Polynomial<U> &u,const Polynomial<V> &v) |
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215 | { |
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216 | return !(u==v); |
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217 | } |
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218 | |
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219 | ///\e |
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220 | |
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221 | ///\relates Polynomial |
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222 | /// |
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223 | template<class U,class V> |
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224 | Polynomial<U> operator+(const Polynomial<U> &u,const Polynomial<V> &v) |
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225 | { |
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226 | Polynomial<U> tmp=u; |
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227 | tmp+=v; |
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228 | return tmp; |
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229 | } |
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230 | |
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231 | ///\e |
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232 | |
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233 | ///\relates Polynomial |
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234 | /// |
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235 | template<class U,class V> |
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236 | Polynomial<U> operator-(const Polynomial<U> &u,const Polynomial<V> &v) |
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237 | { |
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238 | Polynomial<U> tmp=u; |
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239 | tmp-=v; |
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240 | return tmp; |
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241 | } |
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242 | |
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243 | ///\e |
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244 | |
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245 | ///\relates Polynomial |
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246 | /// |
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247 | template<class U,class V> |
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248 | Polynomial<U> operator*(const Polynomial<U> &u,const Polynomial<V> &v) |
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249 | { |
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250 | Polynomial<U> tmp(u.deg()+v.deg()); |
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251 | for(int i=0;i<=v.deg();i++) |
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252 | for(int j=0;j<=u.deg();j++) |
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253 | tmp[i+j]+=v[i]*u[j]; |
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254 | return tmp; |
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255 | } |
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256 | ///\e |
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257 | |
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258 | ///\relates Polynomial |
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259 | /// |
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260 | template<class U,class V> |
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261 | Polynomial<U> operator+(const Polynomial<U> &u,const V &v) |
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262 | { |
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263 | Polynomial<U> tmp=u; |
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264 | tmp+=v; |
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265 | return tmp; |
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266 | } |
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267 | ///\e |
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268 | |
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269 | ///\relates Polynomial |
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270 | /// |
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271 | template<class U,class V> |
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272 | Polynomial<U> operator+(const V &v,const Polynomial<U> &u) |
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273 | { |
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274 | Polynomial<U> tmp=u; |
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275 | tmp+=v; |
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276 | return tmp; |
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277 | } |
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278 | ///\e |
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279 | |
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280 | ///\relates Polynomial |
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281 | /// |
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282 | template<class U,class V> |
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283 | Polynomial<U> operator-(const Polynomial<U> &u,const V &v) |
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284 | { |
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285 | Polynomial<U> tmp=u; |
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286 | tmp-=v; |
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287 | return tmp; |
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288 | } |
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289 | ///\e |
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290 | |
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291 | ///\relates Polynomial |
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292 | /// |
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293 | template<class U> |
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294 | Polynomial<U> operator-(const Polynomial<U> &u) |
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295 | { |
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296 | Polynomial<U> tmp(u.deg()); |
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297 | for(int i=0;i<=u.deg();i++) tmp[i]=-u[i]; |
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298 | return tmp; |
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299 | } |
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300 | ///\e |
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301 | |
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302 | ///\relates Polynomial |
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303 | /// |
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304 | template<class U,class V> |
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305 | Polynomial<U> operator-(const V &v,const Polynomial<U> &u) |
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306 | { |
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307 | Polynomial<U> tmp=-u; |
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308 | tmp+=v; |
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309 | return tmp; |
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310 | } |
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311 | ///\e |
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312 | |
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313 | ///\relates Polynomial |
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314 | /// |
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315 | template<class U,class V> |
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316 | Polynomial<U> operator*(const Polynomial<U> &u,const V &v) |
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317 | { |
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318 | Polynomial<U> tmp=u; |
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319 | tmp*=v; |
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320 | return tmp; |
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321 | } |
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322 | ///\e |
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323 | |
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324 | ///\relates Polynomial |
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325 | /// |
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326 | template<class U,class V> |
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327 | Polynomial<U> operator*(const V &v,const Polynomial<U> &u) |
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328 | { |
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329 | Polynomial<U> tmp=u; |
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330 | tmp*=v; |
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331 | return tmp; |
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332 | } |
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333 | ///\e |
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334 | |
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335 | ///\relates Polynomial |
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336 | /// |
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337 | template<class U,class V> |
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338 | Polynomial<U> operator/(const Polynomial<U> &u,const V &v) |
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339 | { |
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340 | Polynomial<U> tmp=u; |
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341 | tmp/=v; |
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342 | return tmp; |
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343 | } |
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344 | |
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345 | /// @} |
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346 | |
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347 | } //END OF NAMESPACE LEMON |
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348 | |
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349 | #endif // LEMON_POLYNOMIAL_H |
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