ceph/src/boost/libs/math/doc/internals/polynomial.qbk

   1 [section:polynomials Polynomials]
   2
   3 [h4 Synopsis]
   4
   5 ``
   6 #include <boost/math/tools/polynomial.hpp>
   7 ``
   8
   9    namespace boost { namespace math {
  10    namespace tools {
  11
  12    template <class T>
  13    class polynomial
  14    {
  15    public:
  16       // typedefs:
  17       typedef typename std::vector<T>::value_type value_type;
  18       typedef typename std::vector<T>::size_type  size_type;
  19
  20       // construct:
  21       polynomial(){}
  22       template <class U>
  23       polynomial(const U* data, unsigned order);
  24       template <class I>
  25       polynomial(I first, I last);
  26       template <class U>
  27       explicit polynomial(const U& point);
  28       polynomial(std::initializer_list<T> l); // C++11
  29
  30       // access:
  31       size_type size()const;
  32       size_type degree()const;
  33       value_type& operator[](size_type i);
  34       const value_type& operator[](size_type i)const;
  35       std::vector<T> const& data() const;
  36       std::vector<T>& data();
  37       explicit operator bool() const;
  38
  39       // modify:
  40       void set_zero();
  41
  42       // operators:
  43       template <class U>
  44       polynomial& operator +=(const U& value);
  45       template <class U>
  46       polynomial& operator -=(const U& value);
  47       template <class U>
  48       polynomial& operator *=(const U& value);
  49       template <class U>
  50       polynomial& operator /=(const U& value);
  51       template <class U>
  52       polynomial& operator %=(const U& value);
  53       template <class U>
  54       polynomial& operator +=(const polynomial<U>& value);
  55       template <class U>
  56       polynomial& operator -=(const polynomial<U>& value);
  57       template <class U>
  58       polynomial& operator *=(const polynomial<U>& value);
  59       template <class U>
  60       polynomial& operator /=(const polynomial<U>& value);
  61       template <class U>
  62       polynomial& operator %=(const polynomial<U>& value);
  63    };
  64
  65    template <class T>
  66    polynomial<T> operator + (const polynomial<T>& a, const polynomial<T>& b);
  67    template <class T>
  68    polynomial<T> operator - (const polynomial<T>& a, const polynomial<T>& b);
  69    template <class T>
  70    polynomial<T> operator * (const polynomial<T>& a, const polynomial<T>& b);
  71    template <class T>
  72    polynomial<T> operator / (const polynomial<T>& a, const polynomial<T>& b);
  73    template <class T>
  74    polynomial<T> operator % (const polynomial<T>& a, const polynomial<T>& b);
  75
  76    template <class T, class U>
  77    polynomial<T> operator + (const polynomial<T>& a, const U& b);
  78    template <class T, class U>
  79    polynomial<T> operator - (const polynomial<T>& a, const U& b);
  80    template <class T, class U>
  81    polynomial<T> operator * (const polynomial<T>& a, const U& b);
  82    template <class T, class U>
  83    polynomial<T> operator / (const polynomial<T>& a, const U& b);
  84    template <class T, class U>
  85    polynomial<T> operator % (const polynomial<T>& a, const U& b);
  86
  87    template <class U, class T>
  88    polynomial<T> operator + (const U& a, const polynomial<T>& b);
  89    template <class U, class T>
  90    polynomial<T> operator - (const U& a, const polynomial<T>& b);
  91    template <class U, class T>
  92    polynomial<T> operator * (const U& a, const polynomial<T>& b);
  93
  94    template <class T>
  95    polynomial<T> operator - (const polynomial<T>& a);
  96
  97    template <class T>
  98    polynomial<T> operator >>= (const U& a);
  99    template <class T>
 100    polynomial<T> operator >> (polynomial<T> const &a, const U& b);
 101    template <class T>
 102    polynomial<T> operator <<= (const U& a);
 103    template <class T>
 104    polynomial<T> operator << (polynomial<T> const &a, const U& b);
 105
 106    template <class T>
 107    bool operator == (const polynomial<T> &a, const polynomial<T> &b);
 108    template <class T>
 109    bool operator != (const polynomial<T> &a, const polynomial<T> &b);
 110
 111    template <class T>
 112    polynomial<T> pow(polynomial<T> base, int exp);
 113
 114    template <class charT, class traits, class T>
 115    std::basic_ostream<charT, traits>& operator <<
 116       (std::basic_ostream<charT, traits>& os, const polynomial<T>& poly);
 117
 118    template <typename T>
 119    std::pair< polynomial<T>, polynomial<T> >
 120    quotient_remainder(const polynomial<T>& a, const polynomial<T>& b);
 121
 122    } //    namespace tools
 123    }} //    namespace boost { namespace math
 124
 125 [h4 Description]
 126
 127 This is a somewhat trivial class for polynomial manipulation.
 128
 129 See
 130
 131 * [@https://en.wikipedia.org/wiki/Polynomial Polynomial] and
 132 * Donald E. Knuth, The Art of Computer Programming: Volume 2, Third edition, (1998)
 133 Chapter 4.6.1, Algorithm D: Division of polynomials over a field.
 134
 135 Implementation is currently of the "naive" variety, with [bigo](N[super 2])
 136 multiplication, for example.  This class should not be used in
 137 high-performance computing environments: it is intended for the
 138 simple manipulation of small polynomials, typically generated
 139 for special function approximation.
 140
 141 It does has division for polynomials over a [@https://en.wikipedia.org/wiki/Field_%28mathematics%29 field]
 142 (here floating point, complex, etc)
 143 and over a unique factorization domain (integers).
 144 Division of polynomials over a field is compatible with
 145 [@https://en.wikipedia.org/wiki/Euclidean_algorithm Euclidean GCD].
 146
 147 Advanced manipulations: the FFT, factorisation etc are
 148 not currently provided.  Submissions for these are of course welcome :-)
 149
 150 [h4:polynomial_examples  Polynomial Arithmetic Examples]
 151
 152 [import ../../example/polynomial_arithmetic.cpp]
 153
 154 [polynomial_arithmetic_0]
 155 [polynomial_arithmetic_1]
 156
 157 [polynomial_arithmetic_2]
 158 for output:
 159 [polynomial_output_1]
 160
 161 [polynomial_arithmetic_3]
 162 for output
 163 [polynomial_output_2]
 164
 165 [h5 Division, Quotient and Remainder]
 166 [polynomial_arithmetic_4]
 167
 168 The source code is at [@../../example/polynomial_arithmetic.cpp polynomial_arithmetic.cpp]
 169
 170 [endsect] [/section:polynomials Polynomials]
 171
 172 [/
 173   Copyright 2006 John Maddock and Paul A. Bristow.
 174   Copyright 2015 Jeremy William Murphy.
 175
 176   Distributed under the Boost Software License, Version 1.0.
 177   (See accompanying file LICENSE_1_0.txt or copy at
 178   http://www.boost.org/LICENSE_1_0.txt).
 179 ]