mirror of
https://github.com/saitohirga/WSJT-X.git
synced 2024-08-25 07:36:35 -04:00
180 lines
5.8 KiB
Plaintext
180 lines
5.8 KiB
Plaintext
[section:polynomials Polynomials]
|
|
|
|
[h4 Synopsis]
|
|
|
|
``
|
|
#include <boost/math/tools/polynomial.hpp>
|
|
``
|
|
|
|
namespace boost { namespace math {
|
|
namespace tools {
|
|
|
|
template <class T>
|
|
class polynomial
|
|
{
|
|
public:
|
|
// typedefs:
|
|
typedef typename std::vector<T>::value_type value_type;
|
|
typedef typename std::vector<T>::size_type size_type;
|
|
|
|
// construct:
|
|
polynomial(){}
|
|
template <class U>
|
|
polynomial(const U* data, unsigned order);
|
|
template <class I>
|
|
polynomial(I first, I last);
|
|
template <class U>
|
|
explicit polynomial(const U& point);
|
|
polynomial(std::initializer_list<T> l); // C++11
|
|
|
|
// access:
|
|
size_type size()const;
|
|
size_type degree()const;
|
|
value_type& operator[](size_type i);
|
|
const value_type& operator[](size_type i)const;
|
|
std::vector<T> const& data() const;
|
|
std::vector<T>& data();
|
|
explicit operator bool() const;
|
|
|
|
// modify:
|
|
void set_zero();
|
|
|
|
// operators:
|
|
template <class U>
|
|
polynomial& operator +=(const U& value);
|
|
template <class U>
|
|
polynomial& operator -=(const U& value);
|
|
template <class U>
|
|
polynomial& operator *=(const U& value);
|
|
template <class U>
|
|
polynomial& operator /=(const U& value);
|
|
template <class U>
|
|
polynomial& operator %=(const U& value);
|
|
template <class U>
|
|
polynomial& operator +=(const polynomial<U>& value);
|
|
template <class U>
|
|
polynomial& operator -=(const polynomial<U>& value);
|
|
template <class U>
|
|
polynomial& operator *=(const polynomial<U>& value);
|
|
template <class U>
|
|
polynomial& operator /=(const polynomial<U>& value);
|
|
template <class U>
|
|
polynomial& operator %=(const polynomial<U>& value);
|
|
};
|
|
|
|
template <class T>
|
|
polynomial<T> operator + (const polynomial<T>& a, const polynomial<T>& b);
|
|
template <class T>
|
|
polynomial<T> operator - (const polynomial<T>& a, const polynomial<T>& b);
|
|
template <class T>
|
|
polynomial<T> operator * (const polynomial<T>& a, const polynomial<T>& b);
|
|
template <class T>
|
|
polynomial<T> operator / (const polynomial<T>& a, const polynomial<T>& b);
|
|
template <class T>
|
|
polynomial<T> operator % (const polynomial<T>& a, const polynomial<T>& b);
|
|
|
|
template <class T, class U>
|
|
polynomial<T> operator + (const polynomial<T>& a, const U& b);
|
|
template <class T, class U>
|
|
polynomial<T> operator - (const polynomial<T>& a, const U& b);
|
|
template <class T, class U>
|
|
polynomial<T> operator * (const polynomial<T>& a, const U& b);
|
|
template <class T, class U>
|
|
polynomial<T> operator / (const polynomial<T>& a, const U& b);
|
|
template <class T, class U>
|
|
polynomial<T> operator % (const polynomial<T>& a, const U& b);
|
|
|
|
template <class U, class T>
|
|
polynomial<T> operator + (const U& a, const polynomial<T>& b);
|
|
template <class U, class T>
|
|
polynomial<T> operator - (const U& a, const polynomial<T>& b);
|
|
template <class U, class T>
|
|
polynomial<T> operator * (const U& a, const polynomial<T>& b);
|
|
|
|
template <class T>
|
|
polynomial<T> operator - (const polynomial<T>& a);
|
|
|
|
template <class T>
|
|
polynomial<T> operator >>= (const U& a);
|
|
template <class T>
|
|
polynomial<T> operator >> (polynomial<T> const &a, const U& b);
|
|
template <class T>
|
|
polynomial<T> operator <<= (const U& a);
|
|
template <class T>
|
|
polynomial<T> operator << (polynomial<T> const &a, const U& b);
|
|
|
|
template <class T>
|
|
bool operator == (const polynomial<T> &a, const polynomial<T> &b);
|
|
template <class T>
|
|
bool operator != (const polynomial<T> &a, const polynomial<T> &b);
|
|
|
|
template <class T>
|
|
polynomial<T> pow(polynomial<T> base, int exp);
|
|
|
|
template <class charT, class traits, class T>
|
|
std::basic_ostream<charT, traits>& operator <<
|
|
(std::basic_ostream<charT, traits>& os, const polynomial<T>& poly);
|
|
|
|
template <typename T>
|
|
std::pair< polynomial<T>, polynomial<T> >
|
|
quotient_remainder(const polynomial<T>& a, const polynomial<T>& b);
|
|
|
|
} // namespace tools
|
|
}} // namespace boost { namespace math
|
|
|
|
[h4 Description]
|
|
|
|
This is a somewhat trivial class for polynomial manipulation.
|
|
|
|
See
|
|
|
|
* [@https://en.wikipedia.org/wiki/Polynomial Polynomial] and
|
|
* Donald E. Knuth, The Art of Computer Programming: Volume 2, Third edition, (1998)
|
|
Chapter 4.6.1, Algorithm D: Division of polynomials over a field.
|
|
|
|
Implementation is currently of the "naive" variety, with [bigo](N[super 2])
|
|
multiplication, for example. This class should not be used in
|
|
high-performance computing environments: it is intended for the
|
|
simple manipulation of small polynomials, typically generated
|
|
for special function approximation.
|
|
|
|
It does has division for polynomials over a [@https://en.wikipedia.org/wiki/Field_%28mathematics%29 field]
|
|
(here floating point, complex, etc)
|
|
and over a unique factorization domain (integers).
|
|
Division of polynomials over a field is compatible with
|
|
[@https://en.wikipedia.org/wiki/Euclidean_algorithm Euclidean GCD].
|
|
|
|
Advanced manipulations: the FFT, factorisation etc are
|
|
not currently provided. Submissions for these are of course welcome :-)
|
|
|
|
[h4:polynomial_examples Polynomial Arithmetic Examples]
|
|
|
|
[import ../../example/polynomial_arithmetic.cpp]
|
|
|
|
[polynomial_arithmetic_0]
|
|
[polynomial_arithmetic_1]
|
|
|
|
[polynomial_arithmetic_2]
|
|
for output:
|
|
[polynomial_output_1]
|
|
|
|
[polynomial_arithmetic_3]
|
|
for output
|
|
[polynomial_output_2]
|
|
|
|
[h5 Division, Quotient and Remainder]
|
|
[polynomial_arithmetic_4]
|
|
|
|
The source code is at [@../../example/polynomial_arithmetic.cpp polynomial_arithmetic.cpp]
|
|
|
|
[endsect] [/section:polynomials Polynomials]
|
|
|
|
[/
|
|
Copyright 2006 John Maddock and Paul A. Bristow.
|
|
Copyright 2015 Jeremy William Murphy.
|
|
|
|
Distributed under the Boost Software License, Version 1.0.
|
|
(See accompanying file LICENSE_1_0.txt or copy at
|
|
http://www.boost.org/LICENSE_1_0.txt).
|
|
]
|