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- [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,
- typename boost::enable_if<boost::is_convertible<U, T> >::type* = 0);
- template <class Range>
- explicit polynomial(const Range& r,
- typename boost::enable_if<boost::math::tools::detail::is_const_iterable<Range> >::type* = 0); // C++14
- polynomial(std::initializer_list<T> l); // C++11
- polynomial(std::vector<T>&& p);
- // 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;
- polynomial<T> prime() const;
- polynomial<T> integrate() const;
- T operator()(T z) 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].
- Division of polynomials over a UFD is compatible with the subresultant algorithm for GCD (implemented as subresultant_gcd), but a serious word of warning is required: the intermediate value swell of that algorithm will cause single-precision integral types to overflow very easily. So although the algorithm will work on single-precision integral types, an overload of the gcd function is only provided for polynomials with multi-precision integral types, to prevent nasty surprises. This is done somewhat crudely by disabling the overload for non-POD integral types.
- 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).
- ]
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