Pawel Kieliszczyk wrote:
My idea for a GSoC project was to biuld an advanced library for polynomial manipulation. Boost offers a simple class with basic operations here:
http://svn.boost.org/svn/boost/trunk/libs/math/doc/sf_and_dist/html/math_too...
and usefull functions here:
http://svn.boost.org/svn/boost/trunk/libs/math/doc/sf_and_dist/html/math_too...
John Maddock suggested me via e-mail to improve and extend this library. I would like to introduce to you my proposals.
What could be added? - multiplication algorithm using FFT - '/', '/=', '%' and '%=' operators - greatest common divisor of polynomials - factorisation - derivatives and integrals - conversions between various polynomial forms - faster evaluation of a polynomial - finding a polynomial if n points are given (degree of a polynomial is
n-1)
- I am still thinking.
Generally speaking the library would become more advanced.
Hi again. Here are some of proposed ideas for Boost.Polynomial: 1. Now there is a special function for evaluation. I think operator() woudl be comfortable and also intuitive. Short example: int a[] = {3, 4, 5}; polynomial<int> p(a, 2); cout << "p(4) = " << p(4) << endl; // p(4) = 99 2. Fast swap function (in constant time) using vector::swap(). 3. Two versions of functions for evaluating derivatives: polynomial<T> derivative(unsigned k = 1) const; // returns the k-order derivative void replace_by_derivative(unsigned k = 1); // replaces the polynomial by the derivative 4. For integrals: template <class U> polynomial<U> integral(const U& c = 0) const; // returns the integral and c is the coefficient for x^0 template <class U> void replace_by_integral(const U& c = 0); 5. As far as I know a conversion for Chebyshev form has been already done. I would like to add conversion and special functions for Hermitte, Laguerre and Legendre forms. Obviously I wait also for other suggestions. 6. extern function for finding a polynomial based on N points. template <std::size_t N, class T> polynomial<T> create_polynomial(const T(&poly)[N]); Other ideas like new operators and functions seem to be clear. I wait for suggestions or questions and I'm going to send my application in few days. :) Pawel Kieliszczyk.