
From:  Vladislav Malyshkin 
Subject:  Polynomials in arbitrary basis 
Date:  Sat, 16 Jun 2018 15:39:24 0400 
Useragent:  Mozilla/5.0 (X11; Linux x86_64; rv:52.0) Gecko/20100101 Thunderbird/52.8.0 
Octave currently has polynomials manipulation functionality https://octave.org/doc/v4.0.3/PolynomialManipulations.html only in monomials basis: sum c_{k}x^{k }In practice it is often very convenient to have polynomial represented in other polynomials basis: sum c_{k}Q_{k}(x) where the basisĀ Q_{k}(x) is orthogonal polynomials of some kind. There is my implementation of polynomials manipulation functionality (and Gausstype quadratures calculation) in the basis of Chebyshev, Legendre, Laguerre, Hermite bases. The code is available under GPL and is javawritten (however it will not be much a problem to rewrite it in C/C++). You can read about code at https://arxiv.org/pdf/1510.05510 see Appendix A & B. Let me know if you have any interest. Vladislav P.S. From the other alternative basis software I know only matlabwritten http://www.chebfun.org/ by Alex Townsend, but his project has different goals. 
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