
From:  Vladislav Malyshkin 
Subject:  Re: Polynomials in arbitrary basis 
Date:  Sun, 17 Jun 2018 16:06:03 0400 
Useragent:  Mozilla/5.0 (X11; Linux x86_64; rv:52.0) Gecko/20100101 Thunderbird/52.8.0 
Juan,
The code is java written, I do not have octave package. Only java. Earlier version (bundled with other code) is available at https://yadi.sk/d/AtPJ4a8copmZJ?locale=en file AMuseOfCashFlowAndLiquidityDeficit.20_Sept_2017.zip latest code version (minor API changes & code structure) is attached to this email: polynomial_code.zip (this is preferred version to use, I did not release it yet, but changes from Sept 20 1017 version are really minor (few functions renamed)) There are basically two API of interest to you:
Polynomials operations are implemented in com/polytechnik/utils/{Chebyshev,Legendre,HermiteE,Laguerre,LegendreShifted,Monomials}.java with builtin selftest (e.g. run java com/polytechnik/utils/Chebyshev to selftest the class). There are not that much code there, it may be easier to reimplement that code natively in octave, rather than do any javawrapper, especially because my quadraures (not polynomial) code call few lapack subs converted from fortran, it is probably better for octave to call Lapack subs directly). All my code is under GPL. Polynomials manipulation and Gausstype quadratures calculation in generalized basis is described in https://arxiv.org/pdf/1510.05510 , Appendix A & B, page 30. Vladislav P.S. To test the code unzip polynomial_code.zip javac g com/polytechnik/*/*java # then one can run selftest for, say, Legendre Basis & Quadratures calculation in Legendre basis. java com/polytechnik/utils/Legendre java com/polytechnik/utils/OrthogonalPolynomialsLegendreBasis # to run all selftests java com/polytechnik/utils/UnitTests P.P.S. http://www.chebfun.org/docs/guide/chebfun_guide.pdf by Lloyd N. Trefethen is good, but has different goals. On 06/17/2018 02:49 PM, Juan Pablo Carbajal wrote: Hi, Sounds interesting. Could you share the repository where you host your code? Also, you can create a package, compress it and provide an url, this way anybody can install it from within octave pkg install http://your.url needs Octave >= 4.4 On Sat, Jun 16, 2018 at 9:39 PM, Vladislav Malyshkin <address@hidden> wrote:Octave currently has polynomials manipulation functionality https://octave.org/doc/v4.0.3/PolynomialManipulations.html only in monomials basis: sum ckxk In practice it is often very convenient to have polynomial represented in other polynomials basis: sum ckQk(x) where the basis Qk(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. 
polynomial_code.zip
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