{"id":15168554,"url":"https://github.com/antononcube/raku-math-polynomial-chebyshev","last_synced_at":"2026-02-14T10:03:08.670Z","repository":{"id":245189986,"uuid":"817511449","full_name":"antononcube/Raku-Math-Polynomial-Chebyshev","owner":"antononcube","description":"Raku package for functionalities based on Chebyshev 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Math::Polynomial::Chebyshev\n\nRaku package for functionalities based on Chebyshev polynomials.\n\n------\n\n## Installation\n\nFrom Zef ecosystem:\n\n```\nzef install Math::Polynomial::Chebyshev \n```\n\nFrom GitHub:\n\n```\nzef install https://github.com/antononcube/Raku-Math-Polynomial-Chebyshev.git\n```\n\n-------\n\n## Usage examples\n\nEvaluate the numerical value of the Chebyshev polynomial of first kind $T_2(3)$:\n\n```perl6\nuse Math::Polynomial::Chebyshev;\n\nchebyshev-t(2, 0.3)\n```\n\nThe default method is \"recursive\":\n\n```perl6\nchebyshev-t(2, 6, method =\u003e 'recursive')\n```\n\nHere is an invocation of the  \"trigonometric\" method:\n\n```perl6\nchebyshev-t(2, 3, method =\u003e 'trigonometric')\n```\n\n**Remark:** Currently, the trigonometric method is implemented only for the Chebyshev polynomials of first kind\n(Chebyshev-T.)\n\nPlot the 7th Chebyshev-T polynomial:\n\n```perl6\nuse Text::Plot;\n\nmy @x = (-1, -0.99 ... 1);\ntext-list-plot(@x, chebyshev-t(6, @x), width =\u003e 60)\n```\n\nHere we make a Chebyshev-T function:\n\n```perl6\nchebyshev-u(4)\n```\n\nA list of Chebyshev polynomials can be used as a basis for the models in \n[\"Math::Fitting\"](), [AAp2]. \nHere is an example: \n\n```perl6\nuse Math::Fitting;\n\nmy @basis = (^4).map({ chebyshev-t($_) });\nmy @data = [2.rand - 1, 10.rand] xx 20;\n\nmy \u0026lm = linear-model-fit(@data, :@basis);\n```\n\nHere is a plot of the data and the fit:\n\n```perl6\nmy @fit = (-1, -0.98 ... 1).map({ [$_, \u0026lm($_)] });\nsay \u003cfit data\u003e Z=\u003e \u003c* □\u003e;\nsay text-list-plot([@fit, @data])\n```\n\n--------\n\n## References\n\n### Articles\n\n[WK1] Wolfram Koepf,\n[\"Efficient Computation of Chebyshev Polynomials in Computer Algebra\"](https://www.researchgate.net/publication/2321141_Efficient_Computation_of_Chebyshev_Polynomials_in_Computer_Algebra). \n(1999),\nComputer Algebra Systems: A Practical Guide. 79-99.\n\n[Wk1] Wikipedia entry, [Chebyshev polynomials](https://en.wikipedia.org/wiki/Chebyshev_polynomials).\n\n### Packages\n\n[AAp1] Anton Antonov, \n[Text::Plot Raku package](https://github.com/antononcube/Raku-Text-Plot),\n(2022-2023),\n[GitHub/antononcube](https://github.com/antononcube).\n\n[AAp2] Anton Antonov,\n[Math::Fitting Raku package](https://github.com/antononcube/Raku-Math-Fitting),\n(2024),\n[GitHub/antononcube](https://github.com/antononcube).\n\n[SFp1] Solomon Foster,\n[Math::ChebyshevPolynomial Raku package](https://github.com/colomon/Math-ChebyshevPolynomial),\n(2013-2015),\n[GitHub/colomon](https://github.com/colomon).","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fantononcube%2Fraku-math-polynomial-chebyshev","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fantononcube%2Fraku-math-polynomial-chebyshev","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fantononcube%2Fraku-math-polynomial-chebyshev/lists"}