Math::Polynomial::Chebyshev

Raku package for functionalities based on Chebyshev polynomials.

Installation

From Zef ecosystem:

zef install Math::Polynomial::Chebyshev

From GitHub:

zef install https://github.com/antononcube/Raku-Math-Polynomial-Chebyshev.git

Usage examples

Evaluate the numerical value of the Chebyshev polynomial of first kind :

use Math::Polynomial::Chebyshev;

chebyshev-t(2, 0.3)

The default method is "recursive":

chebyshev-t(2, 6, method => 'recursive')

Here is an invocation of the "trigonometric" method:

chebyshev-t(2, 3, method => 'trigonometric')

Remark: Currently, the trigonometric method is implemented only for the Chebyshev polynomials of first kind. (Chebyshev-T).

Plot the 10th Chebyshev-T polynomial:

use Text::Plot;

my @x = (-1, -0.99 ... 1);
text-list-plot(@x, chebyshev-t(6, @x), width => 80)

Here we make a Chebyshev-T function:

chebyshev-u(4)

References

Articles

[WK1] Wolfram Koepf, "Efficient Computation of Chebyshev Polynomials in Computer Algebra". (1999), Computer Algebra Systems: A Practical Guide. 79-99.

[Wk1] Wikipedia entry, Chebyshev polynomials.

Packages

[AAp1] Anton Antonov, Text::Plot Raku package, (2022-2023), GitHub/antononcube.

[AAp2] Anton Antonov, Math::Fitting Raku package, (2024), GitHub/antononcube.

[SFp1] Solomon Foster, Math::ChebyshevPolynomial Raku package, (2013-2015), GitHub/colomon.