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)

# -0.82

The default method is "recursive":

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

# 71

Here is an invocation of the "trigonometric" method:

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

# 17

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)

# +---+-----------------+----------------+-----------------+----------------+----+
# |                                                                              |
# +   *               *****                              *****              *    +  1.00
# |                  **   **                           **    **                  |
# |    *            *       *                          *      **            *    |
# |                **       **                        *        *                 |
# +                *          *                      *          *                +  0.50
# |    *          *           **                    **          **          *    |
# |              **            *                    *            **              |
# |     *        *              *                 **              *        *     |
# +             **               *                *               **             +  0.00
# |     *       *                **              *                 *       *     |
# |     *      **                 *             **                 **      *     |
# +      *     *                   *            *                   *     *      + -0.50
# |      *    **                   **          *                    **    *      |
# |      *   **                      *        *                      *    *      |
# |       *  *                        **    **                        *  *       |
# +       ***                          ******                         ****       + -1.00
# |                                                                              |
# +---+-----------------+----------------+-----------------+----------------+----+
#     -1.00             -0.50            0.00              0.50             1.00

Here we make a Chebyshev-T function:

chebyshev-u(4)

# -> ;; $_? is raw = OUTER::<$_> { #`(Block|5419846387320) ... }

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.