@stdlib/math-base-tools-lucaspoly
v0.2.3TypeScript
Evaluate a Lucas polynomial.
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Published by The Stdlib Authors
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About stdlib...
Lucas Polynomial
[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]
> Evaluate a [Lucas polynomial][fibonacci-polynomials].
A [Lucas polynomial][fibonacci-polynomials] is expressed according to the following recurrence relation
Alternatively, if L(n,k) is the coefficient of x^k in L_n(x), then
We can extend [Lucas polynomials][fibonacci-polynomials] to negative n using the identity
Installation
``bash`
npm install @stdlib/math-base-tools-lucaspoly
Usage
`javascript`
var lucaspoly = require( '@stdlib/math-base-tools-lucaspoly' );
#### lucaspoly( n, x )
Evaluates a [Lucas polynomial][fibonacci-polynomials] at a value x.
`javascript`
var v = lucaspoly( 5, 2.0 ); // => 2^5 + 52^3 + 52
// returns 82.0
#### lucaspoly.factory( n )
Uses code generation to generate a function for evaluating a [Lucas polynomial][fibonacci-polynomials].
`javascript
var polyval = lucaspoly.factory( 5 );
var v = polyval( 1.0 ); // => 1^5 + 5*1^3 + 5
// returns 11.0
v = polyval( 2.0 ); // => 2^5 + 52^3 + 52
// returns 82.0
`
Notes
- For hot code paths, a compiled function will be more performant than lucaspoly().
- While code generation can boost performance, its use may be problematic in browser contexts enforcing a strict [content security policy][mdn-csp] (CSP). If running in or targeting an environment with a CSP, avoid using code generation.
Examples
`javascript
var lucaspoly = require( '@stdlib/math-base-tools-lucaspoly' );
var i;
// Compute the negaLucas and Lucas numbers...
for ( i = -76; i < 77; i++ ) {
console.log( 'L_%d = %d', i, lucaspoly( i, 1.0 ) );
}
`
*
See Also
- [@stdlib/math-base/tools/evalpoly][@stdlib/math/base/tools/evalpoly]: evaluate a polynomial using double-precision floating-point arithmetic.
- [@stdlib/math-base/tools/fibpoly][@stdlib/math/base/tools/fibpoly]: evaluate a Fibonacci polynomial.
*
Notice
This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.
For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].
#### Community
[![Chat][chat-image]][chat-url]
---
License
See [LICENSE][stdlib-license].
Copyright
Copyright © 2016-2026. The Stdlib [Authors][stdlib-authors].
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[test-image]: https://github.com/stdlib-js/math-base-tools-lucaspoly/actions/workflows/test.yml/badge.svg?branch=v0.2.3
[test-url]: https://github.com/stdlib-js/math-base-tools-lucaspoly/actions/workflows/test.yml?query=branch:v0.2.3
[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/math-base-tools-lucaspoly/main.svg
[coverage-url]: https://codecov.io/github/stdlib-js/math-base-tools-lucaspoly?branch=main
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[stdlib]: https://github.com/stdlib-js/stdlib
[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors
[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules
[deno-url]: https://github.com/stdlib-js/math-base-tools-lucaspoly/tree/deno
[deno-readme]: https://github.com/stdlib-js/math-base-tools-lucaspoly/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/math-base-tools-lucaspoly/tree/umd
[umd-readme]: https://github.com/stdlib-js/math-base-tools-lucaspoly/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/math-base-tools-lucaspoly/tree/esm
[esm-readme]: https://github.com/stdlib-js/math-base-tools-lucaspoly/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/math-base-tools-lucaspoly/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-base-tools-lucaspoly/main/LICENSE
[fibonacci-polynomials]: https://en.wikipedia.org/wiki/Fibonacci_polynomials
[mdn-csp]: https://developer.mozilla.org/en-US/docs/Web/HTTP/CSP
[@stdlib/math/base/tools/evalpoly]: https://www.npmjs.com/package/@stdlib/math-base-tools-evalpoly
[@stdlib/math/base/tools/fibpoly]: https://www.npmjs.com/package/@stdlib/math-base-tools-fibpoly