Package polexpr README

Version 0.8.7a of 2022/05/19.

Abstract

The package provides a parser \poldef of algebraic expressions. As it is based on xintexpr the polynomial coefficients are allowed to be arbitrary rational numbers. Operations on declared polynomials, such as computing G.C.D.'s or evaluating definite and indefinite integrals are available directly inside the parser via a functional syntax, or also via dedicated package macros.

Root localization is available via package macros. All real roots can be obtained with arbitrarily long decimal expansions, and all rational rounds found exactly.

In memoriam: Jürgen Gilg

polexpr is dedicated to the memory of Jürgen Gilg (1966-2022).

His question in January 2018 about using xintexpr to compute derivatives of polynomials was the original motivation for the creation of this package. Jointly with Thomas Söll, he used it and kept expressing his interest in it throughout the subsequent years, and provided motivation and encouragements for time-consuming tasks such as (as was done finally in 2021) re-enacting full interoperability with xintexpr after its 1.4 update from 2020.

I will remember with gratitude his generous and unassuming character, which I witnessed during our numerous exchanges on a wide range of topics.

Usage

The package can be used with eTeX based formats via

\input polexpr.sty

or with LaTeX via

\usepackage{polexpr}

xintexpr 1.4h or later is required.

Recent changes

• 0.8 (2021/03/29) Complete refactoring of the package core for better interoperability with xintexpr internal changes at its release 1.4 (2020/01/31). Extension of the functional syntax to cover operations such as G.C.D.'s, derivatives or indefinite integrals previously available via macros.
• 0.8.1 (2021/04/12) Bug fix: a typo broke the 0.8 diff1() and related functions.
• 0.8.2 (2021/05/05) Track xintexpr 1.4e changes
• 0.8.3 (2021/05/27) Track xintexpr 1.4h changes
• 0.8.4 (2021/11/01) Bug fix: PolSturmIsolateZeros** did not declare the square free part of the original polynomial if no real root existed.
• 0.8.5 (2021/11/30) Bug fix: intfrom() was documented at 0.8 but not declared to parser. Track (belatedly) xintexpr 1.4g changes
• 0.8.6 (2022/01/09) Separate polexpr-examples.{tex,pdf} from the polexpr.html reference.
• 0.8.7 (2022/05/14) CSS styling of the html documentation, which is now split over three files. Catcode protection for \poldef now matches long-standing behaviour of \xintdefvar. This fixes issues with babel+french.
• 0.8.7a (2022/05/19) Documentation improvements.

License

Copyright (C) 2018-2022 Jean-François Burnol

See documentation of package xintexpr for contact information.

This Work may be distributed and/or modified under the conditions of the LaTeX Project Public License version 1.3c. This version of this license is in

http://www.latex-project.org/lppl/lppl-1-3c.txt

and version 1.3 or later is part of all distributions of LaTeX version 2005/12/01 or later.

This Work has the LPPL maintenance status author-maintained.

The Author of this Work is Jean-François Burnol.

This Work consists of:

• the package files: polexpr.sty, polexprcore.tex, polexprexpr.tex, polexprsturm.tex,
• this README.md,
• the documentation files: polexpr.html, polexpr-ref.html, polexpr-changes.html, polexpr.css, polexpr-examples.pdf, polexpr.rst.txt, polexpr-ref.rst.txt, polexpr-changes.rst.txt, polexpr-examples.tex