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Directory macros/generic/polexpr

README.md

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 e based formats via

\input polexpr.sty

or with 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 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 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

Download the contents of this package in one zip archive (199.9k).

polexpr – A parser for polynomial expressions

The package provides a parser \poldef of algebraic polynomial expressions. As it is based on xintexpr, the coefficients are allowed to be arbitrary rational numbers.

Once defined, a polynomial is usable by its name either as a numerical function in \xintexpr/\xinteval, or for additional polynomial definitions, or as argument to the package macros. The localization of real roots to arbitrary precision as well as the determination of all rational roots is implemented via such macros.

Since release 0.8, polexpr extends the xintexpr syntax to recognize polynomials as a new variable type (and not only as functions). Functionality which previously was implemented via macros such as the computation of a greatest common divisor is now available directly in \xintexpr, \xinteval or \poldef via infix or functional syntax.

Packagepolexpr
Version0.8.7a 2022-05-19
LicensesThe Project Public License 1.3c
Copyright2018–2022 Jean-François Burnol
MaintainerJean-François Burnol
Contained inTeX Live as polexpr
MiKTeX as polexpr
TopicsCalculation
Generic Macros
Arithmetic
Maths
e-
See alsopolynom
...
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