Package polexpr README

License

Copyright (C) 2018-2020 Jean-François Burnol

See documentation of package xint 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 file polexpr.sty, this README.md and the documentation file polexpr.txt.

Abstract

The package provides \poldef. This a parser of polynomial expressions based upon the \xintdeffunc mechanism of xintexpr.

The parsed expressions use the operations of algebra (inclusive of composition of functions) with standard operators, fractional numbers (possibly in scientific notation) and previously defined polynomial functions or other constructs as recognized by the \xintexpr numerical parser.

The polynomials are then not only genuine \xintexpr (and \xintfloatexpr) numerical functions but additionally are known to the package via their coefficients. This allows dedicated macros to implement polynomial algorithmics.

Releases

• 0.1 (2018/01/11) Initial release (files README, polexpr.sty).
• 0.2 (2018/01/14) Documentation moved to polexpr.{txt,html}.
• 0.3 (2018/01/17) Make polynomials known to \xintfloatexpr and improve documentation.
• 0.3.1 (2018/01/18) Fix two typos in documentation.
• 0.4 (2018/02/16)
  • Revert 0.3 automatic generation of floating point variants.
  • Move CHANGE LOG from README.md to HTML documentation.
  • A few bug fixes and breaking changes. Please refer to polexpr.html.
  • Main new feature: root localization via Sturm Theorem.
• 0.4.1 (2018/03/01) Synced with xint 1.3.
• 0.4.2 (2018/03/03) Documentation fix.
• 0.5 (2018/04/08)
  • new macros \PolMakePrimitive and \PolIContent.
  • main (breaking) change: \PolToSturm creates a chain of primitive integer coefficients polynomials.
• 0.5.1 (2018/04/22) The ' character can be used in polynomial names.
• 0.6 (2018/11/20) New feature: multiplicity of roots.
• 0.7 (2018/12/08), 0.7.1 (bugfix), 0.7.2 (bugfix) (2018/12/09) New feature: finding all rational roots.
• 0.7.3 (2019/02/04) Bugfix: polynomial names ending in digits caused errors. Thanks to Thomas Söll for report.
• 0.7.4 (2019/02/12) Bugfix: 20000000000 is too big for numexpr, shouldn't I know that? Thanks to Jürgen Gilg for report.
• 0.7.5 (2020/01/31) Synced with xint 1.4. Requires it.

Files of 0.7.5 release:

• README.md,
• polexpr.sty (package file),
• polexpr.txt (documentation),
• polexpr.html (conversion via DocUtils rst2html.py)

Acknowledgments

Thanks to Jürgen Gilg whose question about xint usage for differentiating polynomials was the initial trigger leading to this package, and to Jürgen Gilg and Thomas Söll for testing it on some concrete problems.