A package for polynomial reduction and elimination theory over finite fields. It is based on the publication

• Vsevolod Chestnov and Giulio Crisanti, Sampling Polynomial Rational Remainders with SPQR: A new Package for Polynomial Division and Elimination.

SP$\mathbb{Q}$R depends on FiniteFlow, which can be found here. Mathematica 13.1+ is required for SP$\mathbb{Q}$R to function correctly.

To install, open a Mathematica window and run the command

ResourceFunction["GitHubInstall"]["giu989","SPQR"];

The package should now be loadable with

<<SPQR`

If required, the installation directory can be found with

"Location" /. PacletFind["SPQR"][[1]][[1]]

To install from source, clone the git repository to your directory of choice. Then open a Mathematica window and run the command

PacletInstall["/path-to-spqr/build/SPQR-x.x.x.paclet"];

where x-x-x is changed to the desired version. The install location directory can be found as above.

To update to the latest version, simply rerun the automatic install command above. The package should now be updated to the latest available version.

Upon loading the package, extensive documentation can be accessed via the "Open documentation" button (if running via a GUI). Furthermore, all publicly available functions have documentation pages that can be accessed in an identical manner to standard built in functions. Documentation will also be provided in the accompanying manuscript upon release.

To uninstall, open a Mathematica window and run the command

PacletUninstall["SPQR"];