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Ore algebra


A Sage implementation of Ore algebras, Ore polynomials, and differentially finite functions

Main features for the most common algebras include basic arithmetic and actions; gcrd and lclm; D-finite closure properties; creative telescoping; natural transformations between related algebras; guessing; desingularization; solvers for polynomials, rational functions and (generalized) power series. Univariate differential operators also support the numerical computation of analytic solutions with rigorous error bounds and related features.


Distributed under the terms of the GNU General Public License (GPL, see the COPYING file), either version 2 or (at your option) any later version


Sage 8.7 or later is recommended. Some features should work with older versions.


With Sage built from source or binaries from

To download and install the latest development version on a system where Sage was built from source or installed from official packages, run

sage -pip install git+


sage -pip install --user git+

The optional --user flag causes the package to be installed in your .sage directory instead of the Sage installation tree.

Alternatively, run (square brackets indicate optional flags)

sage -pip install [--user] [--editable] .

from the root of a local git checkout. The --editable flag causes the "installed" version to point to your local checkout, making it easier, if you edit the code, to run the modified version. See the pip documentation for more installation options.

Microsoft Windows users should run the above commands in a "SageMath shell", see

Apple macOS users may need additional steps before they are able to add external packages to their Sage installations. See

for more information.

With Sage installed from operating system packages

If your copy of Sage comes from operating system packages (e.g., Debian, Ubuntu, Gentoo, or Arch Linux packages), try replacing sage -pip by pip or pip3 above.

You may need development packages that are not automatically installed as dependencies of the main SageMath package, e.g., a C/C++ compiler, the Cython compiler, and header files for Linbox, Pari, and Singular.

For example, Debian and Ubuntu users need to install the liblinbox-dev, libpari-dev and libsingular-dev packages (and possibly others) in addition to the sagemath package. The command apt build-dep sagemath can be used to install all necessary development packages (and more).

Arch Linux users will need at least the cython and python-pkgconfig packages.

Using ore_algebra without installation

To use ore_algebra directly from a git checkout (without installation), run

sage -python build_ext --inplace

from the checkout, and add the src/ directory to your Python sys.path.

ore_algebra contains compiled (Cython) modules which are automatically built as part of the installation procedure. Installation will fail if they cannot be built. Only some specific features depend on these modules, though, and the core features should work even if Cython modules are unavailable.


The documentation generated from the doc strings is available online at


To run the test suite, install the package and run the command

sage -tp --long --force-lib src/

at the root of the git checkout.


Manuel Kauers