DD-finite functions in Sage

dd_functions is a SageMath package to work with differentiably definable functions.

These generalise the class of differentially finite or "D-finite" functions:

• D-finite functions satisfy linear differential equations with polynomial coefficients
• DD-finite functions satisfy linear differential equations with D-finite functions as coefficients
• differentiably definable functions are obtained by iterating this

This package allows Sage users to naturally use DD-finite functions on the computer.

• author: Antonio Jimenez-Pastor
• license: GNU General Public License v3.0
• home page: https://github.com/Antonio-JP/dd_functions
• documentation: https://antonio-jp.github.io/dd_functions/
• online demo:

This README includes an installation guide.

For extensive documentation, see the documentation link.

Acknowledgements. This package was developed in the research funded by the Austrian Science Fund (FWF): W1214-N15, project DK15.

Installation

There are several ways to install the package (and the online demo requires no installation).

Install from source code

The package can be obtained from the public Git repository on GitHub:

• click here for the webpage view
• or clone the repository by https
• or download the latest zip.

This method allows the user to get the very last version of the code.

After cloning the repository (or getting the zip file and extracting it), change to the main folder and install by running the command

make install

Install via pip

Another option is to install the package using pip, Python's package-management system.

To do so, run the following in a terminal:

sage --pip install git+https://github.com/Antonio-JP/dd_functions.git

Usage

Once installed, start Sage and use appropriate imports:

sage: from ajpastor.dd_functions import *

Or launch the demo notebook dd_functions_demo.ipynb.

The package can also be tried online via Binder, see the "launch Binder" button at the top of this README. This starts a Sage session on an online server without requiring any installation on your computer.

Dependencies

This package

• works on top of SageMath
• installs the ore_algebra Sage package by M. Kauers and M. Mezzarobba.