Sympy code to collect and process terms for various post-Newtonian (PN) equations, and to generate working python/C/C++ code to evolve PN systems.

Sympy is python's library for symbolic math. Though not as mature as Mathematica, it is in many ways ready to replace Mathematica -- and in some important ways, much better already. Plus, it's open source, and fits right in with all the power of python. What's not to love?

The ipython notebook is a general replacement for the notebook interface of Mathematica, and already vastly superior in almost every way. It runs in the web browser, is tremendously powerful, and again is open source. And it just keeps getting better. I believe this is how science should be done on a computer.

This module combines sympy and ipython notebooks, and applies them to the complex issue of post-Newtonian constructions.

If you just want to take a look at the notebooks without downloading them, you can just view the important ones on nbviewer:

• AngularMomentum
• BindingEnergy
• EnergyAbsorption
• Flux
• OrbitalEvolution
• Precession
• Variables
• Variables_Q
• WaveformModes

From the command line, change your directory to this code directory (with all the .ipynb files), and run

ipython notebook --pylab=inline

Your browser should open automatically, and you should see a list of notebooks. (If not, see the Installation section below.) Click one of those notebooks, which should open in a new tab. To run code, just put your cursor in any code cell and hit Shift-Enter, as with Mathematica.

The aim of this project is to provide a simple centralized framework for collecting PN expressions, combining them to automatically calculate, e.g., TaylorTn expressions, and sharing them in a way that can be used by as many people as possible---through LaTeX, C, C++, or Mathematica code.

To be more explicit, the tasks performed by code in this module will:

• Collect various PN expressions, with annotations describing where they come from

• Manipulate and combine partial expressions from different sources into complete expressions appropriate for actual use

• Generate python code for simple (but possibly slow) evaluation of PN systems and waveforms with, e.g., precession effects, or neutron-star tidal effects, etc.

• Export C/C++ code for more efficient evaluation of those systems

• Export expressions to Mathematica

• Export expressions to LaTeX

One important feature of the ipython notebook is that it allows easy description of code, meaning that we can give very explicit citations and other explanations for where to find the collected terms in the literature, including code comments, large sections of text, and even LaTeX equations displayed appropriately. The main notebooks are found in the PNTerms subdirectory, and depend on each other to build up complicated expressions. The rough order of this dependency is as follows.

• Variables_Q.ipynb: Define the fundamental variables, and write all the non-fundamental variables in terms of them. Centralizing these definitions reduces mistakes.

• EnergyAbsorption.ipynb, Flux.ipynb, BindingEnergy.ipynb: Collect the PN expressions for these various quantities, classified by their type and PN order.

• OrbitalEvolution.ipynb: Combine knowledge of the above quantities to compute the orbital evolution, as well as precession.

• C++/OrbitalEvolutionCodeGen.ipynb: Derive the TaylorTn expressions from the notebooks above, and generate C/C++ code to evolve or evaluate them. Note that C++/InspectResults.ipynb gives working examples for PN evolutions.

Some notebooks also come in two flavors: one for the standard evolution system, where vectors are evolved directly; another where quaternions are used for efficiency and robustness. They typically result in identical results, though the quaternion formulation can handle certain special cases better than the other.

Contributions are enthusiastically welcomed. Github has very useful features for enabling collaboration. The basic process is to fork this repository, make the changes in your fork, and then submit a pull request for the author to pull changes back into this main repository. This is easier than it might sound. The links listed here give more than enough information to do this.

All of the code here uses python and various python packages (though C/C++ code is generated). So, you need an up-to-date installation of python (version 2.7 or greater), as well as various python packages. Most package managers (apt, macports, homebrew, etc.) can install these packages for you. For manual installation, install python and pip (python's package manager), and then run

pip install numpy
pip install matplotlib
pip install pandas
pip install sympy
pip install scipy
pip install ipython[notebook]

If these fail, complaining about permissions, simply add --user to each command. For tcsh users, the brackets in the last command will need to be escaped with backslashes.