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https://github.com/moble/postnewtonian

Sympy code to collect and process terms for various post-Newtonian (PN) equations, and to generate working python/C/C++/etc. code to compute PN waveforms
https://github.com/moble/postnewtonian

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

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README 

        
PostNewtonian

=============



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](http://www.sympy.org) 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](http://docs.sympy.org/0.7.1/modules/galgebra/GA/GAsympy.html),

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](http://ipython.org/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.



Just looking

============



If you just want to take a look at the notebooks without downloading them,

you can just view the important ones on `nbviewer`:



  * [AngularMomentum](http://nbviewer.ipython.org/github/MOBle/postnewtonian/blob/master/PNTerms/AngularMomentum.ipynb)

  * [BindingEnergy](http://nbviewer.ipython.org/github/MOBle/postnewtonian/blob/master/PNTerms/BindingEnergy.ipynb)

  * [EnergyAbsorption](http://nbviewer.ipython.org/github/MOBle/postnewtonian/blob/master/PNTerms/EnergyAbsorption.ipynb)

  * [Flux](http://nbviewer.ipython.org/github/MOBle/postnewtonian/blob/master/PNTerms/Flux.ipynb)

  * [OrbitalEvolution](http://nbviewer.ipython.org/github/MOBle/postnewtonian/blob/master/PNTerms/OrbitalEvolution.ipynb)

  * [Precession](http://nbviewer.ipython.org/github/MOBle/postnewtonian/blob/master/PNTerms/Precession.ipynb)

  * [Variables](http://nbviewer.ipython.org/github/MOBle/postnewtonian/blob/master/PNTerms/Variables_Q.ipynb)

  * [Variables_Q](http://nbviewer.ipython.org/github/MOBle/postnewtonian/blob/master/PNTerms/Variables_Q.ipynb)

  * [WaveformModes](http://nbviewer.ipython.org/github/MOBle/postnewtonian/blob/master/PNTerms/WaveformModes.ipynb)



Quick Start

===========



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](#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.



Introduction

============



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.



Contributing

============



Contributions are enthusiastically welcomed.  Github has [very useful

features](https://help.github.com/articles/be-social) for enabling

collaboration.  The basic process is to

[fork](https://help.github.com/articles/fork-a-repo) this repository,

make the changes in your fork, and then submit a [pull

request](https://help.github.com/articles/using-pull-requests) 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.



Installation

============



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



```Shell

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.