I recommend you to start by reading the sage developer guide:

http://doc.sagemath.org/html/en/developer/index.html

It covers all the development process.

I am no expert in Coxeter groups, but from what I see, we already have 
support for them in Sage. So I will assume that your software would provide 
the ability to compute certain properties that are not available in Sage 
already (or maybe a faster implementation of already available ones). In 
that case, you could add CoxIter as an optional package (we usually require 
packages to be optional for one year before becoming standard), and also 
write an interface to it from Sage, together with the corresponding methods 
in CoxeterGroup class to call that interface. The interface can be done 
using pexpect, but if it is possible to adapt your software as a C++ 
library, it would be much faster to just call it through cython. I 
recommend to do all these steps in one ticket.


If you want to take a look at an example of a ticket where something 
similar was done, you can look at: 

https://trac.sagemath.org/ticket/20815

El viernes, 31 de marzo de 2017, 11:18:15 (UTC+2), Rafael Guglielmetti 
escribió:
>
> Dear sage developers,
> During my PhD I developed a C++ program to compute invariants of 
> hyperbolic Coxeter groups.
>
> The program was published in the LMS Journal of Computations and 
> Mathematics and is now on GitHub: https://github.com/rgugliel/CoxIter
>
> I am wondering if it could be included into SAGE? If yes, where should I 
> start?
> I also developed a GAP package, maybe it could also be a way?
>
> Thanks a lot for any hint.
>
> Best,
>
> Rafael Guglielmetti
>

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