Is there a way to start a Sage session from a session of its Python interpreter ?

edit

Yes, I know its sounds silly. But there is a point...

The R library reticulate allows to use a persistent Python session from a R session. One of its main uses is to allow to use Python code as well as R code in the creation of reports or papers. This is really useful for everyday statistics use...

One can do similar things with Sage and SageTeX, but using R and R objects is a bit awkward. Furthermore, the R tools offer abilities not easily emulated from within Sage. One can create composite documents using R facilities for R code (knitr) and SageTeX (or PythonTeX, better maintained nowadays) for supporting Sage code ; but usng such composite documents is a bit awkward : passing from the source to the compiled document entails :

• knit the R code of the .Rnw file, getting a .tex file ;
• \LaTeX the .tex file at least once ;
• sage (or pythontex) the resultant file
• re-\LaTeX the .tex file at least once.

This is a bit hard to automate... The same thing applies with aggravation to Markdown texts : the Sage chunks have to be wrapped in \LaTeX-only chunks, and the sage steps have to be done manually from the command line (or from emacs, which amounts to the same thing).

The availability of a persistent Sage session would solve the problem.

A small trial using Sage's R (launched by sage -R) shows that this is almost possible :

> library(reticulate)
> use_python("/usr/local/sage-8/sage") ## This is the main Sage script file
> repl_python()
Python 2.7.15 (/usr/local/sage-8/sage)
Reticulate 1.10 REPL -- A Python interpreter in R.
>>> 2^3
1

We are in python, no preparsing takes place.

>>> arctan
NameError: name 'arctan' is not defined

arctan is not defined : noting Sage-specific is known.

>>> from sage.all import *
>>> arctan
arctan

The import succeeded.

>>> x
NameError: name 'x' is not defined

But the (default) definition of x as a symbolic variable has not been done.

>>> var("x")
x
>>> x
x
>>> foo=arctan(x).integrate(x)
>>> exit

We are back to R, from which we can access toplevel objects in the Python session :

> py$foo
x*arctan(x) - 1/2*log(x^2 + 1)
> py$latex(py$foo)
x \arctan\left(x\right) - \frac{1}{2} \, \log\left(x^{2} + 1\right)
> py_to_r(py$latex(py$foo))
x \arctan\left(x\right) - \frac{1}{2} \, \log\left(x^{2} + 1\right)

Not a "standard" R characer vector :

> class(py_to_r(py$latex(py$foo)))
[1] "sage.misc.latex.LatexExpr" "python.builtin.str"       
[3] "python.builtin.basestring" "python.builtin.object"

But it can be used as such :

> paste("** ",py$latex(py$foo)," **", sep="")
[1] "** x \\arctan\\left(x\\right) - \\frac{1}{2} \\, \\log\\left(x^{2} + 1\\right) **"

Now, it is possible to insert the loading of a Python module before the launch of the Python REPL : From the doc of repl_python :

module: An (optional) Python module to be imported before the REPL is launched.

So the question is : is it possible to write a module correctly importing sage.all AND whose __init__ function would replace Python's REPL by Sage's ?

ISTR that a few years ago, before the introduction of Sage's Jupyter notebook, such tricks were used in Jupyter to start a Sage session (complete with preparser) from an "ordinary" Jupyter notebook. But for the life of me, I haven't been able to retrieve the relevant pages...

Any thoughts ?

EDIT : A bit of googling using the former name "IPython notebook" led me to this StackOverflow question, whose first answer, by no other than William Stein, tells the user that using %load_ext sage would start Sage from a (conventient) IPython session. Indeed :

charpent@asus16-ec:~$ sage -ipython
Python 2.7.15 (default, May 19 2018, 18:46:27) 
Type "copyright", "credits" or "license" for more information.

IPython 5.5.0 -- An enhanced Interactive Python.
?         -> Introduction and overview of IPython's features.
%quickref -> Quick reference.
help      -> Python's own help system.
object?   -> Details about 'object', use 'object??' for extra details.

In [1]: 2^3
Out[1]: 1

So we are in Python, no preprocessing

In [2]: x
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-2-6fcf9dfbd479> in <module>()
----> 1 x

NameError: name 'x' is not defined

x not defined.

In [3]: %load_ext sage

In [4]: 2^3
Out[4]: 8

We are in Sage !

In [5]: x
Out[5]: x

x has been defined

In [6]: quit()
Exiting Sage (CPU time 0m0.13s, Wall time 0m14.53s).

So this sage notebook extension to IPython still exists, and does what I want. Its dissection should give me what I need to write my helper module.

But for the life of me, I have been unable to divine its source. what is it, and where is it ?

EDIT on 2018-08-13 : that source is in $SAGE_ROOT/src/sage/repl/ipython_extension.py, but is insufficient (to me !) to build a solution. Question re-asked on sage-devel in order to reach new eyeballs...