CASengine

What for? To generate parametrized exercises/texts in LaTeX, from a compact source, while at the same time executing commands in Computer Algebra Systems in a localized namespace (such as sympy, SageMath, maple, mathematica, maxima, gap, ...). Adding one CAS interface should be relatively easy.

OPTIONS:
        --help|-h       Help
        --verbose|-v    Verbose Running
        --output=|-o [FILENAME] explicit output filename
        --sty           Generate the file `casengine.sty` in the current dir.
        --noexec|-n     Do not execute any sympy code.

I do not have time yet to write extensive documentation. Somehow the source is self-explaining?

Just to do, first generate the .sty LaTeX file:

$ casengine.py --sty

Then, write a (La)TeX file with the following commands (simple example):

\documentclass{article}
\usepackage{casengine} % with no CAS, it will be assumed sympy
%%% \usepackage[CAS=maple]{casengine} % sage, maple, math, gap, whatever (see DEFAULT_OPTIONS in src)
\usepackage{enumerate}

\begin{document}
\symexec{CLEAR} % not really necessary. Sometimes.
\symexec{x=Derivative(sqrt(1+x**2))} % syntax-dependent (here it is sympy)
\begin{symfor}{q}{1;Rational(1,2);pi+sqrt(5)}% a list of symbolic expressions, separated by ";"
\begin{symfor}{c}{range(1,3)}% a python range of integers

This is a sentence with $\sym{q} + \sym{x} + \sym{c} = \sym{q+x.doit()+c}$.
\end{symfor}
\end{symfor}
\end{document}

Executing casengine.py on the file yields an outut such as the following (the symfor cycles are cycled through, the \symexec commands executed and the \sym expressions are latexified and printed, as follows:

%File test_symout.tex created by casengine.py (CAS engine: SymPy Version 0.7.4.1)
%Started: 2017-10-10 16:08:37.270242
%Finished: 2017-10-10 16:08:37.499979
%Elapsed time: 0:00:00.229737
\documentclass{article}
\usepackage{casengine} % with no CAS, it will be assumed sympy
%%% \usepackage[CAS=maple]{casengine} % sage, maple, math, gap, whatever (see DEFAULT_OPTIONS in src)
\usepackage{enumerate}

\begin{document}
% ==> NameSpace CLEARED % not really necessary. Sometimes.
%cas_exec: x=Derivative(sqrt(1+x**2)) % syntax-dependent (here it is sympy)
%%sym_for q:
%cas_exec: q=1% a list of symbolic expressions, separated by ";"
%%sym_for c:
%cas_exec: c=1% a python range of integers

This is a sentence with $1 + \frac{d}{d x} \sqrt{x^{2} + 1} + 1 = \frac{x}{\sqrt{x^{2} + 1}} + 2$.
%%end sym_for c
%%sym_for c:
%cas_exec: c=2% a python range of integers

This is a sentence with $1 + \frac{d}{d x} \sqrt{x^{2} + 1} + 2 = \frac{x}{\sqrt{x^{2} + 1}} + 3$.
%%end sym_for c
%%end sym_for q
%%sym_for q:
%cas_exec: q=Rational(1,2)% a list of symbolic expressions, separated by ";"
%%sym_for c:
%cas_exec: c=1% a python range of integers

This is a sentence with $\frac{1}{2} + \frac{d}{d x} \sqrt{x^{2} + 1} + 1 = \frac{x}{\sqrt{x^{2} + 1}} + \frac{3}{2}$.
%%end sym_for c
%%sym_for c:
%cas_exec: c=2% a python range of integers

This is a sentence with $\frac{1}{2} + \frac{d}{d x} \sqrt{x^{2} + 1} + 2 = \frac{x}{\sqrt{x^{2} + 1}} + \frac{5}{2}$.
%%end sym_for c
%%end sym_for q
%%sym_for q:
%cas_exec: q=pi+sqrt(5)% a list of symbolic expressions, separated by ";"
%%sym_for c:
%cas_exec: c=1% a python range of integers

This is a sentence with $\sqrt{5} + \pi + \frac{d}{d x} \sqrt{x^{2} + 1} + 1 = \frac{x}{\sqrt{x^{2} + 1}} + 1 + \sqrt{5} + \pi$.
%%end sym_for c
%%sym_for c:
%cas_exec: c=2% a python range of integers

This is a sentence with $\sqrt{5} + \pi + \frac{d}{d x} \sqrt{x^{2} + 1} + 2 = \frac{x}{\sqrt{x^{2} + 1}} + 2 + \sqrt{5} + \pi$.
%%end sym_for c
%%end sym_for q
\end{document}

Further engines (easy to extend: maple, mathematica, sage, gap, ...): see the examples dir.

A note on elapsed times:

sympy:       Elapsed time: 00:00:00.59
maxima:      Elapsed time: 00:00:12.20
maple:       Elapsed time: 00:00:15.07
mathematica: Elapsed time: 00:00:16.10
sage:        Elapsed time: 00:00:25.66
gap:         Elapsed time: 00:00:18.53

Problem with the new sage

The rich-consolish-interface of the new sage does not work well with pexpect, so that I was not able to upgrade let it work. I should probably read how to run it via ipython, but ...

Inspired by...

The idea was to have an analogue of SageTeX, sympytex or pythontex but more with the idea of parametrized exercises generation than of a math notebook document. This means that it acts as a LaTeX-to-LaTeX filter, allowing freedom to choose the CAS, instead of a LaTeX-to-CAS-language-to-PDF.