September 6, 2023 Compiled on September 6, 2023 at 7:56pm

1 Example using pyconsole

2 Example using pycode

3 Calling python passing it argument to process and getting the Latex back

4 Calling python from latex to solve diﬀerential equations and show its solution

2 Example using pycode

3 Calling python passing it argument to process and getting the Latex back

4 Calling python from latex to solve diﬀerential equations and show its solution

This note describes all the steps to use Python inside Latex. The directions are based on using Linux, since this is the system I tried this on.

Using texlive 2020, this package (pythontex) is already there. There is not additional installation needed. Once you install texlive itself, then you have this package.

Here is the most simple tex ﬁle that uses python

\documentclass[11pt]{article}% \usepackage{pythontex} \begin{document} This document uses Python \end{document}

Now comes the tricky part. To compile it, we have to do the following commands

pdflatex foo.tex /usr/local/texlive/2022/texmf-dist/scripts/pythontex/pythontex.py foo.tex

Which prints on the screen this

>/usr/local/texlive/2022/texmf-dist/scripts/pythontex/pythontex.py python_file.tex This is PythonTeX 0.17 -------------------------------------------------- PythonTeX: python_file - 0 error(s), 0 warning(s)

If you get an error ModuleNotFoundError: No module named 'pygments' then try the following to install pygments: pip install pygments ﬁrst.

Now need to compile the latex ﬁle on more time

pdflatex foo.tex

We have to run the above 3 commands each time. On my installation of texlive 2022, the script pythontex.py was not already in the path, so instead of keep typing the above long command each time, I added an alias to my bashrc

vi $HOME/.bashrc #add this line below to the file alias PYX=/usr/local/texlive/2022/texmf-dist/scripts/pythontex/pythontex.py #after exiting vi, typed source $HOME/.bashrc

So now I can write (less typing) the following

pdflatex foo.tex PYX foo.tex pdflatex foo.tex

Or you can add it to the path. You must have python itself installed. Version 2.7 or better, else none of the above will work.

In the above example, we did not do anything interesting. Let us now make a python variable, raise it to the power 2, and show the result in Latex

\documentclass[11pt]{article}% \usepackage{pythontex} \usepackage{nopageno} \begin{document} \begin{pyconsole} x = 987.27 x = x**2 \end{pyconsole} The variable is $x=\pycon{x}$ \end{document}

Which produces the following PDF ﬁle when compiled

Here is screen shot of the above

In this example we will call Python to do symbolic computation, which is integrating a function, then obtain the latex back of the result. For this sympy is used inside Python.

Create Latex ﬁle like this

\documentclass[11pt]{article}% \usepackage{pythontex} \usepackage{nopageno} \begin{document} \begin{pycode} from sympy import * x=symbols('x') result = latex(integrate("(1+x)**(1/2)",x)) \end{pycode} The result of integrating $\int \sqrt{ 1+x } \, dx$ is given by $\py{result}$ \end{document}

Now compile using the same commands as ﬁrst example above

pdflatex foo.tex /usr/local/texlive/2022/texmf-dist/scripts/pythontex/pythontex.py foo.tex pdflatex foo.tex

Which produces the following PDF ﬁle when compiled

Here is screen shot of the above

In this example, we make a small function inside pycode which takes one argument which is string that represents the integrand to integrate and second argument which is the integration variable.

Create Latex ﬁle like this

\documentclass[11pt]{article}% \usepackage{amsmath} \usepackage{pythontex} \usepackage{nopageno} \begin{document} \begin{pycode} from sympy import * def int(theIntegrand,var): var = symbols(var) anti = integrate(theIntegrand,var) return latex(anti) \end{pycode} The result of integrating $\int \frac{1}{\sqrt{ 1+x }} \, dx$ is given by $\py{int("1/(1+x)**(1/2)","x")}$ Here is some list of integrations to do \begin{align*} \int \frac{1}{\sqrt{ 1+x }} \, dx &= \py{int("1/(1+x)**(1/2)","x")} \\ \int \sin x \, dx &= \py{int("sin(x)","x")} \\ \int x \sin x \, dx &= \py{int("x*sin(x)","x")} \\ \int x^2 \sin x \, dx &= \py{int("x**2 * sin(x)","x")} \\ \int x e^{2 x} \, dx &= \py{int("x*exp(2*x)","x")} \\ \int \frac{1}{1+u} \, du &= \py{int("1/(1+u)","u")} \\ \end{align*} \end{document}

Compiling again using the same commands as the above examples

pdflatex foo.tex /usr/local/texlive/2022/texmf-dist/scripts/pythontex/pythontex.py foo.tex pdflatex foo.tex

Produces the following PDF ﬁle

Here is screen shot of the above

In this example, we make a small function inside pycode which takes and ode to solve, using diﬀerent initial conditions.

Create Latex ﬁle like this

\documentclass[11pt]{article}% \usepackage{amsmath} \usepackage{pythontex} \usepackage{nopageno} \begin{document} \begin{pycode} from sympy import * def solveODE(ode,y,x): x = Symbol(x) y = Function(y) lhs,rhs = ode.split('=') ode = Eq(S(lhs),S(rhs)) sol = dsolve(ode,y(x)) return latex(sol) def solveODEwithIC(ode,y,x,ic): x = Symbol(x) y = Function(y) lhs,rhs = ode.split('=') ode = Eq(S(lhs),S(rhs)) sol = dsolve(ode,y(x),ics= S(ic) ) return latex(sol) \end{pycode} Given the first order differential equation $y'(x)=1+2 x$, it has the solution \[ \py{solveODE("Derivative(y(x),x)=1+2*x","y","x")} \] % When the initial conditions are $y(0)=3$, then the solution becomes \[ \py{solveODEwithIC("Derivative(y(x),x)=1+2*x","y","x","{y(0):3}")} \] We can also solve second order ODE in Latex. For example, given the ode $y''(x)+3 y(x)=1+2 x$ then its solution is \[ \py{solveODE("Derivative(y(x),x,x)+y(x)=1+2*x","y","x")} \] The above solution with initial conditions $y(0)=1$ and $y'(0)=0$ is given by \[ \py{solveODEwithIC("Derivative(y(x),x,x)+y(x)=1+2*x","y","x","{y(0):1,y(x).diff(x).subs(x, 0): 0}")} \] \end{document}

Compiling again using the same commands as the above examples produces the following PDF ﬁle

Here is screen shot of the above

References:

- Pythontex main documenation http://www.ctan.org/pkg/pythontex
- pythontex quickstart PDF
- Pythontex GitHub
- A Gentle Introduction to PythonTeX