% based on example 8 in pythontex_gallery % https://github.com/gpoore/pythontex/ \documentclass[12pt]{pylatex} \usepackage{examples} \begin{document} \section*{Step-by-step integration} This is another nice example drawn from the Pythontex gallery, see \ \url{https://github.com/gpoore/pythontex}. It shows the step-by-step computations of a simple triple integral. \begin{python} from sympy import * x, y, z = symbols('x,y,z') f = Symbol('f(x,y,z)') # Define limits of integration x_max = 2; y_max = 3; z_max = 4; x_min = 0; y_min = 0; z_min = 0; lhs = Integral(f, (x, x_min, x_max), (y, y_min, y_max), (z, z_min, z_max)) # py(lhs.01,lhs) f = x*y + y*sin(z) + cos(x+y) rhs = Integral(f, (x, x_min, x_max), (y, y_min, y_max), (z, z_min, z_max)) # py(rhs.01,rhs) rhs = Integral(Integral(f, (x, x_min, x_max)).doit(), (y, y_min, y_max), (z, z_min, z_max)) # py(rhs.02,rhs) rhs = Integral(Integral(f, (x, x_min, x_max), (y, y_min, y_max)).doit(), (z, z_min, z_max)) # py(rhs.03,rhs) rhs = Integral(f, (x, x_min, x_max), (y, y_min, y_max), (z, z_min, z_max)).doit() # py(rhs.04,rhs) # And now, a numerical approximation rhs = N(rhs) # py(rhs.05,rhs) \end{python} \begin{minipage}[t]{0.65\textwidth} \begin{align*} \py{lhs.01} &= \py{rhs.01}\\ &= \py{rhs.02}\\ &= \py{rhs.03}\\ &= \py{rhs.04}\\[8pt] &\approx \py{rhs.05} \end{align*} \end{minipage} \hskip 1cm \lower16pt\hbox{% \begin{minipage}[t]{0.35\textwidth} \begin{latex} \begin{align*} \py{lhs.01} &= \py{rhs.01}\\ &= \py{rhs.02}\\ &= \py{rhs.03}\\ &= \py{rhs.04}\\[8pt] &\approx \py{rhs.05} \end{align*} \end{latex} \end{minipage}} \end{document}