How to annotate calculations?

Question

I am writing a basic mathematics book and I would like to annotate some calculations, using arrows, underlines, horizontal, vertical and diagonal lines, boxes, circles, etc., with different colors, to provide a visual aid to the reader. Here is an example (please disregard the wrong explanations and visual clutter):

Is there any specific package for this task? (A few weeks ago, I came across a site that explained something along those lines. I don't remember exactly, but it looks like they used the "amsmath" package for that functionality.)

Answer 1

I suggest using tikzmark. The command is \tikzmarknode{<label>}{<content>}. You can use several of these in your equation with different labels. Then use the options remember picture, overlay in a tikzpicture and use TikZ commands to draw the various annotations.

The code uses a variety of libraries other than tikzmark: shapes.geometric is used for the ellipse, shapes.arrows is used for the "result" arrow, fit is used to contain the contents of the red ellipse, blue rectangle and yellow circle, bending is used to improve the arrowhead of the blue arrow.

Remember, when using tikzmark you must compile twice after any changes to the node positions.

\documentclass{article}

\usepackage{tikz}
\usetikzlibrary{tikzmark, shapes.geometric, shapes.arrows, fit, bending}

\begin{document}

\[
\tikzmarknode{a1}{\frac{4}{2}}+\tikzmarknode{a2}{\frac{6}{3}}=
\frac{\tikzmarknode{b1}{(3\times 4)}+\tikzmarknode{b2}{(2\times 6)}}{\tikzmarknode{b3}{2\times 3}}=\tikzmarknode{c1}{\frac{12+12}{6}}=\tikzmarknode{c2}{\frac{24}{6}}=\tikzmarknode{d1}{4}
\]

\begin{tikzpicture}[remember picture, overlay, font=\sffamily]
\draw[red, thick, ->, shorten <=1em, , shorten >=1em](a2.south east)--node[below, pos=.45, scale=.4]{1}(a1.north west);
\node[draw=red, thick, ellipse, fit=(b1), inner ysep=0, inner xsep=-1mm](ell){};
\draw[thick, red] (ell)--++(0,.5)node[above, red, scale=.4]{This is important!};
\draw[red, thick] (b2.south west)--node[above=2mm, red, scale=.5]{\bfseries WRONG!}(b2.north east);
\draw[green!70!black, thick] (b3.east)--node[below]{$\uparrow$}node[below=5mm, align=left, green!70!black, scale=.5]{This multiplication is not\\necessary Try to simplify.}(b3.west) ([yshift=2pt]b3.east)--([yshift=2pt]b3.west);
\node[draw=blue, thick, fit=(c1), inner xsep=1pt](box){};
\draw[blue, thick, ->, shorten >=3pt] (box) to[out=90, in=90] (c2.north);
\node[draw=yellow!70!orange, thick, circle, fit=(d1), inner sep=1pt](cir){};
\node[draw=yellow!70!orange, thick, text=yellow!70!orange, single arrow, shape border rotate=180, anchor=west, scale=.4, single arrow tip angle=40, minimum height=30mm] at (cir.east){\quad RESULT};
\end{tikzpicture}

\end{document}

Answer 2

A simpler (but not as powerful as tikzmark) package would be the annotate-equations package.

Here a short example taken from the package documentation:

\documentclass{article}

\usepackage{mathtools}
\usepackage{annotate-equations}


\begin{document}

\renewcommand{\eqnhighlightheight}{\vphantom{\hat{H}}\mathstrut} 
\begin{equation*}
i \tikzmarknode{hbar}{\mathstrut\hbar} \frac{\partial}{\partial t} \eqnmarkbox[blue]{Psi1}{\Psi(x, t)} = \eqnmark[red]{Hhat}{\hat{H}} \eqnmarkbox[blue]{Psi2}{\Psi(x, t)}
\end{equation*}
\annotate[yshift=3em]{above}{hbar}{$\hbar = \frac{h}{2\pi}$, reduced Planck constant} 
\annotate[yshift=1em]{above}{Hhat}{Hamilton operator} 
\annotatetwo[yshift=-1em]{below}{Psi1}{Psi2}{Wave function}

\end{document}