5

Recently I have discovered the interesting package named luacas (compilable with LuaLaTeX). To pag. 14 of the manual

https://ctan.mirror.garr.it/mirrors/ctan/macros/luatex/latex/luacas/doc/luacas.pdf

I have not understood the necessary packages to put in the preamble to compile the MWE to plot f and f'.

Someone please, can help me?

Here the fragment of the code:

\directlua{
  tex.print(h:tolatex())
}
For Bob’s purposes, \fetch{h} is exactly what he needs:

\begin{tikzpicture}[scale=0.9]
  \begin{axis}[legend pos = north west]
    \addplot [domain=-3.5:1.5,samples=100]
      {\fetch{h}};
    \addlegendentry{$f$};
    \addplot[densely dashed]
      [domain=-3.25:1.25,samples=100]
      {\fetch{dh}};
    \addlegendentry{$df/dx$};
    \addplot[gray,dashed,thick]
      [domain=-3.5:1.5] {0};
  \end{axis}
\end{tikzpicture}

Alternatively, Bob could use \store. The \store command will fetch the contents of its mandatory argument and store it in a macro of the same name.

\store{h}
\store{dh}
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2 Answers 2

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4

As far as I understand, in the preamble it is sufficient to load only

\usepackage{luacas}

For your plotting fragment, you also need the pgfplots package. Then everything works. Here is a minimal example.

\documentclass{article}
\usepackage{luacas}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}

\begin{document}

\begin{CAS}
vars('x')
f = x^2+2*x-2
g = x^2-1
subs = {[x] = f}
dh = expand(substitute(subs,g))
h = simplify(int(dh,x)+10)
\end{CAS}

\noindent
Bob does not need a nicely typeset formula in the text, such as
\[
\print{h}.
\]
For his purpose, he needs the expression produced by
\[
\fetch{h}
\]
instead:


\begin{center}
\begin{tikzpicture}[scale=0.9]
  \begin{axis}[legend pos = north west]
    \addplot [domain=-3.5:1.5,samples=100]
      {\fetch{h}};
    \addlegendentry{$h$};
    \addplot[densely dashed]
      [domain=-3.25:1.25,samples=100]
      {\fetch{dh}};
    \addlegendentry{$h'$};
    \addplot[gray,dashed,thick]
      [domain=-3.5:1.5] {0};
  \end{axis}
\end{tikzpicture}
\end{center}

Here $dh$ is obtained by substituting $f$ into $g$, so $dh(x)=g(f(x))$. The function $h$ is then defined by
\[
h(x)=\int g(f(x))\,dx+10.
\]
\end{document}

enter image description here

Edit.
I have edited the code slightly to make the example more meaningful. The main purpose of the luacas package is to provide symbolic computations directly within LuaLaTeX.

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1
  • 1
    Thank you very very much. Commented 11 hours ago
3

  • you need to load luacas and define the functions you'd like to use

  • load pgfplots for plotting

  • compile with lualatex

A minimal compilable example:

% !TeX TS-program = lualatex -interaction=nonstopmode % | txs:///view-pdf | txs:///view-log

\documentclass{article}

\usepackage{luacas}
\usepackage{pgfplots}

\begin{document}

\begin{CAS}
vars('x')
h=x^2
\end{CAS}

\begin{tikzpicture}
  \begin{axis}[legend pos = north west]
    \addplot [domain=-3.5:1.5,samples=100] {\fetch{h}};
    \addlegendentry{$f$};
  \end{axis}
\end{tikzpicture}
    
\end{document}

enter image description here

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