Definition-time expansiton of command line input

Question

I'm trying to make the following code work correctly. I'm using command line call to python to check whether a number is in a list (no clue how to do this in pure LaTeX(?)). I then want to check whether the result is 'True' or 'False'.

\documentclass{article}

\newcommand{\mysequence}{[2,3,5,7,11,13,17,19,23,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101]}
\makeatletter
\newcommand\isprime[1]{\@@input|"python -c print((#1)in\mysequence)"}
\makeatother

\newcommand{\compare}[1]{%
\def\test{\isprime{#1}}
\def\true{True}
\def\false{False}

Test: \test\par
\ifx\test\true
#1 is PRIME! :D
\else
#1 is not prime ;(
\fi
\vspace{10pt}
}%

\begin{document}
\compare{3} % 3 is prime
\par
\compare{4} % 4 is not prime
\end{document}

As is, I get a correct value of \test, but the \ifx comparison does not seem to expand the \@@input and I get a wrong result. The output looks like that:

I believe I could fix this by using \edef instead of \def, but we I try i make LaTeX very angry and it goes a little bit too far past my knowlegde of it to fix it.

Answer 1

Set up to use the OP's syntax for \mysequence, though I think space separated has certain advantages over comma separated, were I to do it.

\documentclass{article}
\usepackage{listofitems}
\newcommand{\mysequence}{[2,3,5,7,11,13,17,19,23,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101]}
\newcommand\compare[1]{%
  \setsepchar{,#1,||[#1,||,#1]}%
  \readlist\mylist{\mysequence}%
  \ifnum\listlen\mylist[]>1 #1 is PRIME!\else #1 is not prime\fi
}

\begin{document}

\compare{2}

\compare{3} % 3 is prime

\compare{4} % 4 is not prime

\compare{101}
\end{document}

SUPPLEMENT

To handle the case where the argument can also be macro (e.g., \thepage, at least in the arabic case) that fully expands to an integer, try this:

\documentclass{article}
\usepackage{listofitems}
\newcommand{\mysequence}{[2,3,5,7,11,13,17,19,23,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101]}
\newcommand\compare[1]{\edef\tmp{#1}\expandafter\compareaux\expandafter{\tmp}}
\newcommand\compareaux[1]{%
  \setsepchar{,#1,||[#1,||,#1]}%
  \readlist\mylist{\mysequence}%
  \ifnum\listlen\mylist[]>1 #1 is PRIME!\else #1 is not prime\fi
}

\begin{document}

\compare{2}

\compare{3} % 3 is prime

\compare{4} % 4 is not prime

\compare{101}

\compare{\thepage}
\end{document}

If one did not want to rely on \edef, but was satisfied to limit the macro to a single expansion, one could instead define

\newcommand\compare[1]{\expandafter\compareaux\expandafter{#1}}

Answer 2

If you really want a solution that goes through an external program, you can get inspiration from this answer of egreg and do:

\documentclass{article}
\usepackage{etoolbox}
\usepackage{pgffor}

\makeatletter

\newcommand{\mysequence}{%
  [2,3,5,7,11,13,17,19,23,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101]%
}

\newcommand*{\isInList@i}[2]{%
  \begingroup
  \endlinechar=\m@ne\everyeof{\noexpand}%
  \edef\x{\@@input|"python3 -c 'print(#2 in #1)'" }%
  \expandafter
  \endgroup
  \expandafter
  \ifstrequal\expandafter{\x}{True}{%
    #2 is in the list}{%
    #2 is not in the list}.%
}

\newcommand*{\isInList}[1]{%
  \expandafter\isInList@i\expandafter{\mysequence}{#1}%
}

\makeatother

\setlength{\parindent}{0pt}

\begin{document}
\foreach \i in {1,...,23} {%
  \isInList{\i}\par
}
\end{document}

(I didn't want to say “prime” here because the list contained in \mysequence is limited; that would lead to say, for instance, that 103 isn't a prime number...)

Note for the passersby: compiling this requires giving the -shell-escape option to LaTeX (pdflatex, lualatex, xelatex, etc.); otherwise, it will refuse to run the shell command python3 -c '...' contained in the code (this security measure ensures that classes, packages and documents don't run arbitrary shell commands behind your back).