# How to type permutations with commas a bit faster?

Is it possible to use a package or something to make typing permutations a bit faster? I now have to type $(a,b,c,d)$ in the best case, but I'd like to do something like \Pm{a b c d}. Can I do that?

• You mean it puts the commas in automatically? For me, there is no appreciable speed gain from typing \pm{a b c d} over \pm{a,b,c,d}. – jon Nov 7 '13 at 16:35
• @jon: Yes, I'd like the commas to be inserted automatically. Perhaps it's not that faster for a permutation with 4 elements, but I'm working with lots more, so in my opinion, it's a bit quicker when I don't have to type all the commas. By the way, it's typing \pm{a b c d}over $(a,b,c,d)$. – Jeroen Nov 7 '13 at 17:19
• It should be noted that \pm is already used for ±. – Qrrbrbirlbel Nov 7 '13 at 18:22
• Naturally, I meant after defining a macro like \newcommand\pm[1]{\ensuremath{(#1)}} (and making sure I wasn't already competing with a definition for \pm).... – jon Nov 7 '13 at 19:41

It doesn't seem much easier to type than $(a,b,c)$ but

\documentclass{article}

\def\pm#1{$(\xpm{}#1 ! )$}
\def\xpm#1#2 {\ifx!#2\else#1#2\expandafter\xpm\expandafter,\fi}

\begin{document}

\pm{a b c}

\end{document}


or without the space delimiter:

\documentclass{article}

\def\pm#1{$(\xpm{}#1 ! )$}
\def\xpm#1#2{\ifx!#2\else#1#2\expandafter\xpm\expandafter,\fi}

\begin{document}

\pm{abc}

\pm{a{bc}de}

\end{document}

• It would be shorter with a for loop and not type the space! \pm{abcdefg}, that is if the variables are single letters or add commas only if they are not \pm{abcdefg,ze,xb} – Yiannis Lazarides Nov 7 '13 at 19:19
• @YiannisLazarides you could just miss out the space after #2 then it would iterate over single letter variables with no space needed. – David Carlisle Nov 7 '13 at 19:27
• One can delete the -signs code in order to use \pm in a mathematical environment, like displaymath, align*... – Jeroen Nov 7 '13 at 19:43 • @DavidCarlisle Was thinking about a for loop to capture the comma for the second case although maybe can be done with conditionals only. – Yiannis Lazarides Nov 7 '13 at 19:45 • @Jeroen see update using the comma in input would be possible but seems weird to me in a,bc,de why bc one token but not de anyway a{bc}de is easier:-) – David Carlisle Nov 7 '13 at 21:00 You can use a variant of my answer to Permutation cycle notation \documentclass{article} \usepackage{xparse} \ExplSyntaxOn \NewDocumentCommand{\Pm}{ O{~} m O{,} } { ( \jeroen_cycle:nnn { #1 } { #2 } { #3 } ) } \seq_new:N \l_jeroen_cycle_seq \cs_new_protected:Npn \jeroen_cycle:nnn #1 #2 #3 { \seq_set_split:Nnn \l_jeroen_cycle_seq { #1 } { #2 } \seq_use:Nn \l_jeroen_cycle_seq { #3 } } \ExplSyntaxOff \begin{document}\Pm{1 2 3}\Pm[,]{1,2,3}[\;]\Pm{1 2 3}[;]\Pm[,]{1,2,3}\Pm{1 2 3}[;]$\end{document}  The leading optional argument is the input separator (default a space), the trailing one is the output separator (default a comma). Alternatively, you can set up a key-value interface: \documentclass{article} \usepackage{xparse} \ExplSyntaxOn \keys_define:nn { jeroen/perms } { input-separator .tl_set:N = \l_jeroen_perms_input_separator_tl, input-separator .initial:n = { ~ }, output-separator .tl_set:N = \l_jeroen_perms_output_separator_tl, output-separator .initial:n = { , }, } \NewDocumentCommand{\Pm}{ O{} m } { ( \group_begin: \keys_set:nn { jeroen/perms } { #1 } \jeroen_cycle:n { #2 } \group_end: ) } \NewDocumentCommand{\permset}{ m } { \keys_set:nn { jeroen/perms } { #1 } } \seq_new:N \l_jeroen_cycle_seq \cs_new_protected:Npn \jeroen_cycle:n #1 { \seq_set_split:NVn \l_jeroen_cycle_seq \l_jeroen_perms_input_separator_tl { #1 } \seq_use:NV \l_jeroen_cycle_seq \l_jeroen_perms_output_separator_tl } \cs_generate_variant:Nn \seq_set_split:Nnn { NV } \cs_generate_variant:Nn \seq_use:Nn { NV } \ExplSyntaxOff \begin{document}$\Pm{1 2 3}\Pm[output-separator=\;]{1 2 3}\Pm[output-separator=;]{1 2 3}\Pm[input-separator={,}]{1,2,3}$\permset{output-separator=;}$\Pm{1 2 3}$\permset{input-separator=|}$\Pm{1|2|3}\$
\end{document}


Key-value pairs in the optional argument are local to the current permutation, while those in the \permset command are local to the group they appear in. It would be easy to extend this to also change the outer delimiters.