Landau notation with optional argument

Question

I would like to create a command for Landau's notations (small o for example), which would have an optional argument consisting of two elements (the variable and the point) separated by a comma. How do I do this?

Here is an example.

\documentclass[11pt]{article}
\usepackage{amsmath}
\begin{document}
% \petito[x, \infty]{\ln x}. Expected result :
$ \underset{x \rightarrow \infty}{\mathrm{o}} \left( \ln x \right)$
% \petito{\ln x}. Expected result :
$ \mathrm{o} \left( \ln x \right)$
\end{document}

Is there a special reason why this is tagged with expl3, latex3 and xparse? — Jasper Habicht, Mar 08 '23 at 15:17
I thought a simple solution would be to use latex3as here: https://tex.stackexchange.com/questions/87407/iterating-through-comma-separated-arguments — jowe_19, Mar 08 '23 at 15:20

score 2 · Accepted Answer · answered Mar 08 '23 at 15:30

2

To me the \petito[x,\infty]{...} syntax is bad, both to read and to parse, easier to just use [x\to\infty] directly

\documentclass[11pt]{article}
\usepackage{amsmath}
\DeclareMathOperator*{\ooo}{o}
\NewDocumentCommand\petito{o m}{
  \IfNoValueTF{#1}{
    % normal case
    \ooo\left(#2\right)
  }{
    \ooo_{#1}\left(#2\right)
  }
}
\begin{document}
$\petito[x\to\infty]{\ln x}$
[
  \petito[x\to\infty]{\ln x}
]
$ \underset{x \rightarrow \infty}{\mathrm{o}} \left( \ln x \right)$
$\petito{\ln x}$
$ \mathrm{o} \left( \ln x \right)$
\end{document}

Notes: $...$ should never write below, that disturbs the line spacing, thus \DeclareMathOperator* is used to make a macro that behaves like \lim.

Additionally, I'm not a fan of the fence autoscaling, but I've left it here.

answered Mar 08 '23 at 15:30

daleif

54,450

Thank you. Even if it's bad, would it be possible to have a solution with the comma? – jowe_19 Mar 08 '23 at 16:00
@jowe_19 sure, but I don't have the time to provide it. It should be easy enough to add via some expl3 macros. – daleif Mar 08 '23 at 16:16
This can be accomplished using the >{\SplitArgument{...}{...}} syntax. – Gaussler Mar 08 '23 at 16:29

score 1 · Answer 2 · answered Mar 08 '23 at 16:23

I don't see how the proposed syntax would be clearer or easier than

\petito_{x\to\infty}(\log x)

or, if you want to specify in an easier way the size of the parentheses,

\petito_{x\to\infty}{\log x}

with maybe

\petito_{x\to\infty}[big]{\log x}

for larger parentheses or

\petito_{x\to\infty}[*]{\log x}

for autosizing ones.

You can realize the latter syntax quite easily with ltcmd (formerly xparse).

\documentclass{article}
\usepackage{amsmath}
\NewDocumentCommand{\petito}{e{}O{}m}{%
  \genericlandau{o}{#1}{#2}{#3}%
}
\NewDocumentCommand{\grando}{e{}O{}m}{%
  \genericlandau{\mathit{O}}{#1}{#2}{#3}%
}
\ExplSyntaxOn
\NewDocumentCommand{\genericlandau}{mmmm}
 {
  \operatorname*{#1}
  \IfValueT{#2}{\sb{#2}}% the subscript
  \jowe_landau_arg:nn { #3 } { #4 }
 }
\cs_new_protected:Nn \jowe_landau_arg:nn
 {
  \str_case:nnF { #1 }
   {
    {}{\left}
    {}{}
   }
   { \use:c { #1l } } (
  #2
  \str_case:nnF { #1 }
   {
    {}{\right}
    {}{}
   }
   { \use:c { #1r } } )
 }
\ExplSyntaxOff
\begin{document}
\begin{gather}
\petito{\log x} \
\petito[big]{\log x} \
\petito[Big]{\log x} \
\petito[*]{\frac{\sin x}{x}} \
\petito_{x\to\infty}{\log x} \
\petito_{x\to\infty}[big]{\log x} \
\petito_{x\to\infty}[Big]{\log x} \
\petito_{x\to\infty}[*]{\frac{\sin x}{x}} \
\grando{\log x} \
\grando[big]{\log x} \
\grando[Big]{\log x} \
\grando[*]{\frac{\sin x}{x}} \
\grando_{x\to\infty}{\log x} \
\grando_{x\to\infty}[big]{\log x} \
\grando_{x\to\infty}[Big]{\log x} \
\grando_{x\to\infty}[*]{\frac{\sin x}{x}}
\end{gather}
\end{document}

You may want to use \mleft...\mright from the mleftright package or an equivalent construction. — Gaussler, Mar 08 '23 at 16:43

Landau notation with optional argument

2 Answers2