Newcommand with single and double argument (probability function)

Question

I want to define a new command such that when a first and only argument is given it does one thing and when a second argument is given it expands the first argument. The idea is to replicate the probability function. One argument is for probability distribution and two arguments are for conditional probability distribution. I really don't know how to do it.

The (completed) following code

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{amssymb}
\newcommand{\PP}[2]{???}
\begin{document}
$\PP{X}$
$\PP{X}{Y}$
\end{document}

should print

\mathbb{P}{\left({X}\right)}
\mathbb{P}{\left({X}\middle|{Y}\right)}

I wouldn't like to have an optional argument because it would affect the order and readability of the code. I mean, I prefer \PP{X}{Y} over \PP[Y][X].

Could you please help me?

Thanks

How about a syntax like \PP{X,Y}, so that you would only ever need a single argument? — Steven B. Segletes, Sep 15 '20 at 19:43
A different possibility would be to have \PP[X]{Y}. Then you'd just need to check if the optional value is empty or not. — Teepeemm, Sep 15 '20 at 19:48

score 9 · Accepted Answer · answered Sep 15 '20 at 20:15

You can do better, with a much easier user syntax.

\documentclass{article}
\usepackage{amsmath,amssymb}
\usepackage{xparse}
\ExplSyntaxOn
\NewDocumentCommand{\PP}{ s O{} >{\SplitArgument{1}{|}}m }
 {
  \mathbb{P}
  \IfBooleanTF{#1}
   { \PPauto #3 }
   { \PPfixed {#2} #3 }
 }
\NewDocumentCommand{\PPauto}{mm}
 {
  \left(
  \IfNoValueTF{#2} { #1 } { #1 ;\middle|; #2 }
  \right)
 }
\NewDocumentCommand{\PPfixed}{mmm}
 {
  \mathopen{#1(}
  \IfNoValueTF{#3} { #2 } { #2 \mathrel{#1|} #3 }
  \mathclose{#1)}
 }
\ExplSyntaxOff
\begin{document}
[
\PP{X} \quad \PP[\big]{X} \quad \PP{\frac{X}{2}}
]
[
\PP{X|Y} \quad \PP[\big]{X | Y} \quad \PP{\frac{X}{2} | Y}
]
\end{document}

The command \PP has an optional argument for the size (never rely on \left and \right alone) or a * variant for the automatic sizing (use it only if really necessary).

The mandatory argument is split at |, if present. So the input code is much easier to read. Spaces around | are irrelevant.

Steven B. Segletes · Answer 2 · 2020-09-15T20:09:35.803

7

I propose a syntax that uses a single argument only. EDITED to include Mico's spacing suggestion.

\documentclass{article}
\usepackage{listofitems,amssymb}
\newcommand\PP[1]{%
  \readlist\arglist{#1}
  \ifnum1=\arglistlen\relax
    \mathbb{P}{\left(#1\right)}
  \else
    \mathbb{P}{\left(\arglist[1]\;\middle|\;\arglist[2]\right)}
  \fi
}
\begin{document}
$\PP{X}$
$\PP{X,Y}$
\end{document}

edited Sep 15 '20 at 20:09

answered Sep 15 '20 at 19:48

Steven B. Segletes

237,551

2

+1. I'd replace \middle| with \;\middle|\;, though. – Mico Sep 15 '20 at 20:07

score 2 · Answer 3 · answered Sep 16 '20 at 06:45

Inspired of Werner's Answer and similar to Segletes's answer above:

\documentclass{article}
\usepackage{amssymb}
\newcommand{\pp}[1]{\ppaux#1\relax}
\def\ppaux#1#2\relax{%
  \ifnum\pdfstrcmp{#2}{}=0
      \mathbb{P}{\left(#1\right)}
  \else
    \mathbb{P}{\left(#1 \;\middle|\; #2\right)}
  \fi
}
\begin{document}
$\pp{X}$
$\pp{XY}$
$\pp{{XY}}$
\end{document}

Newcommand with single and double argument (probability function)

3 Answers3