How to make an equation more compact?

Question

I have an equation that wastes a lot of space around the union symbol:

\documentclass{article}

\usepackage[cmex10]{amsmath}
\usepackage{amssymb}

\begin{document}
\begin{equation}
RA_U  \left ( new , ref \right ) =
\bigcup_{
  \left\{ 
    i  \text{ such that }  f_i \left(  ref \right) < f_i \left( new \right) 
  \right\} 
}
\left\{ 
  X \in \mathbb{R}^M ; 
  x_i \in \left [ f_i \left(  ref \right) ; f_i \left( new \right) \right ] 
\right\}
\end{equation}
\end{document}

This is especially dreadful, since I am using IEEEtran.cls, which has two columns.

How can I compress the equation around the union symbol?

Answer 1

I recommend you do the following:

• Get rid of all \left and \right directives since they (a) insert undesirable horizontal whitespace and (b) don't actually do anything useful in the present context.

• Use \substack (provided by the amsmath package) to break the line below \bigcup into two parts.

• Use \textup (or \textnormal) instead of the default math italics in the definitions of the variable names "ref" and "new".

• Use \mathclap (provided by the mathtools package) to suppress whitespace to the left and right of \bigcup. (This step is also featured in @karlkoeller's answer.)

\documentclass{article}
\usepackage{mathtools,amssymb}
\newcommand\vnew{\textup{new}}
\newcommand\vref{\textup{ref}}
\begin{document}
Before: 
\begin{equation}
RA_U  \left ( new , ref \right ) =
\bigcup_{
  \left\{
    i  \text{ such that }  f_i \left(  ref \right) < f_i \left( new \right)
  \right\}
}
\left\{
  X \in \mathbb{R}^M ;
  x_i \in \left [ f_i \left(  ref \right) ; f_i \left( new \right) \right ]
\right\}
\end{equation}

After:
\begin{equation}
RA_U (\vnew,\vref) =
\bigcup_{ \mathclap{ \substack{i\text{ such that}\\f_i(\vref) < f_i(\vnew)}} } \,
\bigl\{ X\in\mathbb{R}^M ; x_i \in [ f_i(\vref) ; f_i(\vnew) ] \bigr\}
\end{equation}
\end{document}

Answer 2

You can use \mathclap from mathtools package:

\documentclass{article}

\usepackage[cmex10]{amsmath}
\usepackage{amssymb}
\usepackage{mathtools}

\begin{document}
\begin{equation}
RA_U  ( \mathit{new}, \mathit{ref} ) =
\bigcup_{\mathclap{
  \left\{
    i  \text{ such that }  f_i (\mathit{ref}) < f_i ( \mathit{new} )
  \right\}
}}
\left\{
  X \in \mathbb{R}^M ;
  x_i \in [ f_i ( \mathit{ref} ) ; f_i ( \mathit{new} ) ]
\right\}
\end{equation}
\end{document} 

Output:

Answer 3

This is not new with respect to other answers, but I'd like to introduce a couple of tricks:

\documentclass{article}

\usepackage{amsmath,mathtools}
\usepackage{amssymb}

\newcommand{\V}[1]{\mathrm{#1}} % or \mathit
\newcommand{\numberset}[1]{\mathbb{#1}}
\newcommand{\R}{\numberset{R}}

\begin{document}
This is the original equation
\begin{equation}
RA_{U}(\V{new},\V{ref}) =
\bigcup_{
  \quad
    \mathclap{\substack{
    \text{$i$ such that}\\[\jot]
    f_i(\V{ref}) < f_i(\V{new})
  }}
  \quad
}
\{ 
  X \in \R^{M} : 
  x_i \in [f_i(\V{ref}); f_i(\V{new})] 
\}
\end{equation}

\renewcommand{\V}[1]{\mathit{#1}}
\renewcommand{\numberset}[1]{\mathsf{#1}}

Just to see the effect of changing just a couple of commands
\begin{equation}
RA_{U}(\V{new},\V{ref}) =
\bigcup_{
  \quad
    \mathclap{\substack{
    \text{$i$ such that}\\[\jot]
    f_i(\V{ref}) < f_i(\V{new})
  }}
  \quad
}
\{ 
  X \in \R^{M} : 
  x_i \in [f_i(\V{ref}); f_i(\V{new})] 
\}
\end{equation}
\end{document}

The main trick is the macro \V for typesetting multiletter variables; then also \numberset is defined, which is used indirectly for defining \R (and other number sets). I show how, just changing those definitions, one can change the output.

For the wide subscript I use \substack in a \mathclap, but adding some space around it in order that the union symbol is not adjacent to its surroundings.

Note the \jot used for giving some room between the two lines in the subscript. Also \text{$i$ such that} is handier to type than i\text{ such that}, because spaces are ‘natural’.

Answer 4

Firstly don;t use \left...\right all over the place, it is not a good idea.

Why not just write \{ i \mid f_i ( ref ) < f_i ( new ) \} ( it looks better to add space around the |)

Answer 5

I would write the index to the joint in two lines as

You can obtain this through

\documentclass{article}

\usepackage[cmex10]{amsmath}
\usepackage{amssymb}

\begin{document}
\begin{equation}
RA_U  \left ( new , ref \right ) =
\mkern-36mu
\bigcup_{
  i, \atop f_i \left(  ref \right) < f_i \left( new \right) 
}
\mkern-36mu
\left\{ 
  X \in \mathbb{R}^M ; 
  x_i \in \left [ f_i \left(  ref \right) ; f_i \left( new \right) \right ] 
\right\}
\end{equation}
\end{document}

Note that I addtionally customized the kerning by hand. You can use the mathtools package as well (see @Micos answers for example).

Edit

According to @egregs comment I'd like to present a variety using the \substack command provided by amsmath that yelds better results regarding the size of the index:

\begin{equation}
RA_U  \left ( new , ref \right ) =
\mkern-40mu
\bigcup_{
  \substack{
    i, \\
    f_i \left(  ref \right) < f_i \left( new \right) 
  }
}
\mkern-40mu
\left\{ 
  X \in \mathbb{R}^M ; 
  x_i \in \left [ f_i \left(  ref \right) ; f_i \left( new \right) \right ] 
\right\}
\end{equation}

Answer 6

It is visual formatting, so it's better avoided if you can, but you can do:

\begin{equation}
RA_U  \left ( new , ref \right ) =
\qquad\bigcup_{\mathstrut\makebox[0pt][c]{$
  \left\{ 
    i  \text{ such that }  f_i \left(  ref \right) < f_i \left( new \right) 
  \right\} $}
}
\qquad \left\{ 
  X \in \mathbb{R}^M ; 
  x_i \in \left [ f_i \left(  ref \right) ; f_i \left( new \right) \right ] 
\right\}
\end{equation}

To obtain