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(From these references no 0018 text was directly copied.) 0019 0020 Copyright 2007, 2008, 2009, 2010, 2011, 2012, 2013, 0021 2014, 2015, 2016, 2017, 2018 Karl Berry. 0022 0023 Copyright 1988, 1994, 2007 Stephen Gilmore. 0024 0025 Copyright 1994, 1995, 1996 Torsten Martinsen. 0026 0027 Permission is granted to make and distribute verbatim copies of 0028 this manual provided the copyright notice and this permission notice 0029 are preserved on all copies. 0030 0031 0032 Permission is granted to copy and distribute modified versions of this 0033 manual under the conditions for verbatim copying, provided that the entire 0034 resulting derived work is distributed under the terms of a permission 0035 notice identical to this one. 0036 0037 Permission is granted to copy and distribute translations of this manual 0038 into another language, under the above conditions for modified versions. --> 0039 <!-- Created by GNU Texinfo 6.5, http://www.gnu.org/software/texinfo/ --> 0040 <head> 0041 <meta http-equiv="Content-Type" content="text/html; charset=utf-8"> 0042 <title>\left & \right (LaTeX2e unofficial reference manual (November 2018))</title> 0043 0044 <meta name="description" content="\left & \right (LaTeX2e unofficial reference manual (November 2018))"> 0045 <meta name="keywords" content="\left & \right (LaTeX2e unofficial reference manual (November 2018))"> 0046 <meta name="resource-type" content="document"> 0047 <meta name="distribution" content="global"> 0048 <meta name="Generator" content="makeinfo"> 0049 <link href="index.html#Top" rel="start" title="Top"> 0050 <link href="IndexDocument.html#Index" rel="index" title="Index"> 0051 <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents"> 0052 <link href="Delimiters.html#Delimiters" rel="up" title="Delimiters"> 0053 <link href="_005cbigl-_0026-_005cbigr-etc.html#g_t_005cbigl-_0026-_005cbigr-etc" rel="next" title="\bigl & \bigr etc"> 0054 <link href="Delimiters.html#Delimiters" rel="prev" title="Delimiters"> 0055 <style type="text/css"> 0056 <!-- 0057 /* $Id: latex2e.css 690 2018-09-15 15:20:19Z jimhefferon $ 0058 Minor css for latexrefman. Public domain. 0059 Originally written by Jim Hefferon and Karl Berry, 2018. */ 0060 0061 /* So you can style for yourself */ 0062 @import url("/css/latexreflocal.css"); 0063 0064 0065 0066 a.summary-letter {text-decoration: none} 0067 blockquote.indentedblock {margin-right: 0em} 0068 blockquote.smallindentedblock {margin-right: 0em; font-size: smaller} 0069 blockquote.smallquotation {font-size: smaller} 0070 div.display {margin-left: 3.2em} 0071 div.example {margin-left: 3.2em} 0072 div.lisp {margin-left: 3.2em} 0073 div.smalldisplay {margin-left: 3.2em} 0074 div.smallexample {margin-left: 3.2em} 0075 div.smalllisp {margin-left: 3.2em} 0076 kbd {font-style: oblique} 0077 pre.display {font-family: inherit} 0078 pre.format {font-family: inherit} 0079 pre.menu-comment {font-family: serif} 0080 pre.menu-preformatted {font-family: serif} 0081 pre.smalldisplay {font-family: inherit; font-size: smaller} 0082 pre.smallexample {font-size: smaller} 0083 pre.smallformat {font-family: inherit; font-size: smaller} 0084 pre.smalllisp {font-size: smaller} 0085 span.nolinebreak {white-space: nowrap} 0086 span.roman {font-family: initial; font-weight: normal} 0087 span.sansserif {font-family: sans-serif; font-weight: normal} 0088 ul.no-bullet {list-style: none} 0089 BODY { 0090 margin-top: 1em; 0091 margin-left: 1em; /* auto results in two-digit <ol> lost off left */ 0092 margin-right: 1em; 0093 margin-bottom: 1em; 0094 /* the idea is to use the whole window, unless it is ridiculously 0095 wide, probably with too-small fonts, too. */ 0096 max-width: 64em; 0097 } 0098 0099 /* Because we want @math{... @code ...} to be upright, not slanted, 0100 and Texinfo won't fix it. */ 0101 code {font-style:normal; font-family:monospace; } 0102 0103 /* We put a link to our own home page at the bottom. */ 0104 div.referenceinfo {font-size:small;} 0105 0106 --> 0107 </style> 0108 0109 0110 </head> 0111 0112 <body lang="en"> 0113 <a name="g_t_005cleft-_0026-_005cright"></a> 0114 <div class="header"> 0115 <p> 0116 Next: <a href="_005cbigl-_0026-_005cbigr-etc.html#g_t_005cbigl-_0026-_005cbigr-etc" accesskey="n" rel="next">\bigl & \bigr etc</a>, Up: <a href="Delimiters.html#Delimiters" accesskey="u" rel="up">Delimiters</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="IndexDocument.html#Index" title="Index" rel="index">Index</a>]</p> 0117 </div> 0118 <hr> 0119 <a name="g_t_005cleft-_0026-_005cright-1"></a> 0120 <h4 class="subsubsection">16.2.5.1 <code>\left</code> & <code>\right</code></h4> 0121 0122 <a name="index-delimiters_002c-paired"></a> 0123 <a name="index-paired-delimiters"></a> 0124 <a name="index-matching-parentheses"></a> 0125 <a name="index-matching-brackets"></a> 0126 <a name="index-null-delimiter"></a> 0127 <a name="index-_005cleft"></a> 0128 <a name="index-_005cright"></a> 0129 0130 0131 <p>Synopsis: 0132 </p> 0133 <div class="example"> 0134 <pre class="example">\left <var>delimiter1</var> ... \right <var>delimiter2</var> 0135 </pre></div> 0136 0137 <p>Make matching parentheses, braces, or other delimiters. LaTeX makes 0138 the delimiters tall enough to just cover the size of the formula that 0139 they enclose. 0140 </p> 0141 <p>This makes a unit vector surrounded by parentheses tall enough to cover 0142 the entries. 0143 </p> 0144 <div class="example"> 0145 <pre class="example">\begin{equation} 0146 \left(\begin{array}{c} 0147 1 \\ 0148 0 \\ 0149 \end{array}\right) 0150 \end{equation} 0151 </pre></div> 0152 0153 <p>See <a href="Delimiters.html#Delimiters">Delimiters</a> for a list of the common delimiters. 0154 </p> 0155 <p>Every <code>\left</code> must have a matching <code>\right</code>. In the above 0156 example, leaving out the <code>\left(</code> gets the error message 0157 ‘<samp>Extra \right</samp>’. Leaving out the <code>\right)</code> gets ‘<samp>You 0158 can't use `\eqno' in math mode</samp>’. 0159 </p> 0160 <a name="index-package_002c-amsmath-6"></a> 0161 <a name="index-amsmath-package-6"></a> 0162 0163 <a name="index-package_002c-mathtools-2"></a> 0164 <a name="index-mathtools-package-2"></a> 0165 0166 <p>However, <var>delimiter1</var> and <var>delimiter2</var> need not match. A common 0167 case is that you want an unmatched brace, as below. Use a period, 0168 ‘<samp>.</samp>’, as a null delimiter. 0169 </p> 0170 <div class="example"> 0171 <pre class="example">\begin{equation} 0172 f(n)=\left\{\begin{array}{ll} 0173 1 &\mbox{--if \(n=0\)} \\ 0174 f(n-1)+3n^2 &\mbox{--else} 0175 \end{array}\right. 0176 \end{equation} 0177 </pre></div> 0178 0179 <p>Note that to get a curly brace as a delimiter you must prefix it with a 0180 backslash, <code>\{</code>. (The packages <samp>amsmath</samp> and 0181 <samp>mathtools</samp> allow you to get the above construct through in a 0182 <code>cases</code> environment.) 0183 </p> 0184 <p>The <code>\left ... \right</code> pair make a group. One consequence is that 0185 the formula enclosed in the <code>\left ... \right</code> pair cannot have 0186 line breaks in the output. This includes both manual line breaks and 0187 LaTeX-generated automatic ones. In this example, LaTeX breaks the 0188 equation to make the formula fit the margins. 0189 </p> 0190 <div class="example"> 0191 <pre class="example">Lorem ipsum dolor sit amet 0192 \( (a+b+c+d+e+f+g+h+i+j+k+l+m+n+o+p+q+r+s+t+u+v+w+x+y+z) \) 0193 </pre></div> 0194 0195 <p>But with <code>\left</code> and <code>\right</code> 0196 </p> 0197 <div class="example"> 0198 <pre class="example">Lorem ipsum dolor sit amet 0199 \( \left(a+b+c+d+e+f+g+h+i+j+k+l+m+n+o+p+q+r+s+t+u+v+w+x+y+z\right) \) 0200 </pre></div> 0201 0202 <p>LaTeX won’t break the line, causing the formula to extend into the 0203 margin. 0204 </p> 0205 <p>Because <code>\left ... \right</code> make a group, all the usual grouping 0206 rules hold. Here, the value of <code>\testlength</code> set inside the 0207 equation will be forgotten, and the output is ‘<samp>1.2pt</samp>’. 0208 </p> 0209 <div class="example"> 0210 <pre class="example">\newlength{\testlength} \setlength{\testlength}{1.2pt} 0211 \begin{equation} 0212 \left( a+b=c \setlength{\testlength}{3.4pt} \right) 0213 \the\testlength 0214 \end{equation} 0215 </pre></div> 0216 0217 <p>The <code>\left ... \right</code> pair affect the horizontal spacing of the 0218 enclosed formula, in two ways. The first is that in <code>\( \sin(x) = 0219 \sin\left(x\right) \)</code> the one after the equals sign has more space 0220 around the <code>x</code>. That’s because <code>\left( ... \right)</code> inserts 0221 an inner node while <code>( ... )</code> inserts an opening node. The second 0222 way that the pair affect the horizontal spacing is that because they 0223 form a group, the enclosed subformula will be typeset at its natural 0224 width, with no stretching or shrinking to make the line fit better. 0225 </p> 0226 <p>TeX scales the delimiters according to the height and depth of the 0227 contained formula. Here LaTeX grows the brackets to extend the full 0228 height of the integral. 0229 </p> 0230 <div class="example"> 0231 <pre class="example">\begin{equation} 0232 \left[ \int_{x=r_0}^{\infty} -G\frac{Mm}{r^2}\, dr \right] 0233 \end{equation} 0234 </pre></div> 0235 0236 <p>Manual sizing is often better. For instance, although below the rule 0237 has no depth, TeX will create delimiters that extend far below the 0238 rule. 0239 </p> 0240 <div class="example"> 0241 <pre class="example">\begin{equation} 0242 \left( \rule{1pt}{1cm} \right) 0243 \end{equation} 0244 </pre></div> 0245 0246 <p>TeX can choose delimiters that are too small, as in <code>\( \left| 0247 |x|+|y| \right| \)</code>. It can also choose delimiters that are too large, 0248 as here. 0249 </p> 0250 <div class="example"> 0251 <pre class="example">\begin{equation} 0252 \left( \sum_{0\leq i<n} i^k \right) 0253 \end{equation} 0254 </pre></div> 0255 0256 <p>A third awkward case is when a long displayed formula is on more than 0257 one line and you must match the sizes of the opening and closing 0258 delimiter; you can’t use <code>\left</code> on the first line and 0259 <code>\right</code> on the last because they must be paired. 0260 </p> 0261 <p>To size the delimiters manually, see <a href="_005cbigl-_0026-_005cbigr-etc.html#g_t_005cbigl-_0026-_005cbigr-etc">\bigl & \bigr etc</a>. 0262 </p> 0263 0264 0265 0266 <hr/><div class='referenceinfo'> <a href='https://latexref.xyz/'> <i>Unofficial LaTeX2e reference manual</i></a></div> 0267 </body> 0268 </html>