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<div><a href="index.html" title="">Macaulay2Doc</a> > <a href="___The_sp__Macaulay2_splanguage.html" title="">The Macaulay2 language</a> > <a href="_operators.html" title="">operators</a> > <a href="__vb.html" title="a binary operator, often used for horizontal concatenation">|</a></div>
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<div><h1>| -- a binary operator, often used for horizontal concatenation</h1>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="__vb_vb.html" title="a binary operator, often used for vertical concatenation">||</a> -- a binary operator, often used for vertical concatenation</span></li>
</ul>
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<div class="waystouse"><h2>Ways to use <tt>|</tt> :</h2>
<ul><li><span><a href="___Graded__Module__Map_sp_vb_sp__Graded__Module__Map.html" title="a binary operator, often used for horizontal concatenation">GradedModuleMap | GradedModuleMap</a> -- a binary operator, often used for horizontal concatenation</span></li>
<li><span>Array | Array, see <span><a href="___List_sp_vb_sp__List.html" title="join lists, sequences or arrays">List | List</a> -- join lists, sequences or arrays</span></span></li>
<li><span><a href="___List_sp_vb_sp__List.html" title="join lists, sequences or arrays">List | List</a> -- join lists, sequences or arrays</span></li>
<li><span>Sequence | Sequence, see <span><a href="___List_sp_vb_sp__List.html" title="join lists, sequences or arrays">List | List</a> -- join lists, sequences or arrays</span></span></li>
<li><span><a href="___Matrix_sp_vb_sp__Matrix.html" title="join matrices horizontally">Matrix | Matrix</a> -- join matrices horizontally</span></li>
<li><span>Matrix | RingElement, see <span><a href="___Matrix_sp_vb_sp__Matrix.html" title="join matrices horizontally">Matrix | Matrix</a> -- join matrices horizontally</span></span></li>
<li><span>Matrix | ZZ, see <span><a href="___Matrix_sp_vb_sp__Matrix.html" title="join matrices horizontally">Matrix | Matrix</a> -- join matrices horizontally</span></span></li>
<li><span>RingElement | Matrix, see <span><a href="___Matrix_sp_vb_sp__Matrix.html" title="join matrices horizontally">Matrix | Matrix</a> -- join matrices horizontally</span></span></li>
<li><span>RingElement | RingElement, see <span><a href="___Matrix_sp_vb_sp__Matrix.html" title="join matrices horizontally">Matrix | Matrix</a> -- join matrices horizontally</span></span></li>
<li><span>ZZ | Matrix, see <span><a href="___Matrix_sp_vb_sp__Matrix.html" title="join matrices horizontally">Matrix | Matrix</a> -- join matrices horizontally</span></span></li>
<li><span><a href="___Net_sp_vb_sp__Net.html" title="join strings or nets">Net | Net</a> -- join strings or nets</span></li>
<li><span>String | String, see <span><a href="___Net_sp_vb_sp__Net.html" title="join strings or nets">Net | Net</a> -- join strings or nets</span></span></li>
<li><span>String | ZZ, see <span><a href="___Net_sp_vb_sp__Net.html" title="join strings or nets">Net | Net</a> -- join strings or nets</span></span></li>
<li><span>ZZ | String, see <span><a href="___Net_sp_vb_sp__Net.html" title="join strings or nets">Net | Net</a> -- join strings or nets</span></span></li>
<li><span><a href="___Z__Z_sp_vb_sp__Z__Z.html" title="logical or">ZZ | ZZ</a> -- logical or</span></li>
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<div class="waystouse"><h2>For the programmer</h2>
<p>The object <a href="__vb.html" title="a binary operator, often used for horizontal concatenation">|</a> is <span>a <a href="___Keyword.html">keyword</a></span>.</p>
<div><div><p>This operator may be used as a binary operator in an expression like <tt>x|y</tt>. The user may install <a href="_binary_spmethods.html" title="">binary methods</a> for handling such expressions with code such as</p>
<pre> X | Y := (x,y) -> ...</pre>
<p>where <tt>X</tt> is the class of <tt>x</tt> and <tt>Y</tt> is the class of <tt>y</tt>.</p>
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