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<head><title>/ -- a binary operator, usually used for division</title>
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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="__sl.html" title="a binary operator, usually used for division">/</a></div>
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<div><h1>/ -- a binary operator, usually used for division</h1>
<div class="single"><h2>Synopsis</h2>
<ul><li><div class="list"><dl class="element"><dt class="heading">Usage: </dt><dd class="value"><div><tt>x / y</tt></div>
</dd></dl>
</div>
</li>
</ul>
</div>
<div class="single"><h2>Description</h2>
<div>This operator is currently used in several ways in Macaulay2.<ul><li>division in a ring, yielding a fraction</li>
<li>division in unevaluated expressions</li>
<li>quotient rings, modules and sheaves</li>
<li>applying a function or ring map to every element of a list or set</li>
</ul>
<table class="examples"><tr><td><pre>i1 : 2/3
2
o1 = -
3
o1 : QQ</pre>
</td></tr>
<tr><td><pre>i2 : 2./3
o2 = .666666666666667
o2 : RR (of precision 53)</pre>
</td></tr>
</table>
</div>
</div>
<div class="single"><h2>See also</h2>
<ul><li><span><a href="__sl_sl.html" title="a binary operator, usually used for quotient">//</a> -- a binary operator, usually used for quotient</span></li>
</ul>
</div>
<div class="waystouse"><h2>Ways to use <tt>/</tt> :</h2>
<ul><li>CC / CC</li>
<li>CC / QQ</li>
<li>CC / RR</li>
<li>CC / ZZ</li>
<li>QQ / CC</li>
<li>QQ / QQ</li>
<li>QQ / RR</li>
<li>QQ / ZZ</li>
<li>RR / CC</li>
<li>RR / QQ</li>
<li>RR / RR</li>
<li>RR / ZZ</li>
<li>ZZ / CC</li>
<li>ZZ / QQ</li>
<li>ZZ / RR</li>
<li>ZZ / ZZ</li>
<li><span><a href="___Coherent__Sheaf_sp_sl_sp__Coherent__Sheaf.html" title="quotient of coherent sheaves">CoherentSheaf / CoherentSheaf</a> -- quotient of coherent sheaves</span></li>
<li><span>CoherentSheaf / Ideal, see <span><a href="___Coherent__Sheaf_sp_sl_sp__Coherent__Sheaf.html" title="quotient of coherent sheaves">CoherentSheaf / CoherentSheaf</a> -- quotient of coherent sheaves</span></span></li>
<li><span>Constant / Constant, see <span><a href="___Constant.html" title="">Constant</a></span></span></li>
<li><span>Constant / InexactNumber, see <span><a href="___Constant.html" title="">Constant</a></span></span></li>
<li><span>Constant / Number, see <span><a href="___Constant.html" title="">Constant</a></span></span></li>
<li><span>Constant / RingElement, see <span><a href="___Constant.html" title="">Constant</a></span></span></li>
<li><span>Holder / OneExpression, see <span><a href="___Constant.html" title="">Constant</a></span></span></li>
<li><span>InexactNumber / Constant, see <span><a href="___Constant.html" title="">Constant</a></span></span></li>
<li><span>Number / Constant, see <span><a href="___Constant.html" title="">Constant</a></span></span></li>
<li><span>RingElement / Constant, see <span><a href="___Constant.html" title="">Constant</a></span></span></li>
<li><span>Expression / Expression, see <span><a href="___Expression.html" title="the class of all expressions">Expression</a> -- the class of all expressions</span></span></li>
<li><span><a href="___Ideal_sp_sl_sp__Function.html" title="apply a function to generators of an ideal">Ideal / Function</a> -- apply a function to generators of an ideal</span></li>
<li><span><a href="___Ideal_sp_sl_sp__Ideal.html" title="quotient module">Ideal / Ideal</a> -- quotient module</span></li>
<li><span><tt>InexactNumber / RingElement</tt> (missing documentation<!-- tag: (/,InexactNumber,RingElement) -->)</span></li>
<li><span><a href="___List_sp_sl_sp__Thing.html" title="vector division">List / Thing</a> -- vector division</span></li>
<li><span>Module / Ideal, see <span><a href="___Module_sp_sl_sp__Module.html" title="quotient module">Module / Module</a> -- quotient module</span></span></li>
<li><span>Module / List, see <span><a href="___Module_sp_sl_sp__Module.html" title="quotient module">Module / Module</a> -- quotient module</span></span></li>
<li><span><a href="___Module_sp_sl_sp__Module.html" title="quotient module">Module / Module</a> -- quotient module</span></li>
<li><span>Module / RingElement, see <span><a href="___Module_sp_sl_sp__Module.html" title="quotient module">Module / Module</a> -- quotient module</span></span></li>
<li><span>Module / Sequence, see <span><a href="___Module_sp_sl_sp__Module.html" title="quotient module">Module / Module</a> -- quotient module</span></span></li>
<li><span>Module / Vector, see <span><a href="___Module_sp_sl_sp__Module.html" title="quotient module">Module / Module</a> -- quotient module</span></span></li>
<li><span><a href="___Ring_sp_sl_sp__Ideal.html" title="make a quotient ring">Ring / Ideal</a> -- make a quotient ring</span></li>
<li><span>Ring / List, see <span><a href="___Ring_sp_sl_sp__Ideal.html" title="make a quotient ring">Ring / Ideal</a> -- make a quotient ring</span></span></li>
<li><span>Ring / Module, see <span><a href="___Ring_sp_sl_sp__Ideal.html" title="make a quotient ring">Ring / Ideal</a> -- make a quotient ring</span></span></li>
<li><span>Ring / MonomialIdeal, see <span><a href="___Ring_sp_sl_sp__Ideal.html" title="make a quotient ring">Ring / Ideal</a> -- make a quotient ring</span></span></li>
<li><span>Ring / RingElement, see <span><a href="___Ring_sp_sl_sp__Ideal.html" title="make a quotient ring">Ring / Ideal</a> -- make a quotient ring</span></span></li>
<li><span>Ring / Sequence, see <span><a href="___Ring_sp_sl_sp__Ideal.html" title="make a quotient ring">Ring / Ideal</a> -- make a quotient ring</span></span></li>
<li><span>Ring / ZZ, see <span><a href="___Ring_sp_sl_sp__Ideal.html" title="make a quotient ring">Ring / Ideal</a> -- make a quotient ring</span></span></li>
<li><span><tt>RingElement / InexactNumber</tt> (missing documentation<!-- tag: (/,RingElement,InexactNumber) -->)</span></li>
<li><span><a href="___Ring__Element_sp_sl_sp__Ring__Element.html" title="fraction">RingElement / RingElement</a> -- fraction</span></li>
<li><span>List / Command, see <span><a href="___Visible__List_sp_sl_sp__Function.html" title="apply a function to elements of a list">VisibleList / Function</a> -- apply a function to elements of a list</span></span></li>
<li><span>List / Function, see <span><a href="___Visible__List_sp_sl_sp__Function.html" title="apply a function to elements of a list">VisibleList / Function</a> -- apply a function to elements of a list</span></span></li>
<li><span>List / RingMap, see <span><a href="___Visible__List_sp_sl_sp__Function.html" title="apply a function to elements of a list">VisibleList / Function</a> -- apply a function to elements of a list</span></span></li>
<li><span>Tally / Command, see <span><a href="___Visible__List_sp_sl_sp__Function.html" title="apply a function to elements of a list">VisibleList / Function</a> -- apply a function to elements of a list</span></span></li>
<li><span>Tally / Function, see <span><a href="___Visible__List_sp_sl_sp__Function.html" title="apply a function to elements of a list">VisibleList / Function</a> -- apply a function to elements of a list</span></span></li>
<li><span>VisibleList / Command, see <span><a href="___Visible__List_sp_sl_sp__Function.html" title="apply a function to elements of a list">VisibleList / Function</a> -- apply a function to elements of a list</span></span></li>
<li><span><a href="___Visible__List_sp_sl_sp__Function.html" title="apply a function to elements of a list">VisibleList / Function</a> -- apply a function to elements of a list</span></li>
<li><span>VisibleList / SelfInitializingType, see <span><a href="___Visible__List_sp_sl_sp__Function.html" title="apply a function to elements of a list">VisibleList / Function</a> -- apply a function to elements of a list</span></span></li>
</ul>
</div>
<div class="waystouse"><h2>For the programmer</h2>
<p>The object <a href="__sl.html" title="a binary operator, usually used for division">/</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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