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<head><title>? -- comparison operator</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="__qu.html" title="comparison operator">?</a></div>
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<div><h1>? -- comparison operator</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>
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</li>
<li><div class="single">Inputs:<ul><li><span><tt>x</tt></span></li>
<li><span><tt>y</tt></span></li>
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</li>
<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Boolean.html">Boolean value</a></span></span></li>
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<div class="single"><h2>Description</h2>
<div>Compares <tt>x</tt> and <tt>y</tt> (of the same type), returning <tt>symbol <</tt>, <tt>symbol ></tt>, <tt>symbol ==</tt>, or <a href="_incomparable.html" title="a result indicating incomparability">incomparable</a>.<p/>
Many types of objects may be compared. Numbers are handled as one would expect, and strings, lists and sequences are generally compared lexicographically.<table class="examples"><tr><td><pre>i1 : 3 ? 4
o1 = <
o1 : Keyword</pre>
</td></tr>
<tr><td><pre>i2 : "book" ? "boolean"
o2 = <
o2 : Keyword</pre>
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<tr><td><pre>i3 : 3 ? 3.
o3 = ==
o3 : Keyword</pre>
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<tr><td><pre>i4 : {1,2,3} ? {4,5}
o4 = <
o4 : Keyword</pre>
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<p/>
Polynomials from the same ring may also be compared. The order depends on the monomial order in the ring.<table class="examples"><tr><td><pre>i5 : R = ZZ[a,b,c]
o5 = R
o5 : PolynomialRing</pre>
</td></tr>
<tr><td><pre>i6 : a*c ? b^2
o6 = <
o6 : Keyword</pre>
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A set is smaller than another if it is a subset; for tallies, corresponding counts should all be smaller.<table class="examples"><tr><td><pre>i7 : set {1,2} ? set {2,3}
o7 = incomparable
o7 : Symbol</pre>
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<tr><td><pre>i8 : set {1,2} ? set {1,2,3}
o8 = <
o8 : Keyword</pre>
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<tr><td><pre>i9 : tally {1,1,2} ? tally {1,2,3}
o9 = incomparable
o9 : Symbol</pre>
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<tr><td><pre>i10 : tally {1,1,2} ? tally {1,1,2,3}
o10 = <
o10 : Keyword</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_sort.html" title="sort a list or columns of a matrix">sort</a> -- sort a list or columns of a matrix</span></li>
<li><span><a href="_rsort.html" title="sort a list or matrix in reverse order">rsort</a> -- sort a list or matrix in reverse order</span></li>
</ul>
</div>
<div class="waystouse"><h2>Ways to use <tt>?</tt> :</h2>
<ul><li>IndexedVariable ? IndexedVariable</li>
<li>List ? List</li>
<li>Symbol ? IndexedVariable</li>
<li>Tally ? Tally</li>
<li><span>Bag ? Bag, see <span><a href="___Bag.html" title="the class of all bags">Bag</a> -- the class of all bags</span></span></li>
</ul>
</div>
<div class="waystouse"><h2>For the programmer</h2>
<p>The object <a href="__qu.html" title="comparison operator">?</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>
</div>
<div><p>This operator may be used as a prefix unary operator in an expression like <tt>?y</tt>. The user may <a href="_installing_spmethods.html">install a method</a> for handling such expressions with code such as</p>
<pre> ? Y := (y) -> ...</pre>
<p>where <tt>Y</tt> is the class of <tt>y</tt>.</p>
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