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<head><title>degree(RingElement)</title>
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<div><h1>degree(RingElement)</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>degree f</tt></div>
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<li><span>Function: <a href="_degree.html" title="">degree</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>f</tt>, <span>a <a href="___Ring__Element.html">ring element</a></span>, a <a href="___Ring__Element.html">ring element</a>or <a href="___Vector.html">vector</a></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___List.html">list</a></span>, the degree or multidegree of <tt>f</tt></span></li>
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<div class="single"><h2>Description</h2>
<div>In Macaulay2, the degree of a polynomial is a list of integers. This is to accomodate polynomial rings having multigradings. The usual situation is when the ring has the usual grading: each variable has length 1.<table class="examples"><tr><td><pre>i1 : R = QQ[a..d];</pre>
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<tr><td><pre>i2 : degree (a^3-b-1)^2
o2 = {6}
o2 : List</pre>
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When not dealing with multigraded rings, obtaining the degree as a number is generally more convenient:<table class="examples"><tr><td><pre>i3 : first degree (a^3-b-1)^2
o3 = 6</pre>
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<table class="examples"><tr><td><pre>i4 : S = QQ[a..d,Degrees=>{1,2,3,4}];</pre>
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<tr><td><pre>i5 : first degree (a+b+c^3)
o5 = 9</pre>
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<table class="examples"><tr><td><pre>i6 : T = QQ[a..d,Degrees=>{{0,1},{1,0},{-1,1},{3,4}}];</pre>
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<tr><td><pre>i7 : degree c
o7 = {-1, 1}
o7 : List</pre>
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In a multigraded ring, the degree of a polynomial whose terms have different degrees is perhaps non-intuitive: it is the maximum (in each of the component degree) over each term:<table class="examples"><tr><td><pre>i8 : degree c^5
o8 = {-5, 5}
o8 : List</pre>
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<tr><td><pre>i9 : degree d
o9 = {3, 4}
o9 : List</pre>
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<tr><td><pre>i10 : degree (c^5+d)
o10 = {3, 5}
o10 : List</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_is__Homogeneous.html" title="whether something is homogeneous (graded)">isHomogeneous</a> -- whether something is homogeneous (graded)</span></li>
<li><span><a href="_degree__Length.html" title="the number of degrees">degreeLength</a> -- the number of degrees</span></li>
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