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<head><title>degrees(Ring) -- degrees of generators</title>
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<div><h1>degrees(Ring) -- degrees of generators</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>degrees A</tt></div>
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<li><span>Function: <a href="_degrees.html" title="degrees of generators">degrees</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>A</tt>, <span>a <a href="___Ring.html">ring</a></span>, <span>an <a href="___Ideal.html">ideal</a></span>, <span>a <a href="___Module.html">module</a></span>, <span>a <a href="___Coherent__Sheaf.html">coherent sheaf</a></span>, or <span>a <a href="___Monoid.html">monoid</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___List.html">list</a></span>, the list of multi-degrees for the generators of <tt>A</tt></span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : R = ZZ/101[x,y,z];</pre>
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<tr><td><pre>i2 : degrees R
o2 = {{1}, {1}, {1}}
o2 : List</pre>
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<tr><td><pre>i3 : S = ZZ/101[x,y,z,Degrees => {{2,3},{1,2},{2,0}}];</pre>
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<tr><td><pre>i4 : degrees S
o4 = {{2, 3}, {1, 2}, {2, 0}}
o4 : List</pre>
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This function also applies to ideals, modules, and sheaves.<table class="examples"><tr><td><pre>i5 : I = ideal"xy2,xyz,y3"
2 3
o5 = ideal (x*y , x*y*z, y )
o5 : Ideal of S</pre>
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<tr><td><pre>i6 : degrees I
o6 = {{4, 7}, {5, 5}, {3, 6}}
o6 : List</pre>
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<table class="examples"><tr><td><pre>i7 : degrees R^5
o7 = {{0}, {0}, {0}, {0}, {0}}
o7 : List</pre>
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<tr><td><pre>i8 : degrees R^{1,2,3,4}
o8 = {{-1}, {-2}, {-3}, {-4}}
o8 : List</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_degree__Length.html" title="the number of degrees">degreeLength</a> -- the number of degrees</span></li>
<li><span><a href="_degrees__Ring.html" title="the ring of degrees">degreesRing</a> -- the ring of degrees</span></li>
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