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<head><title>betti(Ideal) -- gives the degrees of generators.</title>
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<div><h1>betti(Ideal) -- gives the 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>betti I</tt></div>
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<li><span>Function: <a href="_betti.html" title="display degrees">betti</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>I</tt>, <span>an <a href="___Ideal.html">ideal</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Betti__Tally.html">Betti tally</a></span>, a diagram showing the degrees of the generators of the modules in <tt>C</tt></span></li>
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<li><div class="single"><a href="_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:<ul><li><span><a href="_betti_lp..._cm_sp__Weights_sp_eq_gt_sp..._rp.html">Weights => ...</a>, </span></li>
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<div class="single"><h2>Description</h2>
<div>The output is the degrees of generators and relations of the quotient of the ambient ring by the ideal.<table class="examples"><tr><td><pre>i1 : S = ZZ/10007[x,y];</pre>
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<tr><td><pre>i2 : I = ideal(x^2,y^3);
o2 : Ideal of S</pre>
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<tr><td><pre>i3 : betti I
0 1
o3 = total: 1 2
0: 1 .
1: . 1
2: . 1
o3 : BettiTally</pre>
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For an explanation of the diagram, see <a href="_betti_lp__Graded__Module_rp.html" title="display of degrees in a graded module">betti(GradedModule)</a>.</div>
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