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<head><title>resolution(Ideal) -- compute a projective resolution of (the quotient ring corresponding to) an ideal</title>
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<div><h1>resolution(Ideal) -- compute a projective resolution of (the quotient ring corresponding to) an ideal</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>resolution I</tt></div>
</dd></dl>
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<li><span>Function: <a href="_resolution.html" title="projective resolution">resolution</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>I</tt>, <span>an <a href="___Ideal.html">ideal</a></span>, an ideal in a ring <tt>R</tt>, say</span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Chain__Complex.html">chain complex</a></span>, a resolution of <tt>R/I</tt> by projective <tt>R</tt>-modules</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="_resolution_lp..._cm_sp__Degree__Limit_sp_eq_gt_sp..._rp.html">DegreeLimit => ...</a>, -- compute only up to this degree</span></li>
<li><span><a href="_resolution_lp..._cm_sp__Hard__Degree__Limit_sp_eq_gt_sp..._rp.html">HardDegreeLimit => ...</a>, </span></li>
<li><span><a href="_resolution_lp..._cm_sp__Length__Limit_sp_eq_gt_sp..._rp.html">LengthLimit => ...</a>, -- stop when the resolution reaches this length</span></li>
<li><span><a href="_resolution_lp..._cm_sp__Pair__Limit_sp_eq_gt_sp..._rp.html">PairLimit => ...</a>, -- stop when this number of pairs has been handled</span></li>
<li><span><a href="_resolution_lp..._cm_sp__Sort__Strategy_sp_eq_gt_sp..._rp.html">SortStrategy => ...</a>, </span></li>
<li><span><a href="_resolution_lp..._cm_sp__Stop__Before__Computation_sp_eq_gt_sp..._rp.html">StopBeforeComputation => ...</a>, -- whether to stop the computation immediately</span></li>
<li><span><a href="_resolution_lp..._cm_sp__Strategy_sp_eq_gt_sp..._rp.html">Strategy => ...</a>, </span></li>
<li><span><a href="_resolution_lp..._cm_sp__Syzygy__Limit_sp_eq_gt_sp..._rp.html">SyzygyLimit => ...</a>, -- stop when this number of syzygies are obtained</span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : R = ZZ[a..d]
o1 = R
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : I = ideal(a,b,c,d)
o2 = ideal (a, b, c, d)
o2 : Ideal of R</pre>
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<tr><td><pre>i3 : C = res I
1 4 6 4 1
o3 = R <-- R <-- R <-- R <-- R <-- 0
0 1 2 3 4 5
o3 : ChainComplex</pre>
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<tr><td><pre>i4 : C_2
6
o4 = R
o4 : R-module, free, degrees {2, 2, 2, 2, 2, 2}</pre>
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<tr><td><pre>i5 : C.dd_2
o5 = {1} | -b 0 -c 0 0 -d |
{1} | a -c 0 0 -d 0 |
{1} | 0 b a -d 0 0 |
{1} | 0 0 0 c b a |
4 6
o5 : Matrix R <--- R</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="___Chain__Complex_sp_us_sp__Z__Z.html" title="component">ChainComplex _ ZZ</a> -- component</span></li>
<li><span><a href="_dd.html" title="differential in a chain complex">dd</a> -- differential in a chain complex</span></li>
<li><span><a href="_resolution.html" title="projective resolution">resolution</a> -- projective resolution</span></li>
<li><span><a href="_ideal.html" title="make an ideal">ideal</a> -- make an ideal</span></li>
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