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<head><title>resolution(Matrix) -- given a module map represented by a matrix, produce a comparison map between resolutions of its source and target</title>
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<div><h1>resolution(Matrix) -- given a module map represented by a matrix, produce a comparison map between resolutions of its source and target</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 f</tt></div>
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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>f</tt>, <span>a <a href="___Matrix.html">matrix</a></span>, a module homomorphism <tt>N <--- M</tt></span></li>
</ul>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Chain__Complex__Map.html">chain complex map</a></span>, a chain map from a projective resolution of the source of <tt>f</tt> to a resolution of the target of <tt>f</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="_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[x,y,z]
o1 = R
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : N = R^1/(x,y,z)
o2 = cokernel | x y z |
1
o2 : R-module, quotient of R</pre>
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<tr><td><pre>i3 : M = R^1/(x^2,y^2,x*y*z,z^2)
o3 = cokernel | x2 y2 xyz z2 |
1
o3 : R-module, quotient of R</pre>
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<tr><td><pre>i4 : f = map(N,M,1)
o4 = | 1 |
o4 : Matrix</pre>
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<tr><td><pre>i5 : res f
1 1
o5 = 0 : R <--------- R : 0
| 1 |
3 4
1 : R <-------------------- R : 1
{1} | x 0 yz 0 |
{1} | 0 y 0 0 |
{1} | 0 0 0 z |
3 6
2 : R <---------------------------- R : 2
{2} | xy yz 0 0 0 0 |
{2} | 0 0 0 yz 0 0 |
{2} | 0 0 0 0 yz xz |
1 3
3 : R <------------------ R : 3
{3} | 0 yz 0 |
4 : 0 <----- 0 : 4
0
o5 : ChainComplexMap</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_free_spresolutions_spof_spmodules.html" title="">free resolutions of modules</a></span></li>
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