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<head><title>localsyz -- find syzygies</title>
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<div><h1>localsyz -- find syzygies</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>localsyz m</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>m</tt>, <span>a <a href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span>, giving minimal generators of the syzygies taking into account the local structure</span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : R = ZZ/32003[x,y,z,w,SkewCommutative=>true]
o1 = R
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : m = matrix{{x,y*z},{z*w,x}}
o2 = | x yz |
| zw x |
2 2
o2 : Matrix R <--- R</pre>
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<tr><td><pre>i3 : setMaxIdeal(ideal(x,y,z,w))
o3 = ideal (x, y, z, w)
o3 : Ideal of R</pre>
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<tr><td><pre>i4 : localsyz m
o4 = {2} | -yz -x |
{2} | x zw |
2 2
o4 : Matrix R <--- R</pre>
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<tr><td><pre>i5 : m * localsyz m
o5 = 0
2 2
o5 : Matrix R <--- R</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_set__Max__Ideal.html" title="set the maximal ideal for local ring methods">setMaxIdeal</a> -- set the maximal ideal for local ring methods</span></li>
<li><span><a href="_local__Complement.html" title="find the splitting of the target of a map">localComplement</a> -- find the splitting of the target of a map</span></li>
<li><span><a href="_local__Mingens.html" title="finds a minimal set of generators">localMingens</a> -- finds a minimal set of generators</span></li>
<li><span><a href="_local__Modulo.html" title="find the pre-image (pullback) of image of a map over a local ring">localModulo</a> -- find the pre-image (pullback) of image of a map over a local ring</span></li>
<li><span><a href="_local__Prune.html" title="find a minimal presentation">localPrune</a> -- find a minimal presentation</span></li>
<li><span><a href="_local__Resolution.html" title="find a resolution over a local ring">localResolution</a> -- find a resolution over a local ring</span></li>
<li><span><tt>residueMap</tt> (missing documentation<!-- tag: residueMap -->)</span></li>
<li><span><tt>maxIdeal</tt> (missing documentation<!-- tag: maxIdeal -->)</span></li>
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<div class="waystouse"><h2>Ways to use <tt>localsyz</tt> :</h2>
<ul><li>localsyz(Matrix)</li>
</ul>
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