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<head><title>syz(Matrix) -- compute the syzygy matrix</title>
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<div><h1>syz(Matrix) -- compute the syzygy matrix</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>syz h</tt></div>
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<li><span>Function: <a href="_syz.html" title="the syzygy matrix">syz</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>h</tt>, <span>a <a href="___Matrix.html">matrix</a></span>, a matrix</span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Matrix.html">matrix</a></span>, the matrix of minimal or trimmed generators for the syzygies among the columns of <tt>h</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><tt>Algorithm => </tt><span><span>default value Inhomogeneous</span>, see <a href="_gb.html" title="compute a Gröbner basis">gb(..., Algorithm => ...)</a></span></span></li>
<li><span><tt>BasisElementLimit => </tt><span><span>default value infinity</span>, see <a href="_gb.html" title="compute a Gröbner basis">gb(..., BasisElementLimit => ...)</a></span></span></li>
<li><span><tt>DegreeLimit => </tt><span><span>default value {}</span>, see <a href="_gb.html" title="compute a Gröbner basis">gb(..., DegreeLimit => ...)</a></span></span></li>
<li><span><tt>GBDegrees => </tt><span><span>default value null</span>, see <a href="_gb.html" title="compute a Gröbner basis">gb(..., GBDegrees => ...)</a></span></span></li>
<li><span><tt>HardDegreeLimit => </tt><span><span>default value null</span>, see <a href="_gb.html" title="compute a Gröbner basis">gb(..., HardDegreeLimit => ...)</a></span></span></li>
<li><span><tt>MaxReductionCount => </tt><span><span>an <a href="___Z__Z.html">integer</a></span>, <span>default value 10</span>, the maximum number of reductions of an S-pair done before requeueing it, if the <tt>Inhomogeneous</tt> algorithm is in use</span></span></li>
<li><span><tt>PairLimit => </tt><span><span>default value infinity</span>, see <a href="_gb.html" title="compute a Gröbner basis">gb(..., PairLimit => ...)</a></span></span></li>
<li><span><tt>StopBeforeComputation => </tt><span><span>default value false</span>, see <a href="_gb.html" title="compute a Gröbner basis">gb(..., StopBeforeComputation => ...)</a></span></span></li>
<li><span><tt>Strategy => </tt><span><span>default value {}</span>, see <a href="_gb.html" title="compute a Gröbner basis">gb(..., Strategy => ...)</a></span></span></li>
<li><span><tt>SyzygyLimit => </tt><span><span>default value infinity</span>, see <a href="_gb.html" title="compute a Gröbner basis">gb(..., SyzygyLimit => ...)</a></span></span></li>
<li><span><tt>SyzygyRows => </tt><span><span>default value infinity</span>, see <a href="_gb.html" title="compute a Gröbner basis">gb(..., SyzygyRows => ...)</a></span></span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : R = QQ[a..g];</pre>
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<tr><td><pre>i2 : I = ideal"ab2-c3,abc-cef,ade-cfg"
2 3
o2 = ideal (a*b - c , a*b*c - c*e*f, a*d*e - c*f*g)
o2 : Ideal of R</pre>
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<tr><td><pre>i3 : syz gens I
o3 = {3} | -abc+cef 0 -ade+cfg de2f-bcfg |
{3} | ab2-c3 -ade+cfg 0 -c2de+b2fg |
{3} | 0 abc-cef ab2-c3 bc3-b2ef |
3 4
o3 : Matrix R <--- R</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_gb.html" title="compute a Gröbner basis">gb</a> -- compute a Gröbner basis</span></li>
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