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<head><title>forceGB(..., SyzygyMatrix => ...) -- specify the syzygy matrix</title>
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<div><h1>forceGB(..., SyzygyMatrix => ...) -- specify 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>forceGB(f,SyzygyMatrix=>z,...)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>z</tt>, <span>a <a href="___Matrix.html">matrix</a></span></span></li>
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<li><div class="single">Consequences:<ul><li>A request for the syzygy matrix of <tt>f</tt> will return <tt>z</tt></li>
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<div class="single"><h2>Description</h2>
<div>In the following example, the only computation being performed when asked to compute the <a href="_kernel.html" title="kernel of a ringmap, matrix, or chain complex">kernel</a> or <a href="_syz.html" title="the syzygy matrix">syz</a> of <tt>f</tt> is the minimal generator matrix of <tt>z</tt>.<table class="examples"><tr><td><pre>i1 : gbTrace = 3
o1 = 3</pre>
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<tr><td><pre>i2 : R = ZZ[x,y,z];
-- registering polynomial ring 4 at 0x8414510</pre>
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<tr><td><pre>i3 : f = matrix{{x^2-3, y^3-1, z^4-2}};
1 3
o3 : Matrix R <--- R</pre>
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<tr><td><pre>i4 : z = koszul(2,f)
o4 = {2} | -y3+1 -z4+2 0 |
{3} | x2-3 0 -z4+2 |
{4} | 0 x2-3 y3-1 |
3 3
o4 : Matrix R <--- R</pre>
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<tr><td><pre>i5 : g = forceGB(f, SyzygyMatrix=>z);</pre>
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<tr><td><pre>i6 : syz g -- no extra computation
o6 = {2} | -y3+1 -z4+2 0 |
{3} | x2-3 0 -z4+2 |
{4} | 0 x2-3 y3-1 |
3 3
o6 : Matrix R <--- R</pre>
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<tr><td><pre>i7 : syz f
-- registering gb 1 at 0x912f260
-- [gb]{2}(1)m{3}(1)m{4}(1)m{5}(1)z{6}(1)z{7}(1)z
-- number of (nonminimal) gb elements = 3
-- number of monomials = 9
-- ncalls = 0
-- nloop = 0
-- nsaved = 0
--
o7 = {2} | -y3+1 -z4+2 0 |
{3} | x2-3 0 -z4+2 |
{4} | 0 x2-3 y3-1 |
3 3
o7 : Matrix R <--- R</pre>
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<tr><td><pre>i8 : kernel f
o8 = image {2} | -y3+1 -z4+2 0 |
{3} | x2-3 0 -z4+2 |
{4} | 0 x2-3 y3-1 |
3
o8 : R-module, submodule of R</pre>
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If you know that the columns of z already form a set of minimal generators, then one may use <a href="_force__G__B.html" title="declare that the columns of a matrix are a Gröbner basis">forceGB</a> once again.</div>
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<h2>Further information</h2>
<ul><li><span>Default value: <a href="_null.html" title="the unique member of the empty class">null</a></span></li>
<li><span>Function: <span><a href="_force__G__B.html" title="declare that the columns of a matrix are a Gröbner basis">forceGB</a> -- declare that the columns of a matrix are a Gröbner basis</span></span></li>
<li><span>Option name: <span><a href="___Syzygy__Matrix.html" title="name for an optional argument">SyzygyMatrix</a> -- name for an optional argument</span></span></li>
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<div class="single"><h2>Caveat</h2>
<div>If the columns of <tt>z</tt> do not generate the syzygy module of <tt>f</tt>, nonsensical answers may result</div>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="___Gröbner_spbases.html" title="">Gröbner bases</a></span></li>
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