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<head><title>gbRemove -- remove Gröbner basis</title>
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<div><h1>gbRemove -- remove Gröbner basis</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>gbRemove M</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>M</tt>, <span>an <a href="___Ideal.html">ideal</a></span>, <span>a <a href="___Matrix.html">matrix</a></span>, or <span>a <a href="___Module.html">module</a></span></span></li>
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<li><div class="single">Consequences:<ul><li>all Gröbner bases computed for M are removed</li>
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<div class="single"><h2>Description</h2>
<div>This is a simple way to remove the space associated with large Gröbner bases that are no longer needed.<table class="examples"><tr><td><pre>i1 : R = ZZ[a]/(a^2-3)[x,y]
o1 = R
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : F = y^2-x*(x-1)*(x-a)
3 2 2
o2 = - x + (a + 1)x + y - a*x
o2 : R</pre>
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<tr><td><pre>i3 : J = ideal(diff(x,F),diff(y,F),F)
2 3 2 2
o3 = ideal (- 3x + (2a + 2)x - a, 2y, - x + (a + 1)x + y - a*x)
o3 : Ideal of R</pre>
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<tr><td><pre>i4 : gens gb J
o4 = | 12 6a+6 2y 4x-2a+6 2xa+2x+2a+6 y2+2x-a-3 x2+3a |
1 7
o4 : Matrix R <--- R</pre>
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<tr><td><pre>i5 : peek J.generators.cache
o5 = CacheTable{GroebnerBasisOptions{HardDegreeLimit => null} => GroebnerBasis[status: done; S-pairs encountered up to degree 5]}
Syzygies => false
SyzygyRows => 0
image => image | -3x2+2xa+2x-a 2y -x3+x2a+x2+y2-xa |
isHomogeneous => false</pre>
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<tr><td><pre>i6 : gbRemove J</pre>
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<tr><td><pre>i7 : peek J.generators.cache
o7 = CacheTable{image => image | -3x2+2xa+2x-a 2y -x3+x2a+x2+y2-xa |}
isHomogeneous => false</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>
<li><span><a href="_gb__Trace.html" title="provide tracing output during various computations in the engine.">gbTrace</a> -- provide tracing output during various computations in the engine.</span></li>
<li><span><a href="_gb__Snapshot.html" title="the Gröbner basis matrix as so far computed">gbSnapshot</a> -- the Gröbner basis matrix as so far computed</span></li>
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<div class="waystouse"><h2>Ways to use <tt>gbRemove</tt> :</h2>
<ul><li>gbRemove(Ideal)</li>
<li>gbRemove(Matrix)</li>
<li>gbRemove(Module)</li>
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