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<head><title>forceGB -- declare that the columns of a matrix are a Gröbner basis</title>
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<div><h1>forceGB -- declare that the columns of a matrix are a 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>forceGB f</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>f</tt>, <span>a <a href="___Matrix.html">matrix</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Groebner__Basis.html">Groebner basis</a></span></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="_force__G__B_lp..._cm_sp__Change__Matrix_sp_eq_gt_sp..._rp.html">ChangeMatrix => ...</a>, -- inform Macaulay2 about the change of basis matrix from GB to generators</span></li>
<li><span><a href="_force__G__B_lp..._cm_sp__Minimal__Matrix_sp_eq_gt_sp..._rp.html">MinimalMatrix => ...</a>, -- specify the minimal generator matrix</span></li>
<li><span><a href="_force__G__B_lp..._cm_sp__Syzygy__Matrix_sp_eq_gt_sp..._rp.html">SyzygyMatrix => ...</a>, -- specify the syzygy matrix</span></li>
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<div class="single"><h2>Description</h2>
<div>Declares that the columns of the matrix <tt>f</tt> constitute a Gröbner basis, autoreduces it, minimizes it, sorts it, and returns a Gröbner basis object declaring itself complete, without computing any S-pairs.<p/>
Sometimes one knows that a set of polynomials (or columns of such) form a Gröbner basis, but <em>Macaulay2</em> doesn't. This is the way to inform the system of this fact.<table class="examples"><tr><td><pre>i1 : gbTrace = 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 : g = forceGB f
o4 = GroebnerBasis[status: done; S-pairs encountered up to degree 0]
o4 : GroebnerBasis</pre>
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This Gröbner basis object is stored with the matrix and can be obtained as usual:<table class="examples"><tr><td><pre>i5 : g === gb(f, StopBeforeComputation=>true)
o5 = true</pre>
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Requesting a Gröbner basis for <tt>f</tt> requires no computation.<table class="examples"><tr><td><pre>i6 : gens gb f
o6 = | x2-3 y3-1 z4-2 |
1 3
o6 : Matrix R <--- R</pre>
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<p>If an autoreduced Gröbner basis is desired, replace <tt>f</tt> by <tt>gens forceGB f</tt> first.</p>
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<div class="single"><h2>Caveat</h2>
<div>If the columns do not form a Gröbner basis, 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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<div class="waystouse"><h2>Ways to use <tt>forceGB</tt> :</h2>
<ul><li>forceGB(Matrix)</li>
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