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<head><title>gbSnapshot -- the Gröbner basis matrix as so far computed</title>
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<div><h1>gbSnapshot -- the Gröbner basis matrix as so far computed</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>gbSnapshot 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">Outputs:<ul><li><span><span>a <a href="___Matrix.html">matrix</a></span>, the Gröbner basis as so far computed</span></li>
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<div class="single"><h2>Description</h2>
<div>This routine is useful to be able to obtain partial results from a partially computed Gröbner basis. Little computation is done (although a minimalization, auto-reduction and sort is performed). <table class="examples"><tr><td><pre>i1 : R = ZZ/101[a..d]
o1 = R
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : I = intersect((ideal(a,b,c^3-d^3))^2,ideal(a^2-c^2,b^2-d^2))
2 2 2 2 2 3 3 3 3 3 2
o2 = ideal (b c - a d , a b*c - b*c - b d + b*d , a c - a*c - a*b d +
------------------------------------------------------------------------
3 4 2 2 3 2 2 2 2 2 3 2 4 2 2
a*d , b - b d , a*b - a*b*d , a b - a d , a b - a*b*c , a - a c ,
------------------------------------------------------------------------
2 4 6 2 3 3 3 2 4 6
a c - c - 2a c*d + 2c d + b d - d )
o2 : Ideal of R</pre>
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<tr><td><pre>i3 : gb(I, BasisElementLimit=>5)
o3 = GroebnerBasis[status: BasisElementLimit; all S-pairs handled up to degree 3]
o3 : GroebnerBasis</pre>
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<tr><td><pre>i4 : gbSnapshot I
o4 = | b2c2-a2d2 a2bc-bc3-b3d+bd3 a3c-ac3-ab2d+ad3 b4-b2d2 ab3-abd2 |
1 5
o4 : Matrix R <--- R</pre>
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<tr><td><pre>i5 : gb(I, BasisElementLimit=>10)
o5 = GroebnerBasis[status: done; S-pairs encountered up to degree 6]
o5 : GroebnerBasis</pre>
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<tr><td><pre>i6 : gbSnapshot I
o6 = | b2c2-a2d2 a2bc-bc3-b3d+bd3 a3c-ac3-ab2d+ad3 b4-b2d2 ab3-abd2 a2b2-a2d2
------------------------------------------------------------------------
a3b-abc2 a4-a2c2 a2c4-c6-2a2cd3+2c3d3+b2d4-d6 |
1 9
o6 : Matrix R <--- R</pre>
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<tr><td><pre>i7 : gens gb I
o7 = | b2c2-a2d2 a2bc-bc3-b3d+bd3 a3c-ac3-ab2d+ad3 b4-b2d2 ab3-abd2 a2b2-a2d2
------------------------------------------------------------------------
a3b-abc2 a4-a2c2 a2c4-c6-2a2cd3+2c3d3+b2d4-d6 |
1 9
o7 : 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>
<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__Remove.html" title="remove Gröbner basis">gbRemove</a> -- remove Gröbner basis</span></li>
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<div class="waystouse"><h2>Ways to use <tt>gbSnapshot</tt> :</h2>
<ul><li>gbSnapshot(Ideal)</li>
<li>gbSnapshot(Matrix)</li>
<li>gbSnapshot(Module)</li>
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