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<head><title>pointsByIntersection -- computes ideal of point set by intersecting maximal ideals</title>
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<div><h1>pointsByIntersection -- computes ideal of point set by intersecting maximal ideals</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>pointsByIntersection(M,R)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>M</tt>, <span>a <a href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span>, in which each column consists of the coordinates of a point</span></li>
<li><span><tt>R</tt>, <span>a <a href="../../Macaulay2Doc/html/___Polynomial__Ring.html">polynomial ring</a></span>, coordinate ring of the affine space containing the points</span></li>
</ul>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, grobner basis for ideal of a finite set of points</span></li>
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<div class="single"><h2>Description</h2>
<div>This function computes the ideal of a finite set of points by intersecting the ideals for each point. The coordinates of the points are the columns in the input matrix <tt>M</tt>.<table class="examples"><tr><td><pre>i1 : M = random(ZZ^3, ZZ^5)
o1 = | 3 7 7 4 5 |
| 1 6 1 3 7 |
| 7 1 6 1 5 |
3 5
o1 : Matrix ZZ <--- ZZ</pre>
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<tr><td><pre>i2 : R = QQ[x,y,z]
o2 = R
o2 : PolynomialRing</pre>
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<tr><td><pre>i3 : pointsByIntersection(M,R)
2 2
o3 = {31y*z + 60z + 72x - 103y - 523z + 391, 31x*z + 64z - 103x + 72y -
------------------------------------------------------------------------
2 2 2
593z + 601, 31y - 3z - 16x - 263y - 25z + 602, 31x*y - 48z - 101x -
------------------------------------------------------------------------
2 2 3 2
209y + 344z + 363, 31x - 19z - 339x - 2y + 131z + 754, 31z - 414z +
------------------------------------------------------------------------
24x - 24y + 1541z - 1182}
o3 : List</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_points.html" title="produces the ideal and initial ideal from the coordinates of a finite set of points">points</a> -- produces the ideal and initial ideal from the coordinates of a finite set of points</span></li>
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<div class="waystouse"><h2>Ways to use <tt>pointsByIntersection</tt> :</h2>
<ul><li>pointsByIntersection(Matrix,Ring)</li>
</ul>
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