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<head><title>makeRingMaps -- evaluation on points</title>
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<div><h1>makeRingMaps -- evaluation on points</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>makeRingMaps(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>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, of ring maps corresponding to evaluations at each point</span></li>
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<div class="single"><h2>Description</h2>
<div>Giving the coordinates of a point in affine space is equivalent to giving a ring map from the polynomial ring to the ground field: evaluation at the point. Given a finite collection of points encoded as the columns of a matrix, this function returns a corresponding list of ring maps.<table class="examples"><tr><td><pre>i1 : M = random(ZZ^3, ZZ^5)
o1 = | 6 9 9 9 2 |
| 5 1 6 4 9 |
| 5 0 0 0 8 |
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 : phi = makeRingMaps(M,R)
o3 = {map(QQ,R,{6, 5, 5}), map(QQ,R,{9, 1, 0}), map(QQ,R,{9, 6, 0}),
------------------------------------------------------------------------
map(QQ,R,{9, 4, 0}), map(QQ,R,{2, 9, 8})}
o3 : List</pre>
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<tr><td><pre>i4 : apply (gens(R),r->phi#2 r)
o4 = {9, 6, 0}
o4 : List</pre>
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<tr><td><pre>i5 : phi#2
o5 = map(QQ,R,{9, 6, 0})
o5 : RingMap QQ <--- R</pre>
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<div class="waystouse"><h2>Ways to use <tt>makeRingMaps</tt> :</h2>
<ul><li>makeRingMaps(Matrix,Ring)</li>
</ul>
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