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<head><title>map(Ring,Matrix) -- make a ring map</title>
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<div><h1>map(Ring,Matrix) -- make a ring map</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>map(R,m)</tt></div>
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<li><span>Function: <a href="_map.html" title="make a map">map</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>R</tt>, <span>a <a href="___Ring.html">ring</a></span></span></li>
<li><span><tt>m</tt>, <span>a <a href="___Matrix.html">matrix</a></span>, a one row matrix</span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Ring__Map.html">ring map</a></span>, A ring map <tt>f : R --> (ring m)</tt>, where the entries of <tt>m</tt> are the images of the variables of <tt>R</tt>.</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="_map_lp..._cm_sp__Degree_sp_eq_gt_sp..._rp.html">Degree => ...</a>, -- set the degree of a map</span></li>
<li><span><a href="_map_lp__Ring_cm__Ring_cm__Matrix_rp.html">DegreeLift => ...</a>, -- make a ring map</span></li>
<li><span><a href="_map_lp__Ring_cm__Ring_cm__Matrix_rp.html">DegreeMap => ...</a>, -- make a ring map</span></li>
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<div class="single"><h2>Description</h2>
<div>This is equivalent to <tt>map(ring m, R, m)</tt>.<table class="examples"><tr><td><pre>i1 : R = QQ[a..d];</pre>
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<tr><td><pre>i2 : S = QQ[s,t];</pre>
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<tr><td><pre>i3 : F = map(R,matrix{{s^4,s^3*t,s*t^3,t^4}})
4 3 3 4
o3 = map(S,R,{s , s t, s*t , t })
o3 : RingMap S <--- R</pre>
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<tr><td><pre>i4 : kernel F
3 2 2 2 3 2
o4 = ideal (b*c - a*d, c - b*d , a*c - b d, b - a c)
o4 : Ideal of R</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_substitution_spand_spmaps_spbetween_springs.html" title="">substitution and maps between rings</a></span></li>
<li><span><a href="_map_lp__Ring_cm__Ring_cm__Matrix_rp.html" title="make a ring map">map(Ring,Ring,Matrix)</a> -- make a ring map</span></li>
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