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<head><title>map(Module,ZZ,List) -- create a matrix by giving a sparse or dense list of entries</title>
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<div><a href="_map.html" title="make a map">map</a> > <a href="_map_lp__Module_cm__Z__Z_cm__List_rp.html" title="create a matrix by giving a sparse or dense list of entries">map(Module,ZZ,List)</a></div>
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<div><h1>map(Module,ZZ,List) -- create a matrix by giving a sparse or dense list of entries</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(M,n,v)</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>M</tt>, <span>a <a href="___Module.html">module</a></span></span></li>
<li><span><tt>n</tt>, <span>an <a href="___Z__Z.html">integer</a></span></span></li>
<li><span><tt>v</tt>, <span>a <a href="___List.html">list</a></span></span></li>
</ul>
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</li>
<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Matrix.html">matrix</a></span>, A matrix <tt>M <-- R^n</tt> whose entries are obtained from <tt>v</tt>, where R is the ring of M, and the source of the result is a graded free module chosen in an attempt to make the result homogeneous of degree zero</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>The list <tt>v</tt> is either a doubly nested list of ring elements, or a list of elements <tt>(i,j) => f</tt>. The first version provides all of the elements of the output matrix, row by row. The second form provides only the non-zero elements of the output matrix <tt>h: h_(i,j) = f</tt>, for every <tt>(i,j) => f</tt> in the list <tt>v</tt>.<p/>
The ring elements appearing in <tt>v</tt> should be be in <tt>R</tt>, or in a base ring of <tt>R</tt>.<p/>
In the first form, each list in v gives a row of the matrix. The length of the list <tt>v</tt> should be the number of generators of <tt>M</tt>, and the length of each element of <tt>v</tt> (which is itself a list of ring elements) should be the number of generators of the source module <tt>N</tt>.<table class="examples"><tr><td><pre>i1 : R = ZZ/101[x,y,z];</pre>
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<tr><td><pre>i2 : p = map(R^2,3,{{x^2,0,3},{0,y^2,5}})
o2 = | x2 0 3 |
| 0 y2 5 |
2 3
o2 : Matrix R <--- R</pre>
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<tr><td><pre>i3 : isHomogeneous p
o3 = true</pre>
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In the second form, if an index (i,j) occurs more than once, only the last is taken.<table class="examples"><tr><td><pre>i4 : p = map(R^2,3,{(0,0) => x+y, (1,1) => x^2, (0,2) => x-1, (0,0) => x-y})
o4 = | x-y 0 x-1 |
| 0 x2 0 |
2 3
o4 : Matrix R <--- R</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_matrix.html" title="make a matrix">matrix</a> -- make a matrix</span></li>
<li><span><a href="_map_lp__Module_cm__Nothing_cm__List_rp.html" title="create a matrix by giving a doubly nested list of ring elements">map(Module,Nothing,List)</a> -- create a matrix by giving a doubly nested list of ring elements</span></li>
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