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<head><title>map(Module,ZZ,Function) -- create a matrix from a free module by specifying a function that gives each entry</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__Function_rp.html" title="create a matrix from a free module by specifying a function that gives each entry">map(Module,ZZ,Function)</a></div>
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<div><h1>map(Module,ZZ,Function) -- create a matrix from a free module by specifying a function that gives each entry</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,f)</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>f</tt>, <span>a <a href="___Function.html">function</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>, a map from a graded free module of rank <tt>n</tt> to the module <tt>M</tt> whose matrix entry <tt>h_(i,j)</tt> is obtained from the function <tt>f</tt> by evaluating <tt>f(i,j)</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 the same as calling map(M,R^n,f), except that the degrees of the basis elements of the source module are chosen in an attempt to ensure that the resulting map is homogeneous of degree zero.<table class="examples"><tr><td><pre>i1 : R = GF(9,Variable=>a)[x,y,z];</pre>
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<tr><td><pre>i2 : f = map(R^1, 3, (i,j) -> (a^j * x - y)^(j+1))
o2 = | x-y (a+1)x2+axy+y2 (-a-1)x3-y3 |
1 3
o2 : Matrix R <--- R</pre>
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<tr><td><pre>i3 : source f
3
o3 = R
o3 : R-module, free, degrees {1, 2, 3}</pre>
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<tr><td><pre>i4 : isHomogeneous f
o4 = true</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_map_lp__Module_cm__Module_cm__Function_rp.html" title="create a matrix by specifying a function that gives each entry">map(Module,Module,Function)</a> -- create a matrix by specifying a function that gives each entry</span></li>
<li><span><a href="_source_lp__Matrix_rp.html" title="find the source module of matrix">source(Matrix)</a> -- find the source module of matrix</span></li>
<li><span><a href="_is__Homogeneous.html" title="whether something is homogeneous (graded)">isHomogeneous(Matrix)</a> -- whether something is homogeneous (graded)</span></li>
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