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<head><title>map(Matrix) -- make a matrix with a different degree</title>
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<div><a href="_map.html" title="make a map">map</a> > <a href="_map_lp__Matrix_rp.html" title="make a matrix with a different degree">map(Matrix)</a></div>
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<div><h1>map(Matrix) -- make a matrix with a different degree</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(f, Degree => d)</tt></div>
</dd></dl>
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</li>
<li><span>Function: <a href="_map.html" title="make a map">map</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>f</tt>, <span>a <a href="___Matrix.html">matrix</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 map identical to <tt>f</tt>, except that it has degree <tt>d</tt>, and the source module has been tensored by a graded free module of rank 1 of the appropriate degree.</span></li>
</ul>
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</li>
<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>
</ul>
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</li>
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<div class="single"><h2>Description</h2>
<div>The input <tt>d</tt> should be <span>an <a href="___Z__Z.html">integer</a></span>, or a list of integers.<p/>
This routine is often used to take a matrix that has a non-zero degree, and make the degree zero.<p/>
For example, multiplication of a matrix by a scalar increases the degree, leaving the source and target fixed:<table class="examples"><tr><td><pre>i1 : R = QQ[a,b];</pre>
</td></tr>
<tr><td><pre>i2 : f1 = matrix{{a,b}}
o2 = | a b |
1 2
o2 : Matrix R <--- R</pre>
</td></tr>
<tr><td><pre>i3 : f = a * f1
o3 = | a2 ab |
1 2
o3 : Matrix R <--- R</pre>
</td></tr>
<tr><td><pre>i4 : degree f
o4 = {1}
o4 : List</pre>
</td></tr>
<tr><td><pre>i5 : source f == source f1
o5 = true</pre>
</td></tr>
</table>
One solution is to change the degree:<table class="examples"><tr><td><pre>i6 : g = map(f, Degree => 0)
o6 = | a2 ab |
1 2
o6 : Matrix R <--- R</pre>
</td></tr>
<tr><td><pre>i7 : degree g
o7 = {0}
o7 : List</pre>
</td></tr>
<tr><td><pre>i8 : source g == (source f) ** R^{-1}
o8 = true</pre>
</td></tr>
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An alternate solution would be to use tensor product with the scalar.<table class="examples"><tr><td><pre>i9 : g2 = a ** matrix{{a,b}}
o9 = | a2 ab |
1 2
o9 : Matrix R <--- R</pre>
</td></tr>
<tr><td><pre>i10 : degree g2
o10 = {0}
o10 : List</pre>
</td></tr>
<tr><td><pre>i11 : isHomogeneous g2
o11 = true</pre>
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