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<head><title>matrix(Matrix) -- the matrix between generators</title>
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<div><h1>matrix(Matrix) -- the matrix between generators</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>matrix f</tt></div>
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<li><span>Function: <a href="_matrix.html" title="make a matrix">matrix</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>f</tt>, <span>a <a href="___Matrix.html">matrix</a></span>, a map of modules</span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Matrix.html">matrix</a></span>, If the source and target of f are free, then the result is f itself. Otherwise, the source and target will be replaced by the free modules whose basis elements correspond to the generators of the modules.</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="_matrix_lp__List_rp.html">Degree => ...</a>, -- create a matrix from a doubly-nested list of ring elements or matrices</span></li>
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<div class="single"><h2>Description</h2>
<div>Each homomorphism of modules f : M → N in Macaulay2 is induced from a matrix f0 : (cover M) →(cover N). This function returns this matrix.<table class="examples"><tr><td><pre>i1 : R = QQ[a..d];</pre>
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<tr><td><pre>i2 : I = ideal(a^2,b^2,c*d)
2 2
o2 = ideal (a , b , c*d)
o2 : Ideal of R</pre>
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<tr><td><pre>i3 : f = basis(3,I)
o3 = {2} | a b c d 0 0 0 0 0 0 0 0 |
{2} | 0 0 0 0 a b c d 0 0 0 0 |
{2} | 0 0 0 0 0 0 0 0 a b c d |
o3 : Matrix</pre>
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<tr><td><pre>i4 : source f
12
o4 = R
o4 : R-module, free, degrees {3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3}</pre>
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<tr><td><pre>i5 : target f
o5 = image | a2 b2 cd |
1
o5 : R-module, submodule of R</pre>
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The map f is induced by the following 3 by 12 matrix from R^12 to the 3 generators of <tt>I</tt>.<table class="examples"><tr><td><pre>i6 : matrix f
o6 = {2} | a b c d 0 0 0 0 0 0 0 0 |
{2} | 0 0 0 0 a b c d 0 0 0 0 |
{2} | 0 0 0 0 0 0 0 0 a b c d |
3 12
o6 : Matrix R <--- R</pre>
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To obtain the map that is the composite of this with the inclusion of I onto R, use <a href="_super.html" title="get the ambient module">super(Matrix)</a>.<table class="examples"><tr><td><pre>i7 : super f
o7 = | a3 a2b a2c a2d ab2 b3 b2c b2d acd bcd c2d cd2 |
1 12
o7 : Matrix R <--- R</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_cover.html" title="get the covering free module">cover</a> -- get the covering free module</span></li>
<li><span><a href="_super.html" title="get the ambient module">super</a> -- get the ambient module</span></li>
<li><span><a href="_basis.html" title="basis of all or part of a module or ring">basis</a> -- basis of all or part of a module or ring</span></li>
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