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<head><title>factor(Module) -- factor a ZZ-module</title>
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<div><h1>factor(Module) -- factor a ZZ-module</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>factor M</tt></div>
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<li><span>Function: <a href="_factor.html" title="factor a ring element or a ZZ-module">factor</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>
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<li><div class="single">Outputs:<ul><li><span>a symbolic expression describing the decomposition of <tt>M</tt> into a direct sum of principal modules</span></li>
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<div class="single"><h2>Description</h2>
<div>The ring of <tt>M</tt> must be <a href="___Z__Z.html" title="the class of all integers">ZZ</a>.<p/>
In the following example we construct a module with a known (but disguised) factorization.<table class="examples"><tr><td><pre>i1 : f = random(ZZ^6, ZZ^4)
o1 = | 9 4 3 9 |
| 5 3 4 0 |
| 5 7 4 1 |
| 7 5 7 5 |
| 7 2 9 7 |
| 5 6 3 8 |
6 4
o1 : Matrix ZZ <--- ZZ</pre>
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<tr><td><pre>i2 : M = subquotient ( f * diagonalMatrix{2,3,8,21}, f * diagonalMatrix{2*11,3*5*13,0,21*5} )
o2 = subquotient (| 18 12 24 189 |, | 198 780 0 945 |)
| 10 9 32 0 | | 110 585 0 0 |
| 10 21 32 21 | | 110 1365 0 105 |
| 14 15 56 105 | | 154 975 0 525 |
| 14 6 72 147 | | 154 390 0 735 |
| 10 18 24 168 | | 110 1170 0 840 |
6
o2 : ZZ-module, subquotient of ZZ</pre>
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<tr><td><pre>i3 : factor M
ZZ ZZ ZZ
o3 = ZZ + -- + -- + ----
5 11 5*13
o3 : Expression of class Sum</pre>
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