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<head><title>random(Module,Module) -- make a random module map</title>
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<div><h1>random(Module,Module) -- make a random module map</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>f = random(F,G)</tt></div>
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<li><span>Function: <a href="_random.html" title="get a random element">random</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>F</tt>, <span>a <a href="___Module.html">module</a></span>, a free module</span></li>
<li><span><tt>G</tt>, <span>a <a href="___Module.html">module</a></span>, a free module</span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>f</tt>, <span>a <a href="___Matrix.html">matrix</a></span>, a random, graded, degree <tt>0</tt> map, from <tt>G</tt> to <tt>F</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><tt>MaximalRank => </tt><span><span>default value false</span>, whether to ensure that the resulting map has maximal rank: designed mostly for use with matrices of numbers: for polynomial rings, returns inhomogeneous results</span></span></li>
<li><span><tt>Density => </tt><span><span>a <a href="___R__R.html">real number</a></span>, <span>default value 1</span>, the proportion of entries to set</span></span></li>
<li><span><tt>UpperTriangular => </tt><span><span>a <a href="___Boolean.html">Boolean value</a></span>, <span>default value false</span>, whether to set just entries strictly above the diagonal</span></span></li>
<li><span><a href="_random_lp__Type_rp.html">Height => ...</a>, -- random element of a type</span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : R = ZZ/101[x,y];</pre>
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<tr><td><pre>i2 : random(R^{1,2,3},R^{1,2,3})
o2 = {-1} | 41 0 0 |
{-2} | -9x-18y 35 0 |
{-3} | 17x2-37xy+39y2 -49x-36y 8 |
3 3
o2 : Matrix R <--- R</pre>
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<tr><td><pre>i3 : random(ZZ^3,ZZ^6,MaximalRank=>true)
o3 = | 10234796479 28887529183 9374509155 439476 480620491 9469997744 |
| 3633391864 10255183258 3327986576 156016 170622111 3361885390 |
| 9028006437 25481385970 8269156027 387658 423950285 8353385508 |
3 6
o3 : Matrix ZZ <--- ZZ</pre>
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<tr><td><pre>i4 : random(ZZ^3,ZZ^10,Density=>.3)
o4 = | 4 0 0 3 8 0 0 0 0 0 |
| 0 3 8 8 7 0 8 4 5 0 |
| 0 0 0 0 0 0 0 0 0 0 |
3 10
o4 : Matrix ZZ <--- ZZ</pre>
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<tr><td><pre>i5 : random(ZZ^6,ZZ^6,UpperTriangular=>true)
o5 = | 0 6 1 1 3 4 |
| 0 0 1 8 9 0 |
| 0 0 0 0 8 5 |
| 0 0 0 0 3 8 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
6 6
o5 : Matrix ZZ <--- ZZ</pre>
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<div class="single"><h2>Caveat</h2>
<div>Over a polynomial ring, specifying <tt>MaximalRank=>true</tt> will yield a non-homogeneous matrix.</div>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_set__Random__Seed.html" title="set starting point for random number generator">setRandomSeed</a> -- set starting point for random number generator</span></li>
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