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<head><title>clean -- Set to zero elements that are approximately zero</title>
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<div><h1>clean -- Set to zero elements that are approximately zero</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>clean(epsilon,M)</tt><br/><tt>clean_epsilon M</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>epsilon</tt>, <span>a <a href="___R__R.html">real number</a></span></span></li>
<li><span><tt>M</tt>, <span>a <a href="___Matrix.html">matrix</a></span>, or a <span>a <a href="___Ring__Element.html">ring element</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>, or <span>a <a href="___Ring__Element.html">ring element</a></span></span></li>
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<div class="single"><h2>Description</h2>
<div><p>If the input is <span>a <a href="___Matrix.html">matrix</a></span> or <span>a <a href="___Ring__Element.html">ring element</a></span>, then the result has the same type, where each real or complex number coefficient that is less than <tt>epsilon</tt> in absolute value is replaced with zero.</p>
<table class="examples"><tr><td><pre>i1 : e = 1e-11;</pre>
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<tr><td><pre>i2 : M = random(RR^4,RR^4)
o2 = | .142767 .650468 .34431 .831079 |
| .344396 .477573 .35125 .50691 |
| .249144 .62852 .344489 .741366 |
| .0586825 .0463371 .60071 .690786 |
4 4
o2 : Matrix RR <--- RR
53 53</pre>
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<tr><td><pre>i3 : M * (M + 1) + 1 - M^2 - M
o3 = | 1 0 0 -1.11022e-16 |
| 0 1 1.11022e-16 0 |
| 5.55112e-17 -1.11022e-16 1 1.11022e-16 |
| 2.77556e-17 0 -1.11022e-16 1 |
4 4
o3 : Matrix RR <--- RR
53 53</pre>
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<tr><td><pre>i4 : clean_e oo
o4 = | 1 0 0 0 |
| 0 1 0 0 |
| 0 0 1 0 |
| 0 0 0 1 |
4 4
o4 : Matrix RR <--- RR
53 53</pre>
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Cleaning a polynomial is a way to get rid of small terms.<table class="examples"><tr><td><pre>i5 : CC[x];</pre>
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<tr><td><pre>i6 : f = product(5,j -> x - exp(2*pi*j*ii/5))
5 4 3
o6 = x + (2.22045e-16 - 1.11022e-16*ii)x - 1.11022e-16*ii*x + (-
------------------------------------------------------------------------
2
1.11022e-16 - 1.11022e-16*ii)x - 1.11022e-16*ii*x - 1 + 5.55112e-16*ii
o6 : CC [x]
53</pre>
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<tr><td><pre>i7 : clean_e f
5
o7 = x - 1
o7 : CC [x]
53</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_norm.html" title="">norm</a></span></li>
<li><span><a href="___R__R.html" title="the class of all real numbers">RR</a> -- the class of all real numbers</span></li>
<li><span><a href="___C__C.html" title="the class of all complex numbers">CC</a> -- the class of all complex numbers</span></li>
<li><span><a href="_fill__Matrix.html" title="fill a mutable matrix with random numbers">fillMatrix</a> -- fill a mutable matrix with random numbers</span></li>
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<div class="waystouse"><h2>Ways to use <tt>clean</tt> :</h2>
<ul><li>clean(RR,Matrix)</li>
<li>clean(RR,MutableMatrix)</li>
<li>clean(RR,Number)</li>
<li>clean(RR,RingElement)</li>
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