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<div><h1>norm</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>norm M</tt><br/><tt>norm(p,M)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>M</tt>, <span>a <a href="___Mutable__Matrix.html">mutable matrix</a></span>, <span>a <a href="___Matrix.html">matrix</a></span>, <span>a <a href="___Ring__Element.html">ring element</a></span>, <span>a <a href="___Number.html">number</a></span>, <span>a <a href="___Vector.html">vector</a></span>, or <span>a <a href="___List.html">list</a></span></span></li>
<li><span><tt>p</tt>, <span>a <a href="___R__R.html">real number</a></span> or <span>an <a href="___Infinite__Number.html">infinite number</a></span>, specifying which norm to compute. Currently, only <tt>p=infinity</tt> is accepted.</span></li>
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<li><div class="single">Outputs:<ul><li><span>the <i>L<sup>p</sup></i>-norm of M computed to the minimum of the precisions of M and of p.</span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : printingPrecision = 2
o1 = 2</pre>
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<tr><td><pre>i2 : R = RR_100
o2 = RR
100
o2 : RealField</pre>
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<tr><td><pre>i3 : M = 10*random(R^3,R^10)
o3 = | 9.4 8.5 3.2 2.7 9.9 9 7 5.6 6.6 1.3 |
| 6.6 6.6 9.5 2.3 2.3 6.9 .98 4.6 8 4.6 |
| 5.7 3.6 7.7 9.4 4 9.1 9.5 4.9 8.1 2.3 |
3 10
o3 : Matrix R <--- R</pre>
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<tr><td><pre>i4 : norm M
o4 = 9.91463968904013992720181916376
o4 : RR (of precision 100)</pre>
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<tr><td><pre>i5 : norm_(numeric_20 infinity) M
o5 = 9.91464
o5 : RR (of precision 20)</pre>
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<tr><td><pre>i6 : norm {3/2,4,-5}
o6 = 5</pre>
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The norm of a polynomial is the norm of the vector of its coefficients.<table class="examples"><tr><td><pre>i7 : RR[x]
o7 = RR [x]
53
o7 : PolynomialRing</pre>
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<tr><td><pre>i8 : (1+x)^5
5 4 3 2
o8 = x + 5x + 10x + 10x + 5x + 1
o8 : RR [x]
53</pre>
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<tr><td><pre>i9 : norm oo
o9 = 10
o9 : RR (of precision 53)</pre>
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<div class="waystouse"><h2>Ways to use <tt>norm</tt> :</h2>
<ul><li>norm(InexactField,MutableMatrix)</li>
<li>norm(InfiniteNumber,Matrix)</li>
<li>norm(InfiniteNumber,Number)</li>
<li>norm(InfiniteNumber,RingElement)</li>
<li>norm(List)</li>
<li>norm(Matrix)</li>
<li>norm(MutableMatrix)</li>
<li>norm(Number)</li>
<li>norm(RingElement)</li>
<li>norm(RR,Matrix)</li>
<li>norm(RR,MutableMatrix)</li>
<li>norm(RR,Number)</li>
<li>norm(RR,RingElement)</li>
<li>norm(Vector)</li>
</ul>
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