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<head><title>RingElement ^ ZZ -- power</title>
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<div><h1>RingElement ^ ZZ -- power</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^n</tt></div>
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<li><span>Operator: <a href="_^.html" title="a binary operator, usually used for powers">^</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>f</tt>, <span>a <a href="___Ring__Element.html">ring element</a></span></span></li>
<li><span><tt>n</tt>, <span>an <a href="___Z__Z.html">integer</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Ring__Element.html">ring element</a></span>, <tt>f^n</tt></span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : R = ZZ/7[x]/(x^46-x-1);</pre>
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<tr><td><pre>i2 : (x+4)^(7^100)
45 43 42 41 38 37 36 35 34 33 32
o2 = - x - x - x + 3x + 3x - 2x + 2x + 3x + x - 3x + 3x
------------------------------------------------------------------------
31 30 29 28 27 26 25 23 22 21 20
- 2x + 2x + x - x + x - 3x + 2x + x + 3x - x - 2x
------------------------------------------------------------------------
19 18 17 16 15 14 13 12 11 10 9
- 2x - x + 3x - 3x - 3x + 2x + x + 2x - 3x - x - 3x
------------------------------------------------------------------------
8 7 6 5 4 2
- 2x + 3x - 2x + 3x - x + 2x - 3x + 3
o2 : R</pre>
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If the ring allows inverses, negative values may be used.<table class="examples"><tr><td><pre>i3 : S = ZZ[t,Inverses=>true,MonomialOrder=>RevLex];</pre>
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<tr><td><pre>i4 : t^-1
-1
o4 = t
o4 : S</pre>
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<tr><td><pre>i5 : T = frac(ZZ[a,b,c]);</pre>
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<tr><td><pre>i6 : (a+b+c)^-1
1
o6 = ---------
a + b + c
o6 : T</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_frac.html" title="construct a fraction field">frac</a> -- construct a fraction field</span></li>
<li><span><a href="_polynomial_springs.html" title="">polynomial rings</a></span></li>
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