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<head><title>Ideal ^ ZZ -- power</title>
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<div><h1>Ideal ^ 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>I^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>I</tt>, <span>an <a href="___Ideal.html">ideal</a></span></span></li>
<li><span><tt>n</tt>, <span>an <a href="___Z__Z.html">integer</a></span>, at least zero</span></li>
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<li><div class="single">Outputs:<ul><li><span><span>an <a href="___Ideal.html">ideal</a></span>, the ideal <tt>I^n</tt></span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : R = QQ[a..d];</pre>
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<tr><td><pre>i2 : I = ideal(a^2, b^2-c*d);
o2 : Ideal of R</pre>
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<tr><td><pre>i3 : I^3
6 4 2 4 2 4 2 2 2 2 2 6 4 2 2 2
o3 = ideal (a , a b - a c*d, a b - 2a b c*d + a c d , b - 3b c*d + 3b c d
------------------------------------------------------------------------
3 3
- c d )
o3 : Ideal of R</pre>
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The generators produced are often not minimal. Use <a href="_trim_lp__Ideal_rp.html" title="">trim(Ideal)</a> or <a href="_mingens_lp__Module_rp.html" title="minimal generator matrix">mingens(Ideal)</a> to find a smaller generating set.<table class="examples"><tr><td><pre>i4 : trim I^3
6 4 2 2 2 3 3 2 4 2 2 2 2 2 4 2
o4 = ideal (b - 3b c*d + 3b c d - c d , a b - 2a b c*d + a c d , a b -
------------------------------------------------------------------------
4 6
a c*d, a )
o4 : Ideal of R</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_ideals.html" title="">ideals</a></span></li>
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