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<head><title>isHolonomic -- determines whether a D-module (or ideal in Weyl algebra) is holonomic</title>
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<div><h1>isHolonomic -- determines whether a D-module (or ideal in Weyl algebra) is holonomic</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>isHolonomic M, isHolonomic I</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>M</tt>, <span>a <a href="../../Macaulay2Doc/html/___Module.html">module</a></span>, over the Weyl algebra <em>D</em></span></li>
<li><span><tt>I</tt>, <span>an <a href="../../Macaulay2Doc/html/___Ideal.html">ideal</a></span>, which represents the module <em>M = D/I</em></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="../../Macaulay2Doc/html/___Boolean.html">Boolean value</a></span></span></li>
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<div class="single"><h2>Description</h2>
<div>A module is holonomic if it has dimension <em>n</em>, the number of variables in the Weyl algebra <em>D = </em><b>C</b><<em>x<sub>1</sub>,...,x<sub>n</sub>,d<sub>1</sub>,...,d<sub>n</sub></em>><table class="examples"><tr><td><pre>i1 : A = matrix{{1,1,1},{0,1,2}}
o1 = | 1 1 1 |
| 0 1 2 |
2 3
o1 : Matrix ZZ <--- ZZ</pre>
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<tr><td><pre>i2 : b = {3,4}
o2 = {3, 4}
o2 : List</pre>
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<tr><td><pre>i3 : I = gkz(A,b)
2
o3 = ideal (D - D D , x D + x D + x D - 3, x D + 2x D - 4)
2 1 3 1 1 2 2 3 3 2 2 3 3
o3 : Ideal of QQ[x , x , x , D , D , D ]
1 2 3 1 2 3</pre>
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<tr><td><pre>i4 : isHolonomic I
o4 = true</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="___Ddim.html" title="dimension of a D-module">Ddim</a> -- dimension of a D-module</span></li>
<li><span><a href="_holonomic__Rank.html" title="rank of a D-module">holonomicRank</a> -- rank of a D-module</span></li>
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<div class="waystouse"><h2>Ways to use <tt>isHolonomic</tt> :</h2>
<ul><li>isHolonomic(Ideal)</li>
<li>isHolonomic(Module)</li>
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