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<head><title>RatAnn -- annihilator of a rational function in Weyl algebra</title>
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<div><h1>RatAnn -- annihilator of a rational function in Weyl algebra</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>RatAnn f, RatAnn(g,f)</tt></div>
</dd></dl>
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</li>
<li><div class="single">Inputs:<ul><li><span><tt>f</tt>, <span>a <a href="../../Macaulay2Doc/html/___Ring__Element.html">ring element</a></span>, polynomial</span></li>
<li><span><tt>g</tt>, <span>a <a href="../../Macaulay2Doc/html/___Ring__Element.html">ring element</a></span>, polynomial</span></li>
</ul>
</div>
</li>
<li><div class="single">Outputs:<ul><li><span><span>an <a href="../../Macaulay2Doc/html/___Ideal.html">ideal</a></span>, left ideal of the Weyl algebra</span></li>
</ul>
</div>
</li>
</ul>
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<div class="single"><h2>Description</h2>
<div><tt>RatAnn f</tt> computes the annihilator ideal in the Weyl algebra of the rational function 1/f<br/><tt>RatAnn(g,f)</tt> computes the annihilator ideal in the Weyl algebra of the rational function g/f<table class="examples"><tr><td><pre>i1 : W = QQ[x,y,Dx,Dy, WeylAlgebra => {x=>Dx, y=>Dy}]
o1 = W
o1 : PolynomialRing</pre>
</td></tr>
<tr><td><pre>i2 : f = x^2-y^3
3 2
o2 = - y + x
o2 : W</pre>
</td></tr>
<tr><td><pre>i3 : g = 2*x*y
o3 = 2x*y
o3 : W</pre>
</td></tr>
<tr><td><pre>i4 : I = RatAnn (g,f)
3 2 2 2 2 2 2 3
o4 = ideal (3x*Dx + 2y*Dy + 1, y Dy - x Dy + 6y Dy + 6y, 9y Dx Dy - 4y*Dy
------------------------------------------------------------------------
2 2 3 2 2 2
+ 27y*Dx + 2Dy , 9y Dx - 4y Dy + 10y*Dy - 10)
o4 : Ideal of W</pre>
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<div class="single"><h2>Caveat</h2>
<div>The inputs f and g should be elements of a Weyl algebra, and not elements of a commutative polynomial ring. However, f and g should only use the commutative variables.</div>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="___Poly__Ann_lp__Ring__Element_rp.html" title="annihilator of a polynomial in Weyl algebra">PolyAnn</a> -- annihilator of a polynomial in Weyl algebra</span></li>
</ul>
</div>
<div class="waystouse"><h2>Ways to use <tt>RatAnn</tt> :</h2>
<ul><li>RatAnn(RingElement)</li>
<li>RatAnn(RingElement,RingElement)</li>
</ul>
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