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<head><title>diff(RingElement,RingElement) -- differentiation</title>
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<div><a href="_diff.html" title="differentiate or take difference">diff</a> > <a href="_diff_lp__Ring__Element_cm__Ring__Element_rp.html" title="differentiation">diff(RingElement,RingElement)</a></div>
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<div><h1>diff(RingElement,RingElement) -- differentiation</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>diff(x,f)</tt></div>
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<li><span>Function: <a href="_diff.html" title="differentiate or take difference">diff</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>x</tt>, <span>a <a href="___Ring__Element.html">ring element</a></span>, a polynomial</span></li>
<li><span><tt>f</tt>, <span>a <a href="___Ring__Element.html">ring element</a></span>, a polynomial in the same ring as <tt>x</tt></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>, the result of differentiating <tt>f</tt> by the differential operator corresponding to <tt>x</tt>.</span></li>
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<div class="single"><h2>Description</h2>
<div>If <tt>x</tt> is an indeterminate this is simply the usual differentiation.<table class="examples"><tr><td><pre>i1 : R = QQ[x,y,z];</pre>
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<tr><td><pre>i2 : diff(x,x^7 + 4*x^3*y - 3*y)
6 2
o2 = 7x + 12x y
o2 : R</pre>
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<tr><td><pre>i3 : diff(x^2+y^2+z^2, y^2*z^2 - x^3 - 1)
2 2
o3 = 2y + 2z - 6x
o3 : R</pre>
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Here is a shortcut that can save some typing.<table class="examples"><tr><td><pre>i4 : diff_x x^6
5
o4 = 6x
o4 : R</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_contract.html" title="contract one matrix by another">contract</a> -- contract one matrix by another</span></li>
<li><span><a href="_jacobian.html" title="the Jacobian matrix of partial derivatives">jacobian</a> -- the Jacobian matrix of partial derivatives</span></li>
<li><span><a href="_diff_spand_spcontract.html" title="">diff and contract</a></span></li>
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