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<div><a href="_diff.html" title="differentiate or take difference">diff</a> > <a href="_diff_lp__Matrix_cm__Ring__Element_rp.html" title="differentiation">diff(Matrix,RingElement)</a></div>
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<div><h1>diff(Matrix,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(f,g)</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>f</tt>, <span>a <a href="___Matrix.html">matrix</a></span>, a matrix</span></li>
<li><span><tt>g</tt>, <span>a <a href="___Ring__Element.html">ring element</a></span>, a polynomial with the same ring as <tt>f</tt></span></li>
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<li><div class="single">Outputs:<ul><li><span>the result of differentiating <tt>g</tt> by the differential operator corresponding to each entry of <tt>f</tt>.</span></li>
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<div class="single"><h2>Description</h2>
<div>The shape of the resulting matrix is the same as the shape of f, but the degrees of the source module are different in an attempt to ensure that the result is homogeneous.<table class="examples"><tr><td><pre>i1 : R = QQ[x,y,z,q];</pre>
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<tr><td><pre>i2 : f = vars R
o2 = | x y z q |
1 4
o2 : Matrix R <--- R</pre>
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<tr><td><pre>i3 : diff(f, (x+y-z)^2)
o3 = | 2x+2y-2z 2x+2y-2z -2x-2y+2z 0 |
1 4
o3 : Matrix R <--- R</pre>
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<tr><td><pre>i4 : f2 = genericMatrix(R,2,2)
o4 = | x z |
| y q |
2 2
o4 : Matrix R <--- R</pre>
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<tr><td><pre>i5 : diff(f2, (x+y-z)^2)
o5 = | 2x+2y-2z -2x-2y+2z |
| 2x+2y-2z 0 |
2 2
o5 : Matrix R <--- 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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