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<head><title>diff(RingElement,Matrix) -- differentiate each entry of a matrix</title>
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<div><a href="_diff.html" title="differentiate or take difference">diff</a> > <a href="_diff_lp__Ring__Element_cm__Matrix_rp.html" title="differentiate each entry of a matrix">diff(RingElement,Matrix)</a></div>
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<div><h1>diff(RingElement,Matrix) -- differentiate each entry of a matrix</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="___Matrix.html">matrix</a></span>, a matrix between free modules over 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="___Matrix.html">matrix</a></span>, having the same shape as f, whose (i,j) entry is the result of differentiating <tt>f_(i,j)</tt> by the differential operator corresponding to <tt>x</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];</pre>
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<tr><td><pre>i2 : f = matrix{{x^2-y*z, x*y*z + z^4}, {x-1, 2*y^2+z^2-1}}
o2 = | x2-yz z4+xyz |
| x-1 2y2+z2-1 |
2 2
o2 : Matrix R <--- R</pre>
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<tr><td><pre>i3 : diff(x,f)
o3 = | 2x yz |
| 1 0 |
2 2
o3 : Matrix R <--- R</pre>
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<tr><td><pre>i4 : diff(x^2-y*z,f)
o4 = | 3 -x |
| 0 0 |
2 2
o4 : 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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