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<head><title>diff(Matrix,Matrix) -- differentiate a matrix by a matrix</title>
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<div><a href="_diff.html" title="differentiate or take difference">diff</a> > <a href="_diff_lp__Matrix_cm__Matrix_rp.html" title="differentiate a matrix by a matrix">diff(Matrix,Matrix)</a></div>
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<div><h1>diff(Matrix,Matrix) -- differentiate a matrix by 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(m,n)</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>m</tt>, <span>a <a href="___Matrix.html">matrix</a></span>, a map <tt>m : F <--- P</tt> between free modules of ranks f and p.</span></li>
<li><span><tt>n</tt>, <span>a <a href="___Matrix.html">matrix</a></span>, a map <tt>n : G <--- Q</tt> between free modules of ranks g and q.</span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Matrix.html">matrix</a></span>, with the shape <tt>h : dual F ** G <--- dual P ** Q</tt>, whose entry in the slot <tt>h<sub>g*i+j,q*k+l</sub></tt> is the result of differentiating <tt>n<sub>j,l</sub></tt> by the differential operator corresponding to <tt>m<sub>i,k</sub>.</tt></span></li>
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<div class="single"><h2>Description</h2>
<div>The arguments <tt>m</tt> and <tt>n</tt> may also be vectors or ring elements.<table class="examples"><tr><td><pre>i1 : R = QQ[a,b,c][x,y,z]
o1 = R
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : m = transpose vars R
o2 = {-1, 0} | x |
{-1, 0} | y |
{-1, 0} | z |
3 1
o2 : Matrix R <--- R</pre>
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<tr><td><pre>i3 : n = matrix{{x^2-a*y^3, x^3-z^2*y, x*y-b, x*z-c}}
o3 = | -y3a+x2 x3-yz2 xy-b xz-c |
1 4
o3 : Matrix R <--- R</pre>
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<tr><td><pre>i4 : diff(m,n)
o4 = {1, 0} | 2x 3x2 y z |
{1, 0} | -3y2a -z2 x 0 |
{1, 0} | 0 -2yz 0 x |
3 4
o4 : Matrix R <--- R</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_diff_sq_lp__Matrix_cm__Matrix_rp.html" title="differentiate a matrix by a matrix, the dual notion">diff'</a> -- differentiate a matrix by a matrix, the dual notion</span></li>
<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="_diff_spand_spcontract.html" title="">diff and contract</a></span></li>
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