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<head><title>diff -- differentiate or take difference</title>
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<div><h1>diff -- differentiate or take difference</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) or diff(P) or diff(P,i)</tt></div>
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<div class="single"><h2>Description</h2>
<div>This function has two different uses. The most common use is for differentiation: differentiate the second input by the first.<p/>
The second use, less common but sometimes useful, is to compute the difference polynomial of a Hilbert polynomial.<p/>
The arguments can also be ring elements or vectors.<table class="examples"><tr><td><pre>i1 : R = ZZ[x,y,z]
o1 = R
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : f = vars R ** vars R
o2 = | x2 xy xz xy y2 yz xz yz z2 |
1 9
o2 : Matrix R <--- R</pre>
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<tr><td><pre>i3 : diff(transpose vars R, f)
o3 = {1} | 2x y z y 0 0 z 0 0 |
{1} | 0 x 0 x 2y z 0 z 0 |
{1} | 0 0 x 0 0 y x y 2z |
3 9
o3 : Matrix R <--- R</pre>
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<tr><td><pre>i4 : diff(x, f)
o4 = | 2x y z y 0 0 z 0 0 |
1 9
o4 : Matrix R <--- R</pre>
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<tr><td><pre>i5 : diff(y, f)
o5 = | 0 x 0 x 2y z 0 z 0 |
1 9
o5 : Matrix R <--- R</pre>
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<tr><td><pre>i6 : diff(z, f)
o6 = | 0 0 x 0 0 y x y 2z |
1 9
o6 : Matrix R <--- R</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_diff_spand_spcontract.html" title="">diff and contract</a></span></li>
<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="_jacobian.html" title="the Jacobian matrix of partial derivatives">jacobian</a> -- the Jacobian matrix of partial derivatives</span></li>
<li><span><a href="_hilbert__Polynomial.html" title="compute the Hilbert polynomial">hilbertPolynomial</a> -- compute the Hilbert polynomial</span></li>
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<div class="waystouse"><h2>Ways to use <tt>diff</tt> :</h2>
<ul><li><span><a href="_diff_lp__Matrix_cm__Matrix_rp.html" title="differentiate a matrix by a matrix">diff(Matrix,Matrix)</a> -- differentiate a matrix by a matrix</span></li>
<li><span>diff(Matrix,Vector), see <span><a href="_diff_lp__Matrix_cm__Matrix_rp.html" title="differentiate a matrix by a matrix">diff(Matrix,Matrix)</a> -- differentiate a matrix by a matrix</span></span></li>
<li><span>diff(RingElement,Vector), see <span><a href="_diff_lp__Matrix_cm__Matrix_rp.html" title="differentiate a matrix by a matrix">diff(Matrix,Matrix)</a> -- differentiate a matrix by a matrix</span></span></li>
<li><span>diff(Vector,Matrix), see <span><a href="_diff_lp__Matrix_cm__Matrix_rp.html" title="differentiate a matrix by a matrix">diff(Matrix,Matrix)</a> -- differentiate a matrix by a matrix</span></span></li>
<li><span>diff(Vector,RingElement), see <span><a href="_diff_lp__Matrix_cm__Matrix_rp.html" title="differentiate a matrix by a matrix">diff(Matrix,Matrix)</a> -- differentiate a matrix by a matrix</span></span></li>
<li><span>diff(Vector,Vector), see <span><a href="_diff_lp__Matrix_cm__Matrix_rp.html" title="differentiate a matrix by a matrix">diff(Matrix,Matrix)</a> -- differentiate a matrix by a matrix</span></span></li>
<li><span><a href="_diff_lp__Matrix_cm__Ring__Element_rp.html" title="differentiation">diff(Matrix,RingElement)</a> -- differentiation</span></li>
<li><span><a href="_diff_lp__Projective__Hilbert__Polynomial_rp.html" title="">diff(ProjectiveHilbertPolynomial)</a></span></li>
<li><span><a href="_diff_lp__Projective__Hilbert__Polynomial_cm__Z__Z_rp.html" title="">diff(ProjectiveHilbertPolynomial,ZZ)</a></span></li>
<li><span><a href="_diff_lp__Ring__Element_cm__Matrix_rp.html" title="differentiate each entry of a matrix">diff(RingElement,Matrix)</a> -- differentiate each entry of a matrix</span></li>
<li><span><a href="_diff_lp__Ring__Element_cm__Ring__Element_rp.html" title="differentiation">diff(RingElement,RingElement)</a> -- differentiation</span></li>
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<div><h3>Menu</h3>
<h4>differentiation</h4>
<ul><li><span><a href="_diff_lp__Ring__Element_cm__Ring__Element_rp.html" title="differentiation">diff(RingElement,RingElement)</a> -- differentiation</span></li>
<li><span><a href="_diff_lp__Ring__Element_cm__Matrix_rp.html" title="differentiate each entry of a matrix">diff(RingElement,Matrix)</a> -- differentiate each entry of a matrix</span></li>
<li><span><a href="_diff_lp__Matrix_cm__Ring__Element_rp.html" title="differentiation">diff(Matrix,RingElement)</a> -- differentiation</span></li>
<li><span><a href="_diff_lp__Matrix_cm__Matrix_rp.html" title="differentiate a matrix by a matrix">diff(Matrix,Matrix)</a> -- differentiate a matrix by a matrix</span></li>
</ul>
<h4>difference operator for Hilbert polynomials</h4>
<ul><li><span><a href="_diff_lp__Projective__Hilbert__Polynomial_rp.html" title="">diff(ProjectiveHilbertPolynomial)</a></span></li>
<li><span><a href="_diff_lp__Projective__Hilbert__Polynomial_cm__Z__Z_rp.html" title="">diff(ProjectiveHilbertPolynomial,ZZ)</a></span></li>
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