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<head><title>jacobian(Ideal) -- the Jacobian matrix of the generators of an ideal</title>
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<div><h1>jacobian(Ideal) -- the Jacobian matrix of the generators of an ideal</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>jacobian I</tt></div>
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<li><span>Function: <a href="_jacobian.html" title="the Jacobian matrix of partial derivatives">jacobian</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>I</tt>, <span>an <a href="___Ideal.html">ideal</a></span>, in a polynomial ring</span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Matrix.html">matrix</a></span>, the Jacobian matrix of partial derivatives of the generators of <tt>I</tt></span></li>
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<div class="single"><h2>Description</h2>
<div>This is identical to <tt>jacobian generators I</tt>. See <a href="_jacobian_lp__Matrix_rp.html" title="the matrix of partial derivatives of polynomials in a matrix">jacobian(Matrix)</a> for more information.<table class="examples"><tr><td><pre>i1 : R = QQ[x,y,z];</pre>
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<tr><td><pre>i2 : I = ideal(y^2-x*(x-1)*(x-13))
3 2 2
o2 = ideal(- x + 14x + y - 13x)
o2 : Ideal of R</pre>
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<tr><td><pre>i3 : jacobian I
o3 = {1} | -3x2+28x-13 |
{1} | 2y |
{1} | 0 |
3 1
o3 : Matrix R <--- R</pre>
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If the ring of <tt>I</tt> is a polynomial ring over a polynomial ring, then indeterminates in the coefficient ring are treated as constants.<table class="examples"><tr><td><pre>i4 : R = ZZ[a,b,c][x,y,z]
o4 = R
o4 : PolynomialRing</pre>
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<tr><td><pre>i5 : jacobian ideal(a*y*z+b*x*z+c*x*y)
o5 = {1, 0} | yc+zb |
{1, 0} | xc+za |
{1, 0} | xb+ya |
3 1
o5 : Matrix R <--- R</pre>
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