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<head><title>discriminant(RingElement,RingElement)</title>
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<div><h1>discriminant(RingElement,RingElement)</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>discriminant(f,x)</tt></div>
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<li><span>Function: <a href="_discriminant_lp__Ring__Element_cm__Ring__Element_rp.html" title="">discriminant</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>f</tt>, <span>a <a href="../../Macaulay2Doc/html/___Ring__Element.html">ring element</a></span>, a polynomial</span></li>
<li><span><tt>x</tt>, <span>a <a href="../../Macaulay2Doc/html/___Ring__Element.html">ring element</a></span>, a variable in the same ring</span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="../../Macaulay2Doc/html/___Ring__Element.html">ring element</a></span>, the discriminant of <tt>f</tt> with respect to <tt>x</tt></span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : R = ZZ/101[x,a,b,c,d]
o1 = R
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : f = x^2+a*x+b
2
o2 = x + x*a + b
o2 : R</pre>
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<tr><td><pre>i3 : g = x^2+c*x+d
2
o3 = x + x*c + d
o3 : R</pre>
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<tr><td><pre>i4 : time eliminate(x,ideal(f,g))
-- used 0.003 seconds
2 2 2 2
o4 = ideal(a*b*c - b*c - a d + a*c*d - b + 2b*d - d )
o4 : Ideal of R</pre>
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<tr><td><pre>i5 : time ideal resultant(f,g,x)
-- used 0.000999 seconds
2 2 2 2
o5 = ideal(- a*b*c + b*c + a d - a*c*d + b - 2b*d + d )
o5 : Ideal of R</pre>
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<tr><td><pre>i6 : sylvesterMatrix(f,g,x)
o6 = {0} | b 0 d 0 |
{1} | a b c d |
{2} | 1 a 1 c |
{3} | 0 1 0 1 |
4 4
o6 : Matrix R <--- R</pre>
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<tr><td><pre>i7 : discriminant(f,x)
2
o7 = - a + 4b
o7 : R</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_resultant_lp__Ring__Element_cm__Ring__Element_cm__Ring__Element_rp.html" title="">resultant</a></span></li>
<li><span><a href="_eliminate.html" title="">eliminate</a></span></li>
<li><span><a href="index.html" title="eliminating specified variables, and Sylvester resultant">Elimination</a> -- eliminating specified variables, and Sylvester resultant</span></li>
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