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<head><title>coefficient -- coefficient of a monomial</title>
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<div><h1>coefficient -- coefficient of a monomial</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>coefficient(m,f)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>m</tt>, <span>a <a href="___Ring__Element.html">ring element</a></span>, a monomial</span></li>
<li><span><tt>f</tt>, <span>a <a href="___Ring__Element.html">ring element</a></span>, in the same ring <tt>R</tt> as <tt>m</tt></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Ring__Element.html">ring element</a></span>, the coefficient of the monomial <tt>m</tt> in <tt>f</tt> as an element of the coefficient ring of <tt>R</tt></span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : R = GF(25,Variable=>a)[x,y,z];</pre>
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<tr><td><pre>i2 : f = ((a+1)*x+a*y+a^2*z)^2
2 2
o2 = (- 2a - 1)x + (- a + 1)x*y + (a - 2)y + 2x*z + (- 2a + 1)y*z + (2a +
------------------------------------------------------------------------
2
2)z
o2 : R</pre>
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<tr><td><pre>i3 : coefficient(y^2,f)
o3 = a - 2
o3 : GF 25</pre>
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The returned value is an element of the coefficient ring, even in the case when that ring is another polynomial ring.<table class="examples"><tr><td><pre>i4 : S = R[r,s,t];</pre>
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<tr><td><pre>i5 : coefficient(r,a*x*(r+a*s))
o5 = a*x
o5 : R</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_coefficients.html" title="monomials and their coefficients">coefficients</a> -- monomials and their coefficients</span></li>
<li><span><a href="_monomials.html" title="matrix of monomials in a ring element or matrix">monomials</a> -- matrix of monomials in a ring element or matrix</span></li>
<li><span><a href="_coefficient__Ring.html" title="get the coefficient ring">coefficientRing</a> -- get the coefficient ring</span></li>
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