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<head><title>topCoefficients -- first variable and its coefficient of a polynomial or matrix</title>
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<div><h1>topCoefficients -- first variable and its coefficient of a polynomial or 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>(lf, cf) = topCoefficients f</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>f</tt>, <span>a <a href="___Ring__Element.html">ring element</a></span> or <span>a <a href="___Matrix.html">matrix</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>lf</tt>, <span>a <a href="___Ring__Element.html">ring element</a></span>, or <span>a <a href="___Matrix.html">matrix</a></span>, the power of the lowest index variable occurring in f, if f is a ring element, or the one row matrix of these powers for each column, if f is a matrix.</span></li>
<li><span><tt>cf</tt>, <span>a <a href="___Ring__Element.html">ring element</a></span>, or <span>a <a href="___Matrix.html">matrix</a></span>, the cofficient of lf in f, if f is a ring element, or the matrix of these coefficients for each column of f</span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : A = ZZ[x]
o1 = A
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : (lf,cf) = topCoefficients (7*x^4-13*x^3+x+1)
4
o2 = (x , 7)
o2 : Sequence</pre>
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<tr><td><pre>i3 : v = first support lf
o3 = x
o3 : A</pre>
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<tr><td><pre>i4 : e = first degree lf
o4 = 4</pre>
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The polynomial ring may have more variables.<table class="examples"><tr><td><pre>i5 : B = ZZ[x,y,z]
o5 = B
o5 : PolynomialRing</pre>
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<tr><td><pre>i6 : f = y^4*(3*z^3-z^2-1) - y^3*z^7 + y + z^12
12 3 7 4 3 4 2 4
o6 = z - y z + 3y z - y z - y + y
o6 : B</pre>
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<tr><td><pre>i7 : (lf,cf) = topCoefficients f
4 3 2
o7 = (y , 3z - z - 1)
o7 : Sequence</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_pseudo__Remainder.html" title="compute the pseudo-remainder">pseudoRemainder</a> -- compute the pseudo-remainder</span></li>
</ul>
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<div class="waystouse"><h2>Ways to use <tt>topCoefficients</tt> :</h2>
<ul><li>topCoefficients(Matrix)</li>
<li>topCoefficients(RingElement)</li>
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