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<head><title>terms -- provide a list of terms of a polynomial</title>
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<div><h1>terms -- provide a list of terms of a polynomial</h1>
<div class="single"><h2>Description</h2>
<div><div><h2>Synopsis</h2>
<ul><li><div class="list"><dl class="element"><dt class="heading">Usage: </dt><dd class="value"><div><tt>terms f</tt></div>
</dd></dl>
</div>
</li>
<li>Inputs:<ul><li><span><tt>f</tt>, <span>a <a href="___Ring__Element.html">ring element</a></span>, in a polynomial ring <tt>R</tt> with coefficient ring <tt>A</tt></span></li>
</ul>
</li>
<li>Outputs:<ul><li><span>the list of terms of <tt>f</tt></span></li>
</ul>
</li>
</ul>
Each term is an element of the coefficient ring <tt>A</tt>, multiplied with a monomial in the variables of <tt>R</tt>.<table class="examples"><tr><td><pre>i1 : R = QQ[a..d];</pre>
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<tr><td><pre>i2 : terms(a+d^2-1+a*b*c)
2
o2 = {a*b*c, d , a, -1}
o2 : List</pre>
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In the situtation where the ring is a polynomial ring over another polynomial ring, the polynomial is split using the monomials of the outer ring.<table class="examples"><tr><td><pre>i3 : S = R[x,y];</pre>
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<tr><td><pre>i4 : terms(a*x+b*x+c*x*y+c*x^3+1+a)
3
o4 = {c*x , c*x*y, (a + b)x, a + 1}
o4 : List</pre>
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<div><h2>Synopsis</h2>
<ul><li><div class="list"><dl class="element"><dt class="heading">Usage: </dt><dd class="value"><div><tt>terms(k,f)</tt></div>
</dd></dl>
</div>
</li>
<li>Inputs:<ul><li><span><tt>k</tt>, <span>a <a href="___Ring.html">ring</a></span></span></li>
<li><span><tt>f</tt>, <span>a <a href="___Ring__Element.html">ring element</a></span>, in a polynomial ring <tt>R</tt></span></li>
</ul>
</li>
<li>Outputs:<ul><li><span>the list of terms of <tt>f</tt> with <tt>k</tt> regarded as the coefficient ring</span></li>
</ul>
</li>
</ul>
<p>Each term is an element of the coefficient ring <tt>k</tt>, multiplied with a monomial in the variables of <tt>R</tt>. This is useful in the situation where the polynomial <tt>R</tt> is built from <tt>k</tt> by a sequence of extensions.</p>
<table class="examples"><tr><td><pre>i5 : R = QQ[a][d];</pre>
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<tr><td><pre>i6 : f = (1+a+d)^3
3 2 2 3 2
o6 = d + (3a + 3)d + (3a + 6a + 3)d + a + 3a + 3a + 1
o6 : R</pre>
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<tr><td><pre>i7 : terms f
3 2 2 3 2
o7 = {d , (3a + 3)d , (3a + 6a + 3)d, a + 3a + 3a + 1}
o7 : List</pre>
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<tr><td><pre>i8 : terms(QQ,f)
3 2 2 2 3 2
o8 = {d , 3a*d , 3d , 3a d, 6a*d, 3d, a , 3a , 3a, 1}
o8 : List</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="_some__Terms.html" title="select some terms of a polynomial">someTerms</a> -- select some terms of a polynomial</span></li>
</ul>
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<div class="waystouse"><h2>Ways to use <tt>terms</tt> :</h2>
<ul><li>terms(Ring,RingElement)</li>
<li>terms(RingElement)</li>
</ul>
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