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<head><title>part(ZZ,ZZ,VisibleList,RingElement) -- select terms of a polynomial by degree or weight</title>
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<div><h1>part(ZZ,ZZ,VisibleList,RingElement) -- select terms of a polynomial by degree or weight</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>part(lo,hi,wt,f)</tt></div>
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<li><span>Function: <a href="_part.html" title="select terms of a polynomial by degree or weight">part</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>lo</tt>, <span>an <a href="___Z__Z.html">integer</a></span></span></li>
<li><span><tt>hi</tt>, <span>an <a href="___Z__Z.html">integer</a></span></span></li>
<li><span><tt>wt</tt>, <span>a <a href="___Visible__List.html">visible list</a></span>, whose elements are integers (after splicing)</span></li>
<li><span><tt>f</tt>, <span>a <a href="___Ring__Element.html">ring element</a></span></span></li>
</ul>
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</li>
<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Ring__Element.html">ring element</a></span>, the sum of those terms of <tt>f</tt> whose weights, with respect to <tt>wt</tt>, are in the range <tt>lo..hi</tt></span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : R = QQ[x,y,z,Degrees=>{3,2,1}];</pre>
</td></tr>
<tr><td><pre>i2 : f = (1+x+y+z)^3
3 2 2 2 2 3 2 2 2
o2 = x + 3x y + 3x*y + 3x z + 3x + y + 6x*y*z + 6x*y + 3y z + 3x*z + 3y
------------------------------------------------------------------------
2 3 2
+ 6x*z + 3y*z + 3x + 6y*z + z + 3y + 3z + 3z + 1
o2 : R</pre>
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<tr><td><pre>i3 : part(0,1,3:1,f)
o3 = 3x + 3y + 3z + 1
o3 : R</pre>
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<tr><td><pre>i4 : part(0,1,1..3,f)
o4 = 3x + 1
o4 : R</pre>
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<tr><td><pre>i5 : part(7,9,1..3,f)
2 2 2 3
o5 = 3y z + 3x*z + 3y*z + z
o5 : R</pre>
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<p>If <tt>wt</tt> is omitted, and the ring is singly graded, then the degrees of the variables are used as the weights.</p>
<table class="examples"><tr><td><pre>i6 : gens R
o6 = {x, y, z}
o6 : List</pre>
</td></tr>
<tr><td><pre>i7 : degree \ oo
o7 = {{3}, {2}, {1}}
o7 : List</pre>
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<tr><td><pre>i8 : part(7,9,f)
3 2 2 2
o8 = x + 3x y + 3x*y + 3x z
o8 : R</pre>
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<p>If <tt>lo</tt> or <tt>hi</tt> is omitted, but not the corresponding comma, then there is no corresponding bound on the weights of the terms provided.</p>
<table class="examples"><tr><td><pre>i9 : part(7,,f)
3 2 2 2
o9 = x + 3x y + 3x*y + 3x z
o9 : R</pre>
</td></tr>
<tr><td><pre>i10 : part(,3,f)
3 2
o10 = 3x + 6y*z + z + 3y + 3z + 3z + 1
o10 : R</pre>
</td></tr>
<tr><td><pre>i11 : part(,3,1..3,f)
3 2
o11 = x + 3x + 6x*y + 3x + 3y + 3z + 1
o11 : R</pre>
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<p>The bounds may be infinite.</p>
<table class="examples"><tr><td><pre>i12 : part(7,infinity,f)
3 2 2 2
o12 = x + 3x y + 3x*y + 3x z
o12 : R</pre>
</td></tr>
<tr><td><pre>i13 : part(-infinity,3,f)
3 2
o13 = 3x + 6y*z + z + 3y + 3z + 3z + 1
o13 : R</pre>
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<tr><td><pre>i14 : part(-infinity,infinity,1..3,f)
3 2 2 2 2 3 2 2
o14 = x + 3x y + 3x*y + 3x z + 3x + y + 6x*y*z + 6x*y + 3y z + 3x*z +
-----------------------------------------------------------------------
2 2 3 2
3y + 6x*z + 3y*z + 3x + 6y*z + z + 3y + 3z + 3z + 1
o14 : R</pre>
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<p>If just one limit is provided, terms whose weight are equal to it are provided.</p>
<table class="examples"><tr><td><pre>i15 : part(7,f)
2 2
o15 = 3x*y + 3x z
o15 : R</pre>
</td></tr>
<tr><td><pre>i16 : part(7,1..3,f)
2 2
o16 = 3y z + 3x*z
o16 : R</pre>
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<p>For polynomial rings over polynomial rings, all of the variables participate.</p>
<table class="examples"><tr><td><pre>i17 : S = QQ[a][x];</pre>
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<tr><td><pre>i18 : g = (1+a+x)^3
3 2 2 3 2
o18 = x + (3a + 3)x + (3a + 6a + 3)x + a + 3a + 3a + 1
o18 : S</pre>
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<tr><td><pre>i19 : part(2,{1,1},g)
2 2
o19 = 3x + 6a*x + 3a
o19 : S</pre>
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<tr><td><pre>i20 : part(2,{1,0},g)
2
o20 = (3a + 3)x
o20 : S</pre>
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<tr><td><pre>i21 : part(2,,{0,1},g)
2 3 2
o21 = 3a x + a + 3a
o21 : S</pre>
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