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<head><title>taylor -- Gives the nth differential in the Taylor resolution of a monomial ideal I.</title>
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<div><h1>taylor -- Gives the nth differential in the Taylor resolution of a monomial ideal I.</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>T = taylor(n,I)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>n</tt>, </span></li>
<li><span><tt>I</tt>, </span></li>
</ul>
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<li><div class="single">Outputs:<ul><li><span>T, the nth differential in the Taylor Resolution of I.</span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : R = ZZ/101[a,b]
o1 = R
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : I = monomialIdeal (ideal vars R)^3
3 2 2 3
o2 = monomialIdeal (a , a b, a*b , b )
o2 : MonomialIdeal of R</pre>
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<tr><td><pre>i3 : T2 = taylor(2,I)
o3 = {3} | -b -b2 0 -b3 0 0 |
{3} | a 0 -b 0 -b2 0 |
{3} | 0 a2 a 0 0 -b |
{3} | 0 0 0 a3 a2 a |
4 6
o3 : Matrix R <--- R</pre>
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<tr><td><pre>i4 : T3 = taylor(3,I)
o4 = {4} | b b2 0 0 |
{5} | -1 0 b 0 |
{4} | a 0 0 b |
{6} | 0 -1 -1 0 |
{5} | 0 a 0 -1 |
{4} | 0 0 a2 a |
6 4
o4 : Matrix R <--- R</pre>
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<div class="waystouse"><h2>Ways to use <tt>taylor</tt> :</h2>
<ul><li>taylor(ZZ,MonomialIdeal)</li>
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