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<head><title>bott(List,ZZ,ZZ) -- cohomology table of Schur functor of tautolgical bundle on P^n</title>
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<div><h1>bott(List,ZZ,ZZ) -- cohomology table of Schur functor of tautolgical bundle on P^n</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>bott(L,lowDegree,highDegree)</tt></div>
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<li><span>Function: <a href="_bott.html" title="cohomology of Schur functors of tautological bundle on P^n">bott</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>L</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, a non-increasing sequence of integers</span></li>
<li><span><tt>lowDegree</tt>, <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span></span></li>
<li><span><tt>highDegree</tt>, <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span></span></li>
</ul>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Cohomology__Tally.html">Cohomology tally</a></span></span></li>
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<div class="single"><h2>Description</h2>
<div>Produces a <a href="___Cohomology__Tally.html" title="cohomology table">CohomologyTally</a> of the vector bundle <tt>S_L(Q)</tt>, between the column whose index is <tt>lowDegree</tt> and the column whose index is <tt>highDegree</tt>. See <a href="_bott_lp__List_cm__Z__Z_rp.html" title="cohomology of Schur functor of tautological bundle on P^n">bott(List,ZZ)</a> for the definition of <tt>Q</tt>.<table class="examples"><tr><td><pre>i1 : C1 = bott({3,2,1},-10,10)
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
o1 = 3: 924 640 420 256 140 64 20 . . . . . . . . . . .
2: . . . . . . . 4 . . . . . . . . . .
1: . . . . . . . . 4 . . . . . . . . .
0: . . . . . . . . . 20 64 140 256 420 640 924 1280 1716
------------------------------------------------------------------------
8 9 10
. . .
. . .
. . .
2240 2860 3584
o1 : CohomologyTally</pre>
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<tr><td><pre>i2 : C2 = pureCohomologyTable({-2,-4,-6},-10,10)
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
o2 = 3: 231 160 105 64 35 16 5 . . . . . . . . . . . . .
2: . . . . . . . 1 . . . . . . . . . . . .
1: . . . . . . . . 1 . . . . . . . . . . .
0: . . . . . . . . . 5 16 35 64 105 160 231 320 429 560 715
------------------------------------------------------------------------
10
.
.
.
896
o2 : CohomologyTally</pre>
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<tr><td><pre>i3 : C1 == 4 * C2
o3 = true</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_bott_lp__List_cm__Z__Z_rp.html" title="cohomology of Schur functor of tautological bundle on P^n">bott(List,ZZ)</a> -- cohomology of Schur functor of tautological bundle on P^n</span></li>
<li><span><a href="_pure__Cohomology__Table_lp__List_cm__Z__Z_cm__Z__Z_rp.html" title="pure cohomology table given zeros of Hilbert polynomial">pureCohomologyTable</a> -- pure cohomology table given zeros of Hilbert polynomial</span></li>
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