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<head><title>base -- an abstract variety, defined with some parameters and some bundles</title>
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<div><h1>base -- an abstract variety, defined with some parameters and some bundles</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>X=base() or X=base(p) or base(n,p) or base(n,p,q,..,Bundle=>(A,r,a),..)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>n</tt>, <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span></span></li>
<li><span><tt>p</tt>, <span>a <a href="../../Macaulay2Doc/html/___Symbol.html">symbol</a></span></span></li>
<li><span><tt>q</tt>, <span>a <a href="../../Macaulay2Doc/html/___Symbol.html">symbol</a></span></span></li>
<li><span><tt>A</tt>, <span>a <a href="../../Macaulay2Doc/html/___Symbol.html">symbol</a></span></span></li>
<li><span><tt>r</tt>, <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span></span></li>
<li><span><tt>a</tt>, <span>a <a href="../../Macaulay2Doc/html/___Symbol.html">symbol</a></span></span></li>
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<li><div class="single">Consequences:<ul><li><div>X has dimension n (if n is present; else 0) and has symbols p,q... defined in its Chow ring (if they are present. A is a bundle defined on X with rank r and chern classes a<sub>1</sub>..a<sub>r</sub> (if this option is present).</div>
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<li><div class="single">Outputs:<ul><li><span><tt>X</tt>, <span>an <a href="___Abstract__Variety.html">abstract variety</a></span></span></li>
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<div class="single"><h2>Description</h2>
<div><div>The symbols p,q... can be used as integer variables in Chow ring computations</div>
<table class="examples"><tr><td><pre>i1 : X=base(1,p,q,Bundle=>(A,1,a), Bundle=>(B,1,b))
o1 = X
o1 : an abstract variety of dimension 1</pre>
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<tr><td><pre>i2 : Y=projectiveSpace(3,X,VariableName=>H)
o2 = Y
o2 : a flag bundle with ranks {3, 1}</pre>
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<tr><td><pre>i3 : f=Y.StructureMap
o3 = f
o3 : a map to X from Y</pre>
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<tr><td><pre>i4 : x=chern f_*((f^*(OO_X(p*a_1)))*OO_Y(q*H))
1 3 2 11
o4 = 1 + (-p*q a + p*q a + --p*q*a + p*a )
6 1 1 6 1 1
o4 : QQ[p, q, a , b ]
1 1</pre>
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<tr><td><pre>i5 : y=chern f_*OO_Y((f^*(p*a_1))+q*H)
1 3 2 11
o5 = 1 + (-p*q a + p*q a + --p*q*a + p*a )
6 1 1 6 1 1
o5 : QQ[p, q, a , b ]
1 1</pre>
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<tr><td><pre>i6 : x==y
o6 = true</pre>
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<div class="single"><h2>Caveat</h2>
<div><div>Be sure that A... are symbols; if they have already been defined there will be trouble.</div>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_projective__Space.html" title="Makes an AbstractVariety representing projective space">projectiveSpace</a> -- Makes an AbstractVariety representing projective space</span></li>
</ul>
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<div class="waystouse"><h2>Ways to use <tt>base</tt> :</h2>
<ul><li><span><tt>base(Sequence)</tt> (missing documentation<!-- tag: (base,Sequence) -->)</span></li>
<li><span><tt>base(Thing)</tt> (missing documentation<!-- tag: (base,Thing) -->)</span></li>
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