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<head><title>mirrorSphere -- Example how to compute the mirror sphere.</title>
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<div><h1>mirrorSphere -- Example how to compute the mirror sphere.</h1>
<div class="single"><h2>Description</h2>
<div><p>Example how to compute the mirror sphere as an <a href="___Complex.html" title="The class of all embedded complexes.">Complex</a>.</p>
<p>This is work in progress. Many interesting pieces are not yet implemented.</p>
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<table class="examples"><tr><td><pre>i1 : R=QQ[x_0..x_4]
o1 = R
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : I=ideal(x_0*x_1,x_2*x_3*x_4)
o2 = ideal (x x , x x x )
0 1 2 3 4
o2 : Ideal of R</pre>
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<tr><td><pre>i3 : C=idealToComplex I
o3 = 2: x x x x x x x x x x x x x x x x x x
0 2 3 1 2 3 0 2 4 1 2 4 0 3 4 1 3 4
o3 : complex of dim 2 embedded in dim 4 (printing facets)
equidimensional, simplicial, F-vector {1, 5, 9, 6, 0, 0}, Euler = 1</pre>
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<tr><td><pre>i4 : PT1C=PT1 C
o4 = 4: y y y y y y y y y y
0 1 2 3 4 5 6 7 8 9
o4 : complex of dim 4 embedded in dim 4 (printing facets)
equidimensional, non-simplicial, F-vector {1, 10, 24, 25, 11, 1}, Euler = 0</pre>
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<tr><td><pre>i5 : tropDefC=tropDef(C,PT1C)
o5 = 1: y y y y y y y y y y
0 4 8 9 3 7 2 6 1 5
o5 : co-complex of dim 1 embedded in dim 4 (printing facets)
equidimensional, non-simplicial, F-vector {0, 0, 5, 9, 6, 1}, Euler = -1</pre>
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<tr><td><pre>i6 : tropDefC.grading
o6 = | -1 0 0 0 |
| 1 0 0 0 |
| -1 2 0 0 |
| -1 0 2 0 |
| 0 -1 -1 -1 |
| 3 -1 -1 -1 |
| 0 2 -1 -1 |
| 0 -1 2 -1 |
| -1 0 0 2 |
| 0 -1 -1 2 |
10 4
o6 : Matrix ZZ <--- ZZ</pre>
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<tr><td><pre>i7 : B=dualize tropDefC
o7 = 2: v v v v v v v v v v v v v v v v v v
2 4 7 2 4 8 9 2 5 7 9 4 5 7 8 5 8 9
o7 : complex of dim 2 embedded in dim 4 (printing facets)
equidimensional, non-simplicial, F-vector {1, 6, 9, 5, 0, 0}, Euler = 1</pre>
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<tr><td><pre>i8 : B.grading
o8 = | -1 0 0 0 |
| 0 -1 0 0 |
| -1 -1 0 0 |
| 1 1 1 0 |
| 0 0 -1 0 |
| -1 0 -1 0 |
| 1 1 0 1 |
| 1 0 1 1 |
| 1 1 1 1 |
| 0 0 0 -1 |
| -1 0 0 -1 |
11 4
o8 : Matrix ZZ <--- ZZ</pre>
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<tr><td><pre>i9 : fvector C
o9 = {1, 5, 9, 6, 0, 0}
o9 : List</pre>
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<tr><td><pre>i10 : fvector B
o10 = {1, 6, 9, 5, 0, 0}
o10 : List</pre>
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<div class="single"><h2>Caveat</h2>
<div><p>The implementation of testing whether a face is tropical so far uses a trick to emulate higher order. For very complicated (non-complete intersections and non-Pfaffians) examples this may lead to an incorrect result. Use with care. This will be fixed at some point.</p>
<div>If using <a href="../../Polyhedra/html/index.html" title="for computations with convex polyhedra, cones, and fans">Polyhedra</a> to compute convex hulls and its faces instead of <i>ConvexInterface</i> you are limited to rather simple examples.</div>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="___P__T1.html" title="Compute the deformation polytope associated to a Stanley-Reisner complex.">PT1</a> -- Compute the deformation polytope associated to a Stanley-Reisner complex.</span></li>
<li><span><a href="_trop__Def.html" title="The co-complex of tropical faces of the deformation polytope.">tropDef</a> -- The co-complex of tropical faces of the deformation polytope.</span></li>
<li><span><a href="___H__H_sp__Complex.html" title="Compute the homology of a complex.">HH Complex</a> -- Compute the homology of a complex.</span></li>
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<div class="waystouse"><h2>For the programmer</h2>
<p>The object <a href="_mirror__Sphere.html" title="Example how to compute the mirror sphere.">mirrorSphere</a> is <span>a <a href="../../Macaulay2Doc/html/___Symbol.html">symbol</a></span>.</p>
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