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<head><title>PT1 -- Compute the deformation polytope associated to a Stanley-Reisner complex.</title>
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<div><h1>PT1 -- Compute the deformation polytope associated to a Stanley-Reisner complex.</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>PT1(C)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>C</tt>, <span>an <a href="___Complex.html">embedded complex</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>an <a href="___Complex.html">embedded complex</a></span></span></li>
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<li><div class="single"><a href="../../Macaulay2Doc/html/_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:<ul><li><span><a href="_file.html">file => ...</a>, -- Store result of a computation in a file.</span></li>
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<div class="single"><h2>Description</h2>
<div><p>Compute the deformation polytope of C, i.e., the convex hull of all homogeneous (i.e., <a href="_degree_lp__First__Order__Deformation_rp.html" title="The small torus degree of a deformation.">degree(FirstOrderDeformation)</a> zero) deformations associated to C, considering them as lattice monomials (i.e., their preimages under C.grading).</p>
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<table class="examples"><tr><td><pre>i1 : R=QQ[x_0..x_3]
o1 = R
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : I=ideal(x_0*x_1,x_2*x_3)
o2 = ideal (x x , x x )
0 1 2 3
o2 : Ideal of R</pre>
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<tr><td><pre>i3 : C=idealToComplex I
o3 = 1: x x x x x x x x
0 2 1 2 0 3 1 3
o3 : complex of dim 1 embedded in dim 3 (printing facets)
equidimensional, simplicial, F-vector {1, 4, 4, 0, 0}, Euler = -1</pre>
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<tr><td><pre>i4 : PT1C=PT1 C
o4 = 3: y y y y y y y y
0 1 2 3 4 5 6 7
o4 : complex of dim 3 embedded in dim 3 (printing facets)
equidimensional, non-simplicial, F-vector {1, 8, 14, 8, 1}, Euler = 0</pre>
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<div class="single"><h2>Caveat</h2>
<div><div>To homogenize the denominators of deformations (which are supported inside the link) we use globalSections to deal with the toric case. The speed of this should be improved. For ordinary projective space homogenization with support on F is done much faster.</div>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_deformations__Face.html" title="Compute the deformations associated to a face.">deformationsFace</a> -- Compute the deformations associated to a face.</span></li>
<li><span><a href="_link.html" title="The link of a face of a complex.">link</a> -- The link of a face of a complex.</span></li>
<li><span><a href="_global__Sections.html" title="The global sections of a toric divisor.">globalSections</a> -- The global sections of a toric divisor.</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>
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<div class="waystouse"><h2>Ways to use <tt>PT1</tt> :</h2>
<ul><li>PT1(Complex)</li>
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