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SRdeformations :: PT1

PT1 -- Compute the deformation polytope associated to a Stanley-Reisner complex.

Synopsis

Description

Compute the deformation polytope of C, i.e., the convex hull of all homogeneous (i.e., degree(FirstOrderDeformation) zero) deformations associated to C, considering them as lattice monomials (i.e., their preimages under C.grading).

i1 : R=QQ[x_0..x_3]

o1 = R

o1 : PolynomialRing
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
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
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

Caveat

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.

See also

Ways to use PT1 :