Computes the co-complex of tropical faces of the deformation polytope.
This is work in progress.
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 |
i5 : tropDefC=tropDef(C,PT1C) o5 = 1: y y y y y y y y 0 3 6 7 2 5 1 4 o5 : co-complex of dim 1 embedded in dim 3 (printing facets) equidimensional, non-simplicial, F-vector {0, 0, 4, 4, 1}, Euler = -1 |
i6 : tropDefC.grading o6 = | -1 0 0 | | 1 0 0 | | -1 2 0 | | 0 -1 -1 | | 2 -1 -1 | | 0 1 -1 | | 0 -1 1 | | -1 0 2 | 8 3 o6 : Matrix ZZ <--- ZZ |
The implementation of testing whether a face is tropical so far uses a trick to emulate higher order. For 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.