mirrorSphere -- Example how to compute the mirror sphere.

i1 : R=QQ[x_0..x_4]

o1 = R

o1 : PolynomialRing

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

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

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

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

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

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

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

i9 : fvector C

o9 = {1, 5, 9, 6, 0, 0}

o9 : List

i10 : fvector B

o10 = {1, 6, 9, 5, 0, 0}

o10 : List