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SRdeformations :: dim(Complex)

dim(Complex) -- Compute the dimension of a complex or co-complex.

Synopsis

Description

Computes the dimension of a complex.

i1 : R=QQ[x_0..x_4]

o1 = R

o1 : PolynomialRing
i2 : addCokerGrading R

o2 = | -1 -1 -1 -1 |
     | 1  0  0  0  |
     | 0  1  0  0  |
     | 0  0  1  0  |
     | 0  0  0  1  |

              5        4
o2 : Matrix ZZ  <--- ZZ
i3 : C=simplex R

o3 = 4: x x x x x  
         0 1 2 3 4

o3 : complex of dim 4 embedded in dim 4 (printing facets)
     equidimensional, simplicial, F-vector {1, 5, 10, 10, 5, 1}, Euler = 0
i4 : dim C

o4 = 4
i5 : bC=boundaryOfPolytope C

o5 = 3: x x x x  x x x x  x x x x  x x x x  x x x x  
         0 1 2 3  0 1 2 4  0 1 3 4  0 2 3 4  1 2 3 4

o5 : complex of dim 3 embedded in dim 4 (printing facets)
     equidimensional, simplicial, F-vector {1, 5, 10, 10, 5, 0}, Euler = -1
i6 : dim bC

o6 = 3
i7 : dbC=dualize bC

o7 = 0: v  v  v  v  v  
         0  1  2  3  4

o7 : co-complex of dim 0 embedded in dim 4 (printing facets)
     equidimensional, simplicial, F-vector {0, 5, 10, 10, 5, 1}, Euler = 1
i8 : dim dbC

o8 = 0

See also