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SRdeformations :: complement(Complex)

complement(Complex) -- Compute the complement CoComplex.

Synopsis

Description

Given a Complex it returns the CoComplex of complement Faces and vice versa.

The complement (co)complex cC is remembered in C.complementComplex=cC and cC.complementComplex=C.

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 : bC=boundaryOfPolytope C

o4 = 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

o4 : complex of dim 3 embedded in dim 4 (printing facets)
     equidimensional, simplicial, F-vector {1, 5, 10, 10, 5, 0}, Euler = -1
i5 : cbC=complement bC

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

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

o6 = true

See also