minimalNonFaces -- The minimal non-faces of a complex.

Synopsis

• Usage:

  minimalNonFaces(C)

• Inputs:
  • C, an embedded complex
• Optional inputs:
  • embedded => ..., default value null, Use only faces of the embedding complex.
• Outputs:
  • a list

Description

i1 : R=QQ[x_0..x_4];

i2 : I=ideal(x_0*x_1,x_1*x_2,x_2*x_3,x_3*x_4,x_4*x_0);

o2 : Ideal of R

i3 : C=idealToComplex I

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

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

i4 : minimalNonFaces C

o4 = {x x , x x , x x , x x , x x }
       0 1   1 2   2 3   0 4   3 4

o4 : List

See also

• idealToComplex -- The complex associated to a reduced monomial ideal.
• complexToIdeal -- The monomial ideal associated to a complex.
• embeddingComplex -- The embedding complex of a complex or co-complex.