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

- 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

The minimal non-faces of a complex. All subsets of the variables of simplexRing(C) are tested as standard.

If the option embedded=>true is specified then only faces of embeddingComplex(C) are tested.

    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.

## Ways to use minimalNonFaces:

- `minimalNonFaces(Complex)`

## For the programmer

The object minimalNonFaces is a method function with options.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/SRdeformations.m2:7497:0.