Face -- The class of faces of simplicial complexes.

Description

The class of faces of simplicial complexes on the variables of a polynomial ring. The faces are lists of variables of the PolynomialRing

The maximal faces can be obtained from a simplicial Complex by the method facets

i1 : K=QQ;

i2 : R=K[x_0..x_4];

i3 : face {x_0,x_1}

o3 = x  x  
      0  1

o3 : face with 2 vertices

i4 : I=ideal(x_0*x_1,x_1*x_2,x_2*x_3,x_3*x_4,x_4*x_0);

o4 : Ideal of R

i5 : D =idealToComplex I

o5 = {x  x  , x  x  , x  x  , x  x  , x  x  }
       2  4    0  3    0  2    1  3    1  4

o5 : complex with 5 facets on the vertices x  x  x  x  x  
                                            0  1  2  3  4

i6 : fc=facets D

o6 = {x  x  , x  x  , x  x  , x  x  , x  x  }
       2  4    0  3    0  2    1  3    1  4

o6 : List

i7 : fc#0

o7 = x  x  
      2  4

o7 : face with 2 vertices

Methods that use an object of class Face :

dimension(Face), see dimension -- The dimension of a simplicial complex or a face of a simplicial complex.
Face == Face -- Compare two faces.
isSubface(Face,Face), see isSubface -- Test whether a face is a subface of another face.
net(Face) -- Printing faces or cones.
simplexRing(Face), see simplexRing -- The underlying polynomial ring of a simplicial complex, face, fan or cone.
substituteFace(Face,PolynomialRing), see substituteFace -- Substitute a face to a different ring.
vertices(Face), see vertices -- The vertices of a face of a simplicial complex.

For the programmer

The object Face is a type, with ancestor classes List < VisibleList < BasicList < Thing.

Face -- The class of faces of simplicial complexes.

Description

See also

Methods that use an object of class Face :

For the programmer