ring(Complex) -- The underlying polynomial ring of a simplicial complex.

i1 : K=QQ;

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

i3 : I=ideal(x_0*x_1,x_1*x_2,x_2*x_3,x_3*x_4,x_4*x_0)

o3 = ideal (x x , x x , x x , x x , x x )
             0 1   1 2   2 3   3 4   0 4

o3 : Ideal of R

i4 : D=idealToComplex I

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

o4 : complex with 5 facets on the vertices x  x  x  x  x  
                                            0  1  2  3  4

i5 : ring D

o5 = R

o5 : PolynomialRing

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 : ring fc#0

o7 = R

o7 : PolynomialRing

i8 : S=complex {(entries vars R)#0}

o8 = {{x , x , x , x , x }}
        0   1   2   3   4

o8 : complex with 1 facets on the vertices x  x  x  x  x  
                                            0  1  2  3  4

i9 : complexToIdeal S

o9 = ideal ()

o9 : Ideal of R