substituteComplex -- Substitute a complex to a different ring.

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 of R

i4 : C=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 : simplexRing C

o5 = R

o5 : PolynomialRing

i6 : S=R**K[y]

o6 = S

o6 : PolynomialRing

i7 : C1=substituteComplex(C,S)

o7 = {x  x  , x  x  , x  x  , x  x  , x  x  }
       2  4    0  3    0  2    1  3    1  4

o7 : complex with 5 facets on the vertices x  x  x  x  x  y 
                                            0  1  2  3  4

i8 : simplexRing C1

o8 = S

o8 : PolynomialRing