-- -*- M2-comint -*- hash: 15922380373430664361

i1 : R = QQ[x_1..x_6];

i2 : G = graph({x_1*x_2,x_2*x_3,x_3*x_4,x_4*x_5,x_1*x_5,x_1*x_6,x_5*x_6}) --5-cycle and a triangle

o2 = Graph{"edges" => {{x , x }, {x , x }, {x , x }, {x , x }, {x , x }, {x , x }, {x , x }}}
                         1   2     2   3     3   4     1   5     4   5     1   6     5   6
           "ring" => R
           "vertices" => {x , x , x , x , x , x }
                           1   2   3   4   5   6

o2 : Graph

i3 : DeltaG = hyperGraphToSimplicialComplex G

o3 = simplicialComplex | x_5x_6 x_1x_6 x_4x_5 x_1x_5 x_3x_4 x_2x_3 x_1x_2 |

o3 : SimplicialComplex

i4 : hyperGraphDeltaG = simplicialComplexToHyperGraph DeltaG

o4 = HyperGraph{"edges" => {{x , x }, {x , x }, {x , x }, {x , x }, {x , x }, {x , x }, {x , x }}}
                              1   2     2   3     3   4     1   5     4   5     1   6     5   6
                "ring" => R
                "vertices" => {x , x , x , x , x , x }
                                1   2   3   4   5   6

o4 : HyperGraph

i5 : GPrime = graph(hyperGraphDeltaG)

o5 = Graph{"edges" => {{x , x }, {x , x }, {x , x }, {x , x }, {x , x }, {x , x }, {x , x }}}
                         1   2     2   3     3   4     1   5     4   5     1   6     5   6
           "ring" => R
           "vertices" => {x , x , x , x , x , x }
                           1   2   3   4   5   6

o5 : Graph

i6 : G === GPrime

o6 = true

i7 : 
