-- -*- M2-comint -*- {* hash: 781880079 *}

i1 : S = QQ[a..e];

i2 : c5 = cycle S

o2 = Graph{edges => {{a, b}, {b, c}, {c, d}, {d, e}, {a, e}}}
           ring => S
           vertices => {a, b, c, d, e}

o2 : Graph

i3 : edgeIdeal c5

o3 = monomialIdeal (a*b, b*c, c*d, a*e, d*e)

o3 : MonomialIdeal of S

i4 : graph flatten entries gens edgeIdeal c5 == c5

o4 = true

i5 : k5 = completeGraph S

o5 = Graph{edges => {{a, b}, {a, c}, {a, d}, {a, e}, {b, c}, {b, d}, {b, e}, {c, d}, {c, e}, {d, e}}}
           ring => S
           vertices => {a, b, c, d, e}

o5 : Graph

i6 : edgeIdeal k5

o6 = monomialIdeal (a*b, a*c, b*c, a*d, b*d, c*d, a*e, b*e, c*e, d*e)

o6 : MonomialIdeal of S

i7 : S = QQ[z_1..z_8];

i8 : h = hyperGraph {{z_1,z_2,z_3},{z_2,z_3,z_4,z_5},{z_4,z_5,z_6},{z_6,z_7,z_8}}

o8 = HyperGraph{edges => {{z , z , z }, {z , z , z , z }, {z , z , z }, {z , z , z }}}
                            1   2   3     2   3   4   5     4   5   6     6   7   8
                ring => S
                vertices => {z , z , z , z , z , z , z , z }
                              1   2   3   4   5   6   7   8

o8 : HyperGraph

i9 : edgeIdeal h

o9 = monomialIdeal (z z z , z z z z , z z z , z z z )
                     1 2 3   2 3 4 5   4 5 6   6 7 8

o9 : MonomialIdeal of S

i10 :