-- -*- M2-comint -*- {* hash: -525951033 *}

i1 : R = QQ[a..f]

o1 = R

o1 : PolynomialRing

i2 : E = {{a,b,c},{b,c,d},{c,d,e},{e,d,f}}

o2 = {{a, b, c}, {b, c, d}, {c, d, e}, {e, d, f}}

o2 : List

i3 : h = hyperGraph (R,E)

o3 = HyperGraph{edges => {{a, b, c}, {b, c, d}, {c, d, e}, {e, d, f}}}
                ring => R
                vertices => {a, b, c, d, e, f}

o3 : HyperGraph

i4 : S = QQ[z_1..z_8]

o4 = S

o4 : PolynomialRing

i5 : E1 = {{z_1,z_2,z_3},{z_2,z_4,z_5,z_6},{z_4,z_7,z_8},{z_5,z_7,z_8}}

o5 = {{z , z , z }, {z , z , z , z }, {z , z , z }, {z , z , z }}
        1   2   3     2   4   5   6     4   7   8     5   7   8

o5 : List

i6 : E2 = {{z_2,z_3,z_4},{z_4,z_5}}

o6 = {{z , z , z }, {z , z }}
        2   3   4     4   5

o6 : List

i7 : h1 = hyperGraph E1

o7 = HyperGraph{edges => {{z , z , z }, {z , z , z , z }, {z , z , z }, {z , z , z }}}
                            1   2   3     2   4   5   6     4   7   8     5   7   8
                ring => S
                vertices => {z , z , z , z , z , z , z , z }
                              1   2   3   4   5   6   7   8

o7 : HyperGraph

i8 : h2 = hyperGraph E2

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

o8 : HyperGraph

i9 : T = QQ[w,x,y,z]

o9 = T

o9 : PolynomialRing

i10 : e = {w*x*y,w*x*z,w*y*z,x*y*z}

o10 = {w*x*y, w*x*z, w*y*z, x*y*z}

o10 : List

i11 : h = hyperGraph e

o11 = HyperGraph{edges => {{w, x, y}, {w, x, z}, {w, y, z}, {x, y, z}}}
                 ring => T
                 vertices => {w, x, y, z}

o11 : HyperGraph

i12 : C = QQ[p_1..p_6]

o12 = C

o12 : PolynomialRing

i13 : i = monomialIdeal (p_1*p_2*p_3,p_3*p_4*p_5,p_3*p_6)

o13 = monomialIdeal (p p p , p p p , p p )
                      1 2 3   3 4 5   3 6

o13 : MonomialIdeal of C

i14 : hyperGraph i

o14 = HyperGraph{edges => {{p , p , p }, {p , p , p }, {p , p }}}
                             1   2   3     3   4   5     3   6
                 ring => C
                 vertices => {p , p , p , p , p , p }
                               1   2   3   4   5   6

o14 : HyperGraph

i15 : j = ideal (p_1*p_2,p_3*p_4*p_5,p_6)

o15 = ideal (p p , p p p , p )
              1 2   3 4 5   6

o15 : Ideal of C

i16 : hyperGraph j

o16 = HyperGraph{edges => {{p , p }, {p , p , p }, {p }}}
                             1   2     3   4   5     6
                 ring => C
                 vertices => {p , p , p , p , p , p }
                               1   2   3   4   5   6

o16 : HyperGraph

i17 : D = QQ[r_1..r_5]

o17 = D

o17 : PolynomialRing

i18 : g = graph {r_1*r_2,r_2*r_4,r_3*r_5,r_5*r_4,r_1*r_5}

o18 = Graph{edges => {{r , r }, {r , r }, {r , r }, {r , r }, {r , r }}}
                        1   2     2   4     1   5     3   5     4   5
            ring => D
            vertices => {r , r , r , r , r }
                          1   2   3   4   5

o18 : Graph

i19 : h = hyperGraph g

o19 = HyperGraph{edges => {{r , r }, {r , r }, {r , r }, {r , r }, {r , r }}}
                             1   2     2   4     1   5     3   5     4   5
                 ring => D
                 vertices => {r , r , r , r , r }
                               1   2   3   4   5

o19 : HyperGraph

i20 : E = QQ[m,n,o,p]

o20 = E

o20 : PolynomialRing

i21 : hyperGraph(E, {})

o21 = HyperGraph{edges => {}             }
                 ring => E
                 vertices => {m, n, o, p}

o21 : HyperGraph

i22 : hyperGraph monomialIdeal(0_E)  -- the zero element of E (do not use 0)

o22 = HyperGraph{edges => {}             }
                 ring => E
                 vertices => {m, n, o, p}

o22 : HyperGraph

i23 : hyperGraph ideal (0_E)

o23 = HyperGraph{edges => {}             }
                 ring => E
                 vertices => {m, n, o, p}

o23 : HyperGraph

i24 :