-- -*- M2-comint -*- {* hash: -314497192 *}

i1 : G = {{1,2},{2,3},{3,4},{4,1}}; -- a four-cycle

i2 : AG = graphic G

o2 = {- x  + x , - x  + x , - x  + x , x  - x }
         1    2     2    3     3    4   1    4

o2 : Hyperplane Arrangement 

i3 : describe AG

o3 = {- x  + x , - x  + x , - x  + x , x  - x }
         1    2     2    3     3    4   1    4

i4 : rank AG -- the number of vertices minus number of components

o4 = 3

i5 : ring AG

o5 = QQ[x , x , x , x ]
         1   2   3   4

o5 : PolynomialRing

i6 : ring graphic(G,ZZ[x,y,z,w])

o6 = ZZ[x, y, z, w]

o6 : PolynomialRing

i7 :