-- -*- M2-comint -*- {* hash: -693359219 *}

i1 : S = ZZ[w,x,y,z];

i2 : A3 = arrangement {w-x,w-y,w-z,x-y,x-z,y-z}

o2 = {w - x, w - y, w - z, x - y, x - z, y - z}

o2 : Hyperplane Arrangement 

i3 : describe A3

o3 = {w - x, w - y, w - z, x - y, x - z, y - z}

i4 : R = S/ideal(w+x+y+z)

o4 = R

o4 : QuotientRing

i5 : A3' = arrangement({w-x,w-y,w-z,x-y,x-z,y-z},R)

o5 = {- 2x - y - z, - x - 2y - z, - x - y - 2z, x - y, x - z, y - z}

o5 : Hyperplane Arrangement 

i6 : describe A3'

o6 = {- 2x - y - z, - x - 2y - z, - x - y - 2z, x - y, x - z, y - z}

i7 : trivial = arrangement({},S)

o7 = {}

o7 : Hyperplane Arrangement 

i8 : describe trivial

o8 = {}

i9 : ring trivial

o9 = S

o9 : PolynomialRing

i10 :