-- -*- M2-comint -*- {* hash: 477883254 *}

i1 : R = QQ[x,y,z];

i2 : der arrangement {x,y,z,x-y,x-z,y-z}

o2 = {1} | 1 -x+y+z -xz+z2      |
     {1} | 1 z      -yz+z2      |
     {1} | 1 y      0           |
     {1} | 1 0      0           |
     {1} | 1 -x+y   0           |
     {1} | 1 -x+z   xy-xz-yz+z2 |

             6       3
o2 : Matrix R  <--- R

i3 : prune image der typeA(3)

                         3
o3 = (QQ[x , x , x , x ])
          1   2   3   4

o3 : QQ[x , x , x , x ]-module, free, degrees {1, 2, 3}
         1   2   3   4

i4 : prune image der typeB(4) -- A is said to be free if der(A) is a free module

                         4
o4 = (QQ[x , x , x , x ])
          1   2   3   4

o4 : QQ[x , x , x , x ]-module, free, degrees {1, 3, 5, 7}
         1   2   3   4

i5 : R = QQ[x,y,z];

i6 : A = arrangement {x,y,z,x+y+z}

o6 = {x, y, z, x + y + z}

o6 : Hyperplane Arrangement 

i7 : betti res prune image der A

            0 1
o7 = total: 4 1
         1: 1 .
         2: 3 1

o7 : BettiTally

i8 : R = QQ[x,y]

o8 = R

o8 : PolynomialRing

i9 : prune image der arrangement {x,y,x-y,y-x,y,2*x}   -- rank 2 => free

      2
o9 = R

o9 : R-module, free, degrees {3, 3}

i10 : prune image der(arrangement {x,y,x-y}, {2,2,2})  -- same thing

       2
o10 = R

o10 : R-module, free, degrees {3, 3}

i11 :