-- -*- M2-comint -*- hash: 225959624181674163

i1 : PG22 = projectiveGeometry(2, 2)

o1 = a "matroid" of rank 3 on 7 elements

o1 : Matroid

i2 : PG22 == specificMatroid "fano"

o2 = true

i3 : A = transpose sub(matrix toList(((3:0)..(3:2-1))/toList), ZZ/2) -- all vectors in (ZZ/2)^3

o3 = | 0 0 0 0 1 1 1 1 |
     | 0 0 1 1 0 0 1 1 |
     | 0 1 0 1 0 1 0 1 |

             ZZ 3      ZZ 8
o3 : Matrix (--)  <-- (--)
              2         2

i4 : areIsomorphic(PG22, simpleMatroid matroid A)

o4 = true

i5 : PG32 = projectiveGeometry(3, 2)

o5 = a "matroid" of rank 4 on 15 elements

o5 : Matroid

i6 : getRepresentation PG32

o6 = | 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 |
     | 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 |
     | 0 0 1 1 0 0 1 1 0 0 1 1 1 1 0 |
     | 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 |

             ZZ 4      ZZ 15
o6 : Matrix (--)  <-- (--)
              2         2

i7 : H = first hyperplanes PG32

o7 = set {8, 9, 10, 11, 12, 13, 14}

o7 : Set

i8 : areIsomorphic(affineGeometry(3, 2), PG32 \ H)

o8 = true

i9 : 
