-- -*- M2-comint -*- hash: 7019241680152760062

i1 : M = uniformMatroid(2,4) + uniformMatroid(1,4)

o1 = a "matroid" of rank 3 on 4 elements

o1 : Matroid

i2 : peek M

o2 = Matroid{bases => {set {0, 1, 2}, set {0, 1, 3}, set {0, 2, 3}, set {1, 2, 3}}}
             cache => CacheTable{...1...}
             groundSet => set {0, 1, 2, 3}
             rank => 3

i3 : M == uniformMatroid(3, 4)

o3 = true

i4 : M0 = uniformMatroid(2, 4) + matroid completeGraph 4

o4 = a "matroid" of rank 5 on 10 elements

o4 : Matroid

i5 : M0 == uniformMatroid(2, 4) ++ matroid completeGraph 4

o5 = true

i6 : M1 = matroid completeGraph 4 ++ uniformMatroid(2, 4)

o6 = a "matroid" of rank 5 on 10 elements

o6 : Matroid

i7 : M0 == M1

o7 = false

i8 : areIsomorphic(M0, M1)

o8 = true

i9 : M0 = matroid({a,b,c,d}, {{a},{b},{c}})

o9 = a "matroid" of rank 1 on 4 elements

o9 : Matroid

i10 : M1 = matroid({a,b,c,d}, {{b},{c},{d}})

o10 = a "matroid" of rank 1 on 4 elements

o10 : Matroid

i11 : M0 + M1 == uniformMatroid(2,4)

o11 = true

i12 : F7 = specificMatroid "fano"

o12 = a "matroid" of rank 3 on 7 elements

o12 : Matroid

i13 : NF = specificMatroid "nonfano"

o13 = a "matroid" of rank 3 on 7 elements

o13 : Matroid

i14 : all({F7 + NF, F7 + F7, NF + NF}, M -> M == uniformMatroid(6, 7))

o14 = true

i15 : A = matrix{{0,1,1,1},{0,0,1,1}}

o15 = | 0 1 1 1 |
      | 0 0 1 1 |

               2       4
o15 : Matrix ZZ  <-- ZZ

i16 : M = matroid A

o16 = a "matroid" of rank 2 on 4 elements

o16 : Matroid

i17 : M_*

o17 = {0, | 1 |, | 1 |, | 1 |}
          | 0 |  | 1 |  | 1 |

o17 : List

i18 : unique M_*

o18 = {0, | 1 |, | 1 |}
          | 0 |  | 1 |

o18 : List

i19 : M0 = matroid(M_{0,1,2} | {d}, bases M)

o19 = a "matroid" of rank 2 on 4 elements

o19 : Matroid

i20 : M == M0

o20 = true

i21 : B = matrix{{0,1,2},{0,1,2}}

o21 = | 0 1 2 |
      | 0 1 2 |

               2       3
o21 : Matrix ZZ  <-- ZZ

i22 : N = matroid B

o22 = a "matroid" of rank 1 on 3 elements

o22 : Matroid

i23 : U = M0 + N

o23 = a "matroid" of rank 3 on 5 elements

o23 : Matroid

i24 : peek U

o24 = Matroid{bases => {set {4, 1, 2}, set {1, 2, 3}, set {4, 1, 3}}}
              cache => CacheTable{...1...}
              groundSet => set {0, 1, 2, 3, 4}
              rank => 3

i25 : U_*

o25 = {0, | 1 |, | 1 |, d, | 2 |}
          | 0 |  | 1 |     | 2 |

o25 : List

i26 : 
