-- -*- M2-comint -*- hash: 4054958036312350465

i1 : M = matroid({a,b,c,d}, {{a,b},{a,c}})

o1 = a "matroid" of rank 2 on 4 elements

o1 : Matroid

i2 : peek M

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

i3 : M = matroid({a,b,c,d},{}, EntryMode => "nonbases") -- defaults to uniform matroid of full rank

o3 = a "matroid" of rank 4 on 4 elements

o3 : Matroid

i4 : peek M

o4 = Matroid{bases => {set {0, 1, 2, 3}}  }
             cache => CacheTable{...2...}
             groundSet => set {0, 1, 2, 3}
             rank => 4

i5 : N = matroid({a,b,c,d}, {{b,c}}, EntryMode => "circuits")

o5 = a "matroid" of rank 3 on 4 elements

o5 : Matroid

i6 : peek N

o6 = Matroid{bases => {set {0, 2, 3}, set {0, 1, 3}}}
             cache => CacheTable{...3...}
             groundSet => set {0, 1, 2, 3}
             rank => 3

i7 : M = matroid {{a,b},{a,c}}

o7 = a "matroid" of rank 2 on 3 elements

o7 : Matroid

i8 : peek M

o8 = Matroid{bases => {set {0, 1}, set {0, 2}}}
             cache => CacheTable{...1...}
             groundSet => set {0, 1, 2}
             rank => 2

i9 : matroid(toList(0..<8), {{0,1,2,3},{2,3,4,5},{0,1,6,7},{4,5,6,7}}, 4) == swirl 4

o9 = true

i10 : M = matroid random(ZZ^3, ZZ^5)

o10 = a "matroid" of rank 3 on 5 elements

o10 : Matroid

i11 : peek M

o11 = Matroid{bases => {set {0, 1, 2}, set {0, 1, 3}, set {0, 2, 3}, set {1, 2, 3}, set {4, 0, 1}, set {4, 0, 2}, set {4, 1, 2}, set {4, 0, 3}, set {4, 1, 3}, set {4, 2, 3}}}
              cache => CacheTable{...3...}
              groundSet => set {0, 1, 2, 3, 4}
              rank => 3

i12 : M = matroid completeGraph 3

o12 = a "matroid" of rank 2 on 3 elements

o12 : Matroid

i13 : peek M

o13 = Matroid{bases => {set {1, 2}, set {0, 2}, set {0, 1}}}
              cache => CacheTable{...6...}
              groundSet => set {0, 1, 2}
              rank => 2

i14 : M = matroid(completeGraph 3, ParallelEdges => {set{0,1},set{0,1},set{1,2}}, Loops => {0,2})

o14 = a "matroid" of rank 2 on 8 elements

o14 : Matroid

i15 : peek M

o15 = Matroid{bases => {set {4, 5}, set {5, 3}, set {5, 1}, set {0, 5}, set {4, 2}, set {4, 1}, set {2, 3}, set {1, 3}, set {1, 2}, set {0, 2}, set {0, 1}}}
              cache => CacheTable{...5...}
              groundSet => set {0, 1, 2, 3, 4, 5, 6, 7}
              rank => 2

i16 : circuits M

o16 = {set {0, 1, 2}, set {1, 2, 3}, set {0, 3}, set {4, 1, 2}, set {4, 3},
      -----------------------------------------------------------------------
      set {4, 0}, set {0, 5, 1}, set {5, 1, 3}, set {4, 5, 1}, set {5, 2},
      -----------------------------------------------------------------------
      set {6}, set {7}}

o16 : List

i17 : R = QQ[x_0..x_4]

o17 = R

o17 : PolynomialRing

i18 : I = monomialIdeal (x_0*x_1*x_3,x_1*x_2*x_4,x_0*x_2*x_3*x_4)

o18 = monomialIdeal (x x x , x x x , x x x x )
                      0 1 3   1 2 4   0 2 3 4

o18 : MonomialIdeal of R

i19 : M = matroid I

o19 = a "matroid" of rank 3 on 5 elements

o19 : Matroid

i20 : peek M

o20 = Matroid{bases => {set {4, 2, 3}, set {4, 1, 3}, set {4, 0, 3}, set {4, 0, 2}, set {4, 0, 1}, set {1, 2, 3}, set {0, 2, 3}, set {0, 1, 2}}}
              cache => CacheTable{...2...}
              groundSet => set {0, 1, 2, 3, 4}
              rank => 3

i21 : 
