isQuotient -- whether a matroid is a quotient of another matroid

i1 : N = matroid completeGraph 6;

i2 : T2N = truncate(2, N)

o2 = a "matroid" of rank 3 on 15 elements

o2 : Matroid

i3 : partition(F -> rank(T2N, F), flats T2N)

o3 = HashTable{0 => {set {}}                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  }
               1 => {set {14}, set {13}, set {12}, set {11}, set {10}, set {9}, set {8}, set {7}, set {6}, set {5}, set {4}, set {3}, set {2}, set {1}, set {0}}
               2 => {set {12, 13, 14}, set {10, 11, 14}, set {9, 14}, set {7, 8, 14}, set {6, 14}, set {5, 14}, set {3, 4, 14}, set {2, 14}, set {1, 14}, set {0, 14}, set {9, 11, 13}, set {10, 13}, set {6, 8, 13}, set {7, 13}, set {5, 13}, set {2, 4, 13}, set {3, 13}, set {1, 13}, set {0, 13}, set {11, 12}, set {9, 10, 12}, set {8, 12}, set {6, 7, 12}, set {5, 12}, set {4, 12}, set {2, 3, 12}, set {1, 12}, set {0, 12}, set {5, 8, 11}, set {7, 11}, set {6, 11}, set {1, 4, 11}, set {3, 11}, set {2, 11}, set {0, 11}, set {8, 10}, set {5, 7, 10}, set {6, 10}, set {4, 10}, set {1, 3, 10}, set {2, 10}, set {0, 10}, set {8, 9}, set {7, 9}, set {5, 6, 9}, set {4, 9}, set {3, 9}, set {1, 2, 9}, set {0, 9}, set {0, 4, 8}, set {3, 8}, set {2, 8}, set {1, 8}, set {4, 7}, set {0, 3, 7}, set {2, 7}, set {1, 7}, set {4, 6}, set {3, 6}, set {0, 2, 6}, set {1, 6}, set {4, 5}, set {3, 5}, set {2, 5}, set {0, 1, 5}}
               3 => {set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}}

o3 : HashTable

i4 : isQuotient(T2N, N)

o4 = true