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

## Synopsis

• Usage:
isQuotient(M, N)
• Inputs:
• M,
• N,
• Outputs:
• , whether the first matroid is a quotient of the second

## Description

This function is provided by the package Matroids.

A matroid M is a quotient of a matroid N if the matroids have the same ground set and every flat of M is a flat of N.

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