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FlMatchingField == FlMatchingField -- equality of flag matching fields

Description

Two matching fields are said to be equal if their tuples are equal. In the case of flag matching fields, the $kList$s must be equal.

i1 : L1 = diagonalMatchingField({1,2}, 4)

o1 = Flag Matching Field for Fl(1, 2; 4)

o1 : FlMatchingField
 
i2 : getWeightMatrix L1

o2 = | 0 0 0 0 |
     | 4 3 2 1 |

              2       4
o2 : Matrix ZZ  <-- ZZ
 
i3 : getTuples L1

o3 = {{{1}, {2}, {3}, {4}}, {{1, 2}, {1, 3}, {2, 3}, {1, 4}, {2, 4}, {3, 4}}}

o3 : List
 
i4 : L2 = flMatchingField({1,2}, matrix {{0,0,0,0}, {8,4,2,1}})

o4 = Flag Matching Field for Fl(1, 2; 4)

o4 : FlMatchingField
 
i5 : getWeightMatrix L2

o5 = | 0 0 0 0 |
     | 8 4 2 1 |

              2       4
o5 : Matrix ZZ  <-- ZZ
 
i6 : getTuples L2

o6 = {{{1}, {2}, {3}, {4}}, {{1, 2}, {1, 3}, {2, 3}, {1, 4}, {2, 4}, {3, 4}}}

o6 : List
 
i7 : L1 == L2

o7 = true
 
i8 : L3 = flMatchingField({1,2}, 4, {{{1}, {4}, {3}, {2}}, {{3,4},{2,4},{1,4},{2,3},{1,3},{1,2}}})

o8 = Flag Matching Field for Fl(1, 2; 4)

o8 : FlMatchingField
 
i9 : L3 == L1

o9 = true

See also

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Ways to use this method:

The source of this document is in MatchingFields.m2:2993:0.