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MatchingField == MatchingField -- equality of matching fields

Description

Two matching fields are said to be equal if their tuples are equal.

i1 : L1 = diagonalMatchingField(2, 4)

o1 = Grassmannian Matching Field for Gr(2, 4)

o1 : GrMatchingField
 
i2 : getWeightMatrix L1

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

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

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

o3 : List
 
i4 : L2 = grMatchingField matrix {{0,0,0,0}, {8,4,2,1}}

o4 = Grassmannian Matching Field for Gr(2, 4)

o4 : GrMatchingField
 
i5 : getWeightMatrix L2

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

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

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

o6 : List
 
i7 : L1 == L2

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

o8 = Grassmannian Matching Field for Gr(2, 4)

o8 : GrMatchingField
 
i9 : L3 == L1

o9 = true

In the case of flag matching fields, the $tupleSizeList$s must be equal.

i10 : L1 = diagonalMatchingField({1,2}, 4)

o10 = Flag Matching Field for Fl(1, 2; 4)

o10 : FlMatchingField
 
i11 : getWeightMatrix L1

o11 = | 0 0 0 0 |
      | 4 3 2 1 |

               2       4
o11 : Matrix ZZ  <-- ZZ
 
i12 : getTuples L1

o12 = {{1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {2, 3}, {1, 4}, {2, 4}, {3, 4}}

o12 : List
 
i13 : L2 = flMatchingField({1,2}, matrix {{0,0,0,0}, {8,4,2,1}})

o13 = Flag Matching Field for Fl(1, 2; 4)

o13 : FlMatchingField
 
i14 : getWeightMatrix L2

o14 = | 0 0 0 0 |
      | 8 4 2 1 |

               2       4
o14 : Matrix ZZ  <-- ZZ
 
i15 : getTuples L2

o15 = {{1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {2, 3}, {1, 4}, {2, 4}, {3, 4}}

o15 : List
 
i16 : L1 == L2

o16 = true
 
i17 : L3 = flMatchingField({1,2}, 4, {
              {1}, {4}, {3}, {2},
              {3,4}, {2,4}, {1,4}, {2,3}, {1,3}, {1,2}
              })

o17 = Flag Matching Field for Fl(1, 2; 4)

o17 : FlMatchingField
 
i18 : L3 == L1

o18 = true

See also

Menu

Ways to use this method:

The source of this document is in MatchingFields.m2:2921:0.