GrMatchingField == GrMatchingField -- equality of Grassmannian matching fields

Operator: ==
Usage:

result = L1 == L2
Inputs:
- L1, an instance of the type GrMatchingField,
- L2, an instance of the type GrMatchingField,
Outputs:
- result, a Boolean value, are the matching fields equal

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

The source of this document is in MatchingFields.m2:3027:0.