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algebraicMatroidCircuits -- The bases of the algebraic matroid

Synopsis

Description

Displays the circuits of the algebraic matroid associated to the Grassmannian Gr$(k,n)$ matching field in terms of the $k$-subsets of $[n]$. For more details about the matroid, see the function algebraicMatroid.

i1 : L = diagonalMatchingField(2, 5)

o1 = Grassmannian Matching Field for Gr(2, 5)

o1 : GrMatchingField
 
i2 : netList algebraicMatroidCircuits L

     +----------------------------------------------------+
o2 = |set {{1, 3}, {2, 3}, {1, 4}, {2, 4}}                |
     +----------------------------------------------------+
     |set {{1, 3}, {2, 3}, {1, 5}, {2, 5}}                |
     +----------------------------------------------------+
     |set {{1, 4}, {2, 4}, {1, 5}, {2, 5}}                |
     +----------------------------------------------------+
     |set {{3, 5}, {1, 4}, {1, 5}, {3, 4}}                |
     +----------------------------------------------------+
     |set {{3, 5}, {1, 3}, {2, 3}, {1, 5}, {2, 4}, {3, 4}}|
     +----------------------------------------------------+
     |set {{3, 5}, {1, 3}, {1, 4}, {2, 3}, {2, 5}, {3, 4}}|
     +----------------------------------------------------+
     |set {{3, 5}, {2, 4}, {2, 5}, {3, 4}}                |
     +----------------------------------------------------+

See also

Ways to use algebraicMatroidCircuits :

For the programmer

The object algebraicMatroidCircuits is a method function.

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