elementary_vectors.supports¶

Supports of circuits and cocircuits¶

For some applications, it is sufficient to compute only the supports of the circuits. Compare also with the circuits of linear matroids.

Functions

`circuit_supports`(matrix)	Compute the supports of the circuits of a matrix.
`cocircuit_supports`(matrix)	Compute the supports of the cocircuits of a matrix.

Classes

CircuitSupportEnumerator(matrix)

Circuit support enumerator.

class elementary_vectors.supports.CircuitSupportEnumerator(matrix: matrix)¶: Circuit support enumerator.

elementary_vectors.supports.circuit_supports(matrix: matrix) → List[List[int]]¶

Compute the supports of the circuits of a matrix.

See also

cocircuit_supports()

EXAMPLES:

sage: from elementary_vectors import *
sage: M = matrix([[1, 2, 0, 0], [0, 1, 2, 3]])
sage: M
[1 2 0 0]
[0 1 2 3]
sage: circuit_supports(M)
[[0, 1, 2], [0, 1, 3], [2, 3]]

TESTS:

This generates the empty list:

sage: M = matrix([[1, 0, 0, 0], [0, 1, 0, 0]])
sage: M
[1 0 0 0]
[0 1 0 0]
sage: circuit_supports(M)
[[2], [3]]

elementary_vectors.supports.cocircuit_supports(matrix: matrix) → List[List[int]]¶

Compute the supports of the cocircuits of a matrix.