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searchRepresentation -- search for a representation of a matroid over a finite field

Synopsis

Description

This function performs a brute-force search for a representation of a matroid, over a given finite field (essentially repeatedly testing random candidates until one is found).

The maximum number of attempts is specified by the optional argument Attempts (default 1000).

Over GF(2), this function is guaranteed to (quickly) find a representation, if one exists. (Over larger finite fields, there is no such guarantee.)

i1 : searchRepresentation(uniformMatroid(2, 4), GF 2)
 
i2 : searchRepresentation(matroid completeGraph 5, GF 3, Attempts => 2000)

o2 = | 1 1 1 1 0  0  0 0  0 0 |
     | 1 0 0 0 1  1  1 0  0 0 |
     | 0 1 0 0 -1 0  0 1  1 0 |
     | 0 0 1 0 0  -1 0 -1 0 1 |

                  4           10
o2 : Matrix (GF 3)  <-- (GF 3)

See also

Ways to use searchRepresentation:

For the programmer

The object searchRepresentation is a method function with options.