Timeline for Checking if a matroid is binary(Detecting $U^2_4$ minor in a matroid)
Current License: CC BY-SA 3.0
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| Feb 23, 2014 at 9:59 | comment | added | Rudi Pendavingh | Also, the single-element extension approach is generously supported in Sage right now. If M is a BinaryMatroid in sage, then M.linear_extensions(..) will generate the binary matroids extending M. The isomorphism test for binary matroids is fairly efficient as well. | |
| Feb 23, 2014 at 9:53 | comment | added | Rudi Pendavingh | I did implement a M.has_line_minor(k) routine in Sage, which essentially enumerates the flats F of rank r-2 to see if the simplification of M/F has k or more elements. So M.has_line_minor(4) will test if M is nonbinary. This comes quite close to approach b) suggested by Jayant Apte above. | |
| Nov 19, 2013 at 3:41 | history | edited | Tony Huynh | CC BY-SA 3.0 |
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| Nov 19, 2013 at 2:05 | comment | added | Gordon Royle | Ack, except that I was talking through my chapeau. After a long day of marking exam scripts, I confused "binary" and "graphic" so in fact, the "is_graphic" routine is the one that is implemented and not the "is_binary" (although of course it should be). Sorry for that, and reminder to self never to post in the evening. | |
| Nov 18, 2013 at 14:41 | comment | added | Tony Huynh | Thanks Gordon. Nice to hear this has been implemented. I guess this is probably the best routine available without having to reinvent the wheel. | |
| Nov 18, 2013 at 14:40 | history | edited | Tony Huynh | CC BY-SA 3.0 |
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| Nov 18, 2013 at 13:08 | comment | added | Gordon Royle | In Sage you should use is_binary() rather than the general purpose minor routine. It uses an effective, though not asymptotically the most efficient method due to Geelen and Gerards and implemented by Rudi Pendavingh. | |
| Nov 17, 2013 at 2:09 | history | edited | Tony Huynh | CC BY-SA 3.0 |
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| Nov 17, 2013 at 1:58 | history | answered | Tony Huynh | CC BY-SA 3.0 |