Timeline for Reference Request: Smith Normal Form for maps between free _graded_ modules
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 11, 2012 at 18:01 | comment | added | Martin Brandenburg | @Thomas: -1 since you don't address the question. When you don't understand it (whatever is the reason), leave a comment first. | |
| Apr 11, 2012 at 13:50 | comment | added | Mikael Vejdemo-Johansson | The presence of a grading means, for instance, that you cannot use all the tricks available for doing Gaussian reduction on the kinds of matrices I'm interested in — you could not reduce rows in lower degrees using rows in higher degrees. I suspect that similar restrictions are in place for computing Smith normal forms, but also that the restrictions do not actually limit things very much. | |
| Apr 11, 2012 at 13:20 | comment | added | Thomas Kahle | I guess I don't see what you question is. The smith normal form of a given matrix exists and can be computed using elimination. If you are asking for the complexity, then that is measured usually in ring operations, so it depends on how fast you can do ring operations. I don't understand the meaning of the sentence "The presence of a grading seems to imply one should take some minute care". | |
| Apr 11, 2012 at 12:15 | comment | added | Mikael Vejdemo-Johansson | I know this, and as I mentioned, I expect this to actually be rather easy — which is why it's a reference request, not a question; but in my setting, the rows of the matrix have inherent degrees, and I worry somewhat about keeping everything compatible with the grading. | |
| Apr 11, 2012 at 11:59 | history | answered | Thomas Kahle | CC BY-SA 3.0 |