Timeline for Real solutions to underdetermined system of polynomial equations
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| Jun 22, 2022 at 8:14 | history | edited | CommunityBot |
replaced http://www.math.uga.edu/~pete with http://alpha.math.uga.edu/~pete
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| Aug 4, 2010 at 23:09 | comment | added | Pete L. Clark | @Raisa: you're welcome. Your followup is very interesting (and I can't answer it!). From the description of the Real Nullstellensatz I gave in my notes, it is not even clear that it is algorithmic, but it is: for instance, this follows from the decidability of real-closed fields. The algorithm that you would get by looking at it that way (e.g. via explicit quantifier elimination) is probably painfully slow. I am pretty sure that finding better algorithms for solving real polynomial systems is an active research field. I encourage you to ask another question about this. | |
| Aug 4, 2010 at 22:37 | comment | added | Raisa | Thank you. This was a very helpful answer. But now I have a related question. How practical is Real Nullstellensatz for analyzing large systems with e.g. 12 equations and 12-15 unknowns, 16 equations and 16-24 unknowns, etc. Or is using this theorem similar to computing Groebner Basis and quickly becomes infeasible? | |
| Aug 4, 2010 at 22:19 | vote | accept | Raisa | ||
| Aug 3, 2010 at 6:06 | history | edited | Pete L. Clark | CC BY-SA 2.5 |
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| Aug 3, 2010 at 6:00 | history | answered | Pete L. Clark | CC BY-SA 2.5 |