On Friday, February 17, 2017 at 4:51:49 AM UTC, john_perry_usm wrote: > > On Thursday, February 16, 2017 at 1:46:18 AM UTC-6, Dima Pasechnik wrote: >> >> >> >> On Thursday, February 16, 2017 at 6:59:04 AM UTC, William wrote: >>> >>> **Disclaimer: I consider myself very naive about computational >>> commutative algebra, especially with floating point numbers. Dima, >>> thanks for answering the question, but I think you are maybe jumping >>> to wronc conclusions. See below. ** >>> ... >> >> >>> Just because you think it's nuts to use floating point numbers in the >>> context of commutative algebra doesn't mean it is... It's a whole >>> research area, e.g., >>> >>> http://link.springer.com/chapter/10.1007/978-3-540-87827-8_23 >>> >> >> a paper from 2008 with one citation and one self-citation is not a "whole >> research area", come on... >> > > Okay, how about this: > > http://www.springer.com/us/book/9783211993132 > > http://www.sciencedirect.com/science/article/pii/S0378475496000274 > > http://link.springer.com/chapter/10.1007/978-3-662-43799-5_10 > > > http://library.wolfram.com/infocenter/Conferences/7536/ApproximateGroebnerBases.pdf > > http://hal.upmc.fr/hal-01336590v1 > > > http://www.risc.jku.at/publications/download/risc_273/Nr.7_paper-revised.pdf > > http://dl.acm.org/citation.cfm?doid=258726.258763 > > DOI 10.1145/780506.780540 <https://doi.org/10.1145/780506.780540> > > I don't mean to quibble with the underlying premise that Gröbner bases may > not be the best tool with approximate coefficients, and yes, maybe William > should have given a better reference, but come on, when you see names like > Faugère, Kreuzer, Lichtblau, Robbiano, and Traverso publishing on the > topic, it's kind of hard to deny it's a whole research area. (I leave > Sasaki out of that list only because he doesn't seem to impress Dima, but > my understanding is that Sasaki is an expert on the topic -- he certainly > gave a great talk on it at ISSAC'11.) >
I agree that I have missed a large part of this floating point Groebner bases activity, sorry. However, note that most of these references are 5+-10+ years old, or not really Groebner basis-only things. Approximate commutative algebra/polynomial system solving has largely moved onto greener pastures (numerical homotopy methods and sums of squares based methods), leaving behind systems that cannot correctly compute Groebner basis even in semi-trivial cases: https://trac.sagemath.org/ticket/22387#comment:2 Dima > > john perry > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
