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.) 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.
