Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Ah, so the failure is about path-connectedness and not about the number of connected components of the complement, which is (I think) what Geoffrey Irving had in mind.
Hi, I'm no algebraist and I look for a reference that I can cite in a paper about what you prove above. Or is it so trivial that I can simply assert it?
Hi. This question looks a great deal like this one: mathoverflow.net/questions/443310/…. If you're the same author, you may wish to request a merging of your accounts. Observe though that it'd be preferable to have a little bit more context in order to motivate people to try to answer it.
@ZoltánCsáti is right. IPE is super easy to learn and you put in LaTeX. Inkscape seems to me much less valuable regarding doing maths figures. With a little work, you may even directly export IPE xml files from any code you'd like to write yourself to generate data for your graphics.
Hi, you should look at what is called "differential algebra" and also "computer algebra" for actual implementations. Yet beware that, with more than 2 variables, these questions are highly non-trivial (e.g. Poinacré question about existence of rational first-integrals in planar polynomial vector fields).
@AndrejBauer: can't one define the reals as right-unlimited string of digits, in a stable form with unique writing (inspired from the non-adjacent form, say), so that Cauchy sequences correspond to convergence of strings for the lexicographic order? I agree, though, that this differs from the definition of constructive reals, and I haven't put enough thought in this, but I thought it could be relevant.
