ASKSAGE: Sage Q&A Forum - Latest question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 27 Oct 2015 04:26:42 -0500Reformulation of a semialgebraic set, without quantifiershttps://ask.sagemath.org/question/30287/reformulation-of-a-semialgebraic-set-without-quantifiers/According to wikipedia:
> The [Tarskiâ€“Seidenberg](https://en.wikipedia.org/wiki/Tarski%E2%80%93Seidenberg_theorem) theorem states that a set in (n + 1)-dimensional space defined by polynomial equations and inequalities can be projected down onto n-dimensional space, and the resulting set is still definable in terms of polynomial identities and inequalities.
That's great, and my question is if it can be done in practice, in a particular case. I have read that the original Tarskiâ€“Seidenberg algorithm is of little practical use, but maybe my problem is tractable with another algorithm:
We have a finite set of points in C^2 (z_i,w_i), and I want to project onto the first C coordinate the intersection of the cones {(z,w): |z-z_i|>|w-w_i|}. It would be awesome, for example for plotting the set, if I could actually get the polynomial inequalities that define the projection. Getting only the higher dimensional strata is fine (an open set in C).
Any idea? Thanks in advance.pangTue, 27 Oct 2015 04:26:42 -0500https://ask.sagemath.org/question/30287/