All Questions
5 questions
9
votes
0
answers
290
views
Computer algebra tools for finding real dimension of an algebraic variety
I have a system of polynomial equations with the unknowns being real numbers. The set of solutions is infinite. What software can I use to compute the real dimension of the solution set?
The CAD-based ...
8
votes
0
answers
229
views
Nearest point to a real algebraic set
Suppose I have a compact bounded real algebraic (eventually: or analytic or semialgebraic or semianalytic set) $V \subset \mathbb R^3$ and a point $x\in\mathbb R^3 \setminus V$. How much do we know ...
7
votes
1
answer
362
views
Does generic projection into $\mathbb{R}^3$ preserve real-algebraic-curve-ness?
I'm interested in the topological properties of certain real algebraic curves in high-dimensional spaces. I want to visualize these curves (say, like this), and so I'm pursuing dimensionality ...
5
votes
1
answer
169
views
Connectedness of semialgebraic sets via CAD
I do not know whether there is a standard or some traditional ways to decide whether a semialgebraic set is connected or not.
One way I know is the cylindrical algebraic decomposition (CAD) algorithm. ...
5
votes
0
answers
350
views
Are nearby points in an algebraic curve necessarily connected?
I would like a result of the following form:
For every algebraic curve $C$ in $\mathbb{R}\mathbf{P}^{n-1}$, there exists an
explicit and easy-to-compute $\epsilon=\epsilon(C)>0$ such that ...