All Questions

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 ...

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. ...

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 ...

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 ...

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 ...