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 ...

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 ...

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 ...

Suppose I have a polynomial Morse function $f: \mathbb{R}^n \to \mathbb{R}$. Consider the ideal $I(\nabla f)$ generated by the partial derivatives $\partial_i f$, and assume that the real zero-set of ...

Suppose an irreducible smooth $p \in \mathbb{R}[x_1,x_2]$ is given, and we would like to find finite sets $S_1 , S_2 \subset \mathbb{R}$ such that $p(S_1 \times S_2)=0$ and $|S_1 \times S_2|$ is as ...