All Questions

For each integer $n$ I am looking for a real-valued polynomial in two variables, $A_n(x,y)$, such that $A_n(x,y) = 0$ defines a curve with precisely $n$ closed components in the plane $\mathbb{R}^2$. ...

Let $R$ be an (irreducible) plane real algebraic curve (without isolated points). Consider Zarissky closure of $R$ in ${\mathbb C}P^1$ (as real variety). Suppose that $\lambda\in R \Rightarrow\...

Assume we are given the set $S$ of $n$ points on the real plane and want to draw a parametrized cubic curve (actually a segment of Bézier spline) with fixed startpoint in such a way, that the ...