Let $\mathcal{C}_d\subset \mathbb{C}^{d+1}$ be the space of non-singular, univariate polynomials degree $d$. The Vi\`{e}te map $\mathscr{V} : \mathcal{C}_d \rightarrow Sym_d(\mathbb{C})$ sends a polynomial to its unordered set roots. It is classical fact that induced $\mathscr{V}_*$ at level fundamental groups realises an isomorphism between $\pi_1(\mathcal{C}_d)$ and Artin braid group $B_d$. F...

In this paper we approximate large sets of univariate data by piecewise linear functions which interpolate subsets of the data using adaptive thinning strategies Rather than minimize the global error at each removal AT we propose a much cheaper thinning strategy AT which only minimizes errors locally Interestingly the two strategies are equivalent in all our numerical tests and we prove this to...

Among several implicitization methods, the method based on resultant computation is a simple and direct one, but it often brings extraneous factors which are difficult to remove. This paper studies a class of rational space curves and rational surfaces by implicitization with univariate resultant computations. This method is more efficient than the other algorithms in finding implicit equations...

We present explicit worst case degree and height bounds for the rational univariate representation of the isolated roots of polynomial systems based on mixed volume. We base our estimations on height bounds of resultants and we consider the case of 0-dimensional, positive dimensional, and parametric polynomial systems. CCS Concepts •Computing methodologies→ Symbolic calculus algorithms;