On the one dimensional polynomial and regular images of $\R^n$

TL;DR

This paper provides a complete geometric characterization of 1-dimensional polynomial and regular images of ^n, including the computation of key invariants, advancing the understanding of their structure and properties.

Contribution

It offers a full geometric description of 1D polynomial and regular images of ^n and calculates their invariants, extending previous theoretical frameworks.

Findings

Complete geometric characterization of 1D polynomial and regular images

Explicit computation of invariants p(S) and r(S) for these images

Enhanced understanding of the structure of polynomial and regular images

Abstract

In this work we present a full geometric characterization of the 1-dimensional polynomial and regular images $S$ of $\R^n$ and we compute for all of them the invariants ${\rm p(S)}$ and ${\rm r}(S)$, already introduced in \cite{fg2}.