Algorithmic detection of hypercircles (Q417959)

The authors consider a characteristic zero base field \(\mathbb{K}\) and an algebraic extension of degree \(d\), \(\mathbb{K}(\alpha)\), and introduce algorithms to detect whether a curve parametrized by an element of \(\mathbb{K}(\alpha)(t)^d\) is a hypercircle (i.e., a generalization of the concept of circle in \(\mathbb{K}(\alpha)\)), and, if so, to identify the transformation yielding that hypercircle (provided that they are able to find a \(\mathbb{K}\)-point on the given curve).