Symmetry detection of rational space curves from their curvature and torsion

•The paper presents a novel, deterministic, and efficient method to detect whether a given rational space curve is symmetric.•The method is significantly faster, simpler, and more general than earlier methods addressing similar problems.•An analysis of the arithmetic complexity of the algorithm and timings from an implementation in Sage are included.

We present a novel, deterministic, and efficient method to detect whether a given rational space curve is symmetric. By using well-known differential invariants of space curves, namely the curvature and torsion, the method is significantly faster, simpler, and more general than an earlier method addressing a similar problem (Alcázar et al., 2014b). To support this claim, we present an analysis of the arithmetic complexity of the algorithm and timings from an implementation in Sage.