Symmetry Detection of Rational Space Curves from their Curvature and   Torsion
  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. To support this claim, we present an analysis of the arithmetic complexity of the algorithm and timings from an implementation in Sage. 
Juan Gerardo Alc\'azar, Carlos Hermoso, Georg Muntingh
math.AG