Wang, HaohaoGoldman, Ron2018-10-312018-10-312018Wang, Haohao and Goldman, Ron. "Syzygies for translational surfaces." <i>Journal of Symbolic Computation,</i> 89, (2018) Elsevier: 73-93. https://doi.org/10.1016/j.jsc.2017.11.004.https://hdl.handle.net/1911/103240A translational surface is a rational tensor product surface generated from two rational space curves by translating one curve along the other curve. Translational surfaces are invariant under rigid motions: translating and rotating the two generating curves translates and rotates the translational surface by the same amount. We construct three special syzygies for a translational surface from a μ-basis of one of the generating space curves, and we show how to compute the implicit equation of a translational surface from these three special syzygies. Examples are provided to illustrate our theorems and flesh out our algorithms.engThis is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Elsevier.Journal articleTranslational surfaceSyzygyμ-basisImplicit equationhttps://doi.org/10.1016/j.jsc.2017.11.004