Computation of canonical forms for ternary cubics

Authors:
Irina A. Kogan;Marc Moreno Maza
Affiliations:
Yale University, New Haven, CT;Université Lille I, LIFL, 59655 Villeneuve d'Ascq, France
Venue:
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Year:
2002

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Abstract

In this paper we conduct a careful study of the equivalence classes of ternary cubics under general complex linear changes of variables. Our new results are based on the method of moving frames and involve triangular decompositions of algebraic varieties. We provide a computationally efficient algorithm that matches an arbitrary ternary cubic with its canonical form and explicitly computes a corresponding linear change of coordinates. We also describe a classification of the symmetry groups of ternary cubics.