Procedure `ToCanonical`, by I. Kogan and M. Moreno Maza.

This code classifies ternary cubics (homogeneous polynomial in three variables) with respect to general complex linear changes of variables.

INPUT: inhomogeneous version (z=1) of a ternary cubic: e.g f:=(p,q)->p*q for x*y*z or f:=(p,q)-> p^3+q+1 for x^3+y*z^2+z^3.

OUTPUT: the corresponding  canonical form as listed in Theorem 5  of Computation of Canonical Forms for Ternary Cubics,  I. Kogan and  M.Moreno Maza. Proceedings of the International Symposium on Symbolic and Algebraic Computations, Lille, 2002, 151--160   

Click here to download Maple worksheet (http://www.math.ncsu.edu/~iakogan/mapleHTML/ToCanonical01.mw)

Code

Examples

Irreducible

Reducible