Full paper in PDF:
$%A. Jacquemard and M. A. Teixeira, Effective algebraic geometry and normal forms of reversible mappings, Rev. Mat. Complut. 15 (2002), no. 1, 3155.%$

Effective Algebraic Geometry and Normal Forms of Reversible Mappings
Alain JACQUEMARD and Marco Antonio TEIXEIRA
Laboratoire de Topologie
Université de Bourgogne
BP 47870 21078 DIJON cedex — France
Departamento de Matemática
Universidade Estadual de Campinas
13081-970, Campinas, SP — Brazil

Received: November 2, 1999
Revised: May 3, 2001


We present a new method to compute normal forms, applied to the germs of reversible mappings. We translate the classification problem of these germs to the theory of ideals in the space of the coefficients of their jets. Integral factorization coupled with Gröbner basis construction is the key factor that makes the process efficient. We also show that a language with typed objects like AXIOM is very convenient to solve these kinds of problems.

2000 Mathematics Subject Classification: 14-04, 14B05, 58F36.