Full paper in PDF:
$%A. Jacquemard and M. A. Teixeira, Effective algebraic geometry and normal forms of reversible
mappings, Rev. Mat. Complut. 15 (2002), no. 1, 31–55.%$
UMR 5584 CNRS Laboratoire de Topologie Université de Bourgogne BP 47870 21078 DIJON cedex — France | Departamento de Matemática IMECC Universidade Estadual de Campinas 13081-970, Campinas, SP — Brazil |
ABSTRACT
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.