On reconstruction of polynomial automorphisms

Paweł Gniadek

Annales Polonici Mathematici (1996)

  • Volume: 64, Issue: 1, page 61-69
  • ISSN: 0066-2216

Abstract

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We extend results on reconstructing a polynomial automorphism from its restriction to the coordinate hyperplanes to some wider class of algebraic surfaces. We show that the algorithm proposed by M. Kwieciński in [K2] and based on Gröbner bases works also for this class of surfaces.

How to cite

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Paweł Gniadek. "On reconstruction of polynomial automorphisms." Annales Polonici Mathematici 64.1 (1996): 61-69. <http://eudml.org/doc/269984>.

@article{PawełGniadek1996,
abstract = {We extend results on reconstructing a polynomial automorphism from its restriction to the coordinate hyperplanes to some wider class of algebraic surfaces. We show that the algorithm proposed by M. Kwieciński in [K2] and based on Gröbner bases works also for this class of surfaces.},
author = {Paweł Gniadek},
journal = {Annales Polonici Mathematici},
keywords = {polynomial automorphisms; reconstruction of polynomial automorphisms; Gröbner bases; identity set of two polynomial automorphisms},
language = {eng},
number = {1},
pages = {61-69},
title = {On reconstruction of polynomial automorphisms},
url = {http://eudml.org/doc/269984},
volume = {64},
year = {1996},
}

TY - JOUR
AU - Paweł Gniadek
TI - On reconstruction of polynomial automorphisms
JO - Annales Polonici Mathematici
PY - 1996
VL - 64
IS - 1
SP - 61
EP - 69
AB - We extend results on reconstructing a polynomial automorphism from its restriction to the coordinate hyperplanes to some wider class of algebraic surfaces. We show that the algorithm proposed by M. Kwieciński in [K2] and based on Gröbner bases works also for this class of surfaces.
LA - eng
KW - polynomial automorphisms; reconstruction of polynomial automorphisms; Gröbner bases; identity set of two polynomial automorphisms
UR - http://eudml.org/doc/269984
ER -

References

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  1. [A-E] K. Adjamagbo and A. van den Essen, A resultant criterion and formula for the inversion of a polynomial map in two variables, J. Pure Appl. Algebra 64 (1990), 1-6. 
  2. [E] A. van den Essen, A criterion to decide if a polynomial map is invertible and to compute the inverse, Comm. Algebra 18 (1990), 3183-3186. Zbl0718.13008
  3. [E-K] A. van den Essen and M. Kwieciński, On the reconstruction of polynomial automorphisms from their face polynomials, J. Pure Appl. Algebra 80 (1992), 327-336. Zbl0763.14004
  4. [B] B. Buchberger, Gröbner bases: An algorithmic method in polynomial ideal theory, in: Multidimensional Systems Theory, N. Bose (ed.), Reidel, Dordrecht, 1985, 164-232. Zbl0587.13009
  5. [J1] Z. Jelonek, Identity sets for polynomial automorphisms, J. Pure Appl. Algebra 76 (1991), 333-337. Zbl0752.14010
  6. [J2] Z. Jelonek, Irreducible identity sets for polynomial automorphisms, Math. Z. 212 (1993), 601-617. Zbl0806.14011
  7. [K1] M. Kwieciński, A Gröbner basis criterion for isomorphisms of algebraic varieties, J. Pure Appl. Algebra 74 (1991), 275-279. Zbl0754.13021
  8. [K2] M. Kwieciński, Automorphisms from face polynomials via two Gröbner bases, J. Pure Appl. Algebra 82 (1992), 65-70. Zbl0805.13009
  9. [L-J] M. Lejeune-Jalabert, Effectivité de Calculs Polynomiaux, Cours de D.E.A., Univ. de Grenoble, 1986. 
  10. J. McKay and S. Wang, An inversion formula for two polynomials in two variables, J. Pure Appl. Algebra 52 (1988), 103-119. Zbl0664.13001
  11. [P-P] F. Pauer and M. Pheifhofer, The theory of Gröbner bases, Enseign. Math. 34 (1988), 215-232. 
  12. [W] T. Winiarski, Application of Gröbner bases in the theory of polynomial mappings, XIV Instructional Conf. in the Theory of Extremal Problems, Łódź Univ., 1993 (in Polish). Zbl0806.13009

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