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1996 | 64 | 1 | 61-69

Tytuł artykułu

On reconstruction of polynomial automorphisms

Autorzy

Treść / Zawartość

Języki publikacji

EN

Abstrakty

EN
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.

Rocznik

Tom

64

Numer

1

Strony

61-69

Daty

wydano
1996
otrzymano
1995-02-27
poprawiono
1995-06-05

Twórcy

  • Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

Bibliografia

  • [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.
  • [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.
  • [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.
  • [B] B. Buchberger, Gröbner bases: An algorithmic method in polynomial ideal theory, in: Multidimensional Systems Theory, N. Bose (ed.), Reidel, Dordrecht, 1985, 164-232.
  • [J1] Z. Jelonek, Identity sets for polynomial automorphisms, J. Pure Appl. Algebra 76 (1991), 333-337.
  • [J2] Z. Jelonek, Irreducible identity sets for polynomial automorphisms, Math. Z. 212 (1993), 601-617.
  • [K1] M. Kwieciński, A Gröbner basis criterion for isomorphisms of algebraic varieties, J. Pure Appl. Algebra 74 (1991), 275-279.
  • [K2] M. Kwieciński, Automorphisms from face polynomials via two Gröbner bases, J. Pure Appl. Algebra 82 (1992), 65-70.
  • [L-J] M. Lejeune-Jalabert, Effectivité de Calculs Polynomiaux, Cours de D.E.A., Univ. de Grenoble, 1986.
  • J. McKay and S. Wang, An inversion formula for two polynomials in two variables, J. Pure Appl. Algebra 52 (1988), 103-119.
  • [P-P] F. Pauer and M. Pheifhofer, The theory of Gröbner bases, Enseign. Math. 34 (1988), 215-232.
  • [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).

Identyfikator YADDA

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