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On reconstruction of polynomial automorphisms

Paweł Gniadek — 1996

Annales Polonici Mathematici

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.

On reconstructing algebraic sets and ideals

Paweł Gniadek — 2007

Annales Polonici Mathematici

We generalize some results on reconstructing sets to the case of ideals of 𝕜[X₁,...,Xₙ]. We show that reconstructing sets can be approximated by finite subsets having the property of reconstructing automorphisms of bounded degree.

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