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On reconstruction of polynomial automorphisms. (English) Zbl 0860.14010

A subset \(X \subseteq k^n\) is called identity set of two polynomial automorphisms of \(k^n\), which coincide on \(X\), are equal. If \(k\) is the field of complex numbers, then a generic algebraic hypersurface of degree \(d\geq n \geq 2\) in \(k^n\) is an identity set. A. van den Essen and M. Kwiecinski developed algorithms based on Gröbner bases techniques to reconstruct an automorphism from the restriction to the union of the coordinate hyperplanes. Their results are extended to some greater class of algebraic subsets of \(k^n\).

MSC:

14H37 Automorphisms of curves
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
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