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Polynomial Automorphisms and Gröbner Reductions

✍ Scribed by Vladimir Shpilrain; Jie-Tai Yu

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
173 KB
Volume
197
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

Let P s K x , . . . , x be the polynomial algebra over a field K of characterisn 1 n tic 0. We show that applying an automorphism to a given polynomial p g P is n mimicked by Grobner transformations of a basis of the ideal of P generated by ¨n partial derivatives of this polynomial. In the case of P , this yields a miraculously 2 simple algorithm for deciding whether or not a given polynomial from P is part of 2 a basis. Another application is an algorithm which, given a polynomial p g P that 2 is part of a basis, finds a sequence of elementary automorphisms that reduces p to x . We also speculate on how our method may be used for constructing a possible 1 counterexample to the Jacobian conjecture in higher dimensions.

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