Equivalence of polynomials under automorphisms of C2

✍ Scribed by Penelope G. Wightwick

• Book ID: 104152276
• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 323 KB
• Volume: 157
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(00)00014-1

✦ Synopsis

We provide an e ective and e cient algorithm to decide, given two polynomials in p; q ∈ C[x; y], whether there is an automorphism of C[x; y] taking p to q, and to ÿnd this automorphism if it exists. For p(x; y) = x an algorithm is implicit in the proofs of the Abhyankar-Moh=Suzuki embedding theorem, and a di erent and interesting explicit algorithm was given in 1997 by Shpilrain and Yu (J. Alg. 197 (2) (1997) 546 -558). Other special cases are done in a preprint of Shpilrain and Yu (to appear in J. Alg.).