Algorithms for recognizing coordinates in two variables over UFD's

ABSTRACT

We give an easy and efficient algorithm to check whether a given polynomial f in K[x,y] is a coordinate, where K be a commutative field of characteristic zero, and if so to compute a coordinate's mate of f. Then we treat the same problem replacing the ground field K by a unique factorization domain A of characteristic zero. A notable feature of our method is that it always produces a mate of minimum degree.

REFERENCES

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INDEX TERMS

Primary Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.1 Numerical Algorithms and Problems
          Subjects: Computations on polynomials

General Terms:
Algorithms

Keywords:
coordinate, locally nilpotent derivation, slice