Computing with Polynomials Given By Black Boxes for Their Evaluations: Greatest Common Divisors, Factorization, Separation of Numerators and Denominators

@article{Kaltofen1990ComputingWP,
  title={Computing with Polynomials Given By Black Boxes for Their Evaluations: Greatest Common Divisors, Factorization, Separation of Numerators and Denominators},
  author={Erich Kaltofen and Barry M. Trager},
  journal={J. Symb. Comput.},
  year={1990},
  volume={9},
  pages={301-320}
}
Algorithms are developed that adopt a ,ovel implicit representation ibr multivariate polynomials and rational functions with rational coefficients, that of black boxes for their evaluation. We show tha t within this representation the polynomial greatest common divisor and factorization problems, as well as the problem of extracting the numerator and denominator of a rational function, can all be solved in random polynomial-tlme. Since we can convert black boxes efficiently to sparse format… CONTINUE READING
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