Direct proof of a theorem by Kalkbrener, Sweedler, and Taylor

  • Authors:

  • Erich Kaltofen

  • Affiliations:

  • -

  • Venue:
  • ACM SIGSAM Bulletin
  • Year:
  • 1993

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Abstract

For given f1,..., fm ∈ K[x] that are relatively prime, where K is a field, Kalkbrener, Sweedler, and Taylor (1993) present degree bounds on the ai needed to express 1 (and other low degree polynomials) as Σaifi. Their bounds are an improvement on bounds given by Kakié (1976). This note presents a direct proof of the following fact.