Contents

• 1 Introduction
  • 1.1 Exemplifying the Chinese remainder theorem
  • 1.2 Exemplifying the decomposition of rational functions
  • 1.3 Organization of this paper
• 2 Algorithms to compute the Bezout's coefficients
  • 2.1 Euclidean versus principal
  • 2.2 Euclidean algorithm, then back
  • 2.3 Straightforward Bezout's algorithm
  • 2.4 Matricial writing
  • 2.5 Centered algorithm
• 3 Polynomials
• 4 Continued fractions
  • 4.1 Confrac expansion of a rational
  • 4.2 Some theorems about centered convergents
  • 4.3 Periodic expansion of
  • 4.4 Interval arithmetic and rationality checking
• 5 Padé approximants
  • 5.1 Obtaining Padé approximants
  • 5.2 Quotients in arithmetical progression
• 6 Accelerations
  • 6.1 Describing some experiments
  • 6.2 Almost but not everywhere
  • 6.3 Divide and conquer
• 7 Concluding remarks
• Bibliography
• Bibliography
• Contents