Computer Algebra System - Mathematics Used in Computer Algebra Systems

Mathematics Used in Computer Algebra Systems

  • Symbolic integration - Risch algorithm
  • Hypergeometric summation - Gosper's algorithm
  • Limit computation - Gruntz's algorithm
  • Polynomial factorization. Over finite fields, Berlekamp's algorithm or Cantor–Zassenhaus algorithm is used.
  • Greatest common divisor - Euclidean algorithm
  • Gaussian elimination
  • Gröbner basis - Buchberger's algorithm; generalization of Euclidean algorithm and Gaussian elimination
  • Padé approximant
  • Schwartz–Zippel lemma and testing polynomial identities
  • Chinese remainder theorem
  • Diophantine equations
  • Quantifier elimination over real numbers - Tarski's method/Cylindrical algebraic decomposition
  • Landau's algorithm
  • Derivatives of elementary and special functions (e.g. see Incomplete Gamma function)

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