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)
Read more about this topic: Computer Algebra System
Famous quotes containing the words mathematics, computer, algebra and/or systems:
“Why does man freeze to death trying to reach the North Pole? Why does man drive himself to suffer the steam and heat of the Amazon? Why does he stagger his mind with the mathematics of the sky? Once the question mark has arisen in the human brain the answer must be found, if it takes a hundred years. A thousand years.”
—Walter Reisch (1903–1963)
“Family life is not a computer program that runs on its own; it needs continual input from everyone.”
—Neil Kurshan (20th century)
“Poetry has become the higher algebra of metaphors.”
—José Ortega Y Gasset (1883–1955)
“We have done scant justice to the reasonableness of cannibalism. There are in fact so many and such excellent motives possible to it that mankind has never been able to fit all of them into one universal scheme, and has accordingly contrived various diverse and contradictory systems the better to display its virtues.”
—Ruth Benedict (1887–1948)