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:
“Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don’t happen to have all the data. In mathematics we have all the data ... and yet we don’t understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.”
—Simone Weil (1909–1943)
“The computer takes up where psychoanalysis left off. It takes the ideas of a decentered self and makes it more concrete by modeling mind as a multiprocessing machine.”
—Sherry Turkle (b. 1948)
“Poetry has become the higher algebra of metaphors.”
—José Ortega Y Gasset (1883–1955)
“The skylines lit up at dead of night, the air- conditioning systems cooling empty hotels in the desert and artificial light in the middle of the day all have something both demented and admirable about them. The mindless luxury of a rich civilization, and yet of a civilization perhaps as scared to see the lights go out as was the hunter in his primitive night.”
—Jean Baudrillard (b. 1929)