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 dont happen to have all the data. In mathematics we have all the data ... and yet we dont 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 (19091943)
“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 (18831955)
“No civilization ... would ever have been possible without a framework of stability, to provide the wherein for the flux of change. Foremost among the stabilizing factors, more enduring than customs, manners and traditions, are the legal systems that regulate our life in the world and our daily affairs with each other.”
—Hannah Arendt (19061975)