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:
“The three main medieval points of view regarding universals are designated by historians as realism, conceptualism, and nominalism. Essentially these same three doctrines reappear in twentieth-century surveys of the philosophy of mathematics under the new names logicism, intuitionism, and formalism.”
—Willard Van Orman Quine (b. 1908)
“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)
“Our little systems have their day;
They have their day and cease to be:
They are but broken lights of thee,
And thou, O Lord, art more than they.”
—Alfred Tennyson (1809–1892)