Computer algebra Computer algebra In mathematics and computer algebra, automatic differentiation, or AD, sometimes alternatively called algorithmic differentiation, is a method to numerically evaluate the derivative of a function specified by a computer program. Two classical ways of doing this are: ...more on Wikipedia about "Automatic differentiation"
In differential algebra, an elementary function is a function built from a finite number of exponentials, logarithms, constants, one variable, and roots of equations through composition and combinations using the four elementary operations (+ − × ÷). The trigonometric functions and their inverses are assumed to be included in the elementary functions by using complex variables ...more on Wikipedia about "Elementary function (differential algebra)"
In algebraic geometry, elimination theory is the classical name for algorithmic approaches to eliminating between polynomials of several variables. ...more on Wikipedia about "Elimination theory"
In computer algebra, computational algebraic geometry, and computational commutative algebra, a Gröbner basis G (named after Wolfgang Gröbner) is a particular kind of generating subset of an ideal I in a polynomial ring R. One can view it as a multivariate, non-linear generalization of: ...more on Wikipedia about "Gröbner basis"
Record linkage refers to the task of finding identical entries in two or more files. The initial idea goes back to Halbert L. Dunn ("Record Linkage" in: American Journal of Public Health, Vol. 36 (1946), 1412-1416). In the 1950s, Howard Borden Newcombe laid the probabilistic foundations of modern record linkage theory. ...more on Wikipedia about "Record linkage"
The Risch algorithm is an algorithm for the calculus operation of indefinite integration (i.e. finding antiderivatives). The algorithm transforms the problem of integration into a problem in algebra. It is based on the form of the function being integrated and on methods for integrating rational functions, radicals, logarithms, and exponential functions. Robert Risch, who developed the algorithm in 1968, called it a decision procedure, because it is a method for deciding if a function has a simple-looking function as an indefinite integral; and also, if it does, determining it. The Risch-Norman algorithm, a faster but less powerful technique, was developed in 1976. ...more on Wikipedia about "Risch algorithm"
Symbolic integration is the application of computer software to solving problems in mathematics of find the integral of an expression, but finding an expression rather than a value. ...more on Wikipedia about "Symbolic integration"
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Symbolic mathematics, or symbolic math, relates to the use of computers to manipulate mathematical equations and expressions in symbolic form, as opposed to manipulating the approximations of specific numerical quantities represented by those symbols. Such a system might be used for symbolic integration or differentiation, substitution of one expression into another, simplification of an expression, etc. ...more on Wikipedia about "Symbolic mathematics"
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