Search results
Results From The WOW.Com Content Network
In calculus, symbolic integration is the problem of finding a formula for the antiderivative, or indefinite integral, of a given function f(x), i.e. to find a formula for a differentiable function F(x) such that
The following tables provide a comparison of computer algebra systems (CAS). [1] [2] [3] A CAS is a package comprising a set of algorithms for performing symbolic manipulations on algebraic objects, a language to implement them, and an environment in which to use the language.
MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages. Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the MuPAD symbolic engine allowing access to symbolic computing abilities.
Symbolic integration via e.g. Risch algorithm or Risch–Norman algorithm; Hypergeometric summation via e.g. Gosper's algorithm; Limit computation via e.g. Gruntz's algorithm; Polynomial factorization via e.g., over finite fields, [21] Berlekamp's algorithm or Cantor–Zassenhaus algorithm. Greatest common divisor via e.g. Euclidean algorithm
Chebfun is a free/open-source software system written in MATLAB for numerical computation with functions of a real variable. It is based on the idea of overloading MATLAB's commands for vectors and matrices to analogous commands for functions and operators.
Octave (aka GNU Octave) is an alternative to MATLAB. Originally conceived in 1988 by John W. Eaton as a companion software for an undergraduate textbook, Eaton later opted to modify it into a more flexible tool. Development begun in 1992 and the alpha version was released in 1993. Subsequently, version 1.0 was released a year after that in 1994.
In symbolic computation, the Risch algorithm is a method of indefinite integration used in some computer algebra systems to find antiderivatives.It is named after the American mathematician Robert Henry Risch, a specialist in computer algebra who developed it in 1968.
Just as the definite integral of a positive function of one variable represents the area of the region between the graph of the function and the x-axis, the double integral of a positive function of two variables represents the volume of the region between the surface defined by the function (on the three-dimensional Cartesian plane where z = f(x, y)) and the plane which contains its domain. [1]