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This free software had an earlier incarnation, Macsyma. Developed by Massachusetts Institute of Technology in the 1960s, it was maintained by William Schelter from 1982 to 2001. In 1998, Schelter obtained permission to release Maxima as open-source software under the GNU General Public license and the source code was released later that year ...
Wolfram Mathematica is a software system with built-in libraries for several areas of technical computing that allows machine learning, statistics, symbolic computation, data manipulation, network analysis, time series analysis, NLP, optimization, plotting functions and various types of data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in ...
The Wolfram Language (/ ˈ w ʊ l f r əm / WUUL-frəm) is a proprietary, [7] general-purpose, very high-level multi-paradigm programming language [8] developed by Wolfram Research.It emphasizes symbolic computation, functional programming, and rule-based programming [9] and can employ arbitrary structures and data. [9]
Wolfram Language WolframAlpha ( / ˈ w ʊ l f . r əm -/ WUULf-rəm- ) is an answer engine developed by Wolfram Research . [ 1 ] It is offered as an online service that answers factual queries by computing answers from externally sourced data.
Free CeCILL (GPL-compatible) until version 5.5.2 GPL v2.0 since version 6.0.2 MATLAB alternative. SINGULAR: University of Kaiserslautern: 1984 1997 4-3-0: 14 January 2022: Free GNU GPL: Computer algebra system for polynomial computations, with special emphasis on commutative and non-commutative algebra, algebraic geometry, and singularity ...
That is, df is the unique 1-form such that for every smooth vector field X, df (X) = d X f , where d X f is the directional derivative of f in the direction of X. The exterior product of differential forms (denoted with the same symbol ∧) is defined as their pointwise exterior product.
The rate of change of f with respect to x is usually the partial derivative of f with respect to x; in this case, ∂ f ∂ x = y . {\displaystyle {\frac {\partial f}{\partial x}}=y.} However, if y depends on x , the partial derivative does not give the true rate of change of f as x changes because the partial derivative assumes that y is fixed.
h := sqrt(eps) * x; xph := x + h; dx := xph - x; slope := (F(xph) - F(x)) / dx; However, with computers, compiler optimization facilities may fail to attend to the details of actual computer arithmetic and instead apply the axioms of mathematics to deduce that dx and h are the same.