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SymPy is an open-source Python library for symbolic computation.It provides computer algebra capabilities either as a standalone application, as a library to other applications, or live on the web as SymPy Live [2] or SymPy Gamma. [3]
Risch developed a method that allows one to consider only a finite set of functions of Liouville's form. The intuition for the Risch algorithm comes from the behavior of the exponential and logarithm functions under differentiation. For the function f e g, where f and g are differentiable functions, we have
PARI/GP is a computer algebra system that facilitates number-theory computation. Besides support of factoring, algebraic number theory, and analysis of elliptic curves, it works with mathematical objects like matrices, polynomials, power series, algebraic numbers, and transcendental functions. [3]
C/C++ based numerical computing and graphical plotting [1] DADiSP: DSP Development 1984 1987 6.7 B02 17 January 2017: $1995 (commercial), $129 (academic), Free (student) Proprietary: Numeric computations for science and engineering featuring a spreadsheet like interface. Dyalog APL: Dyalog Ltd. 1981 1983 18.0 10 June 2020
plotting graphs and parametric plots of functions in two and three dimensions, and animating them; drawing charts and diagrams; APIs for linking it on an external program such as a database, or using in a programming language to use the computer algebra system; string manipulation such as matching and searching
Given a function: from a set X (the domain) to a set Y (the codomain), the graph of the function is the set [4] = {(, ()):}, which is a subset of the Cartesian product.In the definition of a function in terms of set theory, it is common to identify a function with its graph, although, formally, a function is formed by the triple consisting of its domain, its codomain and its graph.
The first two steps of the Gram–Schmidt process. In mathematics, particularly linear algebra and numerical analysis, the Gram–Schmidt process or Gram-Schmidt algorithm is a way of finding a set of two or more vectors that are perpendicular to each other.
A plot of the smoothstep(x) and smootherstep(x) functions, using 0 as the left edge and 1 as the right edgeSmoothstep is a family of sigmoid-like interpolation and clamping functions commonly used in computer graphics, [1] [2] video game engines, [3] and machine learning.