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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] SymPy is simple to install and to inspect because it is written entirely in Python with few dependencies.
Fresnel integral. Plots of S(x) and C(x). The maximum of C(x) is about 0.977 451 424. If the integrands of S and C were defined using π 2 t2 instead of t2, then the image would be scaled vertically and horizontally (see below). The Fresnel integrals S(x) and C(x) are two transcendental functions named after Augustin-Jean Fresnel that are ...
The Gram–Schmidt process takes a finite, linearly independent set of vectors for k ≤ n and generates an orthogonal set that spans the same -dimensional subspace of as . The method is named after Jørgen Pedersen Gram and Erhard Schmidt, but Pierre-Simon Laplace had been familiar with it before Gram and Schmidt. [1]
Escape time algorithm. The simplest algorithm for generating a representation of the Mandelbrot set is known as the "escape time" algorithm. A repeating calculation is performed for each x, y point in the plot area and based on the behavior of that calculation, a color is chosen for that pixel.
Smoothstep. Smoothstep is a family of sigmoid-like interpolation and clamping functions commonly used in computer graphics, [1][2] video game engines, [3] and machine learning. [4] The function depends on three parameters, the input x, the "left edge" and the "right edge", with the left edge being assumed smaller than the right edge.
Vectorized array operations. Some compiled languages such as Ada and Fortran, and some scripting languages such as IDL, MATLAB, and S-Lang, have native support for vectorized operations on arrays. For example, to perform an element by element sum of two arrays, a and b to produce a third c, it is only necessary to write.
uBLAS is a C++ template class library that provides BLAS level 1, 2, 3 functionality for dense, packed and sparse matrices. Eigen is a C++ template library for linear algebra: matrices, vectors, numerical solvers, and related algorithms. Fastor is a high performance tensor (fixed multi-dimensional array) library for modern C++.
Array programming. In computer science, array programming refers to solutions that allow the application of operations to an entire set of values at once. Such solutions are commonly used in scientific and engineering settings. Modern programming languages that support array programming (also known as vector or multidimensional languages) have ...