The library includes mathematical tools like differentiation for functions of any number of variables up to any order; numerical integration; a Newton-Raphson method for numerical root finding; non-linear least squares fitting; and several other capabilities. Another Python resource is SciPy. This is another library containing modules for optimization, linear algebra, integration, interpolation, special functions, FFTs, signal and image processing, differential equation solvers, and other tasks common in science and engineering.
SageMath previously Sage or SAGE, System for Algebra and Geometry Experimentation is a computer algebra system covering many aspects of mathematics, including algebra, combinatorics, graph theory, numerical analysis, number theory, calculus and statistics. It builds on top of several other open-source Python packages that include SciPy and many more. It accesses them through a common, Python-based language or directly via interfaces or wrappers.
There are many other free math programs that aim a bit lower, computationally. All calculations are entered in a sheet UI. Users can define custom variables and functions and graph the results. The program can express calculations with arithmetic, conditional, logical and bitwise operators and includes around built-in mathematical, physical and conditional constants.
There are around 60 built-in functions for analysis, arithmetic, complex numbers, hyperbolic functions, statistics, trig, and others. The Euler Math Toolbox was also inspired by Matlab, but the syntax is not exactly compatible.
Like Matlab, Euler is a matrix language designed to handle vectors and matrices, in most cases without explicit loops. Euler does symbolic math with the help of another free program called Maxima. One good thing: Euler is still actively developed with two updates released earlier this year. Math Mechanixs lets users type in equations as they might write them on a piece of paper. It includes a scientific calculator and an integrated variables and functions list window to simplify the tracking of defined variables and functions.
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