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Like any series, an alternating series is a convergent series if and only if the sequence of partial sums of the series converges to a limit. The alternating series test guarantees that an alternating series is convergent if the terms a n converge to 0 monotonically, but this condition is not necessary for convergence.
PARI is a C library, allowing for fast computations, and which can be called from a high-level language application (for instance, written in C, C++, Pascal, Fortran, Perl, or Python). gp is an easy-to-use interactive command line interface giving access to the PARI functions.
Genius (also known as the Genius Math Tool) is a free open-source numerical computing environment and programming language, [2] similar in some aspects to MATLAB, GNU Octave, Mathematica and Maple. Genius is aimed at mathematical experimentation rather than computationally intensive tasks. It is also very useful as just a calculator.
Both binaries and source code are available for SageMath from the download page. If SageMath is built from source code, many of the included libraries such as OpenBLAS, FLINT, GAP (computer algebra system), and NTL will be tuned and optimized for that computer, taking into account the number of processors, the size of their caches, whether there is hardware support for SSE instructions, etc.
An infinite series of any rational function of can be reduced to a finite series of polygamma functions, by use of partial fraction decomposition, [8] as explained here. This fact can also be applied to finite series of rational functions, allowing the result to be computed in constant time even when the series contains a large number of terms.
An unpublished computational program written in Pascal called Abra inspired this open-source software. Abra was originally designed for physicists to compute problems present in quantum mechanics. Kespers Peeters then decided to write a similar program in C computing language rather than Pascal, which he renamed Cadabra. However, Cadabra has ...
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A simple arithmetic calculator was first included with Windows 1.0. [5]In Windows 3.0, a scientific mode was added, which included exponents and roots, logarithms, factorial-based functions, trigonometry (supports radian, degree and gradians angles), base conversions (2, 8, 10, 16), logic operations, statistical functions such as single variable statistics and linear regression.