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PARI/GP online calculator - https://pari.math.u-bordeaux.fr/gp.html (PARI/GP is a widely used computer algebra system designed for fast computations in number theory (factorizations, algebraic number theory, elliptic curves, modular forms, L functions...), but also contains a large number of other useful functions to compute with mathematical ...
The PARI/GP system consists of the following standard components: 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
The original use of interpolation polynomials was to approximate values of important transcendental functions such as natural logarithm and trigonometric functions.Starting with a few accurately computed data points, the corresponding interpolation polynomial will approximate the function at an arbitrary nearby point.
The main computer algebra systems (Maple, Mathematica, SageMath, PARI/GP) have each a variant of this method as the default algorithm for the real roots of a polynomial. The class of methods is based on converting the problem of finding polynomial roots to the problem of finding eigenvalues of the companion matrix of the polynomial, [ 1 ] in ...
The nth element of an arithmetico-geometric sequence is the product of the nth element of an arithmetic sequence and the nth element of a geometric sequence. [1] An arithmetico-geometric series is a sum of terms that are the elements of an arithmetico-geometric sequence.
Geometric programming is closely related to convex optimization: any GP can be made convex by means of a change of variables. [2] GPs have numerous applications, including component sizing in IC design, [ 3 ] [ 4 ] aircraft design, [ 5 ] maximum likelihood estimation for logistic regression in statistics , and parameter tuning of positive ...
ALGLIB has an implementations in C++ / C# / VBA / Pascal. GSL has a polynomial interpolation code in C; SO has a MATLAB example that demonstrates the algorithm and recreates the first image in this article; Lagrange Method of Interpolation — Notes, PPT, Mathcad, Mathematica, MATLAB, Maple; Lagrange interpolation polynomial on www.math-linux.com
If m is a power of 2, then a − 1 should be divisible by 4 but not divisible by 8, i.e. a ≡ 5 (mod 8). [ 1 ] : §3.2.1.3 Indeed, most multipliers produce a sequence which fails one test for non-randomness or another, and finding a multiplier which is satisfactory to all applicable criteria [ 1 ] : §3.3.3 is quite challenging. [ 8 ]