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A generalized continued fraction is an expression of the form. where the an ( n > 0) are the partial numerators, the bn are the partial denominators, and the leading term b0 is called the integer part of the continued fraction. The successive convergents of the continued fraction are formed by applying the fundamental recurrence formulas :
Firstly, the computation of x** (n-1) in exact arithmetics is expensive if x is a large integer, so every iteration takes a long time. Secondly, the method needs a lot of iterations. For instance, nthroot (1234567890123456789012345**10, 10) requires 4725 iterations (note that I replaced 100 in your example with 10), while a binary search ...
Hensel's lemma. In mathematics, Hensel's lemma, also known as Hensel's lifting lemma, named after Kurt Hensel, is a result in modular arithmetic, stating that if a univariate polynomial has a simple root modulo a prime number p, then this root can be lifted to a unique root modulo any higher power of p. More generally, if a polynomial factors ...
In mathematical logic and type theory, the λ-cube (also written lambda cube) is a framework introduced by Henk Barendregt [1] to investigate the different dimensions in which the calculus of constructions is a generalization of the simply typed λ-calculus. Each dimension of the cube corresponds to a new kind of dependency between terms and types.
In abstract algebra and number theory, Kummer theory provides a description of certain types of field extensions involving the adjunction of n th roots of elements of the base field. The theory was originally developed by Ernst Eduard Kummer around the 1840s in his pioneering work on Fermat's Last Theorem. The main statements do not depend on ...
Some authors use the name square root or the notation A1/2 only for the specific case when A is positive semidefinite, to denote the unique matrix B that is positive semidefinite and such that BB = BTB = A (for real-valued matrices, where BT is the transpose of B ). Less frequently, the name square root may be used for any factorization of a ...
Muhamed (horse) Muhamed was a German horse reportedly able to mentally extract the cube roots of numbers, which he would then tap out with his hooves. Raised in the town of Elberfeld by Karl Krall in the late 19th and early 20th centuries, he was one of several supposedly gifted horses, the others being Kluge Hans, Zarif, Amassis, and later ...
Fast inverse square root, sometimes referred to as Fast InvSqrt () or by the hexadecimal constant 0x5F3759DF, is an algorithm that estimates , the reciprocal (or multiplicative inverse) of the square root of a 32-bit floating-point number in IEEE 754 floating-point format. The algorithm is best known for its implementation in 1999 in Quake III ...