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Many algorithms have been devised for determining the prime factors of a given number (a process called prime factorization). They vary quite a bit in sophistication and ...
The study of efficient algorithms for solving geometric problems. Examples of problems treated by computational geometry include determination of the convex hull and Voronoi ...
Computational number theory is the branch of number theory concerned with finding and implementing efficient computer algorithms for solving various problems in number ...
A sequence of approximations a/b to sqrt(n) can be derived by factoring a^2-nb^2=+/-1 (1) (where -1 is possible only if -1 is a quadratic residue of n). Then ...
While many computations admit shortcuts that allow them to be performed more rapidly, others cannot be sped up. Computations that cannot be sped up by means of any shortcut ...
The computational paradigm is a term introduced by Wolfram (2002, 2021) to describe the idea of using simple programs rather than mathematical equations (the latter of which ...
Some computations allow shortcuts which can be used to speed them up. Consider the operation of raising a number to a positive integer power. It is possible, for example, to ...
Almost all processes that are not obviously simple can be viewed as computations of equivalent sophistication (Wolfram 2002, pp. 5 and 716-717). More specifically, the ...
The number of single operations (of addition, subtraction, and multiplication) required to complete an algorithm.
A problem is assigned to the P (polynomial time) class if there exists at least one algorithm to solve that problem, such that the number of steps of the algorithm is bounded ...
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