Factoring in astrocytes

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Factoring in Quadratic Fields

This is closed under addition, subtraction, multiplication, and also division by nonzero numbers. Similarly, set Z[ √ d] = {a+ b √ d : a, b ∈ Z}. This is closed under addition, subtraction, and multiplication, but not usually division. We will define a concept of “integers” for K, which will play the same role in K as the ordinary integers Z do in Q. The integers of K will contain Z[ √ d] but m...

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Factoring Proofs

Logic programs, when total, realize proofs via a realizability interpretation similar to the Curry Howard isomorphism. The challenge in statically deciding totality lies in checking for termination and for coverage. For Elf logic programs, sophisticated algorithms exist for both problems. However, those solutions only apply to a much smaller subset of logic programs than a programmer is typical...

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Factoring Polynomials

Factoring polynomials over the rational numbers, real numbers, and complex numbers has long been a standard topic of high school algebra. With the advent of computers and the resultant development of error-correcting codes, factoring over finite fields (e.g., Zp, for p a prime number) has become important as well. To understand this discussion, you need to know what polynomials are, and how to ...

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Factoring & Primality

In this lecture we will discuss the problem of integer factorization and primality testing, two problems that have been the focus of a great amount of research over the years. These problems started receiving attention in the mathematics community far before the appearance of computer science, however the emergence of the latter has given them additional importance. Gauss himself wrote in 1801 ...

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On Factoring

This is a survey article on factoring. Given the importance of factoring, or rather the difficulty thereof, in the security of RSA and other cryptosystems, it is worth having an overview of the area. Mathematics Subject Classification: Primary: 11A41; Secondary: 11A51

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ژورنال

عنوان ژورنال: Nature Reviews Neuroscience

سال: 2015

ISSN: 1471-003X,1471-0048

DOI: 10.1038/nrn3908