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{{Short description|Number-theoretic algorithm}} In [[computational number theory]], '''Cornacchia's algorithm''' is an [[algorithm]] for solving the ...

* ''p'', an odd [[Prime number|prime]] {{number theoretic algorithms}} ...

...hm''' is an algorithm for computing the [[modular square root]] of a given number.<ref>Adolf Kunerth, "Sitzungsberichte. Academie Der Wissenschaften" vol 78( ...he modulus, and uses modular operations that are often easy when the given number is prime. ...

...-8_15|doi = 10.1007/978-981-15-5191-8_15|chapter = A Survey of Solving SVP Algorithms and Recent Strategies for Solving the SVP Challenge|title = International S |title=Boosted KZ and LLL Algorithms ...

...]] are very important in the study of [[information theory]]. There are a number of different contexts in which these inequalities appear. == Machine based proof checker of information-theoretic inequalities== ...

==Set-theoretic definition== ...model theory. Here we define a structure on a nonempty set ''M'' in a set-theoretic manner, as a sequence ''S''&nbsp;=&nbsp;(''S''_''n''), ''n''&nbsp ...

...as the set of finite graphs, modulo isomorphism) where each element has a number of ''realizers'', which are understood as its algorithmic representations. ...e context of realizability, it is useful not to restrict the definition to algorithms in the [[Church–Turing thesis|Church–Turing sense]]. Instead, assemblies ar ...

...onal reconstruction''' is a method that allows one to recover a [[rational number]] from its value [[modular arithmetic|modulo]] a [[sufficiently large]] [[i ...teger with the property that <math>ns\equiv r\pmod{m}</math>. The rational number <math>r/s</math> is unknown, ...

...''b'', the algorithm finishes in at most 5''k'' steps, where ''k'' is the number of digits (decimal) of ''b''.<ref>{{Cite web |last=Weisstein |first=Eric W. ...>u\,\!</math> and <math>v\,\!</math> is less than <math>5</math> times the number of decimal digits of <math>\min(u,v)\,\!</math>. ...

| related to = FFT-based algorithms ...integer, and let {{Math|''p'' > 0}} be a modulus (not necessarily [[Prime number|prime]], but is convenient to choose it prime). Define {{Mvar|R}} to be the ...

{{short description|Method in number theory}} ...979.<ref name=":1">{{cite journal |author = M. Rabin |title= Probabilistic Algorithms in Finite Fields |journal= SIAM Journal on Computing |year= 1980 |volume= 9 ...

...n the input, and also has other conditions that must be met. A [[composite number|composite]] passing this test is a [[Frobenius pseudoprime]], but the conve ...title = A Probable Prime Test With High Confidence | journal = Journal of Number Theory | volume = 72 | issue = 1 | pages = 32–47 | date = 1998 | doi = 10.1 ...

...onentiation]] of numbers: {{math|''G''{{sup|2}}}} is called the ''[[Square number|square]]'' of {{mvar|G}}, {{math|''G''{{sup|3}}}} is called the ''[[Cube (a | title = Graph-theoretic concepts in computer science ...

The algorithms based on the method FEE include the algorithms for fast calculation of any elementary [[transcendental function]] for any [[Algebraic number|algebraic]] values of the argument and parameters, the [[Riemann zeta funct ...

...The framework has been used to provide tight worst-case guarantees on the number of required iterations, for several important classes of optimization probl ...''oracle complexity'' of this class of optimization problems: Namely, the number of iterations such that on one hand, there is an algorithm that provably re ...

In [[computational number theory]], '''Cipolla's algorithm''' is a technique for solving a [[Congruen ...''x'', and where <math>p</math> is an [[Parity (mathematics)|odd]] [[Prime number|prime]]. Here <math>\mathbf{F}_p</math> denotes the finite [[Field (mathema ...

...milar items map to the same "buckets" in memory with high probability (the number of buckets being much smaller than the universe of possible input items). I ...subadditivity]] (or the triangle inequality). In practice, metric learning algorithms ignore the condition of identity of indiscernibles and learn a pseudo-metri ...

...e FFTs of datasets with billions of elements (when applied to the [[number-theoretic transform]], the datasets of the order of 10¹² elements were pro ...ngruent Number Theta Coefficients to 10¹² | title = Algorithmic Number Theory | series = Lecture Notes in Computer Science | date = 2010 | volume ...

...Bob]] are each given a (potentially different) string, what is the minimal number of bits that they need to exchange in order for Alice to approximately comp ...orithm for Estimating the Entropy of a Stream|journal= ACM Transactions on Algorithms|volume=6|issue=3|pages=1–21|doi=10.1145/1798596.1798604|issn=1549-6325|cite ...

...] in 1983. Currently he is a professor at the Institute for Analysis and Number Theory at TU Graz. Previous positions include head of the Department of Ma ...s]] and [[Actuarial mathematics]], and in particular with number theoretic algorithms, digital expansions, [[diophantine equation|diophantine]] problems, combina ...