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...0002-9947-1980-0570778-7|issn=0002-9947|doi-access=free}}</ref> Given the polynomial ''p'', the matrices ''A'' and ''B'' can be found by elementary methods.<ref The polynomial ''x''² + ''y''² is irreducible over '''R'''[''x'',''y ...

...thms have worst-case runtime. They have the property of being [[reducible polynomial|reducible]] [[modulo]] every prime, while being irreducible over the ration ...ber]]s, the Swinnerton-Dyer polynomial associated to <math>P</math> is the polynomial: ...

{{Short description|Algorithm for factorization of polynomials}} ...ov's algorithm''', named after [[Sergei Evdokimov]], is an algorithm for [[factorization of polynomials]] over [[finite field]]s. It was the fastest algorithm known ...

...only if]] a perfect matching exists. (This polynomial is not the [[Tutte polynomial]] of ''G''.) *{{cite book|author=R. Motwani, P. Raghavan |title=Randomized Algorithms|publisher=Cambridge University Press|year=1995|page=167}} ...

{{Short description|Factorization under function composition}} .... [[Algorithms]] are known for decomposing [[univariate polynomial]]s in [[polynomial time]]. ...

The algorithm does not require the factorization of the modulus, and uses modular operations that are often easy when the gi #:The parameters of the polynomial expansion are quite flexible, in that <math>((67 z+r)^2+X\cdot \text{RSA260 ...

...979.<ref name=":1">{{cite journal |author = M. Rabin |title= Probabilistic Algorithms in Finite Fields |journal= SIAM Journal on Computing |year= 1980 |volume= 9 ...sed by [[Elwyn Berlekamp]] in his 1970 work<ref name=":0" /> on polynomial factorization over finite fields. His original work lacked a formal [[Correctness (comput ...

...omputation of the factorization by means of an [[algorithm]]. In practice, algorithms have been designed only for polynomials with coefficients in a [[finite fie ...er the rational numbers, reduce the problem to this case; see [[polynomial factorization]]. It is also used for various applications of finite fields, such as [[cod ...

...uses relating to [[stable polynomial]]s. In [[stability theory]], Spectral Factorization has been used to find determinantal matrix representations for bivariate st ...ejér-Riesz_theorem|Fejer–Riesz Theorem]] yields the polynomial '''spectral factorization''' <math>p(t) = q(t)\bar{q}(t)</math>. Results of this form are generically ...

{{broader|Root-finding algorithms}} ...9th century, [[algebra]] meant essentially [[theory of equations|theory of polynomial equations]]. ...

...decomposition''' of a [[polynomial system]] {{mvar|S}} is a set of simpler polynomial systems {{math|''S''₁, ..., ''S_e''}} such that a poin ..., those simpler systems are [[regular chain]]s. If the coefficients of the polynomial systems {{math|''S''₁, ..., ''S_e''}} are real numbers ...

There are many polynomial-time algorithms for list decoding. In this article, we first present an algorithm for [[RS Here is a plot of the rate R and distance <math> \delta</math> for different algorithms. ...

...orithm]] (LLL) to find a polynomial that has the same zeroes as the target polynomial but smaller coefficients. Coppersmith's approach is a reduction of solving modular polynomial equations to solving polynomials over the integers. ...

...true, would have numerous implications in graph theory, including the [[1-factorization conjecture]].<ref>{{citation ==Algorithms== ...

{{Short description|Type of triangular sets of polynomial}} ...}}th polynomial. In other words, regular chains allow solving [[systems of polynomial equations]] by solving successive univariate equations without considering ...

...o solve a version of the [[shortest vector problem]] (SVP) in a lattice (a polynomial-time reduction from this SVP problem to the RLWE problem has been presented ...of two 384-bit primes but not the product of two 512-bit primes. [[Integer factorization]] forms the basis of the widely used [[RSA (cryptosystem)|RSA]] cryptograph ...

...and [[computer scientist]], known for his research on [[algorithm]]s for [[polynomial]]s and [[matrix multiplication]]. ...wn informally as "polynomial Pan" for his pioneering work in the area of [[polynomial]] [[computation]]s. In late 1970s, he immigrated to the [[United States]] a ...

{{Short description|Bound on the coefficients of a factor polynomial}} ...nential function|exponential expression]] involving only the [[degree of a polynomial|degree]] and coefficients of ''f''(''x''), i.e. only depending on ''f''(''x ...

...sense, the notion of "restricted power series" is a generalization of a [[polynomial]]. ...g of restricted power series is defined as the [[projective limit]] of the polynomial rings over <math>A/I_{\lambda}</math>: ...

{{short description|Algorithms for polynomial evaluation}} ...(2,3)= 2\cdot 2\cdot 3 + 2^3+4=24.</math> See also {{slink|Polynomial ring|Polynomial evaluation}} ...