Search results

...t of [[polynomial]] topics''', by Wikipedia page. See also [[trigonometric polynomial]], [[list of algebraic geometry topics]]. *[[Degree of a polynomial|Degree]]: The maximum exponents among the monomials. ...

{{short description|Polynomial with no repeated root}} ...in physics and engineering, a square-free polynomial is commonly called a polynomial with no '''repeated roots'''. ...

{{Short description|Polynomial division computation method}} ...ation]] of the [[Euclidean division]] of a [[polynomial]] by a [[Binomial (polynomial)|binomial]] of the form ''x – r''. It was described by [[Paolo Ruffini (mat ...

...The benefit of this notation is that it simplifies the analysis of these algorithms. The <math>e^{c(\ln n)^\alpha(\ln\ln n)^{1-\alpha}}</math> expresses the d ...complexity and behaviour. The breadth of L-notation, allowing one to span polynomial to exponential growth rates, and its looseness, allowing theorems and heuri ...

...ares]], to the operation of squaring, to terms of the second [[degree of a polynomial|degree]], or equations or formulas that involve such terms. ''Quadratus'' * [[Quadratic function]] (or quadratic polynomial), a polynomial function that contains terms of at most second degree ...

{{short description|Algorithm for generating random numbers with their factorization}} ...[[Random number generation|generating random numbers]] along with their [[factorization]]s. It was published by [[Eric Bach]] in 1988. No algorithm is known that e ...

{{short description|Polynomial without nontrivial factorization}} ...ials|polynomials which are not a composition of polynomials|Indecomposable polynomial}} ...

...r transform]] (FFT) algorithm based on an unusual recursive [[polynomial]]-factorization approach, proposed for powers of two by G. Bruun in 1978 and generalized to ...ovides an interesting perspective on FFTs that permits mixtures of the two algorithms and other generalizations. ...

...gebra]], the '''Cantor–Zassenhaus algorithm''' is a method for factoring [[polynomial]]s over [[finite field]]s (also called Galois fields). The algorithm consists mainly of exponentiation and polynomial [[greatest common divisor|GCD]] computations. It was invented by [[David G. ...

...modular arithmetic|congruence]] commonly used in [[integer factorization]] algorithms. Given a positive [[integer]] ''n'', [[Fermat's factorization method]] relies on finding numbers ''x'' and ''y'' satisfying the [[equatio ...

...algorithm consists mainly of [[matrix (mathematics)|matrix]] reduction and polynomial [[greatest common divisor|GCD]] computations. It was invented by [[Elwyn B ...ring (mathematics)|ring]] of polynomials over a finite field is a [[unique factorization domain]]). ...

{{Short description|Counting polynomial real roots based on coefficients}} ...ve real roots is at most the number of sign changes in the sequence of the polynomial's coefficients (omitting zero coefficients), and the difference between the ...

...ies all the theory of [[factorization of polynomials|factorization]] and [[polynomial greatest common divisor|greatest common divisors of such polynomials]]. ...ite article is used here since, when the coefficients belong to a [[unique factorization domain]], "greatest" refers to the [[preorder]] of divisibility, rather tha ...

...matters, see the [[list of mathematical logic topics]]. See also [[list of algorithms]], [[list of algorithm general topics]]. *[[Polynomial time]] ...

...ion|extending]] the field ''F'' (whence the "rational"), notably without [[factorization of polynomials|factoring polynomials]], this shows that whether two matrice ...quire factorization, and explicitly mentions "primary" when the form using factorization is meant. ...

...the '''special number field sieve''' (SNFS) is a special-purpose [[integer factorization]] algorithm. The [[general number field sieve]] (GNFS) was derived from it. ...t]]; for some time the [[Integer factorization records|records for integer factorization]] have been numbers factored by SNFS. ...

...l</math> is a divisor of the corresponding [[Division polynomials|division polynomial]] used in Schoof's algorithm, and it has significantly lower degree, <math> In the case of an Atkin prime, we can gain some information from the factorization pattern of <math>\Phi_l(X,j(E))</math> in <math>\mathbb{F}_l[X]</math>, whi ...

...ent [[algorithm]] for finding the [[Root of a function|root]]s of a real [[polynomial]] of arbitrary degree. The algorithm first appeared in the appendix of the See [[root-finding algorithm]] for other algorithms. ...

...rization]] algorithm, one of the family of [[algebraic-group factorisation algorithms]]. It was invented by [[Hugh C. Williams]] in 1982. ...it has a prime factor ''p'' such that any ''k''^th [[cyclotomic polynomial]] Φ_''k''(''p'') is [[Smooth number|smooth]].<ref>{{cite journal ...

...ical analysis|numerical algorithm]] for the numerical factorization of a [[polynomial]] and, ultimately, for finding its [[complex number|complex]] [[Root of a f ...omials. With those methods it is possible to construct a factor of a given polynomial <math> p(x) = x^n + p_{n-1}x^{n-1} + \cdots + p_0 </math> for any region of ...