generic polynomial refers usually to a polynomial whose coefficients are indeterminates. For example, if a, b, and c are indeterminates, the generic polynomial...

point that contains all other points Generic polynomial, a polynomial whose coefficients are indeterminates Generic property, a formal definition of a property...

statements, "A generic polynomial does not have a root at zero," or "A generic square matrix is invertible." As another example, a generic property of a...

resultant of two polynomials is a polynomial expression of their coefficients that is equal to zero if and only if the polynomials have a common root...

mathematics, a polynomial lemniscate or polynomial level curve is a plane algebraic curve of degree 2n, constructed from a polynomial p with complex coefficients...

The Chebyshev polynomials are two sequences of orthogonal polynomials related to the cosine and sine functions, notated as T n ( x ) {\displaystyle T_{n}(x)}...

century, is unsolved. There are some permutation groups for which generic polynomials are known, which define all algebraic extensions of Q {\displaystyle...

impossibility theorem) states that there is no solution in radicals to general polynomial equations of degree five or higher with arbitrary coefficients. Here,...

is in GenP (generically polynomial time) if it never gives incorrect answers and if it gives correct answers in polynomial time on a generic set of inputs...

doi:10.2478/jee-2018-0059, S2CID 115440420 "Fast CRC Computation for Generic Polynomials Using PCLMULQDQ Instruction" (PDF). www.intel.com. 2009. Retrieved...

non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since...

it appears in the multiset. For example, the number of times a given polynomial has a root at a given point is the multiplicity of that root. The notion...

precisely, it is a polynomial function of the coefficients of the original polynomial. The discriminant is widely used in polynomial factoring, number...

gen-kill problems, or locally separable problems. Such problems have generic polynomial-time solutions. In addition to the reaching definitions and live variables...

abbreviated as GCD) of two polynomials is a polynomial, of the highest possible degree, that is a factor of both the two original polynomials. This concept is analogous...

"complete", which in modern terminology would translate to generic. Since with generic polynomials, there are no points at infinity, and all multiplicities...

quadratic polynomial, the only ways to rearrange two roots are to either leave them be or to transpose them, so solving a quadratic polynomial is simple...

of any generic polynomial of arbitrary degree [F. Calogero, “Novel differential algorithm to evaluate all the zeros of any generic polynomial”, J. Nonlinear...

det(A+tI) is a polynomial in t with degree at most n, so it has at most n roots. Note that the ijth entry of adj((A+tI)(B)) is a polynomial of at most order...

(xy-yx)^{2}=-\det(xy-yx)I} for any 2-by-2-matrices x and y. Generic matrix ring Formanek, Edward (1991). The polynomial identities and invariants of n×n matrices. Regional...

m = 1 then F 1 {\displaystyle F_{1}} is a polynomial ring in one variable. For example, a central polynomial is an element of the ring F n {\displaystyle...

non-linear irreducible polynomials. In this case, the spectrum consists of one closed point for each monic irreducible polynomial, and a generic point corresponding...

root of a polynomial is sometimes said to be degenerate if it is a multiple root, since generically the n roots of an nth degree polynomial are all distinct...

titled "Polynomial Codes over Certain Finite Fields". The original encoding scheme described in the Reed and Solomon article used a variable polynomial based...

Archived from the original on 2019-08-06. "Fast CRC Computation for Generic Polynomials Using PCLMULQDQ" (PDF). Vlad Krasnov (2015-07-08). "Fighting Cancer:...

This solution does not count as polynomial time in complexity theory because B − A {\displaystyle B-A} is not polynomial in the size of the problem, which...

−1.) This polynomial helps to solve some basic questions; see below. Another polynomial associated with A is the Whitney-number polynomial wA(x, y), defined...

} For a generic 2 × 2 matrix, A = ( a b c d ) , {\displaystyle A={\begin{pmatrix}a&b\\c&d\\\end{pmatrix}},} the characteristic polynomial is given by...

geometry and computational geometry, general position is a notion of genericity for a set of points, or other geometric objects. It means the general...

Consider the submodule K consisting of all those polynomials with zero constant term. Since every polynomial contains only finitely many terms whose coefficients...