theory of equations, the principal form of an irreducible polynomial of degree at least three is a polynomial of the same degree n without terms of degrees...

degree of a polynomial is the highest of the degrees of the polynomial's monomials (individual terms) with non-zero coefficients. The degree of a term is...

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)}...

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

set of polynomials that annihilate a given A form an ideal I in C[x], the principal ideal domain of polynomials with complex coefficients. The monic element...

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...

In linear algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues...

mathematics, especially in the field of algebra, a polynomial ring or polynomial algebra is a ring formed from the set of polynomials in one or more indeterminates...

notably without factoring polynomials, this shows that whether two matrices are similar does not change upon field extensions. The form is named after German...

named after Étienne Bézout who proved it for polynomials, is the following theorem: Bézout's identity—Let a and b be integers with greatest common divisor...

of a polynomial with degree 5 or more. (Generality matters because any polynomial with degree n {\displaystyle n} is the characteristic polynomial of...

^{2}\mid x=0\}} is a principal ideal because it can be written as ⟨ x ⟩ {\displaystyle \langle x\rangle } (the set of polynomials divisible by x {\displaystyle...

In statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable...

principal (that is, is formed by the multiples of a single element). Some authors such as Bourbaki refer to PIDs as principal rings. Principal ideal domains are...

strongly polynomial time was first developed; that is, the number of steps to compute the Hermite normal form is bounded above by a polynomial in the dimensions...

is the minimal polynomial, and the product of invariant factors is the characteristic polynomial. Combined with a standard matrix form for K [ T ] / p...

polynomial, in 1923. In 1969, John Conway showed a version of this polynomial, now called the Alexander–Conway polynomial, could be computed using a skein...

of all of its principal minors. Definite quadratic forms lend themselves readily to optimization problems. Suppose the matrix quadratic form is augmented...

A system of polynomial equations (sometimes simply a polynomial system) is a set of simultaneous equations f1 = 0, ..., fh = 0 where the fi are polynomials...

spectrum of the polynomial ring over a field k: such a polynomial ring is known to be a principal ideal domain and the irreducible polynomials are the prime...

In mathematics, a Tschirnhaus transformation, also known as Tschirnhausen transformation, is a type of mapping on polynomials developed by Ehrenfried...

mathematics, a field F is algebraically closed if every non-constant polynomial in F[x] (the univariate polynomial ring with coefficients in F) has a root in...

is principal (that is, a Bézout domain) satisfies (ACCP) if and only if it is a principal ideal domain. The ring Z+XQ[X] of all rational polynomials with...

In mathematics, Eisenstein's criterion gives a sufficient condition for a polynomial with integer coefficients to be irreducible over the rational numbers...

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...

bound of the degrees occurring in a solution, one may write the unknown polynomials as polynomials with unknown coefficients. Then, as two polynomials are...

the cotangent space over a fixed point x of X, the symbol σ P {\displaystyle \sigma _{P}} defines a homogeneous polynomial of degree k in T x ∗ X {\displaystyle...

every polynomial equation of degree one or higher. Complex numbers thus form an algebraically closed field, where any polynomial equation has a root....

polynomial is homogeneous one can write down concretely any k-form of the closed connection ω as some 2k-form of the associated curvature form Ω of ω...

matrix by computing the Smith normal form, over the ring of polynomials, of the matrix (with polynomial entries) XIn − A (the same one whose determinant defines...