mathematics, the ring of polynomial functions on a vector space V over a field k gives a coordinate-free analog of a polynomial ring. It is denoted by...

polynomial rings. A closely related notion is that of the ring of polynomial functions on a vector space, and, more generally, ring of regular functions on an...

. This function is a homeomorphism (for the Zariski topology of the affine space and of the spectrum of the ring of polynomial functions) of the affine...

numerical analysis to approximate other functions. In advanced mathematics, polynomials are used to construct polynomial rings and algebraic varieties, which are...

elements are neither polynomials nor functions). The ring of quasisymmetric functions, denoted QSym, can be defined over any commutative ring R such as the integers...

fundamental theorems of invariant theory concern the generators and relations of the ring of invariants in the ring of polynomial functions for classical groups...

elementary symmetric polynomials are one type of basic building block for symmetric polynomials, in the sense that any symmetric polynomial can be expressed...

equating the function to 0", and the study of zeros of functions is exactly the same as the study of solutions of equations. Every real polynomial of odd degree...

the ring of symmetric functions is a specific limit of the rings of symmetric polynomials in n indeterminates, as n goes to infinity. This ring serves...

which could be regarded as the ring of polynomial functions f : V → k {\displaystyle f:V\to k} , the global regular functions on V. Grothendieck's innovation...

digital data. Blocks of data entering these systems get a short check value attached, based on the remainder of a polynomial division of their contents. On...

field, the field of fractions of the ring of the polynomial functions over K. A function f {\displaystyle f} is called a rational function if it can be written...

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...

homogeneous function of the coordinates over any basis. A polynomial of degree 0 is always homogeneous; it is simply an element of the field or ring of the 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)}...

particular the ring of symmetric functions, are of great importance in combinatorics and in representation theory. The following polynomials in two variables...

exponential polynomials are functions on fields, rings, or abelian groups that take the form of polynomials in a variable and an exponential function. An exponential...

V_{n}^{2}-\Delta \rangle } , which is the ring of alternating polynomials. Given a polynomial, the Vandermonde polynomial of its roots is defined over the splitting...

x , y ] / ( f ) {\displaystyle \mathbb {C} [x,y]/(f)} is the ring of polynomial functions on the curve { ( x , y ) : f ( x , y ) = 0 } {\displaystyle \{(x...

power sum symmetric polynomials are a type of basic building block for symmetric polynomials, in the sense that every symmetric polynomial with rational coefficients...

the nature of the coefficients that are accepted for the possible factors, that is, the ring to which the coefficients of the polynomial and its possible...

commutative algebra, a Gröbner basis is a particular kind of generating set of an ideal in a polynomial ring K [ x 1 , … , x n ] {\displaystyle K[x_{1},\ldots...

mathematics, an algebraic function is a function that can be defined as the root of an irreducible polynomial equation. Algebraic functions are often algebraic...

may also be non-numerical objects such as polynomials, square matrices, functions, and power series. A ring may be defined as a set that is endowed with...

mathematics, a permutation polynomial (for a given ring) is a polynomial that acts as a permutation of the elements of the ring, i.e. the map x ↦ g ( x )...

homogeneous symmetric polynomials are a specific kind of symmetric polynomials. Every symmetric polynomial can be expressed as a polynomial expression in complete...

regular functions on the affine n-space may be identified with the ring of polynomial functions in n variables over k. Therefore, the set of the regular...

denotes the ring of all polynomials in the variable X with coefficients in the real numbers R, and C denotes the complex numbers, then the function f : R[X]...

polynomial ring Q [ t ] {\displaystyle \mathbb {Q} [t]} of polynomials with rational number coefficients, the subring of integer-valued polynomials is...

representation of positive polynomials as a sum of squares of rational functions Metric tensor Polynomial ring Polynomial SOS, the representation of a non-negative...