Rational Polynomial Coefficients (RPCs) provide a compact representation of a ground-to-image geometry, allowing photogrammetric processing without requiring...

leading coefficient an. The rational root theorem is a special case (for a single linear factor) of Gauss's lemma on the factorization of polynomials. The...

polynomial is a non-zero univariate polynomial (that is, a polynomial in a single variable) in which the leading coefficient (the nonzero coefficient...

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...

of a monic polynomial can alternatively be given as a polynomial expression in the coefficients of the polynomial. Symmetric polynomials also form an...

In mathematics, a polynomial is a mathematical expression consisting of indeterminates (also called variables) and coefficients, that involves only the...

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

also be defined as the monic polynomial with integer coefficients that is the minimal polynomial over the field of the rational numbers of any primitive nth-root...

computation of polynomials with integers or rational coefficients may be reduced to similar computations on integers and primitive polynomials. This is systematically...

improper. Any improper rational fraction can be expressed as the sum of a polynomial (possibly constant) and a proper rational fraction. In the first...

variables) with coefficients in another ring, often a field. Often, the term "polynomial ring" refers implicitly to the special case of a polynomial ring in one...

criterion gives a sufficient condition for a polynomial with integer coefficients to be irreducible over the rational numbers – that is, for it to not be factorizable...

homology, the Poincaré polynomial is defined as the generating function of its Betti numbers, via the polynomial where the coefficient of x n {\displaystyle...

j ( t ) {\displaystyle q_{ij}(t)} is a complex coefficient polynomial or complex coefficient rational function then so are the elements of its conjugate...

of polynomial GCD has been developed to satisfy the need for efficiency of computer algebra systems. Let p and q be polynomials with coefficients in an...

polynomial equation is usually preferred. Some but not all polynomial equations with rational coefficients have a solution that is an algebraic expression that...

computer algebra, factorization of polynomials or polynomial factorization expresses a polynomial with coefficients in a given field or in the integers...

both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers; they may be taken in any field...

number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients. For example, the golden ratio, (...

fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists...

{\tbinom {n}{k}}.} It is the coefficient of the xk term in the polynomial expansion of the binomial power (1 + x)n; this coefficient can be computed by the...

factorizations within the ring of polynomials with rational number coefficients (see factorization of polynomials). A commutative ring possessing the...

is a polynomial in the indeterminates x1, ..., xm, with integer coefficients, or coefficients in some fixed field, often the field of rational numbers...

is an improvement of this method. For polynomials whose coefficients are exactly given as integers or rational numbers, there is an efficient method to...

rational numbers; a rational polynomial may be a polynomial with rational coefficients, although the term "polynomial over the rationals" is generally preferred...

essentially the resultant of a polynomial and its derivative. The resultant of two polynomials with rational or polynomial coefficients may be computed efficiently...

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

Equivalently, a polynomial matrix is a polynomial whose coefficients are matrices. A univariate polynomial matrix P of degree p is defined as: P = ∑...

polytope tP. Ehrhart showed in 1962 that L is a rational polynomial of degree d in t, i.e. there exist rational numbers L 0 ( P ) , … , L d ( P ) {\displaystyle...

In mathematics, a univariate polynomial of degree n with real or complex coefficients has n complex roots (if counted with their multiplicities). They...