of the polynomial. Some of these geometrical properties are related to a single polynomial, such as upper bounds on the absolute values of the roots,...

mathematics, Descartes' rule of signs, described by René Descartes in his La Géométrie, counts the roots of a polynomial by examining sign changes in...

and the zeroes of its derivative. See also geometrical properties of polynomial roots. A cubic polynomial has three zeroes in the complex number plane...

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

zn = z0 = 1 are all of the nth roots of unity, since an nth-degree polynomial equation over a field (in this case the field of complex numbers) has at...

central concepts in algebra and algebraic geometry. The word polynomial joins two diverse roots: the Greek poly, meaning "many", and the Latin nomen, or "name"...

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

"Consideration of the objections raised against the geometrical representation of the square roots of negative quantities". Philosophical Transactions of the Royal...

} Given any polynomial p, a root of p is a number y such that p(y) = 0. For example, the nth roots of x are the roots of the polynomial (in y) y n −...

study by means of algebraic methods of some geometrical shapes, called algebraic sets, and defined as common zeros of multivariate polynomials. Algebraic...

the discriminant of a polynomial is a quantity that depends on the coefficients and allows deducing some properties of the roots without computing them...

Finding the roots of polynomials is a long-standing problem that has been extensively studied throughout the history and substantially influenced the development...

errors, and the roots of a polynomial can be an extremely sensitive function of the coefficients (as exemplified by Wilkinson's polynomial). Even for matrices...

this way he hoped to apply the powerful tools of analysis and algebra for studying the roots of polynomials to the combinatorial coloring problem. Hassler...

terms of square roots of numbers in the coefficient field. Instead, define the 2-root R(c) of c to be a root of the polynomial x2 + x + c, an element of the...

{p}}_{1}z^{n-1}} have the same number of roots in | z | < 1. {\displaystyle |z|<1.} Geometrical properties of polynomial roots Cohn, A (1922). "Über die Anzahl...

least one real root (this is true for all odd-degree polynomial functions). All of the roots of the cubic equation can be found by the following means:...

which a polynomial can be factored into its roots is known as the splitting field of the polynomial. The Galois group of a polynomial is the set of all transformations...

In numerical analysis, polynomial interpolation is the interpolation of a given data set by the polynomial of lowest possible degree that passes through...

multiplicity, exactly n complex roots. The equivalence of the two statements can be proven through the use of successive polynomial division. Despite its name...

to argue about their algebraic properties. Recently (around 2016), the polynomial method has led to the development of remarkably simple solutions to...

solution of period four fixed points functions in bifurcation diagram Geometrical properties of polynomial roots Alan F. Beardon, Iteration of Rational...

all polynomial equations could be solved algebraically (that is, that all roots of a polynomial could be expressed in terms of a finite number of radicals...

location polynomial. The roots of the error location polynomial can be found by exhaustive search. The error locators Xk are the reciprocals of those roots. The...

non-real roots (in the average, a polynomial of degree n has n complex roots, and only log n real roots; see Geometrical properties of polynomial roots § Real...

mathematics, Lill's method is a visual method of finding the real roots of a univariate polynomial of any degree. It was developed by Austrian engineer...

for all usual arithmetic operations, including the computation of the roots of a polynomial, and thus form a real closed field that contains the real algebraic...

field of meromorphic functions on X. The function field of an algebraic variety X (a geometric object defined as the common zeros of polynomial equations)...

many mathematical structures such as numbers, geometric shapes and polynomial roots. Because the concept of groups is ubiquitous in numerous areas both...

"revolutionary"; results which seemed inextricably connected to properties of polynomial rings were shown to follow from a single axiom. Artin, inspired...