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...

Sextic equation (degree = 6) Septic equation (degree = 7) System of linear equations System of polynomial equations Linear Diophantine equation Linear...

equations, System of bilinear equations, System of polynomial equations, System of differential equations, or a System of difference equations Simultaneous...

the theory of equations is the study of algebraic equations (also called "polynomial equations"), which are equations defined by a polynomial. The main...

mathematics, a system of linear equations or a system of polynomial equations is considered underdetermined if there are fewer equations than unknowns...

multivariate polynomial equations (see System of polynomial equations). A system of linear equations (or linear system) is a collection of linear equations involving...

have fewer equations than unknowns and involve finding integers that solve all equations simultaneously. Because such systems of equations define algebraic...

in the argument of a function which is not a polynomial of degree one. In other words, in a nonlinear system of equations, the equation(s) to be solved...

solutions. See System of polynomial equations. The special case where all the polynomials are of degree one is called a system of linear equations, for which...

between polynomials of several variables, in order to solve systems of polynomial equations. Classical elimination theory culminated with the work of Francis...

basis computation is one of the main practical tools for solving systems of polynomial equations and computing the images of algebraic varieties under...

In mathematics, a system of bilinear equations is a special sort of system of polynomial equations, where each equation equates a bilinear form with a...

algebraic variety is defined as the set of solutions of a system of polynomial equations over the real or complex numbers. Modern definitions generalize this...

study of systems of polynomial equations in several variables, the subject of algebraic geometry begins with finding specific solutions via equation solving...

mathematics, a system of equations is considered overdetermined if there are more equations than unknowns.[citation needed] An overdetermined system is almost...

In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same variables. For example...

number theory, the Chevalley–Warning theorem implies that certain polynomial equations in sufficiently many variables over a finite field have solutions...

root algorithm System of polynomial equations – Roots of multiple multivariate polynomials Kantorovich theorem – About the convergence of Newton's method...

properties. An algebraic surface is a two-dimensional set of solutions of a system of polynomial equations. Some mathematical spaces have additional arithmetical...

He showed how to convert a problem stated verbally into a system of polynomial equations (up to the 14th order), by using up to four unknowns: 天 Heaven...

dimension of the algebraic set defined by a given system of polynomial equations. Moreover, the dimension is not changed if the polynomials of the Gröbner...

of differential equations and operators without computing the solutions, similarly as polynomial algebras are used for the study of algebraic varieties...

In the latter, a subset V of Cn is closed if and only if it consists of all solutions to some system of polynomial equations. Since any such V also is...

theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter...

amounts to eliminate variables between polynomial equations. In fact, given a system of polynomial equations, which is homogeneous in some variables...

the 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...

1992 described an algorithm which finds all polynomial solutions of those recurrence equations with polynomial coefficients. The algorithm computes a degree...

roots. (This is also true of quadratic (second-degree) and quartic (fourth-degree) equations, but not for higher-degree equations, by the Abel–Ruffini theorem...

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

numerical analysis to study and manipulate the solutions of systems of polynomial equations. The primary computational method used in numerical algebraic...