polynomial equation - definizione. Che cos'è polynomial equation
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Cosa (chi) è polynomial equation - definizione

MATHEMATICAL CONCEPT
Polynomial equation; Algebraic equations; Polynomial equations; Algebraic root; Solutions of algebraic equations; Solutions of polynomial equations; Methods for solving polynomial equations; Methods for solving algebraic equations

Sextic         
POLYNOMIAL EQUATION OF DEGREE SIX
Sextic; Sextic function; Sextic polynomial; Hexic equation; Sixth degree equation
·adj Of the sixth degree or order.
II. Sextic ·noun A quantic of the sixth degree.
HOMFLY polynomial         
TWO-VARIABLE KNOT POLYNOMIAL, GENERALIZING THE JONES AND ALEXANDER POLYNOMIALS
HOMFLY(PT) polynomial; HOMFLY; LYMPHTOFU polynomial; HOMFLYPT polynomial; Homfly polynomial; FLYPMOTH polynomial; HOMFLY invariant
In the mathematical field of knot theory, the HOMFLY polynomial or HOMFLYPT polynomial, sometimes called the generalized Jones polynomial, is a 2-variable knot polynomial, i.e.
Degree of a polynomial         
HIGHEST POWER OF THE VARIABLES OCCURRING IN A MONOMIAL IN A GIVEN POLYNOMIAL
Total degree; Polynomial degree; Hectic equation; Decic equation; Nonic equation; Octic equation; Octic function; Octic; Degree (polynomials)
In mathematics, the 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 sum of the exponents of the variables that appear in it, and thus is a non-negative integer.

Wikipedia

Algebraic equation

In mathematics, an algebraic equation or polynomial equation is an equation of the form

P = 0 {\displaystyle P=0}

where P is a polynomial with coefficients in some field, often the field of the rational numbers. For many authors, the term algebraic equation refers only to univariate equations, that is polynomial equations that involve only one variable. On the other hand, a polynomial equation may involve several variables. In the case of several variables (the multivariate case), the term polynomial equation is usually preferred to algebraic equation.

For example,

x 5 3 x + 1 = 0 {\displaystyle x^{5}-3x+1=0}

is an algebraic equation with integer coefficients and

y 4 + x y 2 x 3 3 + x y 2 + y 2 + 1 7 = 0 {\displaystyle y^{4}+{\frac {xy}{2}}-{\frac {x^{3}}{3}}+xy^{2}+y^{2}+{\frac {1}{7}}=0}

is a multivariate polynomial equation over the rationals.

Some but not all polynomial equations with rational coefficients have a solution that is an algebraic expression that can be found using a finite number of operations that involve only those same types of coefficients (that is, can be solved algebraically). This can be done for all such equations of degree one, two, three, or four; but for degree five or more it can only be done for some equations, not all. A large amount of research has been devoted to compute efficiently accurate approximations of the real or complex solutions of a univariate algebraic equation (see Root-finding algorithm) and of the common solutions of several multivariate polynomial equations (see System of polynomial equations).