Polynomial in a sentence

He realized that the algebraic solution to a polynomial equation is related to the structure of a group of permutations associated with the roots of the polynomial, the Galois group of the polynomial.

If a polynomial time algorithm calls as a subroutine polynomially many polynomial time algorithms, the resulting algorithm is still polynomial time.

If one or more are found, they can be factored out of the polynomial, resulting in a polynomial of lower degree whose roots are also roots of the original polynomial.

Once the sender has constructed the polynomial in some way, however, instead of sending the values of at all points, the sender computes some related polynomial of degree at most for and sends the coefficients of that polynomial.

Polynomial functions seeAlso A polynomial function is a function that can be defined by evaluating a polynomial.

Polynomial interpolation Plot of the data with polynomial interpolation applied main Polynomial interpolation is a generalization of linear interpolation.

A polynomial of degree zero is a constant polynomial or simply a constant.

Applications Calculus main seeAlso The simple structure of polynomial functions makes them quite useful in analyzing general functions using polynomial approximations.

Conversely, if the Turing Machine is expected polynomial-time (for any given x), then a considerable fraction of the runs must be polynomial-time bounded, and the coin sequence used in such a run will be a witness.

Division of a polynomial by a number, however, yields another polynomial.

Example: let f be a polynomial in one variable; i.e., an element in a polynomial ring R. Then is an element in and is divisible by h in that ring.

Examples The Maclaurin series for any polynomial is the polynomial itself.

Factor error locator polynomial Now that you have the polynomial, its roots can be found in the form by brute force for example using the Chien search algorithm.

For example, in computational complexity theory the phrase polynomial time means that the time it takes to complete an algorithm is bounded by a polynomial function of some variable, such as the size of the input.

For example, : is a univariate algebraic (polynomial) equation with integer coefficients and : is a multivariate polynomial equation over the rational numbers.

Further, for a quadratic polynomial with rational coefficients, it factors over the rationals if and only if the discriminant – which is necessarily a rational number, being a polynomial in the coefficients – is in fact a square.

Important types include: * An algebraic equation or polynomial equation is an equation in which both sides are polynomials (see also system of polynomial equations ).

Integers can be treated as the value of a polynomial evaluated specifically at the number base, with the coefficients of the polynomial corresponding to the digits in that base.

In the case of short proofs (of length bounded by a polynomial in the size of the input) which can be efficiently verified (V is a polynomial-time deterministic Turing machine), the string w is called a witness.

It follows that real algebraic geometry is not only the study of the real algebraic varieties, but has been generalized to the study of the semi-algebraic sets, which are the solutions of systems of polynomial equations and polynomial inequalities.