polynomial love

# polynomial

## Definitions

### from The American Heritage® Dictionary of the English Language, 5th Edition.

• adjective Of, relating to, or consisting of more than two names or terms.
• noun A taxonomic designation consisting of more than two terms.
• noun An algebraic expression consisting of one or more summed terms, each term consisting of a constant multiplier and one or more variables raised to integral powers. For example, x2 − 5x + 6 and 2p3q + y are polynomials.
• noun An expression of two or more terms.

### from The Century Dictionary.

• Containing many names or terms.
• In Zoöl. and botany, Specifically, noting a method of nomenclature in which the technical names of species are not confined to two terms, the generic and the specific, as they are in the binomial system of nomenclature: as, a polynomial name; a polynomial system of nomenclature: contrasted with binomial and mononomial.
• Also multinomial, plurinominal.
• A technical name consisting of more than two terms; a-polyonym.
• An algebraical expression consisting of two or more terms united by addition: as, Also multinomial.

### from the GNU version of the Collaborative International Dictionary of English.

• noun (Alg.) An expression composed of two or more terms, connected by the signs plus or minus; as, a2 - 2ab + b2.
• adjective Containing many names or terms; multinominal.
• adjective Consisting of two or more words; having names consisting of two or more words

• adjective algebra Able to be described or limited by a polynomial.
• adjective taxonomy of a polynomial name or entity
• noun algebra An expression consisting of a sum of a finite number of terms, each term being the product of a constant coefficient and one or more variables raised to a non-negative integer power, such as .
• noun taxonomy A taxonomic designation (such as of a subspecies) consisting of more than two terms.

• noun a mathematical function that is the sum of a number of terms
• adjective having the character of a polynomial

## Etymologies

### from The American Heritage® Dictionary of the English Language, 4th Edition

[poly– + (bi)nomial.]

poly- + -nomial

## Examples

• In the above examples, each piecewise polynomial is defined on an interval with the same length and thus forms a uniform basis.

• The idea was to start a pendulum from several different heights in order to cover a range of velocities and then to use simultaneous algebraic equations to fit a two or three term polynomial to two or three lost-arc data-points, changing the exponents until the polynomial achieved good agreement with the other lost-arc data points.

Newton's Philosophiae Naturalis Principia Mathematica Smith, George 2007

• And there are tons of computational complexity classes above the standard P and NP that represent problems that deterministic and non-deterministic Turing Machines can solve in polynomial time.

• This isn't a trivial difference; a model that can solve a problem in polynomial time really is fundamentally more powerful than one that takes exponential time.

• In this equation, d is called the polynomial's degree.

DevX: Latest Published Articles Rod Stephens 2010

• In this equation, d is called the polynomial's degree.

DevX: Latest Published Articles Rod Stephens 2010

• Also, all such calculations are done modulo another polynomial, which is called the irreducible polynomial for the field.

Softpedia - Windows - All Softpedia Linux 2010

• We call a polynomial p (x) with integer coefficients irreducible if p (x) cannot be written as a product of two polynomials with integer coefficients neither of which is a constant.

• The degree of the polynomial is the degree of the term with highest degree.

• -- Key wireless functions such as polynomial generation and multiply - accumulate for de-spreading functions (up to 16 complex code MACs/cycle) -- High precision FFTs with adaptive range management