Difference between revisions of "Polynomial"
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| − | A polynomial is an [[Algebra|algebraic]] mathematical object. It is any element of a polynomial ring, that is a [[Ring_(mathematics)|ring]] R with one or more [[ | + | A polynomial is an [[Algebra|algebraic]] mathematical object. It is any element of a polynomial ring, that is a [[Ring_(mathematics)|ring]] R with one or more [[variable]]s adjoined. Note that R need not be [[Commutativity|commutative]], nor have [[identity]], nor be [[Associativity|associative]]. |
| − | Examples of polynomials include 0, x and 5xy<sup>2</sup>. Every element of R is also a polynomial, a [[ | + | Examples of polynomials include 0, x and 5xy<sup>2</sup>. Every element of R is also a polynomial, a [[constant]]. |
Polynomials can be evaluated to return an element of the ring R. | Polynomials can be evaluated to return an element of the ring R. | ||
| − | Some [[ | + | Some [[algorithm]]s are said to perform in polynomial time. There are algorithms which can factor polynomials in polynomial time. |
[[Category:Algebra]] | [[Category:Algebra]] | ||
Revision as of 01:47, February 26, 2008
A polynomial is an algebraic mathematical object. It is any element of a polynomial ring, that is a ring R with one or more variables adjoined. Note that R need not be commutative, nor have identity, nor be associative.
Examples of polynomials include 0, x and 5xy2. Every element of R is also a polynomial, a constant.
Polynomials can be evaluated to return an element of the ring R.
Some algorithms are said to perform in polynomial time. There are algorithms which can factor polynomials in polynomial time.