Difference between revisions of "Polynomial"
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| − | A | + | A polynomial in one variable <math>x</math> is a function <math>f(x)</math> of the form: |
| − | + | <math> | |
| + | f(x) = a_n x^n+a_{n-1}x^{n-1}+...+a_1 x + a_0 | ||
| + | </math> | ||
| − | + | In elementary mathematics, the coefficients <math>a_i</math> are typically chosen to be real or complex numbers. However, it makes sense to define a polynomial with coefficients in any [[ring]]. | |
| − | Some [[algorithm]]s are said to perform in polynomial time. There are algorithms which can factor polynomials in polynomial time. | + | The largest power of <math>x</math> that appears in the polynomial is called the degree of the polynomial. |
| + | |||
| + | *Example: <math>f(x) = 4x^3-3x+1</math> is a degree 3 polynomial with integer coefficients. | ||
| + | |||
| + | A polynomial in two variables <math>x,y</math> is, similarly, a finite sum | ||
| + | |||
| + | <math> | ||
| + | \sum a_{ij}x^i y^j | ||
| + | </math>, | ||
| + | where the coefficients <math>a_{ij}</math> are elements of some [[ring]]. Polynomials in 3 or more variables are defined similarly. | ||
| + | |||
| + | Some [[algorithm]]s are said to perform in polynomial time. There are algorithms which can factor polynomials in polynomial time.{{fact}} | ||
[[Category:Algebra]] | [[Category:Algebra]] | ||
Revision as of 02:59, July 6, 2008
A polynomial in one variable 
is a function 
of the form:
In elementary mathematics, the coefficients 
are typically chosen to be real or complex numbers. However, it makes sense to define a polynomial with coefficients in any ring.
The largest power of that appears in the polynomial is called the degree of the polynomial.
- Example:
is a degree 3 polynomial with integer coefficients.
A polynomial in two variables 
is, similarly, a finite sum
,
where the coefficients 
are elements of some ring. Polynomials in 3 or more variables are defined similarly.
Some algorithms are said to perform in polynomial time. There are algorithms which can factor polynomials in polynomial time.[Citation Needed]
