Algebraic number: Difference between revisions
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{{Wikipedia}} | {{Wikipedia|Algebraic number}} | ||
A [http://mathworld.wolfram.com/UnivariatePolynomial.html univariate polynomial] ''a''<sub>0</sub>''x''<sup>''n''</sup> + ''a''<sub>1</sub>''x''<sup>(''n'' - 1)</sup> + … + ''a''<sub>''n''</sub> whose coefficients ''a''<sub>''i''</sub> are integers (or equivalently, rational numbers) has roots which are known as '''algebraic numbers'''. A root is a value ''r'' for which the [[Wikipedia: Polynomial #Polynomial functions|polynomial function]] ''f'' (''x'') = ''a''<sub>0</sub>''x''<sup>''n''</sup> + ''a''<sub>1</sub>''x''<sup>(''n'' - 1)</sup> + … + ''a''<sub>''n''</sub> satisfies ''f'' (''r'') = 0. If ''r'' is a [[Wikipedia: Real number|real number]], it is a ''real algebraic number''. | A [http://mathworld.wolfram.com/UnivariatePolynomial.html univariate polynomial] ''a''<sub>0</sub>''x''<sup>''n''</sup> + ''a''<sub>1</sub>''x''<sup>(''n'' - 1)</sup> + … + ''a''<sub>''n''</sub> whose coefficients ''a''<sub>''i''</sub> are integers (or equivalently, rational numbers) has roots which are known as '''algebraic numbers'''. A root is a value ''r'' for which the [[Wikipedia: Polynomial #Polynomial functions|polynomial function]] ''f'' (''x'') = ''a''<sub>0</sub>''x''<sup>''n''</sup> + ''a''<sub>1</sub>''x''<sup>(''n'' - 1)</sup> + … + ''a''<sub>''n''</sub> satisfies ''f'' (''r'') = 0. If ''r'' is a [[Wikipedia: Real number|real number]], it is a ''real algebraic number''. | ||