Irreducible Polynomial

irreducible polynomial

[‚ir·ə′dü·sə·bəl ‚päl·ə′nō·mē·əl] (mathematics) A polynomial is irreducible over a field K if it cannot be written as the product of two polynomials of lesser degree whose coefficients come from K. Also known as irreducible function.

Irreducible Polynomial

a polynomial that cannot be factored into factors of lower degree. The possibility of factoring a polynomial into factors and the irreducibility property depend on the numbers that can be coefficients of the polynomial. Thus, the polynomial x³ + 2 is irreducible if only rational numbers are admitted as coefficients; but it is factored into the product of two irreducible polynomials

if any real numbers can be taken as the coefficients and into the product of three factors

if complex numbers are the coefficients. In the general case, the concept of irreducibility is defined for polynomials with coefficients belonging to an arbitrary field. A polynomial with rational coefficients that cannot be factored into factors of lower degree with rational coefficients is often called an irreducible polynomial.

REFERENCE

Kurosh, A. G. Kurs vysshei algebry, 9th ed. Moscow, 1968.

单词	irreducible polynomial
释义	Irreducible Polynomial irreducible polynomial [‚ir·ə′dü·sə·bəl ‚päl·ə′nō·mē·əl] (mathematics) A polynomial is irreducible over a field K if it cannot be written as the product of two polynomials of lesser degree whose coefficients come from K. Also known as irreducible function. Irreducible Polynomial a polynomial that cannot be factored into factors of lower degree. The possibility of factoring a polynomial into factors and the irreducibility property depend on the numbers that can be coefficients of the polynomial. Thus, the polynomial x³ + 2 is irreducible if only rational numbers are admitted as coefficients; but it is factored into the product of two irreducible polynomials if any real numbers can be taken as the coefficients and into the product of three factors if complex numbers are the coefficients. In the general case, the concept of irreducibility is defined for polynomials with coefficients belonging to an arbitrary field. A polynomial with rational coefficients that cannot be factored into factors of lower degree with rational coefficients is often called an irreducible polynomial. REFERENCE Kurosh, A. G. Kurs vysshei algebry, 9th ed. Moscow, 1968.
随便看	frederic maitland frederic march frederic mistral frederico fellini frederico garcia lorca frederic ogden nash frederic remington art museum frederic riesz frederic sanger frederic seebohm frederic seebohm (disambiguation) frederiction fredericton fredericton, canada fredericton district soccer association fredericton, nb fredericton, new brunswick fredericton, new brunswick, canada fredericton, new brunswick, canada - fredericton municipal frederic william farrar frederic william goudy frederic william maitland frederik frederika bremer frederik hendrik