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irreducibility of a polynomial

asked 2016-07-26 15:54:08 -0500

nebuckandazzer gravatar image

updated 2016-07-26 15:54:37 -0500

If f $f(x)$ is a polynomial, i know that the command $f.factor()$ gives the factorization of f. But I am interested in knowing whether the polynomial is irreducible or not, not its factors. Is there any command for that ?

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To display inline code, surround it within backticks .... This way you could get f.factor() instead of $f.factor()$.

slelievre gravatar imageslelievre ( 2016-10-18 06:22:51 -0500 )edit

thanks @slelievre

nebuckandazzer gravatar imagenebuckandazzer ( 2016-10-20 16:21:28 -0500 )edit

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answered 2016-07-26 16:51:48 -0500

There is

sage: R = ZZ['x']
sage: x = R.gen()
sage: (x^2 + 2*x + 1).is_irreducible()
False
sage: (x^2 - x + 1).is_irreducible()
True

Note that the irreducibility depends on the base ring (the integers in the example above).

sage: xZZ = polygen(ZZ)
sage: xQQ = polygen(QQ)
sage: (2*xZZ).is_irreducible()
False
sage: (2*xQQ).is_irreducible()
True
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Asked: 2016-07-26 15:54:08 -0500

Seen: 102 times

Last updated: Jul 26 '16