irreducibility of a polynomial

asked 2016-07-26 22:54:08 +0200

nebuckandazzer
177 ●11 ●12 ●19

updated 2016-07-26 22:54:37 +0200

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 ( 2016-10-18 13:22:51 +0200 )edit

thanks @slelievre

nebuckandazzer ( 2016-10-20 23:21:28 +0200 )edit

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answered 2016-07-26 23:51:48 +0200

vdelecroix
7397 ●19 ●81 ●164 http://www.labri.fr/pe...

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 22:54:08 +0200

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Last updated: Jul 26 '16

irreducibility of a polynomial edit