More polynomials should know that they are irreducible

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​847a4e7

Merge develop and 25227

[Julian Rüth]

New commits:

​57e6d44	Teach more rings about irreducible polynomials
​cf4bebf	Merge remote-tracking branch 'trac/u/saraedum/irreducible' into HEAD
​847a4e7	Merge develop and 25227

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​3cf6c75	Merge develop and 25227
​93e8d51	Add docstrings for _is_irreducible_univariate_polynomial()

[git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

​d2bc6fe

Add docstrings for _is_irreducible_univariate_polynomial()

[Frédéric Chapoton]

one doctest failing (typo)

and pyflakes plugin is not happy

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​cacb467	silence pyflakes
​2d43fe7	fix typo

[Julian Rüth]

New commits:

​cacb467	silence pyflakes
​2d43fe7	fix typo

---

New commits:

​cacb467	silence pyflakes
​2d43fe7	fix typo

[Frédéric Chapoton]

red branch => needs work

[Sebastian Oehms]

I rebase the implementation to 9.1.beta5 and insert a dependency to ticket #29266 which fixes a bug of #26421, since the latter one cause one of the doctest to fail.

Note, that the following doctests of the present ticket already worked under the previous stable release 8.1:

┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 8.1, Release Date: 2017-12-07                     │
│ Type "notebook()" for the browser-based notebook interface.        │
│ Type "help()" for help.                                            │
└────────────────────────────────────────────────────────────────────┘
sage: S.<t> = QQ[]
sage: R.<x> = S[]
sage: f = t*x
sage: f.is_irreducible()
False
sage: f = t*x + (t+1)
sage: f.is_irreducible()
True
sage: R.<x> = ZZ[]
sage: f = 2*x
sage: f.is_irreducible()
False
sage: f = 2*x + 3
sage: f.is_irreducible()
True
sage:

Therefore, they don't make clear what is improved by the corresponding implementation. I would replace these doctests by examples which don't work without the implementation of the ticket.

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New commits:

​ffa9302	Merge branch 'u/saraedum/25227' of git://trac.sagemath.org/sage into more_polynomials_irreducible_25227
​004c1c4	29266 initial version
​8977f19	Merge branch 'factorization_integral_domain_29266' into more_polynomials_irreducible_25227