Trac #13781: make all doctests use NTL implementation
15954: replace TypeError with more informative message
Merge branch 'develop' into t/13781/ticket/13781

* develop: (1780 commits)
  Updated Sage version to 6.3.beta3
  Support default arguments when starting the notebook server Warn if starting fails
  Trac #13422: Reintroduce a warning (but not an error) when the user supplies too few ticks to disambiguate the plot scale.
  Trac 8828: fix two other LaTeX errors
  Trac 8828: \eps should be \epsilon
  proofreading and fixing doctest failures
  16420: little tweaks: use module_morphism, sum_of_monomials, ...
  Review tweaks for Young's lattice and RSK thematic tutorial.
  Trac #13422: Reviewer suggestions.
  trac #14953: Moving the .html to EXT_CODE and using DOCTEST_MODE
  16405: fixed trivial doctest failure and ReST indentation
  auto expand log scale to include at least two major ticks
  trac #16323: several fix + doc
  New section for algebraic combinatorics tutorial on Young's lattice and RSK
  fix libgap conversion of huge integers
  changes necessary for the updated gap_packages tarball, which includes GAP's AtlasRep package now - necessary to fix GAP's TomLib package, but also useful on its own
  trac #16323: DF -> difference_family, change errors and more doc
  Trac #14209 - Forget assumptions from earlier doctest
  Trac #14209 - verify Maxima fix for doing improper integral twice changing answer
  Trac #15386 - document that Maxima 5.33 fixes this limit
  ...
Merge branch 't/15954/polyring_fpt_coerce_cannot_handle_polynomial_modn_dense_ntl' into t/13781/ticket/13781

* t/15954/polyring_fpt_coerce_cannot_handle_polynomial_modn_dense_ntl:
  15954: replace TypeError with more informative message
13781: fix doctest
13781: change all 'ntl' to 'NTL'
Trac #13781: Doctests in rings/polynomial/polynomial_modn_dense_ntl.pyx test the wrong implementation

A common doctest in `polynomial_modn_dense_ntl.pyx` goes something like
this:

{{{
sage: R.<x> = Integers(100)[]
sage: (x + 5) * 3
3*x + 15
}}}

At some point, I guess, this used to construct a
Polynomial_dense_modn_ntl_zz. But now it looks like the default
implementation uses flint:

{{{
sage: R.<x> = Integers(100)[]
sage: type((x + 5) * 3)
<type
'sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint'>
}}}

So a large number of the functions in this file are actually untested,
because they're testing the flint implementation instead of the ntl one.
It looks like this is the workaround:

{{{
sage: R.<x> = PolynomialRing(Integers(100), implementation='ntl')
sage: type((x + 5) * 3)
<type 'sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_
modn_ntl_zz'>
}}}

URL: http://trac.sagemath.org/13781
Reported by: mjo
Ticket author(s): Ralf Stephan
Reviewer(s): Martin Albrecht