first try for trac issue #15686:
Improve documentation of constraint_generation in MixedIntegerLinearProgramming
second try for trac issue #15686
first pass at #15722
third try for trac issue #15686
Added special case of q_int(0).
trac #15805 : small enhancement
Trac 13274: Added QQ._factor_univariate_polynomial
Added lift() method.
Merge branch 'develop' into ticket/13274
Added _factor_univariate_polynomial() for QQbar and AA
Added _factor_univariate_polynomial() for CDF and RDF
Trac #13274: Add QQ._factor_univariate_polynomial()

As a part of #11731, transfer the code which does the factorization over
{{{QQ}}} from
{{{sage.rings.polynomial.polynomial_element.Polynomial.factor()}}} to
{{{QQ._factor_univariate_polynomial()}}}.

URL: http://trac.sagemath.org/13274
Reported by: saraedum
Ticket author(s): Julian Rueth
Reviewer(s): Peter Bruin
Trac #13275: Add QQbar._factor_univariate_polynomial()

As a part of #11731, transfer the code which does the factorization over
{{{QQbar}}} and {{{AA}}} from
{{{sage.rings.polynomial.polynomial_element.Polynomial.factor()}}} to
{{{QQbar._factor_univariate_polynomial()}}} and
{{{AA._factor_univariate_polynomial()}}} respectively.

URL: http://trac.sagemath.org/13275
Reported by: saraedum
Ticket author(s): Julian Rueth
Reviewer(s): Peter Bruin
Trac #13276: Add CDF._factor_univariate_polynomial()

As a part of #11731, transfer the code which does the factorization over
{{{CDF}}} and {{{RDF}}} from
{{{sage.rings.polynomial.polynomial_element.Polynomial.factor()}}} to
{{{CDF._factor_univariate_polynomial()}}} and
{{{RDF._factor_univariate_polynomial()}}} respectively.

This will also fix the following bug:
{{{
sage: R.<x> = CDF[]
sage: (x^2).factor()
AssertionError
}}}

URL: http://trac.sagemath.org/13276
Reported by: saraedum
Ticket author(s): Julian Rueth
Reviewer(s): Peter Bruin
Trac #15686: Improve documentation of constraint_generation in MixedIntegerLinearProgramming

As prompted by http://ask.sagemath.org/question/3410, this ticket is
meant for discussion to improve the documentation of the
`constraint_generation` option of MixedIntegerLinearProgramming.

From the ref:
http://www.sagemath.org/doc/reference/numerical/sage/numerical/mip.html:

> constraint_generation – whether to require the returned solver to
support constraint generation (excludes Coin). False by default.

From the source: https://github.com/sagemath/sage/blob/master/src/sage/n
umerical/backends/generic_backend.pyx#L983:

>  - `constraint_generation` (boolean) -- whether the solver returned is
to be used for constraint/variable generation. As the interface with
Coin does not support constraint/variable generation, setting
`constraint_generation` to `False` ensures that the backend to Coin is
not returned when `solver = None`. This is set to `False` by default.

First issue: in the source the phrase “setting `constraint_generation`
to `False` ensures that the backend to Coin is not returned when `solver
= None`” seems incorrect, as setting `constraint_generation` to `False`
is meant to ''allow'' selection of Coin.

Second issue: upon first reading the ref and source documentation, I
understood that Coin would not be selected if `constraint_generation`
were set to `True`, but not what was exactly meant by ‘constraint
generation’ in the context of the module. I thought it would enable
passing a constraint generator. Now I understand that constraint
generation means: after a first call `solve()`, one or more constraints
is added to the solved instance, and then `solve()` is called again.
Perhaps the documentation should be changed to make this clearer.

URL: http://trac.sagemath.org/15686
Reported by: equaeghe
Ticket author(s): Erik Quaeghebeur
Reviewer(s): Nathann Cohen
Trac #15722: Some documentation errata in numerical module

There are some errata (small, usually formatting) mistakes in the
documentation of the numerical formula. The linked branch fixes them.
(Or at least the ones I spotted.)

URL: http://trac.sagemath.org/15722
Reported by: equaeghe
Ticket author(s): Erik Quaeghebeur
Reviewer(s): Nathann Cohen
Trac #15823: Implement conversion map from tropical semiring

Because sometimes one might want to go back:
{{{
sage: T = TropicalSemiring(QQ)
sage: QQ(T(2))
2
}}}

URL: http://trac.sagemath.org/15823
Reported by: tscrim
Ticket author(s): Travis Scrimshaw
Reviewer(s): Darij Grinberg
Trac #15805: the q-integer 0 has no parent.

For uniformity, all q-integers should belong to the polynomial ring in q
over ZZ.

{{{
sage: from sage.combinat.q_analogues import q_int
sage: q_int(1).parent()
Univariate Polynomial Ring in q over Integer Ring
sage: q_int(0).parent()
------------------------------------------------------------------------
---
AttributeError                            Traceback (most recent call
last)
<ipython-input-3-f312dad40f56> in <module>()
----> 1 q_int(Integer(0)).parent()

AttributeError: 'int' object has no attribute 'parent'
}}}

URL: http://trac.sagemath.org/15805
Reported by: chapoton
Ticket author(s): Travis Scrimshaw
Reviewer(s): Frédéric Chapoton