Error in conversion from RR['x,y'] to RR['x']

[defeo]

Conversion of univariate polynomials from the bivariate ring RR['x,y'] fails:

sage: RR['x'](RR['x,y'].0)

----
ValueError                                Traceback (most recent call last)
...
ValueError: max() arg is an empty sequence

This does not seem to affect other rings:

sage: QQ['x'](QQ['x,y'].0)
x
sage: CC['x'](CC['x,y'].0)
x
sage: RDF['x'](RDF['x,y'].0)
x

[bruno]

[EDIT] As one can notice, I messed up the history with some completely unrelated commits. I am trying to undo this... The relevant code is the latest commit only! [/EDIT] Should be OK now!

The problem was not in conversion, but rather in initialization of univariate polynomials over RR, with an empty dictionary. Before:

sage: RR['x']({})
Traceback (most recent call last):
...
ValueError: max() arg is an empty sequence

After:

sage: RR['x']({})
0

As a result, we also have:

sage: RR['x'](RR['x,y'].0)
x

Details

In the initialization of a polynomial over RR, if the "data" is given as a dictionary, this dictionary is converted to a list. Before the patch, there was an attempt to compute max(x.keys()) where x is the dictionary. If x is empty, this yields an error. To correct the error, I could have add a test. Yet, a function is already specifically defined in the class Polynomial to perform this conversion dict -> list. The new code just uses this function.

Note that I corrected some slight formatting issues in the docstring in other (unrelated) parts of the same file src/sage/rings/polynomials/polynomial_real_mpfr_dense.pyx.

---

New commits: (Note: Irrelevant commits. The only correct commit is in comment:5 below)

​98b7ca1	Rebased on 6.9beta1
​6d0da24	One last zero_element removed + correct one doctest
​dbfb518	Remove useless colons
​331c713	#19171: New method divides
​7527104	#19172: Rewrite valuation for dense polynomials
​22d9c67	#19172: valuation for sparse polynomials
​c546e17	#17190: Authorize empty dictionary in initialization of polynomial over RR

[git]

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

​fe6f95c

#17190: Authorize empty dictionary in initialization of polynomial over RR

[tscrim]

LGTM modulo adding a blank line here:

         Check that :trac:`17190` is fixed::
+
             sage: RR['x']({})
             0

Once you make this change, you can set a positive review on my behalf. (Also, could you edit you post above to show the result is 0?)

[git]

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

​6315d74

#17190: Add missing blank line

[bruno]

Replying to tscrim:

LGTM modulo adding a blank line here:

         Check that :trac:`17190` is fixed::
+
             sage: RR['x']({})
             0

Once you make this change, you can set a positive review on my behalf. (Also, could you edit you post above to show the result is 0?)

Thanks for the quick review! (I edited my post to make it correct...)