PolynomialRing's behaviour does not match docstring

[sagetrac-broune]

The docstring for the function PolynomialRing states

    OUTPUT:
        PolynomialRing(base_ring, name, sparse=False) returns a univariate
        polynomial ring; all other input formats return a multivariate
        polynomial ring.

which is not what PolynomialRing actually does, since

sage: PolynomialRing(QQ, names=['x'])
Univariate Polynomial Ring in x over Rational Field

Either PolynomialRing has a bug or the docstring should be corrected.

Component: algebra

Author: Simon King

Reviewer: Martin Albrecht, Mike Hansen

Merged: sage-4.2.1.alpha0

Issue created by migration from https://trac.sagemath.org/ticket/3128

[sagetrac-broune]

comment:1

To be more precise, the problem is that the docstring of PolynomialRing says there is only one way to get a univariate polynomial ring, but in fact PolynomialRing tries to be clever and returns univariate rings in other cases too.

[simon-king-jena]

Attachment: PolynomialRingDoc.patch.gz

Fixing wrong docstring statement and adding more doctests

[simon-king-jena]

comment:2

I think the new doc string covers all use cases. It also provides the corner cases (zero or one variables) as doc tests.

[malb]

comment:3

Note that a multivariate polynomial ring is returned even if the 
given number of variables is zero or one. 

should be replaced with

Note that a multivariate polynomial ring is returned when an explicit number is given.

[mwhansen]

comment:4

Attachment: trac_3128.patch.gz

I rebased the patch and changed the docstring as per malb's suggestion.