On Thursday, February 19, 2015 at 9:53:18 AM UTC-8, Bruno Grenet wrote:
>
>  
> And `PolynomialRing`s are *univariate* polynomial rings, without an order 
> argument. 
>

Indeed, because different term orders are generally uninteresting on 
univariate polynomial rings, unless we're allowing term orders that aren't 
term orders in the usual sense (such as neglex):

A possibility could be to define a *multivariate* polynomial ring in just 
> one variable (!) when an `order` is given. This is possible with the 
> current implementation I think, though the results do not seem to be 
> correct for the particular question of whether (1+t) is a unit:
>
> sage: from sage.rings.polynomial.multi_polynomial_ring import 
> MPolynomialRing_polydict
>

Right idea, wrong type (highlighting even further why we shouldn't expose 
Singular's "local rings" via our normal polynomial ring interface):

sage: 
R.<x>=sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular(QQ,1,order="neglex")
sage: (1+x).is_unit()
True

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