+1 to writing a class for localizations of polynomial rings with respect to 
orderings. 

El jueves, 19 de febrero de 2015, 18:43:15 (UTC+1), Enrique Artal escribió:
>
> I did not know this ticket but it is a related problem. I guess, following 
> also Simon, that the best choice is to create something like 
> LocalPolynomialRing admitting local orderings since even if all the 
> algorithms can be performed inside the polynomials (as Singular does) the 
> actual rings are different. In the example of ticket #10708, the ideal 
> generated by 1-x is the unit ideal, i.e. the total local ring, and hence 
> its Krull dimension is -1.
>
> El jueves, 19 de febrero de 2015, 18:35:51 (UTC+1), Nils Bruin escribió:
>>
>> On Thursday, February 19, 2015 at 8:46:19 AM UTC-8, Enrique Artal wrote:
>>>
>>> For the first one, it was already reported, with an open ticket, but I 
>>> am worried about it since it produces wrong outputs. The problem appears 
>>> working with polynomial rings with local orders, e.g., 
>>> *R.<x,y>=PolynomialRing(QQ,order='neglex')*. If one defines a non 
>>> constant polynomial with constant leading monomial,  e.g. *f=1+x*, the 
>>> output of *1/f* is *1*;
>>>
>> I assume you are referring to http://trac.sagemath.org/ticket/10708 . 
>> Indeed, that is rather worrying behaviour.
>>
>

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