Just for the record, I have created a 
ticket https://trac.sagemath.org/ticket/34758

Regards,
Max

On Monday, October 25, 2021 at 5:26:37 PM UTC-4 Max Alekseyev wrote:

> Btw, another there is another issue related to the order of indeterminates 
> described at 
> https://ask.sagemath.org/question/53319/
>
> Regards,
> Max
>
> On Thu, Sep 9, 2021 at 11:01 AM Max Alekseyev <max...@gmail.com> wrote:
>
>> That would be nice to fix. Btw, there is also the same issue with formal 
>> integration - like in the example below:
>>
>> K.<u> = PolynomialRing(QQ)
>> R.<x> = InfinitePolynomialRing(K)
>> f = x[0] + x[1]
>> integrate(f,x[2])
>>
>> which fails while integrate(f,x[1]) works fine.
>>
>> Regards,
>> Max
>>
>> On Thursday, September 9, 2021 at 2:15:48 AM UTC-4 Simon King wrote:
>>
>>> Hi Nils, 
>>>
>>> can you open a ticket for it? 
>>>
>>> Best regards, 
>>> Simon 
>>>
>>> On 2021-09-08, Nils Bruin <nbr...@sfu.ca> wrote: 
>>> > On Wednesday, 8 September 2021 at 09:24:15 UTC-7 max...@gmail.com 
>>> wrote: 
>>> > 
>>> >> Hi Simon, 
>>> >> 
>>> >> Thank you for your insight, and let me state that I 
>>> >> find InfinitePolynomialRing useful in combinatorics to deal with 
>>> >> (truncated) multivariate generating functions with apriori unknown 
>>> number 
>>> >> of variables, and so basic operations (such as differentiation) on 
>>> >> polynomials would be very welcome here. Btw, is there 
>>> >> InfinitePowerSeriesRing or alike available by any chance? 
>>> >> 
>>> >> From what you said, I think it should be easy to fix (making it work) 
>>> at 
>>> >> least ISSUE#2 -- one just needs to extend the underlying finite 
>>> >> PolynomialRing with the differentiating variable(s) before delegating 
>>> the 
>>> >> actual differentiation to it. 
>>> >> 
>>> > 
>>> > I don't think any extending is required: if the differentiation 
>>> variables 
>>> > do no lie in the parent of the representing finite polynomial ring for 
>>> the 
>>> > actual element then the answer is 0. 
>>> > 
>>> > def derivative(self, *args): 
>>> > R=self._p.parent() 
>>> > try: 
>>> > L=[R(c) for c in args] 
>>> > except TypeError: #perhaps test a little more here 
>>> > return 
>>> > self.parent().zero() 
>>> > return R(self._p.derivative(*L)) 
>>> > 
>>>
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