I think it is an issue to be reported.
So, I wait for someone to respond this question.

To developers of the SageMath module of rings:
Please verify the program in this question, with debugging messages I added.
we ran into a weakness of SageMath either
 in formula processing producing too complicated denominators
 or in SageMath module of quotient of rings, which fail to reduce the 
element of the ring.
I believe the code reported here is an important entry for new students to 
SageMath.
Please program what is going for this program.

2020年4月5日日曜日 5時56分25秒 UTC+9 finotti:
>
> Thanks for the reply!
>
> On Saturday, April 4, 2020 at 1:00:12 PM UTC-4, rana-aere wrote:
>>
>> I modified the code and tried to trace computation.
>>
>> I think you stepped over the weakness of Sagemath.
>>
>
> I was afraid that that would be the case...
>  
>
>>
>> The modified code is quoted below.
>> The line with many minus signs is meant to separate the program in 
>> different cells of jupyter notebook.
>> My impression is that the program computes R, P + Q, LHS = (P + Q) + R 
>> and then Q + R for RHS.
>> After that the data for the outer call of P + (Q + R) becomes too big so 
>> that Sagemath cannot pass the parameters to add_EC.
>>
>
> Thanks for taking the time to do that! I really appreciate.  I wonder if 
> this is an issue that I should report or if it simply "how it is"...
>
> I think we will just stick with Magma for now.  I try to use (and teach 
> with) Sage whenever possible, but in this case I think I will have to stick 
> with Magma.
>
> Thanks again!
>

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