I can only answer one of your questions.

On Saturday, 11 February 2017 17:16:29 UTC+1, Jakob Kroeker wrote:
>
> By default, Singular uses 16 bit exponents. But it is perfectly capable of 
>> working with exponents up to 64 bits. That will be slower of course.
>>
>
> How to change this? Is it runtime or compile-time?
>

I believe it can be set at runtime. Hans surely knows how to change it.
 

> Is it transparent for overflow detection?
>

I don't understand the question.
 

>
> I guess it isn't easy for Sage to change the relevant ring upon overflow 
>> to one using 64 bit exponents.
>>
>
> I have no idea;
>
> Jakob
>

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