On Sunday, 9 October 2016 18:08:29 UTC+2, Dima Pasechnik wrote:
>
>
>
> On Sunday, October 9, 2016 at 3:35:57 PM UTC, Bill Hart 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.
>>
>> why? I presume arithmetic on 16-bit integers is not faster than on 
> 32-bit, or even 64-bit.
>

It's the exponent arithmetic, not the coefficients we are talking about.

The exponents are packed, with four 16 bit field in a 64 bit word. This is 
*much* faster. I use the same trick, as does just about every decent 
computer algebra system out there.

Interestingly, Magma only allows exponents up to about 30 bits, but it 
takes a few minutes to compute x^(2^30 - 1).
 

>  
>  
>
>> I guess it isn't easy for Sage to change the relevant ring upon overflow 
>> to one using 64 bit exponents.
>>
>> I can't say whether it would be easy or hard for Singular to 
>> automatically change the exponent size for you. For basic arithmetic, I 
>> have implemented precisely this in the code I've been writing. But Singular 
>> is almost infinitely more complex than the very simple cases I've been 
>> dealing with in my own code. At this stage I couldn't even hazard a guess.
>>
>> I'll ask Hans if I remember. But either way, I believe this would be an 
>> *extremely* time consuming thing to fix. How important is it?
>>
>> Bill.
>>
>> On Wednesday, 5 October 2016 01:10:31 UTC+2, Jakob Kroeker wrote:
>>>
>>>
>>> https://trac.sagemath.org/ticket/6472
>>>
>>> even for recent singular upgrade 
>>>
>>> https://trac.sagemath.org/ticket/17254
>>>
>>> and it was not(?) reported to upstream...
>>>
>>>
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>>>

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