วันจันทร์ที่ 10 กรกฎาคม พ.ศ. 2560

Re: [sage-devel] Re: [ODK participants] Blog post on fast multivariate arithmetic



On Monday, 10 July 2017 17:05:10 UTC+2, vdelecroix wrote:
On 10/07/2017 16:36, 'Bill Hart' via sage-devel wrote:
>> BTW, it would be good to have them in the post!
>>
>
> It already says in the post that for systems that didn't provide the
> required function, I used quotient with remainder.

I meant code snippets.

I suppose that could be useful, but it's a lot of work for little clear benefit (5 systems, 6 benchmarks). The code is pretty much exactly what Ralph wrote, except that I used a for loop for the operation being timed, and timed that. This was the same in all the systems.

I used quo_rem for division with remainder (for the divisibility test with quotient benchmark) and * for multiplication. For quotient only, I don't recall if I used quo_rem or //. It's clear from the timings I didn't use /, and I do recall checking the documentation very carefully for that.

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[computer] [computer] [computer] [computer] [computer] [computer] [computer] [computer] Re: [sage-devel] Re: [ODK participants] Blog post on fast multivariate arithmetic



On Monday, 10 July 2017 13:31:26 UTC+2, vdelecroix wrote:
On 10/07/2017 12:48, mmarco wrote:
> It is surprising the difference between singular and Sage, considering that
> Sage mostly relies on Singular for multivariate polynomial arithmetic. In
> the case of divisions, I suspect that it has to do with the fact that Sage
> treats division of polynomials as an operation in the fraction field, so it
> would construct the fraction, look for common factors in the numerator and
> denominator, and cancel them. That is probably not what other systems do.

Indeed, for (internal) division one should use // and not /

> Which commands/instructions did you use in your benchmarks?

It looks like I used quo_rem, since you need both the quotient and whether or not it is divisible, for which you need the remainder.
 

BTW, it would be good to have them in the post!

It already says in the post that for systems that didn't provide the required function, I used quotient with remainder. 
 

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[computer] [computer] [computer] [computer] [computer] [computer] [computer] Re: [sage-devel] Re: [ODK participants] Blog post on fast multivariate arithmetic



On Monday, 10 July 2017 13:31:26 UTC+2, vdelecroix wrote:
On 10/07/2017 12:48, mmarco wrote:
> It is surprising the difference between singular and Sage, considering that
> Sage mostly relies on Singular for multivariate polynomial arithmetic. In
> the case of divisions, I suspect that it has to do with the fact that Sage
> treats division of polynomials as an operation in the fraction field, so it
> would construct the fraction, look for common factors in the numerator and
> denominator, and cancel them. That is probably not what other systems do.

Indeed, for (internal) division one should use // and not /

> Which commands/instructions did you use in your benchmarks?

It looks like I used quo_rem, since you need both the quotient and whether or not it is divisible, for which you need the remainder.
 

BTW, it would be good to have them in the post!

It already says in the post that for systems that didn't provide the required function, I used quotient with remainder. 
 

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[computer] [computer] [computer] [computer] [computer] [computer] Re: [sage-devel] Re: [ODK participants] Blog post on fast multivariate arithmetic



On Monday, 10 July 2017 13:31:26 UTC+2, vdelecroix wrote:
On 10/07/2017 12:48, mmarco wrote:
> It is surprising the difference between singular and Sage, considering that
> Sage mostly relies on Singular for multivariate polynomial arithmetic. In
> the case of divisions, I suspect that it has to do with the fact that Sage
> treats division of polynomials as an operation in the fraction field, so it
> would construct the fraction, look for common factors in the numerator and
> denominator, and cancel them. That is probably not what other systems do.

Indeed, for (internal) division one should use // and not /

> Which commands/instructions did you use in your benchmarks?

It looks like I used quo_rem, since you need both the quotient and whether or not it is divisible, for which you need the remainder.
 

BTW, it would be good to have them in the post!

It already says in the post that for systems that didn't provide the required function, I used quotient with remainder. 
 

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[computer] [computer] [computer] [computer] [computer] Re: [sage-devel] Re: [ODK participants] Blog post on fast multivariate arithmetic



On Monday, 10 July 2017 13:31:26 UTC+2, vdelecroix wrote:
On 10/07/2017 12:48, mmarco wrote:
> It is surprising the difference between singular and Sage, considering that
> Sage mostly relies on Singular for multivariate polynomial arithmetic. In
> the case of divisions, I suspect that it has to do with the fact that Sage
> treats division of polynomials as an operation in the fraction field, so it
> would construct the fraction, look for common factors in the numerator and
> denominator, and cancel them. That is probably not what other systems do.

Indeed, for (internal) division one should use // and not /

> Which commands/instructions did you use in your benchmarks?

It looks like I used quo_rem, since you need both the quotient and whether or not it is divisible, for which you need the remainder.
 

BTW, it would be good to have them in the post!

It already says in the post that for systems that didn't provide the required function, I used quotient with remainder. 
 

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[computer] [computer] [computer] [computer] Re: [sage-devel] Re: [ODK participants] Blog post on fast multivariate arithmetic



On Monday, 10 July 2017 13:31:26 UTC+2, vdelecroix wrote:
On 10/07/2017 12:48, mmarco wrote:
> It is surprising the difference between singular and Sage, considering that
> Sage mostly relies on Singular for multivariate polynomial arithmetic. In
> the case of divisions, I suspect that it has to do with the fact that Sage
> treats division of polynomials as an operation in the fraction field, so it
> would construct the fraction, look for common factors in the numerator and
> denominator, and cancel them. That is probably not what other systems do.

Indeed, for (internal) division one should use // and not /

> Which commands/instructions did you use in your benchmarks?

It looks like I used quo_rem, since you need both the quotient and whether or not it is divisible, for which you need the remainder.
 

BTW, it would be good to have them in the post!

It already says in the post that for systems that didn't provide the required function, I used quotient with remainder. 
 

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[computer] [computer] [computer] Re: [sage-devel] Re: [ODK participants] Blog post on fast multivariate arithmetic



On Monday, 10 July 2017 13:31:26 UTC+2, vdelecroix wrote:
On 10/07/2017 12:48, mmarco wrote:
> It is surprising the difference between singular and Sage, considering that
> Sage mostly relies on Singular for multivariate polynomial arithmetic. In
> the case of divisions, I suspect that it has to do with the fact that Sage
> treats division of polynomials as an operation in the fraction field, so it
> would construct the fraction, look for common factors in the numerator and
> denominator, and cancel them. That is probably not what other systems do.

Indeed, for (internal) division one should use // and not /

> Which commands/instructions did you use in your benchmarks?

It looks like I used quo_rem, since you need both the quotient and whether or not it is divisible, for which you need the remainder.
 

BTW, it would be good to have them in the post!

It already says in the post that for systems that didn't provide the required function, I used quotient with remainder. 
 

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