On Saturday, December 8, 2012 11:07:31 AM UTC-6, Santanu wrote:
>
> Thank you. But when I try to solve
> f1=x1 + x2 + x4 + x10 + x31 + x43 + x56 , 
> f2=x2 + x3 + x5 + x11 + x32 +x44 + x57,
>
> it becomes very slow. Is there any faster approach like 
> F4 algorithm available in Sage? 
>

F4 is not yet available in Sage; as far as I know, we're waiting for 
upstream (Singular) to implement it. They've been working on it very hard 
for quite some time, because they're trying to do it right, and it's not as 
easy as one might think. Last I heard, they had both F4 and an F5-like 
algorithm with respectable performance in an internal development branch, 
but they had to integrate it with the regular Singular branch. It's been a 
huge effort to do this, since memory management & other tricky issues come 
into play.

Daniel Cabarcas wrote an open-source implementation of F4 for his Master's 
Thesis, which you might be able to find online. Bjarke Roune & Michael 
Stillman described an open-source F5-like algorithm at ISSAC 2012, and gave 
an address where you can download it in the paper.

All that said, when I look at your system, I wonder if something's wrong 
with the formatting, because it looks to me as if it's either linear or 
univariate. Is that the case?

regards
john perry

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