> Well, to be honest 4 GB isn't much these days and GBasis computations
> tend to be rather large, especially if you use Lex. I often ran out of
> memory on a 24 GB system three years ago doing rather large-ish GB
> computations and none of those ideals were the size you posted. That
> was over various F_p and not boolean rings, so the amount of memory
> needed is different and PolyBoRi is extremely efficient storing
> boolean polynomials.
Wow, this is impressive. When I bought the system, I thought that 4 GB
RAM would be enough because usually I don't need that much. But soon
after that, the problem with GBasis arose and I discover that it's not
enough. To be honest, I never imagined that I needed more.
PolyBoRi is automatically used by Sage for GB computations?
On the other hand I calculated my new ideal and I wonder why it takes
so long for SAGE to evaluate just the ideal and not to compute the GB.
As I said in my previous posts, I only introduced the ideal, pressed
evaluate, waited all night long and nothing. So I didn't even got in
to the GB computation phase.
Is this normal?
And another last question: should I use SAGE via web or installe it on
my system? Which one do you think is faster? Does it matter?
Many thanks!
> > On the other hand, I discovered that the computations that lead my to
> > that ideal were somehow wrong because I discovered that the Grobner
> > Base using DegRevLex is 1(it seems that for Lex, it took very long
> > and never finished but with DegRevLex, in said 1 in 5 seconds) ,
> > which means there is no solution for my system of nonlinear equations,
> > and this is wrong. I'm sure I have solutions, so I have to check again
> > some calculations!
>
> Ok. In theory you can compute the GBasis in Lex for zero dimensional
> ideals by first computing it in some other term ordering like
> DegRevLex and then use FGLM which worst case complexity is much better
> than the GB computation. Other helpful tricks are homogenization, but
> I am not sure if PolyBoRi is doing so internally.
>
> > Thank you very much for your advice! I will be back very soon!
>
> Let us know if you have any more questions.
>
> Cheers,
>
> Michael
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