Hey Simon,

> From Ulrich's timings, it seems like we are still loosing quite a lot in 
> > converting to/from singular. 
>
> Is it really the *conversion*? I wouldn't be surprised if that example 
> would take a long time in Singular without a conversion.


It does take some time, but far less than in pure Singular according to 
Ulrich's timings (which is still much faster than my [faster] CPU). 
Although from looking at the multivariate code, there should really be no 
overhead. So maybe my statement with conversions is not correct.
 

> The polynomials 
> in Singular are not optimised for arithmetics but for Gröbner basis 
> computations, which (as I was told some time ago) are two totally 
> different things. 
>

I also remember reading the same thing, but I cannot seem to find a 
reference for it. From the like I posted, there also seems to be something 
said for dense multivariate polynomials. However, this suggests that we 
should figure out some way to quickly convert to a system that is much 
better at multiplying polynomials.

Best,
Travis




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