Actually, I've now checked and it looks like Fricas uses PSR, which will 
take forever on this problem if you have the variable ordering with x the 
main variable. Of course I'm not terribly familiar with the source code 
layout of Fricas, so I could be wrong here.

Bill.

On Friday, 4 November 2016 17:54:43 UTC+1, Bill Hart wrote:
>
>
>
> On Friday, 4 November 2016 17:38:17 UTC+1, Bill Hart wrote:
>>
>> Sure, if you change the order of the variables it will finish in no time 
>> using PSR.
>>
>
> Sorry, I should have said that x has to be the main variable. I could 
> design some polys for which the timing didn't depend on the main variable, 
> but for now, x has to be the main variable to see how slow this is (at 
> least in Sage and Singular). I'm not sure if the first or last variable is 
> x in Fricas, but if you define your polynomial ring so that the first or 
> last variable is x, you will likely see a big slowdown. Of course Fricas 
> may also just use a really fast algorithm. I didn't check.
>
> Bill. 
>

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