Changing the rewrite order greatly improves performance (though not yet to 
an acceptable level). I tested this using Singular's web-interface. For the 
inhomogeneous cyclic-8,

> int RT = rtimer; int T=timer; size(sba(k,0,0)); rtimer-RT; timer-T; 
372
6369
5304

For the homogeneous cyclic-8,

> int RT = rtimer; int T=timer; size(sba(k,0,0)); rtimer-RT; timer-T; 
1182
6854
5113

There's another option for the module order, but I haven't found a setting 
that makes that improve.

I find this curious, as I had the impression from conversations that things 
were much better than this. In fact, I thought they chose the default for 
the second option because experimental evidence suggested it was better, 
but here we see it getting worse. (I can certainly understand why the 
second option would be worse in practice, but then it shouldn't have ended 
up as the default. Then again, one example does not a standard make.) I 
have inquired & will report back.

john perry

On Sunday, May 8, 2016 at 12:56:32 AM UTC-5, parisse wrote:
>
>
>
> Le dimanche 8 mai 2016 04:08:54 UTC+2, john_perry_usm a écrit :
>>
>> What about homogeneous cyclic-8? I'm not sure it will be any better; I'm 
>> just curious.
>>
>> I do know Singular is working on improving aspects of the sba() 
>> implementation, and I'm a bit surprised it's that slow.
>>
>  
> That's indeed better : about 1mn15s (and 635M). But it's slower than 
> groebner (26s, 4M) and much slower than giac (3.6s).
>

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