hmm...one more question here then I'll stop, as this is turning into more
like a sage-support discussion as opposed to sage-devel.
This does seem to be doing a good job with high enough precision specified.
What is the best way to compare two such interval numbers? The multipliers
(after applying d) will have a bunch of repeat values, but there will be
some minor precision differences. We need to remove those duplicates.
On Monday, November 24, 2014 2:54:24 PM UTC-5, Ben Hutz wrote:
>
> Thanks Vincent. I can give that a try. We did try to approximate earlier
> with CC and the errors were compounding too much (we do a bunch more stuff
> after this), but maybe approximating the roots with CIF will do a better
> job.
>
> It sounds like the recursion depth error is actually expected for numbers
> like this,
>
> (btw, type is defined in the example as 6, but it doesn't really matter)
>
> On Monday, November 24, 2014 1:55:05 PM UTC-5, vdelecroix wrote:
>>
>> Hi Ben,
>>
>> You are dealing with complicated numbers, it is not surprising that
>> things like "exactify" or "__cmp__" lead to maximum recursion errors.
>> If you want something faster than QQbar you can either:
>> - do approximation earlier in the code
>> - try to work with number fields
>>
>> Note that your example can be simplified
>> {{{
>> z = polygen(ZZ)
>> f = z^2 + 3/4
>> g = f
>> for _ in range(5): g = f(g)
>> roots = (g-z).roots(QQbar, multiplicities=False)
>> }}}
>>
>> Then instead of applying "d" I would suggest that you do the
>> approximation now
>> {{{
>> R = ComplexIntervalField(256)
>> approx_roots = [r.interval_exact(R) for r in roots]
>> }}}
>> and start your computation from there.
>>
>> By the way, I was not able to go through your example since "type" is
>> not defined. I tried with type=7 and get quite accurate results (the
>> diameter was < 10^-43).
>>
>> Vincent
>>
>
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