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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