#7598: NumberField embedding slightly off
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Reporter: mhansen | Owner: davidloeffler
Type: defect | Status: new
Priority: major | Milestone: sage-4.3.1
Component: number fields | Keywords:
Work_issues: | Author:
Upstream: N/A | Reviewer:
Merged: |
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Comment(by was):
trac_7598-more_serious_version.patch -- this deals with the problems more
at the root. Unfortunately, there are doctests in this file that fail:
{{{
sage -t devel/sage-main/sage/modular/dirichlet.py # 4 doctests
failed
}}}
and I haven't had time to figure out what is wrong. It probably has to do
with a complex embedding not being defined automatically, whereas before
it was...
The design of embeddings was really bad before and relied on numerical
errors to mess up the order of roots in case of 53 bit precision. This
was potentially *very* buggy and was I think the result of some absolutely
terrible design decisions. This absolutely must be fixed before
releasing sage-4.3. This patch basically fixes it, modulo some small
remaining issue.
Here is an example from sage-4.2.1 that illustrates just how horrendously
bad the previous design was (with using CDF when prec=53 but
ComplexField(prec) otherwise):
{{{
sage: K.<i> = QuadraticField(-1)
sage: i.complex_em
i.complex_embedding i.complex_embeddings
sage: i.complex_embedding()
1.0*I
sage: i.complex_embedding(100)
-1.0000000000000000000000000000*I
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7598#comment:4>
Sage <http://www.sagemath.org>
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