#18836: Make refine_embedding into a method of number fields instead of
stand-alone
-------------------------------------+-------------------------------------
Reporter: cremona | Owner:
Type: enhancement | Status: needs_work
Priority: minor | Milestone: sage-6.8
Component: number fields | Resolution:
Keywords: | Merged in:
Authors: John Cremona | Reviewers: Vincent Delecroix
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/cremona/18836-refine_embedding | 94a1d567b17399c9e39517ab6943004210ee23ba
Dependencies: #20064 | Stopgaps:
-------------------------------------+-------------------------------------
Comment (by lftabera):
You are right, I thought #20064 was already merged, while it is not.
Everything is fine now.
- The code is ok, I miss extending embeddings from number to p-adic
fields, but this issue is out of scope for this ticket.
- Please document that precision cannot decrease.
{{{
sage: N=QQ[sqrt(2)]
sage: e=N.embeddings(RR)[0]
sage: N.refine_embedding(e,16) is e
True
sage: e
Ring morphism:
From: Number Field in sqrt2 with defining polynomial x^2 - 2
To: Real Field with 53 bits of precision
Defn: sqrt2 |--> -1.41421356237310
}}}
Also, it would be nice to note that, when the refinement is not unique, an
"arbitrary" one is returned:
{{{
sage: N=NumberField(x^4 - 199999999/50000000*x^2 +
40000000400000001/10000000000000000,'a')
sage: e = N.embeddings(ComplexField(16))[1]
sage: e
Ring morphism:
From: Number Field in a with defining polynomial x^4 -
199999999/50000000*x^2 + 40000000400000001/10000000000000000
To: Complex Field with 16 bits of precision
Defn: a |--> 1.414
sage: N.refine_embedding(e,32)
Ring morphism:
From: Number Field in a with defining polynomial x^4 -
199999999/50000000*x^2 + 40000000400000001/10000000000000000
To: Complex Field with 32 bits of precision
Defn: a |--> 1.41421356 - 0.0000988882552*I
sage: len(N.embeddings(ComplexField(16)))
2
sage: len(N.embeddings(ComplexField(32)))
4
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/18836#comment:18>
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