#4276: [with patch, needs review] move number fields to new coercion, implement
embeddings
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Reporter: robertwb | Owner: robertwb
Type: defect | Status: new
Priority: major | Milestone: sage-3.2.1
Component: coercion | Resolution:
Keywords: |
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Comment (by robertwb):
Thank you for taking a look at this. I really don't want these patches to
bitrot. I will try to post another patch with more docstrings.
Essentially, the embedding is a specified coercion into another field
(typically RR or CC, though embeddings to any other field can be
specified). This should make what you're trying to do at #4193 trivial (or
at least very easy). The embedding parameter specifies where the generator
of the number field should land (the closest root being taken if the root
is not exact). So by doing
{{{
sage: L.<b> = NumberField(x^5-x+1, embedding=-1.1)
}}}
I am saying I want the number filed defined by {{{x^5-x+1}}} *with* the
embedding into RR defined by sending the generator to the root (closest
to) -1.1. You can test this by calling {{{RR(b)}}} or RR(some other
element of K) and doing stuff like {{{b+1.5}}} whose result should be
about 0.4. Given two number fields K and L with embedding into (say) CC,
one now gets for free morphisms between (subsets of) K and L.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4276#comment:5>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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