#15027: Inconsistent primitive_root_of_unity for number fields
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Reporter: cremona | Owner: cremona
Type: defect | Status: new
Priority: major | Milestone: sage-5.12
Component: number fields | Resolution:
Keywords: number field unit | Merged in:
Authors: John Cremona | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Dependencies:
Stopgaps: |
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Comment (by cremona):
Replying to [comment:3 fwclarke]:
> John,
>
> The patch doesn't seem to eliminate the other inconsistency: between
`-1/2*a + 1/2` and `1/2*a + 1/2`. For when `primitive_root_of_unity` is
called before `unit_group` it selects the primitive with the shortest
string representation. On the other hand, `UnitGroup.__init__` just uses
the element given by Pari's `nfrootsof1`. There are clearly a variety of
ways to sort this out.
Fair comment, but once you have computed the unit group it's quite
important to go with its generators or discrete logs get confused. The
shortest-string business (which I wrote, though I cannot quite remember
the issue which led me to) is less important. But what was really needed
was not to have the root of unity displaying on the lmfdb.org page of a
number field as "u0"!
--
Ticket URL: <http://trac.sagemath.org/ticket/15027#comment:4>
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