#4722: BUG - number field K.hilbert_class_polynomial() is a *lie*
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Reporter: was | Owner: was
Type: defect | Status: new
Priority: major | Milestone: sage-3.2.2
Component: number theory | Resolution:
Keywords: |
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Comment (by kohel):
Replying to [comment:1 was]:
> Who to blame? Either me or David Kohel, since this was done before Sage
was under revision control.
Not me. This is a wrapper for the Pari/gp function quadhilbert.
I find this unanswered question about what it returns:
http://pari.math.u-bordeaux.fr/archives/pari-users-0402/msg00000.html
Certainly it does not return the hilbert class polynomial (minimal
polynomial of the j-invariant), rather it returns a "nicer" polynomial
over QQ which generates the Hilbert class field over K.
I agree that a name change is in order to avoid this confusion, but
I don't have a suggestion other than
hilbert_class_field_[relative_]defining_polynomial
which is a bit long, but descriptive. Note that the hilbert_class_field
does not have this as a defining polynomial (hence the relative_),
since it is formed as a compositum of the quadratic and degree h
extensions rather than a relative extension.
The documentation should also be corrected to say that Schertz's method
is used (only) for D < 0. A reference to Schertz's methods and whatever
method (Stark units?) is used for D > 0 would be desirable.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4722#comment:2>
Sage <http://sagemath.org/>
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