#15552: enumerate_totallyreal_fields_prim does not return polynomial as
elements of
a polynomial ring
-----------------------+----------------------------
Reporter: ppurka | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.1
Component: algebra | Keywords:
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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The function `enumerate_totallyreal_fields_prim` is supposed to return,
according to its description,
{{{
OUTPUT:
the list of fields with entries "[d,f]", where "d" is the
discriminant and "f" is a defining polynomial, sorted by
discriminant.
}}}
Let us look at an output:
{{{
sage: E = enumerate_totallyreal_fields_prim(2, 10); E
[[5, x^2 - x - 1], [8, x^2 - 2]]
sage: E[0][1].parent()
Interface to the PARI C library
}}}
We notice from here that the polynomial does not actually belong to the
polynomial ring of `QQ`. In fact, there is no nice way to directly get the
polynomial, as in an element of `PolynomialRing(QQ)` from `E[0][1]`, which
can be then used to construct the number field.
The only way to do this is this lengthy and tedious procedure:
{{{
sage: Ecoef = [QQ(_) for _ in E[0][1].list()]
sage: x = polygen(QQ)
sage: Epol = sum(x**i * _ for i,_ in enumerate(Ecoef))
sage: Epol, Epol.parent()
(x^2 - x - 1, Univariate Polynomial Ring in x over Rational Field)
}}}
The output of the function itself should give back elements of the
polynomial ring, instead of giving us elements which are simply output of
pari.
--
Ticket URL: <http://trac.sagemath.org/ticket/15552>
Sage <http://www.sagemath.org>
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