#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 | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
---------------------------+------------------------
Old description:
> 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.
New description:
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.
----
Additionally,
1. the first entry of each list should belong to Sage's `Integer` ring
instead of being just a python `int`.
2. the functions `enumerate_totallyreal_fields_all` and
`enumerate_totallyreal_fields_rel` should get the same fix.
--
Comment (by ppurka):
Replying to [comment:1 fwclarke]:
> Yes, this should certainly be changed. And it would also be better if
the integer returned was a Sage `Integer`. At the moment
`E[0][0].factor()` fails.
Indeed.
This is also a problem with all the other `enumerate_totallyreal_*`
functions.
--
Ticket URL: <http://trac.sagemath.org/ticket/15552#comment:2>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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