#5982: Can't construct fraction field
--------------------------------------------------------+-------------------
Reporter: jmbr | Owner: tbd
Type: defect | Status:
needs_review
Priority: major | Milestone:
sage-4.6.2
Component: algebra | Keywords:
Author: Nick Alexander, Juan M. Bello Rivas | Upstream: N/A
Reviewer: William Stein, Mike Hansen, Marco Streng | Merged:
Work_issues: |
--------------------------------------------------------+-------------------
Changes (by mstreng):
* reviewer: William Stein, Mike Hansen => William Stein, Mike Hansen,
Marco Streng
Old description:
> {{{
> ----------------------------------------------------------------------
> | Sage Version 3.4.2, Release Date: 2009-05-04 |
> | Type notebook() for the GUI, and license() for information. |
> ----------------------------------------------------------------------
> sage: R.<x, y> = PolynomialRing(QQ, 2)
> sage: I = (x^2 + y^2 - 1)*R
> sage: Q = R.quotient(I); Q
> Quotient of Multivariate Polynomial Ring in x, y over Rational Field by
> the ideal (x^2 + y^2 - 1)
> sage: Q.fraction_field()
> ---------------------------------------------------------------------------
> NotImplementedError Traceback (most recent call
> last)
> <SNIP>
> }}}
New description:
{{{
----------------------------------------------------------------------
| Sage Version 3.4.2, Release Date: 2009-05-04 |
| Type notebook() for the GUI, and license() for information. |
----------------------------------------------------------------------
sage: R.<x, y> = PolynomialRing(QQ, 2)
sage: I = (x^2 + y^2 - 1)*R
sage: Q = R.quotient(I); Q
Quotient of Multivariate Polynomial Ring in x, y over Rational Field by
the ideal (x^2 + y^2 - 1)
sage: Q.fraction_field()
---------------------------------------------------------------------------
NotImplementedError Traceback (most recent call
last)
<SNIP>
}}}
Apply
* [attachment:trac_5982-ncalexan-with-check.patch]
* [attachment:trac_5982-reviewer.patch]
* [attachment:trac_5982_review2.patch]
--
Comment:
Why is this
{{{
The following is Trac #5982. Note that the quotient ring
is not recognized as being a field at this time, so the
fraction field is not the quotient ring itself::
sage: Q = R.quotient(I); Q
Quotient of Multivariate Polynomial Ring in x, y over Rational
Field by the ideal (x^2 - y^2 - 1)
sage: Q.fraction_field()
Fraction Field of Quotient of Multivariate Polynomial Ring in
x, y over Rational Field by the ideal (x^2 - y^2 - 1)
}}}
part of the documentation of {{{is_prime}}} and not of
{{{fraction_field}}}?
All tests pass with these patches on sage-4.6.2.alpha4. Patches fix the
problem in the ticket description, and all changes look good.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5982#comment:26>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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