#807: construction of function fields
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Reporter: nbruin | Owner: somebody
Type: defect | Status: new
Priority: major | Milestone: sage-5.8
Component: basic arithmetic | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: | Merged in:
Dependencies: | Stopgaps:
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Comment (by nbruin):
Replying to [comment:7 cremona]:
> As I understand it, the . before the < triggers a python error which is
caught and then handled nicely.
The preparser is just a preprocessor, so no python errors are involved.
The string is modified before the python parser ever sees it. Anyway:
{{{
sage: preparse("P1.<t> = QQ['x'].fraction_field()")
"P1 = QQ['x'].fraction_field(names=('t',)); (t,) = P1._first_ngens(1)"
}}}
and supporting it seems straightforward, but this is where things get
questionable: `names` supplied on construction are part of the
construction data, so
{{{
sage: R=QQ['x']
sage: F1=R.fraction_field(names=('u',))
sage: F2=R.fraction_field(names=('v',))
}}}
should produce two fields F1,F2. Both would have coercions from R
installed, since they are constructed as field-of-fractions of R. There
would not be a coercion from F1 to F2. Furthermore, for
{{{
sage: K=QQ['x,u,v'].fraction_field()
}}}
all of R,F1,F2 would coerce into K, but coercion from R to K would not be
compatible with the coercions from F1 and F2 into K, which is bad.
For better of for worse, it was decided that the names of polynomial
variables have meaning in sage. A consequence of that is that you don't
get to choose the name upon applying the function_field functor.
(oh, I didn't realize I made this ticket!)
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/807#comment:8>
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