#15348: "R.<a> =" syntactic sugar incorrect for EquationOrder and ZZ.extension
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Reporter: emassop | Owner:
Type: defect | Status: needs_review
Priority: major | Milestone: sage-7.0
Component: number fields | Resolution:
Keywords: | Merged in:
Authors: Jeroen Demeyer | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/jdemeyer/ticket/15348 | dac0a4cdb957393b282619213dc231f55cf55cc4
Dependencies: | Stopgaps:
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Changes (by jdemeyer):
* status: new => needs_review
* commit: => dac0a4cdb957393b282619213dc231f55cf55cc4
Old description:
> After typing
> {{{
> sage: f = x^2+1
> sage: R.<i> = ZZ.extension(f)
> }}}
> I expect variable {{{i}}} to be the element of {{{R}}} named {{{'i'}}}.
> However, it is not. It is the element 1.
>
> This is due to the generators of an order in Sage being its //module//
> generators (as noted by {{{EquationOrder?}}}):
> {{{
> sage: R.gens()
> [1, i]
> sage: preparse("R.<i> = ZZ.extension(f)")
> "R = ZZ.extension(f, names=('i',)); (i,) = R._first_ngens(1)"
> }}}
>
> I see three ways of fixing this:
> 1) redefine {{{AbsoluteOrder.gens()}}},
> 2) make {{{preparse(...)}}} output {{{i = R._element_constructor('i')}}}
> instead of {{{(i,) = R._first_ngens(1)}}},
> 3) disallow {{{R.<i> = }}} for {{{EquationOrder}}}.
>
> Way (1) might make previously good code produce wrong results, so it is
> not a good idea.
> For way (2), {{{_element_constructor}}} should have ubiquitous support,
> about which I am unsure. I think way (3) might be achieved by renaming
> the argument {{{names}}} of {{{EquationOrder}}} to {{{field_names}}} or
> some such. (For the short term I think {{{names}}} should still be
> accepted, but with a warning.)
New description:
After typing
{{{
sage: f = x^2+1
sage: R.<i> = ZZ.extension(f)
}}}
I expect variable {{{i}}} to be the element of {{{R}}} named {{{'i'}}}.
However, it is not. It is the element 1.
This is due to the generators of an order in Sage being its //module//
generators (as noted by {{{EquationOrder?}}}):
{{{
sage: R.gens()
[1, i]
}}}
We fix this by redefining `_first_ngens()` (which is what the preparser
uses to implement the `R.<x> =` syntax) to use `ring_generators()` if such
an attribute exists.
--
Comment:
New commits:
||[http://git.sagemath.org/sage.git/commit/?id=dac0a4cdb957393b282619213dc231f55cf55cc4
dac0a4c]||{{{Let "R.<x> =" syntax use ring_generators if possible}}}||
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Ticket URL: <http://trac.sagemath.org/ticket/15348#comment:11>
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