#16447: do not use identical var names when constructing rings
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Reporter: rws | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.3
Component: commutative algebra | Keywords:
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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novoselt in comment 17 of #13360:
> By the way, I think that this is a bug:
> {{{
> sage: QQ["t"]["t"]
> Univariate Polynomial Ring in t over Univariate Polynomial Ring in t
over Rational Field
> }}}
> Nobody in mathematics uses the same variable in the same expression with
the same meaning, so there is no reason to support it. Moreover, this may
indicate a logical error and a user would appreciate catching it. So I
think that constructions that "add names" should check that they are
absent in the base ring. This way it would be prohibited to create
`SR["t"]`, but all polynomials can remain coercible to `SR`.
>
> I suppose adding such a check is also not extremely difficult, but care
should be taken when constructing polynomials "for internal purposes".
There should be some standard way to get from a ring a name that can work
as a "new name". And it should raise an exception for SR.
>
> I also think that for any element of any ring we should have `R(str(f))
== f` which is impossible to hope for if we do not insist on distinct
names for generators.
I think it's not the worst solution to silently change `["t"]["t"]` to
`["t1"]["t2"]` automatically.
--
Ticket URL: <http://trac.sagemath.org/ticket/16447>
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