#11126: Fix category of Symbolic Ring
-------------------------------------+-------------------------------------
Reporter: duenez | Owner: burcin
Type: defect | Status: needs_review
Priority: major | Milestone: sage-6.4
Component: symbolics | Resolution:
Keywords: symbolic ring | Merged in:
category | Reviewers:
Authors: Peter Bruin | Work issues:
Report Upstream: N/A | Commit:
Branch: | 82b9860a3d47ee19f944a3b357b9d0e943226a54
u/pbruin/11126-SymbolicRing_not_domain| Stopgaps:
Dependencies: |
-------------------------------------+-------------------------------------
Changes (by {'newvalue': u'Peter Bruin', 'oldvalue': u'duenez'}):
* status: needs_info => needs_review
* commit: => 82b9860a3d47ee19f944a3b357b9d0e943226a54
* branch: => u/pbruin/11126-SymbolicRing_not_domain
* author: duenez => Peter Bruin
Old description:
> The symbolic ring (`SR`) in Sage currently considers itself to be a field
> and therefore also an integral domain:
> {{{
> sage: SR.is_field()
> True
> sage: SR.is_integral_domain()
> True
> }}}
> However, it is confused about its category:
> {{{
> sage: SR.category()
> Category of commutative rings
> sage: SR in PrincipalIdealDomains()
> False
> sage: SR in Fields()
> True
> }}}
> The last command causes the category of `SR` to be refined, and running
> the same commands again gives a different output:
> {{{
> sage: SR.category()
> Category of fields
> sage: SR in PrincipalIdealDomains()
> True
> sage: SR in Fields()
> True
> }}}
> We should either make `SR.is_field()` return `False` (which is the only
> mathematically correct option) or put `SR` in `Fields()` from the
> beginning.
New description:
The symbolic ring (`SR`) in Sage currently considers itself to be a field
and therefore also an integral domain:
{{{
sage: SR.is_field()
True
sage: SR.is_integral_domain()
True
}}}
However, it is confused about its category:
{{{
sage: SR.category()
Category of commutative rings
sage: SR in PrincipalIdealDomains()
False
sage: SR in Fields()
True
}}}
The last command causes the category of `SR` to be refined, and running
the same commands again gives a different output:
{{{
sage: SR.category()
Category of fields
sage: SR in PrincipalIdealDomains()
True
sage: SR in Fields()
True
}}}
This ticket makes `SR.is_field()` and `SR.is_integral_domain()` return
`False`.
Because of this, one now has to indicate explicitly in the code when one
takes the risk of treating the symbolic ring as a field. This is
currently only done for a couple of linear algebra methods and for points
on elliptic curves over the symbolic ring.
A few constructions (which were mathematically meaningless anyway) are now
disallowed:
- quaternion algebras over the symbolic ring
- converting a symbolic expression into a rational function over the
symbolic ring
- minimal polynomials of matrices over the symbolic ring
--
--
Ticket URL: <http://trac.sagemath.org/ticket/11126#comment:14>
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