#11126: Symbolic Ring is_integral_domain() throws exception
------------------------------------+---------------------------------------
Reporter: duenez | Owner: burcin
Type: defect | Status: needs_review
Priority: major | Milestone:
sage-duplicate/invalid/wontfix
Component: symbolics | Resolution:
Keywords: symbolics matrix | Work issues:
Report Upstream: N/A | Reviewers:
Authors: duenez | Merged in:
Dependencies: | Stopgaps:
------------------------------------+---------------------------------------
Comment (by nbruin):
Replying to [comment:5 duenez]:
> I am a bit confused... It seems to me you are suggesting that I should
simply accept that sage might refuse to perform symbolic calculations when
solving systems of linear equations... or worse yet, perform them and be
wrong. Also, I should just deal with it if it doesn't work like I want.
What I suspect is happening is that linear algebra over SR tries to use
generic linear algebra code which wants to know some properties of the
ring it's working over in order to know how to proceed (i.e., is it a
field? an integral domain?). The symbolic ring doesn't really fit such a
rigorous approach and I suspect that most of its benefits stem from that:
It's just an algebra of "expression trees". If SR were honest, and report
it's not a field and not an integral domain, hardly anything would work.
There's a benefit to lying and a lot of things WILL sort of work, because
zero-divisors are relatively hard to construct. However, they do exist in
SR, so I suspect that you can construct linear algebra examples for which
a wrong answer is generated, because the code runs into a zero divisor
(which was promised to not exist by claiming it's an integral domain).
SR is just trying to be a bit too much to expect a rigorous algebraic
approach to apply to it and still end up with something useful. Testing
equality in it is known to be undecidable.
I certainly wouldn't want to stand in the way of an intelligent discussion
to improve the situation. Great mathematics happens in the face of great
problems. I just thought a word of caution to moderate expectations was in
order.
A similar thing happens (for different reasons) with the "numerical"
rings. RR and CC claim to be fields too, but due to the numerical nature
of the representation of their elements, they are not. Operations aren't
even commutative and any float operations that rely on true equality
testing are inherently broken. Linear algebra there is really quite
tenuous and we can't rely on the generic approaches at all.
How to deal with that is an entire field of mathematics.
(now note that SR in fact contains float arithmetic as well to see that
you can't really hope that generic approaches are always safe for SR).
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11126#comment:6>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/sage-trac?hl=en.
