coercion of objects embedded in symbolic expressions

[Ralf Stephan]

Hello,

a long standing issue is

sage: bool(pi<Infinity)
False
sage: bool(SR(3)<Infinity) 
False

http://trac.sagemath.org/ticket/12967

at which I'm having a naive stab (because it interferes with #14801).

Maybe I can learn something?

In the ticket the problem has been said having to do with Pynac,

but I don't think so. It would all work nicely if, instead of the expression

object, its underlying `pyobject` would be compared. But this does not

happen because there is no coerce map from `SR` to `InfinityRing`.

So, can we somehow have an indirect coercion map that uses not

the parent but the parent of something a member function (like `pyobject`)

returns? The problem of SR having no canonical map to anything

in spite of some expressions being well behaved is the source of

much frustration.

Regards,

[Eric Gourgoulhon]

Hi,

Just to tell that no later than two days ago, I had a bug in my code that was caused by
bool(SR(0) < Infinity) returning False.
I was about to post a message to sage-devel, but thanks to your post, I realize this is a known issue.

Best wishes,

Eric.

[Volker Braun]

Just to tell you what you already know, the symbolic ring is the parent of last resort if there is nothing more specific. So its to be expected that you don't have any canonical maps elsewhere.

Pynac should probably unwind the comparison of two wrapped (non-symbolic) python objects to the comparison of the underlying python objects. Haven't tried that, though. You have to be careful about infinite recursions, the comparison might again coerce into the symbolic ring.

[Burcin Erocal]

On Sun, 22 Feb 2015 03:17:13 -0800 (PST)
Volker Braun <vbrau...@gmail.com> wrote:

> Just to tell you what you already know, the symbolic ring is the
> parent of last resort if there is nothing more specific. So its to be
> expected that you don't have any canonical maps elsewhere.
>
> Pynac should probably unwind the comparison of two wrapped
> (non-symbolic) python objects to the comparison of the underlying
> python objects. Haven't tried that, though. You have to be careful
> about infinite recursions, the comparison might again coerce into the
> symbolic ring.

Pynac already calls the Python comparison function if both are
pyobjects. In this case, infinity and constants are not pyobjects. They
are a basic class as in mul, add, symbol, etc.

Cheers,
Burcin

P.S. The infinity class was added to pynac by Volker. :)

[Ralf Stephan]

On Sunday, February 22, 2015 at 1:03:54 PM UTC+1, Burcin Erocal wrote:

Pynac already calls the Python comparison function if both are
pyobjects. In this case, infinity and constants are not pyobjects. They
are a basic class as in mul, add, symbol, etc.

The code need not be fast so my solution is in Python and utilizes

the InfinityRing.

http://trac.sagemath.org/ticket/12967