wrong comparison between RealIntervalField and RealField

[zimmerma]

on some machines we get the following:

sage: RealIntervalField(53)(-1) > RR(1)
False
sage: RealIntervalField(54)(-1) > RR(1)
True

The second answer True is clearly wrong.

If your machine gets the correct answer False in both cases, then it most probably gives:

sage: RealIntervalField(53)(1) > RR(-1)
True
sage: RealIntervalField(54)(1) > RR(-1)
False

where the second answer False is wrong.

[zimmerma]

still wrong with Sage 5.0.beta1 on a 64-bit Core 2 under Ubuntu 10.10 (gcc 4.4.5):

tarte% ./sage
----------------------------------------------------------------------
| Sage Version 5.0.beta1, Release Date: 2012-01-22                   |
| Type notebook() for the GUI, and license() for information.        |
----------------------------------------------------------------------
**********************************************************************
*                                                                    *
* Warning: this is a prerelease version, and it may be unstable.     *
*                                                                    *
**********************************************************************
sage: RealIntervalField(53)(-1) > RR(1)
False
sage: RealIntervalField(54)(-1) > RR(1)
True

Paul

[zimmerma]

Robert, this seems related to the coercion model. Please could you help?

Paul

[zimmerma]

I'm currently building Sage 4.8 on sage.math (where the bug doesn't happen with 4.7.2) to compare with my workstation where the bug happens, and isolate the problem.

Paul

[zimmerma]

after some investigation, the function _richcmp in structure/element.pyx computes r = cmp(type(left), type(right)), which gives r=-1 on sage.math, and r=1 on my workstation (both with Sage 4.8).

Note that the *types* only are compared, thus by swapping the values I can produce a bug on sage.math too:

sage: RealIntervalField(54)(1) > RR(-1)
False

Something is badly wrong by comparing the types, not the values. Here we need help from someone more fluent in the Sage internals.

Paul

[fbissey]

Are we talking about this piece of code (line 840)

            except (TypeError, NotImplementedError):
                r = cmp(type(left), type(right))
                if r == 0:
                    r = -1

As far as I know comparing type when you cannot compare the values is standard python behavior and is implemented in other places such as sets/set.py

    def __cmp__(self, right):
        r"""
        Compare self and right.

        If right is not a Set compare types.  If right is also a Set,
        returns comparison on the underlying objects.

        .. note::

           If `X < Y` is true this does *not* necessarily mean
           that `X` is a subset of `Y`.  Also, any two sets can be
           compared still, but the result need not be meaningful
           if they are not equal. 

        EXAMPLES:
            sage: Set(ZZ) == Set(QQ)
            False
            sage: Set(ZZ) < Set(QQ)
            True
            sage: Primes() == Set(QQ)
            False

        The following is random, illustrating that comparison of
        sets is not the subset relation, when they are not equal::
        
            sage: Primes() < Set(QQ)             # random
            True or False
        """
        if not isinstance(right, Set_object):
            return cmp(type(self), type(right))
        return cmp(self.__object, right.__object)

The comparison of type can be machine dependent as far as I remember which explain the inconsistencies. I guess it would be nice to try to get

• a better answer
• a better comparison

[zimmerma]

Francois,

Are we talking about this piece of code (line 840) [...]

yes exactly. But in this case the comparison of numerical values (the point interval [-1.0, -1.0] and the real 1.0) is well defined, thus I do not understand why the code returns a comparison of *types* which is machine dependent. And moreover I don't understand how the doctests could work before (see comment 50 in #12171).

Paul

[fbissey]

After thinking about it, I agree it should work. So something is wrong with the coercion (line 2774 onward) so we should try to debug what's happening there.

[jdemeyer]

Why is this a blocker?

[zimmerma]

Replying to jdemeyer:

Why is this a blocker?

because this is a wrong result in basic arithmetic, which can yield wrong results in any part of Sage.

William, Robert, are you out there to help fixing this?

Paul

[roed]

I will take a look in the next few hours.

[roed]

Alright. I know what's going on and am working on a fix. I'll try to post a patch tonight.

[roed]

I didn't get to it tonight but will do so in the next couple days. Here's a brief description of the fix.

We need to update the construction functors returned by RIF.construction() and RR.construction() to be able to merge construction functors of different types. So there's a total ordering on the types of real fields, and the pushout of two real fields has type the "minimum" of their types, and precision the minimum of their precisions.

[zimmerma]

David, thanks for your patch, I will review it. A first comment: RQDF is deprecated, thus it should not be considered in the patch. Please can you update this?

Paul

[zimmerma]

There is a new ticket #12458 about obsolete RQDF stuff.

Paul

[zimmerma]

oops there was a typo in the description.

Paul

[roed]

How about the following? I made it clear that it was deprecated and removed it from pushout, but left it as an option in create_RealField where it returns RealField(212)? Let me know if you prefer a different solution.

[zimmerma]

David,

since RQDF is since long time obsolete in Sage, I would prefer we don't add new references to it (see #12458).

Paul

[roed]

Changed.

[zimmerma]

a typo while reading the patch: approrpiate should be appropriate.

Paul

[zimmerma]

also, in We check that #12353 has been resolved, the 3rd and 4th tests are identical (my fault). The 3rd one should be at precision 53:

sage: RealIntervalField(53)(1) > RR(-1) 
True

Paul

[roed]

Fixed

[zimmerma]

I give a positive review since all doctests still work, and the problem is fixed. However I'm not fluent enough in the construction functors to really review the new code. If Robert or William can do this, please go ahead. In the meantime, since this fixes an major defect, I set to positive review.

Paul

[jdemeyer]

Folded both patches into one.