On Tue, Oct 20, 2015 at 1:55 PM, Liu Yue <[email protected]> wrote:
> I'm using sage 6.8.
>
> After I typed: RealSet(pi,pi+1), the answer I got is: (pi+1, pi).
>
> Furthermore: RealSet(pi,pi+1).lower() returns pi+1; RealSet(pi,pi+1).upper()
> returns pi.
>
> Is there anything wrong?

I don't know.  The ? help for RealSet it epically horrible.  Why is
this so utterly broken? (see [1] below).  Using ?? to see the source
code and reading it shows that (1) there is definitely a serious bug,
which you're hitting, and (2) it can be traced to this even more
serious bug:

sage: RLF(pi+1) < RLF(pi)
True   # umh, no!
sage: RLF
Real Lazy Field

Looking at blame [2], it looks like Robert Bradshaw originally wrote
Real Lazy Field in 2008, but then Travis Scrimshaw and Jeroen Demeyer
rewrote the comparison code recently.

William


NOTES:

[2] https://github.com/sagemath/sage/blame/master/src/sage/rings/real_lazy.pyx

[1]

sage: RealSet?
String form:     <class 'sage.sets.real_set.RealSet'>
File:            /projects/sage/sage-6.9/src/sage/misc/lazy_import.pyx
Docstring:
   EXAMPLES:

      sage: from sage.misc.lazy_import import LazyImport
      sage: my_isprime = LazyImport('sage.all', 'is_prime')
      sage: my_isprime(5)
      True
      sage: my_isprime(55)
      False

Class docstring:
   EXAMPLES:

      sage: from sage.misc.lazy_import import LazyImport
      sage: my_integer = LazyImport('sage.rings.all', 'Integer')
      sage: my_integer(4)
      4
      sage: my_integer('101', base=2)
      5
      sage: my_integer(3/2)
      Traceback (most recent call last):
      ...
      TypeError: no conversion of this rational to integer
Init docstring:
   EXAMPLES:

      sage: from sage.misc.lazy_import import LazyImport
      sage: my_isprime = LazyImport('sage.all', 'is_prime')
      sage: my_isprime(5)
      True
      sage: my_isprime(55)
      False
Call docstring:
   Calling self calls the wrapped object.

   EXAMPLES:

      sage: from sage.misc.lazy_import import LazyImport
      sage: my_isprime = LazyImport('sage.all', 'is_prime')
      sage: my_isprime(12)
      False
      sage: my_isprime(13)
      True

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