#11779: python ints vs sage ints with respect to powers weirdness
------------------------+---------------------------------------------------
Reporter: dimpase | Owner: AlexGhitza
Type: defect | Status: needs_review
Priority: major | Milestone: sage-4.7.2
Component: coercion | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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Changes (by leif):
* component: basic arithmetic => coercion
Comment:
Replying to [comment:4 dimpase]:
> Replying to [comment:3 leif]:
> > So what do you expect the result types to be?
> >
> > IMHO the fact that `3r^3` yields a Python `int` is pretty correct;
with negative exponents the interpretation is less straightforward.
>
> in all other operations (see the ticket description),
> the Sage type takes the precedence over Python.
Exponentiation is different, i.e., the ''type'' of the exponent doesn't
matter at all, only its value.
[[BR]]
> I certainly don't mind {{{int(3)^int(3)}}} being int though.
Why should one?
[[BR]]
> in fact, with the patch applied, the behaviour is as follows:
{{{
...
sage: type(int(3)^3)
<type 'sage.rings.integer.Integer'>
...
}}}
which is simply wrong, because `3r^3` is `3r * 3r * 3r`, so the type of
the result should be the ''base's'' type (unless the result is not an
integer, in which case Python's rules should apply, leading to a `float`
result.)
The following is equally wrong for the same reason. ('''This''' is a bug.)
>
{{{
sage: type(int(3)^-3)
<type 'sage.rings.rational.Rational'>
}}}
> this is the behaviour that is much less confusing.
Less confusing to whom? Honestly, every school child should know the
difference.
Ok, one could argue that `3r * 3` could be interpreted as `3r + 3r + 3r`
as well (leading to result type `int` rather than `Integer`), but this
would break commutativity.
Worth a discussion on sage-devel... (quite curious of the opinions :P )
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11779#comment:5>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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