#5188: squaring some factorizations has a bug
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Reporter: was | Owner: tbd
Type: defect | Status: new
Priority: critical | Milestone: sage-3.3
Component: algebra | Resolution:
Keywords: |
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Comment (by was):
Some discussion in email:
{{{
On Thu, Feb 5, 2009 at 1:39 AM, Willem Jan Palenstijn <[email protected]>
wrote:
>
>
> Hi all,
>
> We recently ran into two cases of confusing behaviour of Factorization
> objects.
>
> The first:
>
> sage: f = factor(-1); f
> -1
> sage: f^2
> -1
>
That's terrible! This is now:
http://trac.sagemath.org/sage_trac/ticket/5188
> I traced this to a special case in the powering code for taking powers
> of zero, which f is treated as:
>
> sage: bool(f)
> False
>
> This is because f.__len__() == 0, and f.__nonzero__ is not defined. What
do
> you think the behaviour of __nonzero__() should be? Always return True?
> Return 'not self.value()' ?
The safest is clearly
return self.value().__nonzero__()
But this can be very expensive. Always returning true would be
excellent,
but if we do that we need to put a test in the Factorization constructor
that
all the "primes" are nonzero. That would be reasonable, especially if you
put
a check=False option in, so one can skip checking nontriviality of the
primes
for speed reasons.
> Return 'len(self.__x) > 0 or bool(self.__unit)' ?
> It's not at all clear to me how this should behave.
>
> My main confusion stems from the fact that it's easy to manually create
> Factorization objects that have value 0, even though some methods in
> Factorization don't seem to work properly for such manually created
(non-prime)
> factorizations.
>
> E.g.,
> Factorization([0,1]) and Factorization([(Integers(4)(2),2)]) have value
0, and:
> sage: Factorization([(6,1)]).gcd(factor(2))
> 1
> is unexpected, though understandable.
>
> One solution to this might be documenting the exact behaviour of the
> Factorization object and functions like gcd/lcm to make it clear what
> (not) to expect. In that case, making __nonzero__() always return True
> might be acceptable. (Although I'm not sure if that's acceptable for
> Factorizations of spaces.)
>
>
>
>
>
> The other is a non-commutative +:
>
> sage: f = factor(2)
> sage: f + 7
> 9
> sage: 7 + f
> ...
> TypeError: unsupported operand parent(s) for '+': 'Integer Ring' and
'<class 'sage.structure.factorization.Factorization'>'
>
> Maybe add/sub should be removed entirely as John Cremona suggested in
> http://trac.sagemath.org/sage_trac/ticket/3927 ?
>
> Alternatively, could Factorization objects somehow be hooked into the
coercion
> system through the natural map to their universe where appropriate? Or
does
> them not having a parent make this impossible/hard/undesirable ?
Maybe they should have a parent...
William
>
>
> -Willem Jan
>
> P.S. See also http://groups.google.com/group/sage-
devel/browse_thread/thread/425a8614d5765130 for a previous discussion on
this topic.
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5188#comment:1>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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