On Oct 3, 2009, at 4:08 PM, rjf wrote:
> Then would factoring 2*x-2 also reveal the bug? Or maybe factoring
> 2 ?
Nope.
> It seems to me that for Pari to remove and then ignore the content
> (in Z?) is a bug.
Yep, I consider that strange too (though it does solve the "more
interesting" problem). Right in the users manual it states
Note that PARI tries to guess in a sensible way over which ring you
want to factor. Note
also that factorization of polynomials is done up to multiplication
by a constant. In particular, the
factors of rational polynomials will have integer coefficients, and
the content of a polynomial or
rational function is discarded and not included in the factorization.
If you need it, you can always
ask for the content explicitly.
And trying it out:
GP/PARI CALCULATOR Version 2.3.3 (released)
i386 running darwin (ix86/GMP-4.2.1 kernel) 32-bit version
compiled: Sep 9 2009, gcc-4.0.1 (Apple Computer, Inc. build
5363)
(readline v5.2 enabled, extended help available)
Copyright (C) 2000-2006 The PARI Group
? factor(15*x+3)
%7 =
[5*x + 1 1]
? factor(15.0*x+3)
%8 =
[x + 0.2000000000000000000000000000 1]
That's why we "fix" the result when we get it back from Pari (though,
up till now, a corner case was broken).
> It would make some sense to optionally not factor such a content
> unless you want to also do integer factorization.
I agree, though that's a much smaller issue.
- Robert
>
>
>
>
>
> On Oct 3, 11:51 am, Robert Bradshaw <rober...@math.washington.edu>
> wrote:
>> On Oct 2, 2009, at 9:30 PM, rjf wrote:
>>
>>> hey, factoring-testing guys..
>>> If you make up factoring problems this way, you are probably not
>>> doing
>>> much testing of the real factoring algorithms.
>>
>> Actually, given this bug has been in Sage for so long, the real issue
>> is that for several years no one had tested "easy" factorizations
>> such as this--everyone was worried about timing and testing the
>> "hard" ones.
>>
>>
>>
>>> Repeated factors like
>>> this of different degree are detected by so-called square-free
>>> factorization.
>>> The time to factor F in Maxima is, to the resolution of the clock,
>>> 0.0000 seconds on
>>> a 3GHz Intel machine.
>>
>>> F can also be entirely factored by the sqfr program, which uses a 5
>>> line program involving
>>> differentiation, GCD, and division. So the problem is
>>> essentially no
>>> harder than factoring f and g separately.
>>
>>> There are papers that show how to construct polynomials that are
>>> difficult to factor.
>>
>>> I dunno about the Sage wrapper problem. If that's the difficulty,
>>> maybe the subject line is wrong.
>>
>> Yes, it was all about the wrapper (pari ignores the content, and
>> there was a bug in reconstructing it). The subject perfectly
>> describes the symptom, and was helpful in locating the cause.
>>
>> - Robert
> >
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