On Mar 26, 2007, at 13:02 , David Harvey wrote:
>
>
> On Mar 26, 2007, at 3:57 PM, Timothy Clemans wrote:
>
>>
>> Apparently I was incorrectly defining x as an integer, however, I did
>> not get an error the first I tried.
>>
>> incorrect way: x = PolynomialRing(ZZ)
>> correct way: g.<x> = PolynomialRing(ZZ)
>>
>> The len method works now. Thanks.
>
> Be careful though:
>
> sage: R.<x> = PolynomialRing(ZZ)
>
> sage: f = 2*x^2 + 4*x + 8
>
> sage: f.factor()
> 2 * (x^2 + 2*x + 4)
>
> sage: len(f.factor())
> 2
Just to make matters worse:
sage: f=2*x^2+4*x+8
sage: F=factor(f)
sage: len(F)
1
sage: len(f.factor())
1
sage: F
(2) * (x^2 + 2*x + 4)
In my case, I did not predefined the polynomial ring. Hmmm....this
probably means that in my case, the '2' is viewed as a unit, not a
factor, and 'f' is a rational polynomial, not an integer one. In
fact, type()' gives
<class
'sage.rings.polynomial_element_generic.Polynomial_integer_dense'>
in your case, and
<class
'sage.rings.polynomial_element_generic.Polynomial_rational_dense'>
in mine.
Timothy, this illustrates an issue in developing software: you have
to know what your inputs are. Here's a case where it's unlikely that
the average student, with little sophistication in the use of CAS's,
will know (he can create what appears to be f\in ZZ[x], but in fact,
it's in QQ[x]; and the reason it's important is kind of subtle).
Justin
--
Justin C. Walker, Curmudgeon-At-Large
Director
Institute for the Enhancement of the Director's Income
--------
"Weaseling out of things is what separates us from the animals.
Well, except the weasel."
- Homer J Simpson
--------
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