factoring in a number field

[Joel B. Mohler]

After having been a heavy sage user for several years, I now have
virtually not touched it for several more years. Returning now on a
lark, I'm feeling rather confused because I'd think the following
would obviously work. My goal is to factor a bunch of Gaussian
integers.

sage: K.<I>=QuadraticField(-1)
sage: ((I+1)*(I+1)).factor()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call
last)
/home/joel/.sagelocalrc.py in <module>()
AttributeError: 'sage.rings.number_field.number_field_element_quadr'
object has no attribute 'factor'

Isn't factoring a Gaussian integer about the simplest complex number
theory one might wish to try? And isn't this the most obvious way to
try it?

Joel

[D. S. McNeil]

> sage: K.<I>=QuadraticField(-1)
> sage: ((I+1)*(I+1)).factor()

This may have been fixed since the last time you looked at Sage: what
version are you running? It seems to work for me in both 4.8 and 5.0
beta.

sage: K.<I>=QuadraticField(-1)
sage: ((I+1)*(I+1))

2*I
sage: ((I+1)*(I+1)).factor()
(I + 1)^2

Doug

[Joel B. Mohler]

On Feb 26, 7:35 pm, "Joel B. Mohler" <j...@kiwistrawberry.us> wrote:
> After having been a heavy sage user for several years, I now have
> virtually not touched it for several more years.  Returning now on a
> lark, I'm feeling rather confused because I'd think the following
> would obviously work.  My goal is to factor a bunch of Gaussian
> integers.
>
> sage: K.<I>=QuadraticField(-1)
> sage: ((I+1)*(I+1)).factor()
> ---------------------------------------------------------------------------
> AttributeError                            Traceback (most recent call
> last)
> /home/joel/.sagelocalrc.py in <module>()
> AttributeError: 'sage.rings.number_field.number_field_element_quadr'
> object has no attribute 'factor'

Ok, to answer myself, this appears to work in the cell server on the
sage front page, but does not work in my old install of version 4.3.
Therefore I conclude that I need to upgrade. However, I'm still quite
baffled that this didn't work in sage 4.3.

Joel

[William Stein]

Um, isn't sage 4.3 ancient?  

> Joel
>
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--
William Stein
Professor of Mathematics
University of Washington
http://wstein.org

[Jeroen Demeyer]

I get a nostalgic feeling. Implementing this was the very first patch I
ever made for Sage... an "exercise" by John Cremona.

[Jason Grout]

On 2/26/12 7:13 PM, William Stein wrote:
> Um, isn't sage 4.3 ancient?

From http://sagemath.org/src-old/, it was released on Christmas Eve, 2009.

Jason

[Justin C. Walker]

On Feb 26, 2012, at 17:13 , William Stein wrote:

> On Sunday, February 26, 2012, Joel B. Mohler <jo...@kiwistrawberry.us> wrote:
>> On Feb 26, 7:35 pm, "Joel B. Mohler" <j...@kiwistrawberry.us> wrote:
>>> After having been a heavy sage user for several years, I now have
>>> virtually not touched it for several more years. Returning now on a
>>> lark, I'm feeling rather confused because I'd think the following
>>> would obviously work. My goal is to factor a bunch of Gaussian
>>> integers.
>>>
>>> sage: K.<I>=QuadraticField(-1)
>>> sage: ((I+1)*(I+1)).factor()
>>>
> ---------------------------------------------------------------------------
>>> AttributeError Traceback (most recent call
>>> last)
>>> /home/joel/.sagelocalrc.py in <module>()
>>> AttributeError: 'sage.rings.number_field.number_field_element_quadr'
>>> object has no attribute 'factor'
>>
>> Ok, to answer myself, this appears to work in the cell server on the
>> sage front page, but does not work in my old install of version 4.3.
>> Therefore I conclude that I need to upgrade. However, I'm still quite
>> baffled that this didn't work in sage 4.3.
>>
>
> Um, isn't sage 4.3 ancient?

December, 2009. I think this was fixed in 4.5.3.

Justin

--
Justin C. Walker, Curmudgeon at Large
Institute for the Absorption of Federal Funds
-----------
I'm beginning to like the cut of his jibberish.
-----------

[William Stein]

Any serious number theorist (i.e., most Sage users who would want to
do this sort of thing before 2009?) would have just done:

sage: K.<I>=QuadraticField(-1)
sage: a = K.ideal( ((I+1)*(I+1)))
sage: a.factor()
(Fractional ideal (I + 1))^2