On Wed, Mar 18, 2015 at 10:15 PM, Robert Bradshaw <[email protected]> wrote:
> +1 for the change; this is what both Maple and Mathematica and Most
> Mathematicians do.
No.
- That Pari and Magma *don't* do this is more relevant.
- I think your new claim that Maple represents polynomials or
algebraic numbers from lowest to highest degree is incorrect (see
[1]).
- Here's how Mathematica outputs algebraic numbers (see [2]):
"AlgebraicNumber[Root[#^5 - 7 # + 1 &, 1], {0, 7, 0, 0, 0, -1}]"
Yes, the order of the thing in braces is lowest to highest, but that
has to be the ugliest output format I've ever seen, by far.
- I just did a quick survey (e.g., searching for algebraic number,
looking at google image results, looking at other pages) and the
majority of what I saw that wasn't quadratic was polynomials, which
are mostly written from highest degree to lowest. It's *consistent*
to represent algebraic numbers in the same way that people usually
represent polynomials. I can't imagine how you would argue that we
should change sage to output algebraic numbers in a way that is
backwards from polynomials...
- Ten years of backwards compatibility.
William
[1] http://www.maplesoft.com/support/help/Maple/view.aspx?path=evala
[2] http://reference.wolfram.com/language/tutorial/AlgebraicNumberFields.html
>
> On Wed, Mar 18, 2015 at 9:25 AM, William Stein <[email protected]> wrote:
>> On Wed, Mar 18, 2015 at 5:01 AM, Chris Wuthrich
>> <[email protected]> wrote:
>>> Since I was at the origin of the argument for a change (long time ago
>>> already), I better add my opinion:
>>>
>>> I would change all number field printing by reversing the order. For
>>> instance this feels unnatural to me:
>>>
>>> sage: K = NumberField(x^7-3, "a")
>>> sage: K([1,2,3,4,5,6,7])
>>> 7*a^6 + 6*a^5 + 5*a^4 + 4*a^3 + 3*a^2 + 2*a + 1
>>>
>>> I really believe a large majority of number theorist will write
>>> 1+ zeta + zeta^2
>>> in cyclotomic fields or
>>> 1+ sqrt[3]{7} +...
>>> more generally etc.
>>>
>>> However, it is purely an aesthetic question.
>>
>> -1 to this proposal because what Sage currently does is consistent
>> with what PARI and Magma both currently do. See [1].
>>
>>
>>
>>
>> [1]
>> https://cloud.sagemath.com/projects/2bfce692-d0d8-4b89-968e-d9825f175a0f/files/support/2015-03-18-092139-nf-order.sagews
>>
>>
>>
>> --
>> William (http://wstein.org)
>>
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