On Tue, Sep 13, 2022 at 3:43 AM Jeremy Tan <reddeloo...@gmail.com> wrote:
>
> A simpleton's way of getting out of the problem indeed. PARI/GP's
> documentation says:
>
Let's play nice here, okay?
> ? ?bernvec
> bernvec(n): returns a vector containing, as rational numbers, the Bernoulli
> numbers B_0, B_2, ..., B_{2n}.
> ? bernfrac(3)
> %2 = 0
> ? bernfrac(5)
> %3 = 0
>
> So not only B_1 but also B_3, B_5, etc. have values.
>
> Jeremy Tan / Parcly Taxel
>
> On Tuesday, 13 September 2022 at 15:03:05 UTC+8 vdelecroix wrote:
>>
>> PARI/GP actually has a better convention : only even Bernoulli numbers exist
>>
>> ? bernvec(5)
>> %1 = [1, 1/6, -1/30, 1/42, -1/30, 5/66]
>>
>> And the two conventions can be recovered as evaluations of Bernoulli
>> polynomials at 0 and 1 respectively
>>
>> ? [subst(bernpol(n), x, 0) | n <- [1..6]]
>> %2 = [-1/2, 1/6, 0, -1/30, 0, 1/42]
>> ? [subst(bernpol(n), x, 1) | n <- [1..6]]
>> %3 = [1/2, 1/6, 0, -1/30, 0, 1/42]
>>
>> I second Edgar that I don't see much of the point on doing this
>> change. If we had to do any change I would suggest to raise an error
>> when bernoulli(n) is called with n=1 so that nobody could complain
>> about sage convention choices.
>>
>> Vincent
>
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