On Thu, Sep 15, 2022 at 7:36 PM Kwankyu Lee wrote:
> On Friday, September 16, 2022 at 10:46:09 AM UTC+9 wst...@gmail.com wrote:
>
>> I just happened to stumble again on the original scrap of paper just
>> now where I made up the name
>> Sage back in 2004.
>>
>
> A good photo of it deserves to be
On Friday, September 16, 2022 at 10:46:09 AM UTC+9 wst...@gmail.com wrote:
> I just happened to stumble again on the original scrap of paper just
> now where I made up the name
> Sage back in 2004.
>
A good photo of it deserves to be permanently placed in the history section
of the sagemath
There is now an Arb equivalent of the Sage ticket that implements the
generalised Bernoulli function but nothing else:
https://github.com/fredrik-johansson/arb/pull/438
Any further equivalents (e.g. on mpmath) will be edited into the
description of the Sage ticket rather than being mailed
https://trac.sagemath.org/ticket/34536
There, Luschny!
On why I initially only changed B_1 = +½, I have a rebuttable demand of my
code: *it must be as beautiful as the maths it implements*. Having
bernoulli_gen() (your generalised Bernoulli function as implemented in the
SageMath ticket)
Thank you for coming, Luschny.
I not only wholeheartedly believe B_1 = +½ and that there is no convention
about it, but also that I believe in the reality and usefulness of the
Bernoulli, Euler and other functions you defined in your 2020 paper.
When I implemented those functions in SymPy there
tl;dr, 80 lines, sorry.
I think there is a better alternative than changing the current
implementation of the Bernoulli numbers.
Fredrik: "The sign convention for B_1 is fairly arbitrary, ..."
Calling the question a 'convention' sets a wrong framing from
the start. Conventions are treated
I have no opinions about what B_1 should be, but I am concerned about
potential confusion: some users will expect one value for B_1, others will
expect a different value, and so one group or other will end up being
confused when answers don't come out the way they expect. The safest course
On Tue, 13 Sept 2022, 17:00 David Joyner, wrote:
> Let's play nice here, okay?
Let me explain what I mean in a nicer way. Not defining B_1 looks good on
the surface given the current discussion, but is really a strictly worse
option than defining B_1 = +½ or -½ because then the n = 1 case has
On Tue, Sep 13, 2022 at 10:35 AM Oscar Benjamin
wrote:
>
> On Mon, 12 Sept 2022 at 22:09, Fredrik Johansson
> wrote:
> >
> > The claim "bernoulli_plus admits a natural generalisation to real and
> > complex numbers but bernoulli_minus does not" (made elsewhere in this
> > thread) seems a bit
On Mon, 12 Sept 2022 at 22:09, Fredrik Johansson
wrote:
>
> The claim "bernoulli_plus admits a natural generalisation to real and complex
> numbers but bernoulli_minus does not" (made elsewhere in this thread) seems a
> bit hyperbolic. For B+ this natural generalization is -n*zeta(1-n); for B-
On Tue, Sep 13, 2022 at 3:43 AM Jeremy Tan 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, ...,
A simpleton's way of getting out of the problem indeed. PARI/GP's
documentation says:
? ?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
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,
On Tuesday, 13 September 2022 at 10:00:20 UTC+8 edgardi...@gmail.com wrote:
> The choice of the sign is arbitrary. So why make this change? What is the
> benefit?
> Most recent papers, algebra systems
> (Maple/Mathematica/Magma/Matlab/Oscar), and libraries
> (Pari/Flint/Mpmath/ARB) seemed to
On Mon, Sep 12, 2022 at 7:00 PM edgardi...@gmail.com
wrote:
>
> The choice of the sign is arbitrary. So why make this change? What is the
> benefit?
The answer to that question is what the website
http://luschny.de/math/zeta/The-Bernoulli-Manifesto.html
is all about. I think you have to read
The choice of the sign is arbitrary. So why make this change? What is the
benefit?
Most recent papers, algebra systems (Maple/Mathematica/Magma/Matlab/Oscar),
and libraries (Pari/Flint/Mpmath/ARB) seemed to have picked B_1 = -1/2.
Thus why put work into changing the default value and go against
I'm pretty neutral about this change, but I've received PRs for FLINT and
mpmath (presumably there will be one for Arb as well) so I suppose I will
need to make a decision about merging or closing them sooner or later :-)
The sign convention for B_1 is fairly arbitrary, and the downside of
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