Considering the subsequent replies to my proposal, I'm perfectly happy with implementing B_1 = +½ in Sage with the 1-year deprecation policy. During the deprecation period I would expect an extra boolean keyword argument to bernoulli() enforcing B_1 = +½ if true and relying on the backend libraries if false; at the end of said period the extra argument will be removed and B_1 = +½ will be permanently enforced.
If you want me to, I can fork Sage and make a trac ticket for this, but then I'd need your help in identifying other files/tests to change for the new behaviour. On Sunday, 11 September 2022 at 00:50:44 UTC+8 wst...@gmail.com wrote: > On Sat, Sep 10, 2022 at 7:17 AM Jeremy Tan <redde...@gmail.com> wrote: > > > > My name is Jeremy Tan, or Parcly Taxel in the furry/MLP art scene. As of > this post I am a recent graduate from the National University of Singapore > with two degrees in maths and computer science. > > > > Over the past month I had a good read of Peter Luschny's Bernoulli > Manifesto (http://luschny.de/math/zeta/The-Bernoulli-Manifesto.html) and > was thoroughly convinced that B_1 (the first Bernoulli number) has to be > +½, not -½. (Much of Luschny's argument centres on being able to (1) > interpolate the Bernoulli numbers when B_1 = +½ with an entire function > intimately related to the zeta function, and (2) extend the range of > validity of or simplify several important equations like the > Euler–Maclaurin formula. Have a read yourself though – it is close to > divine truth.) > > > > So I went to SymPy – one of SageMath's dependencies, and where a > discussion on this topic was open ( > https://github.com/sympy/sympy/issues/23866) – and successfully merged > several PRs there (https://github.com/sympy/sympy/pull/23926) > implementing both that change and some functions in Luschny's "An > introduction to the Bernoulli function" (https://arxiv.org/abs/2009.06743 > ). > > > > I thought I was also done with changing B_1 = +½ for SageMath, but then > someone pointed out that the latter currently uses other libraries that all > have B_1 = -½. I have already opened a PR for one such library, FLINT, to > change B_1 = +½ there (https://github.com/wbhart/flint2/pull/1179). > However Fredrik Johansson has advised me that I take the discussion right > here, to sage-devel, because (in his words) > > > > > if FLINT and Arb change their definitions but the Sage developers > decide that they don't like it, they will just treat the new behavior as a > bug and add a special case in the wrapper to return B_1 = -½. > > > > So my proposal is to special-case it the other way – before the backend > selection in Sage's Bernoulli code ( > https://github.com/sagemath/sage/blob/08202bc1ba7caea46327908db8e3715d1adf6f9a/src/sage/arith/misc.py#L349), > > add a check for argument 1 and immediately return +½ if that is the case. > This also has the advantage of bypassing libraries that haven't or don't > want to change. > > > > What do you think? > > It could be done via the "1 year deprecation policy". I.e., return the > current value by default with a warning message > (and note about an option to change it) for the next year, then when > there is a release in late 2023 (?), the default would change. This > would give people time to update their code. > > I have no comment on the pros and cons of this personally, though I'm > curious if the change breaks any code anywhere else in Sage (e.g., > maybe for computing q-expansions of modular forms?)... > > > > > Jeremy Tan / Parcly Taxel > > > > -- > > You received this message because you are subscribed to the Google > Groups "sage-devel" group. > > To unsubscribe from this group and stop receiving emails from it, send > an email to sage-devel+...@googlegroups.com. > > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-devel/CAGYgO94gF%3DBKo7gRnUj8c3H0bJyuLp_Apr%3D8Y9NC%2BFM%2BSZHNOg%40mail.gmail.com > . > > > > -- > William (http://wstein.org) > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/922fe236-74d0-45c4-9a00-e1d659083622n%40googlegroups.com.
