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? 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+unsubscr...@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.
