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 have picked B_1 = -1/2. > Thus why put work into changing the default value and go against the > current norm? > By doing this you will generate a lot of unnecessary work to go from one > arbitrary choice (that most people use) to another that few seem to use. > The people and CAS's who use B_1 = -½ are good, but wrong. The central thesis of Luschny's manifesto is that B_1 = +½ shows the central place of the Bernoulli numbers in all mathematics much better than B_1 = -½. As he puts it in the closing paragraphs: "I believe in the *unity of mathematics* as described by Barry Mazur… In any case mathematics is not a bunch of disparate conventions which must be maintained in its present form just to protect some mathematicians from a possible confusion." Every general-purpose CAS is an embodiment of said unity of mathematics, and should strive to capture – make real – that unity as much as possible. Yes, the Four Heavenly Kings (Magma, Maple, Mathematica, Matlab) may provide B_1 = -½, but this is SageMath, an open-source *alternative* to all of them. We don't have to follow them or any convention. As well as that, SageMath originally stood for System for Algebra and Geometry *Experimentation*. Given the almost excessive number of relations between the Bernoulli numbers with B_1 = +½ and other mathematical entities, I am confident that a secondary school/high school student/undergraduate first introduced to the Bernoulli numbers with B_1 = +½, and given SageMath with B_1 = +½, would have a lot more fun than if B_1 = -½ was initially given instead. Finally I would like to drop a quip from the manifesto: "My impression is that the number of modern authors who use B_1 = +½ is steadily increasing." 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/68f64631-1abb-43d4-91ae-972cc009ce91n%40googlegroups.com.
