Very interesting issue, superbly documented by Kirby, thanks!
May I contribute a slightly streamlined version of the seidel-generator: see attachment. (Please check if everything is correct.) Regards, Gregor kirby urner schrieb:
Just adding to what's on file, not sure this is a "must have" but it's fun to do, especially given the association of Bernoulli Numbers with "the first computer program" as scoped out in Ada's notes: http://www.flickr.com/photos/17157...@n00/3718903352/sizes/o/ (shell view, Akbar font) http://www.4dsolutions.net/ocn/python/ada.py (source code) According to Wikipedia, this is similar to what Knuth recommends i.e. we're staying with integer operations, although I'm using the Fraction type to output results (Bernoulli numbers are fractions with lots of digits once you get into 'em, ideal grist for the mill when learning about Python generators). Kirby 4D
""" Python version: 3.1 author: Kirby Urner, 4D Solutions release: 1.01, July 15, 2009 quick and dirty implementation of Bernoulli numbers as a generator, getting clues from Wikipedia article code of seidel generator slightly streamlined by Gregor Lingl Dedication: "to Ada Byron, with respect and admiration" (hence name ada.py) "In note G of Ada Lovelace's notes on the Analytical engine from 1842, Lovelace describes an algorithm for generating Bernoulli numbers with Babbage's machine [~ 1]. As a result, the Bernoulli numbers have the distinction of being the subject of the first computer program." Wikipedia: http://en.wikipedia.org/wiki/Bernoulli_number Source code (current version): http://www.4dsolutions.net/ocn/python/ada.py """ from fractions import Fraction def seidel(): """ "...in 1877 Philipp Ludwig von Seidel published an ingenious algorithm which makes it extremely simple to calculate Tn." (Ibid, Wikipedia) See OEIS: http://www.research.att.com/~njas/sequences/A000111 """ yield 1 yield 1 row = [1] while True: t = 0 newrow = [] for i in row: t += i newrow.append(t) newrow.append(t) yield t row = reversed(newrow) def bernoulli(): yield Fraction(1,1) yield Fraction(-1,2) seidelgen = seidel() next(seidelgen) sign = 1 n = 2 while True: sign *= -1 denom = 2**n -4**n numer = sign * n * next(seidelgen) next(seidelgen) n += 2 yield Fraction(numer, denom)
_______________________________________________ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig
