Yes, much cooler, thanks! Kirby
On Wed, Jul 15, 2009 at 1:16 PM, Gregor Lingl<gregor.li...@aon.at> wrote: > 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
