On Oct 1, 7:09 pm, andresj <[EMAIL PROTECTED]> wrote: > > > On 2007-10-01, Arnaud Delobelle <[EMAIL PROTECTED]> wrote: > > > > > Finally, arithmetic would become very confusing if there were > > > > three distinct numeric types; it already causes enough > > > > confusion with two! > > Well, yeah... I get what you are saying, that would be confusing... > > Terry Reedy and Laurent Pointal: > I know from __future__ import division changes the behaivour to return > floats instead of ints, but what I meant is to be able to implement a > function (or class/method) which would return what _I_ want/decide. > > Gabriel Genellina, thanks for the suggestion of wrapping my code. I > think it could be one way... But I think it would be too much trouble, > I'll just go with writing fractions/rationals explicitly. > > And thanks to mensanator and Gabriel for the suggestion of gmpy, and > to Nick for the example (It really helps to have an example,
Would you like to see a more thorough example? First, go check out the Wikipedia article: <http://en.wikipedia.org/wiki/Collatz_conjecture> And scroll down the the section "Iterating on rational numbers with odd denominators". I added the section beginning with "The complete cycle being:..." through "And this is because...". Here's the Python program I used to develop that section. import gmpy def calc_pv_xyz(pv): """calculate Hailstone Function Parameters using Parity Vector instead of Sequence Vector (defined using (3n+1)/2) calc_pv_xyz(pv) pv: parity vector returns HailstoneFunctionParameters (x,y,z) """ ONE = gmpy.mpz(1) TWO = gmpy.mpz(2) TWE = gmpy.mpz(3) twee = gmpy.mpz(sum(pv)) twoo = gmpy.mpz(len(pv)) x = TWO**twoo y = TWE**twee z = gmpy.mpz(0) c = gmpy.mpz(sum(pv)-1) for i,j in enumerate(pv): if j: z += TWE**c * TWO**i c -= ONE return (x,y,z) def iterating_on_rational(n): # Collatz for rational numbers # is numerator odd? if n.numer() % 2 == 1: n = (n*3 + 1)/2 else: n = n/2 print n, return n pv = [1,0,1,1,0,0,1] for i in xrange(len(pv)+1): print pv # get Hailstone Function parameters X,Y,Z xyz = calc_pv_xyz(pv) # calculate the Crossover Point Z/(X-Y) cp = gmpy.mpq(xyz[2],xyz[0]-xyz[1]) # as a rational number # start of loop cycle print cp, # start the cycle... n = iterating_on_rational(cp) # ...which MUST return to the starting point # since ALL rationals are valid Crossover Points # not just integers while n != cp: n = iterating_on_rational(n) print print # step through the cyclic permutations p = pv.pop(0) pv.append(p) ## parity vector cyclic permutations ## ## [1, 0, 1, 1, 0, 0, 1] ## 151/47 250/47 125/47 211/47 340/47 170/47 85/47 151/47 ## ## [0, 1, 1, 0, 0, 1, 1] ## 250/47 125/47 211/47 340/47 170/47 85/47 151/47 250/47 ## ## [1, 1, 0, 0, 1, 1, 0] ## 125/47 211/47 340/47 170/47 85/47 151/47 250/47 125/47 ## ## [1, 0, 0, 1, 1, 0, 1] ## 211/47 340/47 170/47 85/47 151/47 250/47 125/47 211/47 ## ## [0, 0, 1, 1, 0, 1, 1] ## 340/47 170/47 85/47 151/47 250/47 125/47 211/47 340/47 ## ## [0, 1, 1, 0, 1, 1, 0] ## 170/47 85/47 151/47 250/47 125/47 211/47 340/47 170/47 ## ## [1, 1, 0, 1, 1, 0, 0] ## 85/47 151/47 250/47 125/47 211/47 340/47 170/47 85/47 ## ## [1, 0, 1, 1, 0, 0, 1] ## 151/47 250/47 125/47 211/47 340/47 170/47 85/47 151/47 > because > it usually takes me hours to get to what I want in the > documentations :). I think I will use that, when i get it working in > Ubuntu. Do you guys know of any pre-made package or guides for getting > it working in Ubuntu? > > Well, I guess my idea was not as good as I thought it was :). But > anyways... I look forward to Python 3.0 (Specially the > __future__.with_statement and the standardization of names-- cStringIO > is just too ugly for my eyes!) -- http://mail.python.org/mailman/listinfo/python-list
