On Friday, 19 October 2012 05:13:55 UTC+8, Ken Ribet wrote: > > Thanks to everyone for the explanation of why my comparison of rational > numbers did not work. I'd like to make two comments: > > 1. I got into this mess by trying to count points above and below the line > in the standard textbook proof of quadratic reciprocity. You have two odd > primes p and q, make the grid of integers whose x-coordinates run between 1 > and (p-1)/2 and whose y-coordinates run between 1 and (q-1)/2, and draw the > line through the origin with slope q/p. I drew a beautiful picture for my > students but then miscounted the points below the line by using a rational > number comparison instead of the apparently equivalent integer comparison > (gotten by cross-multiplying). The count looked more realistic after I > cross-multiplied! > > 2. It occurred to me that the integers that I was dividing were of the > wrong "type." I asked sage what was going on and interpreted the output > <type 'int'> > as referring to a standard sage integer. I had no clue that I should have > been looking for > <type 'sage.rings.integer.Integer'> >
it's possible to handle this in "plain" Python 2, as follows: $ python Python 2.6.6 (r266:84292, Dec 26 2010, 22:31:48) [GCC 4.4.5] on linux2 Type "help", "copyright", "credits" or "license" for more information. >>> from __future__ import division >>> 1/3 0.33333333333333331 >>> > Ken > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-support?hl=en.
