On 11/1/07, [EMAIL PROTECTED] <[EMAIL PROTECTED]> wrote: > > In particular, how does applying (1,2,3)(4,5) to [0,1,2,3,4] > > result in what you claim, i.e., in [1, 2, 0, 4, 3]? > > It should either be an error, or maybe: > > [2,0,1,3,4] > > if say (1,2,3)(4,5) sends the "first entry", i.e., 0th position > > to the 1st, the 1st to 2nd, etc, > > That's what is going on -- I interpret the cycle notation as: > > 1 |--> 2 > 2 |--> 3 > 3 |--> 1 > 4 |--> 5 > 5 |--> 4 > > and I don't know how you arrived at [2,0,1,3,4] -- that looks like (3,2,1) to > me.
OK, consider the permutation (1,2,3), which permutes things as follows: 1 |--> 2 2 |--> 3 3 |--> 1 Thus if the input is v = [a,b,c], then the output is [c,a,b]. I.e., the permutation sends the entry at position 1 to position 2, i.e., the a gets stuck in the middle, the entry at position 2 to position 3, i.e., the b goes to where c is, and the entry at position 3 goes to the front, i.e., to where a is. Thus applied to [0,1,2], we get [2,0,1]. Applying the permutation (1,2,3)(4,5) to [0,1,2,3,4] should either move the entry in position 1 (which happens to be called "0") to position 2, so that the output looks like [*,0,*,*,*] or if we do some weird 1-based thing, it would always fix the first entry, then send the entry in position 1 to position 2 and look like: [0,*,1,*,*] and neither of these are what you claim, i.e., [1, 2, 0, 4, 3]. William --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
