Hi Chris, The convention that I'm familiar with is that the notation (both cycle notation and the two-line notation) represents the exchange of *elements*, not positions. See for example
http://www.math.caltech.edu/~2015-16/1term/ma006a/17.%20More%20permutations.pdf pp. 4--5. So my interpretation of t*s where t=(1,2) and s=(2,3) (multiplying from R to L) would be: 1 -s-> 1 -t-> 2 2 -s-> 3 -t-> 3 3 -s-> 2 -t-> 1, hence (1,2,3) ("1 goes to 2, 2 goes to 3, 3 goes to 1"), or (in list form) [0, 2, 3, 1]. Is transposition of elements from right to left (my interpretation) equivalent to transposition of positions from left to right (your interpretation)? I can't think of any counterexamples, but I'll chew on it. At the very least, I think that just specifying a multiplication direction without specifying what's being permuted (elements or positions) is ambiguous. Thanks again, Alex On Fri, Mar 12, 2021 at 8:29 AM Chris Smith <[email protected]> wrote: > My thinking is expression in the transformations of the original list of > items, [0,1,2,3]. If you first transpose the 2nd and third position you get > [0,1,3,2] and then if you transpose 1st and 2nd position you get [0,3,1,2]. > You'll see my name all over the docs for that module so if you can find the > error in my thinking here, you are close to the source ;-) > > /c > > On Thursday, March 11, 2021 at 9:47:05 PM UTC-6 [email protected] wrote: > >> Hi Chris, >> >> Thanks for your response. When you write, >> >> > If you let `p = Permutation(1,2)(2,3)` then `p.list()` gives `[0, 3, 1, >> 2]` which is consistent with R to L interpretation >> >> I think this is incorrect (and I contend that the docs are incorrect on >> this point as well). >> Multiplying the transpositions (1,2)(2,3) from R to L, we end up with the >> cycle (1,2,3), >> which in list form is [0, 2, 3, 1] (if `p.list()` is the second line of >> 2-line permutation notation). >> >> What do you think? >> >> On Thu, Mar 11, 2021 at 7:33 PM Chris Smith <[email protected]> wrote: >> >>> So documentation here, "The composite of two permutations p*q means >>> first apply p, then q" should read "...apply q, then p", right? This would >>> be an easy issue to open and fix if there is consensus that it is wrong as >>> written. But note that using the composition of function syntax reverses >>> the order, "One can use also the notation p(i) = i^p, but then the >>> composition rule is (p*q)(i) = q(p(i)), not p(q(i)):" >>> >>> /c >>> >>> On Thursday, March 11, 2021 at 8:37:25 PM UTC-6 Chris Smith wrote: >>> >>>> Given elements `0,1,2,3`, `Permutation(1,2)(2,3)` interpreting R to L >>>> gives `0123->0132->0312`; interpreting L to R gives `0123->0213->0231` >>>> >>>> If you let `p = Permutation(1,2)(2,3)` then `p.list()` gives `[0, 3, 1, >>>> 2]` which is consistent with R to L interpretation. So the assumption that >>>> spelling it `Permutation(1,2)*Permutation(2,3)` means left to right must be >>>> wrong? >>>> >>>> /c >>>> >>>> On Monday, February 22, 2021 at 3:51:02 PM UTC-6 [email protected] >>>> wrote: >>>> >>>>> Hi everyone, >>>>> >>>>> I've been experimenting with the "Permutations" module, trying to >>>>> follow the examples in the documentation here: >>>>> >>>>> https://docs.sympy.org/latest/modules/combinatorics/permutations.html >>>>> >>>>> As expected, >>>>> >>>>> Permutation(1, 2)(2, 3) == Permutation(1, 2) * Permutation(2, 3) >>>>> >>>>> But doesn't this mean that the permutations are applied from left to >>>>> right, since (as described in the docs) left-to-right permutation >>>>> multiplication p*q is equivalent to composition q o p? >>>>> >>>>> If so, this contradicts the documentation's claim that "The convention >>>>> is that the permutations are applied from *right to left*". >>>>> >>>>> If not, I must be confused about something, and would appreciate any >>>>> corrections. >>>>> >>>>> Thanks for your help, >>>>> Alex >>>>> >>>>> -- >>> You received this message because you are subscribed to a topic in the >>> Google Groups "sympy" group. >>> To unsubscribe from this topic, visit >>> https://groups.google.com/d/topic/sympy/5MTQFwB7xIo/unsubscribe. >>> To unsubscribe from this group and all its topics, send an email to >>> [email protected]. >>> To view this discussion on the web visit >>> https://groups.google.com/d/msgid/sympy/7556df78-eb14-408c-bf38-326dafaa1318n%40googlegroups.com >>> <https://groups.google.com/d/msgid/sympy/7556df78-eb14-408c-bf38-326dafaa1318n%40googlegroups.com?utm_medium=email&utm_source=footer> >>> . >>> >> -- > You received this message because you are subscribed to a topic in the > Google Groups "sympy" group. > To unsubscribe from this topic, visit > https://groups.google.com/d/topic/sympy/5MTQFwB7xIo/unsubscribe. > To unsubscribe from this group and all its topics, send an email to > [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/b0302a20-7afa-48e7-ac63-2f467c0b164cn%40googlegroups.com > <https://groups.google.com/d/msgid/sympy/b0302a20-7afa-48e7-ac63-2f467c0b164cn%40googlegroups.com?utm_medium=email&utm_source=footer> > . > -- You received this message because you are subscribed to the Google Groups "sympy" group. 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