Re: Tally

*To*: mathgroup at smc.vnet.net*Subject*: [mg86937] Re: Tally*From*: Szabolcs Horvát <szhorvat at gmail.com>*Date*: Wed, 26 Mar 2008 04:56:59 -0500 (EST)*Organization*: University of Bergen*References*: <fsa5eq$adg$1@smc.vnet.net>

Armen Kocharyan wrote: > Dear Group, > > I'm trying the following: > > > *Dlist = {{{0,1},{0,1}},{{1,0},{1,0}},{{1,0},{0,1}},{{0,1},{1,0}}};* > > *Tally[Dlist,(#1=== #2) \[Or] * > > * (#1[[1]][[1]]=== #2[[1]][[2]] \[And] * > > * #1[[1]][[2]]=== #2[[1]][[1]] \[And] * > > * #1[[2]][[1]]=== #2[[2]][[2]] \[And] * > > * #1[[2]][[2]]=== #2[[2]][[1]] )&]* > > > > The output is: > > *{{{{0,1},{0,1}},1},{{{1,0},{1,0}},1},{{{1,0},{0,1}},2}}* > > instead of > > *{{{{0,1},{0,1}},2},{{{1,0},{0,1}},2}}* > > > > If I remove the last member from DList > > *Dlist = {{{0,1},{0,1}},{{1,0},{1,0}},{{1,0},{0,1}}};* > > then I got a correct answer > > *{{{{0,1},{0,1}},2},{{{1,0},{0,1}},1}}.* > > > > Is anything wrong with my original code? I really *hope* that I am wrong, but it seems to me that your code is correct. The test function is a "good" equivalence relation, i.e. it is reflexive, symmetric and transitive, so this cannot be the problem. But something seems to be wrong with Tally: test = #1 === #2 || (#1[[1, 1]] === #2[[1, 2]] && #1[[1, 2]] === #2[[1, 1]] && #1[[2, 1]] === #2[[2, 2]] && #1[[2, 2]] === #2[[2, 1]]) & dlist = {{{0, 1}, {0, 1}}, {{1, 0}, {1, 0}}, {{1, 0}, {0, 1}}, {{0, 1}, {1, 0}}} test2[p_, q_] := With[{val = test[p, q]}, Print[{Position[dlist, p, {1}], Position[dlist, q, {1}], val}]; val] ( Using Position should work because this specific dlist has no repeating elements ) The output of Tally[dlist, test2] is: {{{1}},{{4}},False} {{{3}},{{2}},False} {{{4}},{{2}},False} {{{4}},{{3}},True} {{{1}},{{3}},False} {{{2}},{{4}},False} {{{4}},{{3}},True} {{{3}},{{1}},False} {{{{0, 1}, {0, 1}}, 1}, {{{1, 0}, {1, 0}}, 1}, {{{1, 0}, {0, 1}}, 2}} It looks like Tally never tests element 1 against element 2, but it does test element 4 against element 3 *twice*, even though this is completely unnecessary. This is the kind of bug that severely undermines one's trust in Mathematica. I do not expect that Integrate or some numerical method should always return a correct answer. I know that this is simply not possible. But the algorithms that could be used by Tally are simple enough that I find this bug quite shocking.