FYI, Tally is still broken.
DrMajorBob
December 2007) is unchanged in version 6.0.3.
$Version
"6.0 for Mac OS X x86 (64-bit) (May 21, 2008)"
(Here's a repeat of the same code, without all those >> interruptions.)
Needs["Combinatorica`"];
diagrams::usage = "Calculate diagrams";
basicedges::usage;
wick[a_, b_] := pair[a, b];
wick[a_, b__] :=
Sum[Expand[pair[a, {b}[[i]]] Delete[Unevaluated[wick[b]], i]], {i,
Length[{b}]}];
ham[n_Integer] := (ns = 4*n - 3; {c[ns], c[ns + 1], d[ns + 2], d[ns + 3]});
basicedges[n_] :=
Flatten[Table[{{{i, i + 1}, EdgeColor -> Red}}, {i, 1, 2*n, 2}], 1];
hamserie[n_Integer] := Flatten[Table[ham[i], {i, n}]];
cvertices[n_Integer] := {{n, 1}, {n, 0}};
cvertexserie[n_Integer] := Flatten[Table[cvertices[i], {i, n}], 1];
pair[c[_], c[_]] := 0;
pair[d[_], d[_]] := 0;
pair[a_Integer, b_Integer] /; (a > b) := pair[b, a];
diagrams[n_] :=
Module[{wickli, rep, i, cgraph, cvertices, congraph, le, un, ta},
wickli = wick[Sequence @@ hamserie[n]] /. Plus -> List;
le = Length[wickli[[1]]];
wickli = wickli /. {pair[c[i_], d[j_]] -> pair[i, j],
pair[d[i_], c[j_]] -> pair[i, j]};
graph = {}; While[wickli =!= {},
wickli =
rempar[First[wickli], wickli, n,
le]];(*edge reduction and edgelist construction for use by> >
Combinatorica*)
rep = Dispatch[Flatten[Table[{Rule[2*i - 1, i], Rule[2*i, i]}, {i,
2*n}]]];
graph = (Take[#, -le] /. rep /. pair[a__]^_ -> pair[a]) & /@ graph;
be = basicedges[n];
cgraph = Map[List, (graph /. {pair -> List, Times -> List}), {2}];
cvertices = List /@ cvertexserie[n]; cgraph = Join[be, #] & /@ cgraph;
cgraph = Graph[#, cvertices] & /@ cgraph;(*Now I compare Union and
Tally*)
saved = cgraph; un = Union[cgraph, SameTest -> IsomorphicQ];
Print["Union: number of elements: ", Length[un]]; Print[GraphicsGrid[
Partition[ShowGraph[#] & /@ un, 3, 3, {1, 1}, {}]]];
ta = Sort@Tally[cgraph, IsomorphicQ][[All, 1]];
Print["Tally: Number of Elements: ", Length[ta]];
Print[GraphicsGrid[Partition[ShowGraph /@ ta, 3, 3, {1, 1}, {}]]];
Print[GraphicsGrid[
Partition[ShowGraph /@ ta[[{2, 4}]], 3, 3, {1, 1}, {}]]];
Print["Are 2 and 4 isomorphic? ", IsomorphicQ[ta[[2]], ta[[4]]]];
Print["Are 4 and 2 isomorphic? ", IsomorphicQ[ta[[4]], ta[[2]]]];
]
rempar[li_, wickli_List, n_Integer, le_] :=
Module[{lis, mult, gem, pre, i}, lis = {Take[li, -le]}; pre = Drop[li,
-le];
Do[lis = Join[lis, lis /. {i -> i + 1, i + 1 -> i}], {i, 1, 4*n - 1, 2}];
lis = Union[lis]; mult = Length[lis];
graph = Join[graph, {li*mult}];
Complement[wickli, pre*lis]]
diagrams[3]
Union: number of elements: 8
Tally: Number of Elements: 11
Are 2 and 4 isomorphic? True
Are 4 and 2 isomorphic? True
saved // Length
index = Thread[saved -> Range@Length@saved];
(u = Union[saved, SameTest -> IsomorphicQ]) // Length
(t = Sort@Tally[saved, IsomorphicQ][[All, 1]]) // Length
21
8
11
These are the cgraph indices returned by Union and Tally :
u /. index
t /. index
{1, 11, 4, 21, 8, 18, 15, 6}
{1, 11, 4, 2, 8, 14, 3, 18, 15, 7, 6}
Comparing cgraph[[5]] and cgraph[[10]] is irrelevant, as you can see.
(boo = Boole@Outer[IsomorphicQ, t, t, 1]) // MatrixForm;
boo == Transpose@boo
Cases[Position[boo, 1], {a_, b_} /; a < b, 1]
True
{{2, 4}, {5, 7}, {8, 10}}
Bobby
On Fri, 07 Dec 2007 12:27:32 -0600, Michael Weyrauch
<michael....@gmx.de> wrote:
> Dear Bobby,
>
> thanks for asking.
>
> Yes, indeed, I reported this problem to WRI using official support
> channels (thanks to a service contract of my company).
>
> I got the answer from some WRI support engineer that Tally[] is indeed
> broken,
> and does not function correctly in more complicated cases. However,
> appyling
> it
> repeatedly until nothing changes any more does give the correct result.
> (The last bit I did not yet check for myself.)
>
> In practice I wrote my own Tally[], which works but is probably much
> much
> slower
> than a (correctly working) built-in Tally[].
>
> I hope that in a future version Tally will work correctly, because I
> find it
> very useful in principle.
>
>
> Regards Michael
>
> "DrMajorBob" <drmaj...@bigfoot.com> schrieb im Newsbeitrag
> news:<fjav9f$rjb$1...@smc.vnet.net>...
>> Did we get an answer on whether this is a bug in Tally?
>>
>> Bobby
>>
>> On Sun, 18 Nov 2007 16:09:01 -0600, DrMajorBob <drmaj...@bigfoot.com>
>> wrote:
>>
>> > There is, apparently, something wrong with Tally, but your test wasn't
>> > the right one, since cgraph's 5th and 10th elements were not returned
>> in
>
>>
>> > the Tally results. Here's a modification of your code and some tests:
>> >
>> > Needs["Combinatorica`"];
>> > diagrams::usage = "Calculate diagrams";
>> > basicedges::usage;
>> >
>> > wick[a_, b_] := pair[a, b];
>> > wick[a_, b__] :=
>> > Sum[Expand[pair[a, {b}[[i]]] Delete[Unevaluated[wick[b]], i]], {i,
>> > Length[{b}]}];
>> > ham[n_Integer] := (ns = 4*n - 3; {c[ns], c[ns + 1], d[ns + 2],
>> > d[ns + 3]});
>> > basicedges[n_] :=
>> > Flatten[Table[{{{i, i + 1}, EdgeColor -> Red}}, {i, 1, 2*n, 2}],
>> > 1];
>> > hamserie[n_Integer] := Flatten[Table[ham[i], {i, n}]];
>> > cvertices[n_Integer] := {{n, 1}, {n, 0}};
>> > cvertexserie[n_Integer] := Flatten[Table[cvertices[i], {i, n}], 1];
>> > pair[c[_], c[_]] := 0;
>> > pair[d[_], d[_]] := 0;
>> > pair[a_Integer, b_Integer] /; (a > b) := pair[b, a];
>> >
>> > diagrams[n_] :=
>> > Module[{wickli, rep, i, cgraph, cvertices, congraph, le, un, ta} ,
>> > wickli = wick[Sequence @@ hamserie[n]] /. Plus -> List;
>> > le = Length[wickli[[1]]];
>> > wickli =
>> > wickli /. {pair[c[i_], d[j_]] -> pair[i, j],
>> > pair[d[i_], c[j_]] -> pair[i, j]};
>> > graph = {};
>> > While[wickli =!= {},
>> > wickli = rempar[First[wickli], wickli, n, le]];
>> > (*edge reduction and edgelist construction for use by \
>> > Combinatorica*)
>> > rep = Dispatch[
>> > Flatten[Table[{Rule[2*i - 1, i], Rule[2*i, i]}, {i, 2*n}]]];
>> > graph = (Take[#, -le] /. rep /. pair[a__]^_ -> pair[a]) & /@
>> > graph;
>> > be = basicedges[n];
>> > cgraph = Map[List, (graph /. {pair -> List, Times -> List}), {2} >> ];
>> > cvertices = List /@ cvertexserie[n];
>> > cgraph = Join[be, #] & /@ cgraph;
>> > cgraph = Graph[#, cvertices] & /@ cgraph;
>> > (*Now I compare Union and Tally*)
>> > saved = cgraph;
>> > un = Union[cgraph, SameTest -> IsomorphicQ];
>> > Print["Union: number of elements: ", Length[un]];
>> > Print[GraphicsGrid[
>> > Partition[ShowGraph[#] & /@ un, 3, 3, {1, 1}, {}]]];
>> > ta = Sort@Tally[cgraph, IsomorphicQ][[All, 1]];
>> > Print["Tally: Number of Elements: ", Length[ta]];
>> > Print[GraphicsGrid[Partition[ShowGraph /@ ta, 3, 3, {1, 1},
>> {}]]];=
>>
>> > Print[GraphicsGrid[
>> > Partition[ShowGraph /@ ta[[{2, 4}]], 3, 3, {1, 1}, {}]]];
>> > Print["Are 2 and 4 isomorphic? ", IsomorphicQ[ta[[2]], ta[[4]]]];
>> > Print["Are 4 and 2 isomorphic? ", IsomorphicQ[ta[[4]], ta[[2]]]];
>> > ];
>> >
>> > rempar[li_, wickli_List, n_Integer, le_] :=
>> > Module[{lis, mult, gem, pre, i}, lis = {Take[li, -le]};
>> > pre = Drop[li, -le];
>> > Do[lis = Join[lis, lis /. {i -> i + 1, i + 1 -> i}], {i, 1,
>> > 4*n - 1, 2}];
>> > lis = Union[lis];
>> > mult = Length[lis];
>> > graph = Join[graph, {li*mult}];
>> > Complement[wickli, pre*lis]];
>> >
>> > diagrams[3]
>> > Union: number of elements: 8
>> > Tally: Number of Elements: 11
>> > Are 2 and 4 isomorphic? True
>> > Are 4 and 2 isomorphic? True
>> >
>> > saved // Length
>> > index = Thread[saved -> Range@Length@saved];
>> > (u = Union[saved, SameTest -> IsomorphicQ]) // Length
>> > (t = Sort@Tally[saved, IsomorphicQ][[All, 1]]) // Length
>> >
>> > 21
>> >
>> > 8
>> >
>> > 11
>> >
>> > These are the cgraph indices returned by Union and Tally:
>> >
>> > u /. index
>> > t /. index
>> >
>> > {1, 11, 4, 21, 8, 18, 15, 6}
>> >
>> > {1, 11, 4, 2, 8, 14, 3, 18, 15, 7, 6}
>> >
>> > Comparing cgraph[[5]] and cgraph[[10]] is irrelevant, as you can see.
>> >
>> > (boo = Boole@Outer[IsomorphicQ, t, t, 1]) // MatrixForm;
>> > boo == Transpose@boo
>> > Cases[Position[boo, 1], {a_, b_} /; a < b, 1]
>> >
>> > True
>> >
>> > {{2, 4}, {5, 7}, {8, 10}}
>> >
>> > boo is NOT an identity matrix, so Tally did something very odd.
>> >
>> > Bobby
>> >
>> > On Sun, 18 Nov 2007 03:53:16 -0600, Michael Weyrauch >>
>> > <michael....@gmx.de> wrote:
>> >
>> >> Hello,
>> >>
>> >> in the Mathematica 6.0 documentation it says in the entry for
>> Tally:=
>> =
>>
>> >> Properties and Relations:
>> >>
>> >> "A sorted Tally is equivalent to a list of counts for the Union: "
>> >>
>> >> This is what I indeed expect of Tally and Union, in particular then
>> i=
>> t =
>>
>> >> holds for any list:
>> >> Length[Tally[list]] is equal to Length[Union[list]].
>> >>
>> >> Now, I have an example, where Mathematica 6.0 produces a result
>> where=
>>
>> >> Tally[list] and Union[list] are different in length, which surpris=
es =
>> =
>> me.
>> >> And in fact, the result of Tally[ ] seems wrong to me.
>> >>
>> >> You can reproduce this result using the small Mathematica package =
=
>>
>> >> enclosed, which
>> >> uses Combinatorica. (Sorry for the somewhat complicated example, =
=
>> but=
>> I =
>>
>> >> did not find
>> >> a simpler case showing the effect.)
>> >>
>> >> If you load this package into a notebook and then execute
>> >>
>> >> diagrams[2]
>> >>
>> >> Tally and Union produce the expected result: both lists have equal=
=
>>
>> >> length.
>> >> (The list elements are diagrams.)
>> >>
>> >> However, if you execute
>> >>
>> >> diagrams[3]
>> >>
>> >> Tally and Union produce lists of different length.
>> >>
>> >> To my opinion, it really should never happen that Tally and Union=
>> >> produce lists of different length. I just expect of Tally to tell =
me =
>> =
>> =
>>
>> >> the multpilicities in the equivalence classes, in addition to
>> >> the information produced by Union. (The two list to be compared a=
re =
>> =
>> =
>>
>> >> called "ta" and "un" in the package enclosed.)
>> >>
>> >> Strangely enough, the program compares list elements 5 and 10 ==
>>
>> >> explicitly, and comes to the
>> >> conclusion that element 5 and 10 belong to the same equivalence =
>> class=
>> , =
>>
>> >> nevertheless they are
>> >> both listed seperately in the Tally, but - correctly - lumped up =
in =
>> =
>> =
>>
>> >> the Union.
>> >>
>> >> Do I misinterpret something here or is there a bug in Tally? (Tal=
ly =
>> =
>> is =
>>
>> >> new in Mathematica 6, and I
>> >> would find it extremely useful, if it would do what I expect it to=
=
>> do=
>> .)
>> >>
>> >> Michael
>> >>
>> >> Here comes my little package in order to reproduce the effect....
>> >>
>> >> BeginPackage["wick`"]
>> >>
>> >> Needs["Combinatorica`"];
>> >> diagrams::usage="Calculate diagrams";
>> >> basicedges::usage;
>> >>
>> >> Begin["`Private`"]
>> >>
>> >> wick[a_, b_] := pair[a, b];
>> >> wick[a_, b__]:= Sum[Expand[pair[a, {b}[[i]]] =
>>
>> >> Delete[Unevaluated[wick[b]], i]], {i, Length[{b}]}];
>> >> ham[n_Integer]:=(ns=4*n-3;{c[ns],c[ns+1],d[ns+2],d[ns+3]});
>> >> basicedges[n_]:=Flatten[Table[{{{i,i+1}, EdgeColor->Red}}, ==
>>
>> >> {i,1,2*n,2}],1];
>> >> hamserie[n_Integer]:=Flatten[Table[ham[i],{i,n}]];
>> >> cvertices[n_Integer]:={{n,1},{n,0}};
>> >> cvertexserie[n_Integer]:=Flatten[Table[cvertices[i],{i,n}],1];
>> >> pair[c[_],c[_]]:=0;
>> >> pair[d[_],d[_]]:=0;
>> >> pair[a_Integer,b_Integer]/;(a>b):=pair[b,a];
>> >>
>> >> diagrams[n_]:=Module[{wickli, rep, i, cgraph, cvertices, congrap=
h, =
>> le, =
>>
>> >> un, ta},
>> >>
>> >> wickli=wick[Sequence@@hamserie[n]]/.Plus->List;
>> >> le=Length[wickli[[1]]];
>> >> wickli=wickli/.{pair[c[i_],d[j_]]->pair[i,j],
>> >> pair[d[i_],c[j_]]->pair[i,j]};
>> >> graph={};
>> >> While[wickli=!={},
>> >> wickli=rempar[First[wickli],wickli,n, le]];
>> >>
>> >> (*edge reduction and edgelist construction for use by =
>> Combinatorica=
>> *)
>> >> rep=Dispatch[Flatten[Table[{Rule[2*i-1,i],Rule[2*i,i]},{i,2*n}=
]]]=
>> ;
>> >> graph=(Take[#,-le]/.rep/.pair[a__]^_->pair[a])&/@graph;
>> >>
>> >> be=basicedges[n];
>> >> cgraph=Map[List,(graph/.{pair->List, Times->List}),{2}];
>> >> cvertices=List/@cvertexserie[n];
>> >> cgraph=Join[be,#]&/@cgraph;
>> >> cgraph=Graph[#,cvertices]&/@cgraph;
>> >>
>> >> (* Now I compare Union and Tally *)
>> >> un=Union[cgraph,SameTest->IsomorphicQ];
>> >> Print["Union: number of elements: ", Length[un]];
>> >> Print[GraphicsGrid[Partition[ShowGraph[#]&/@un, 3,3,{1,1},{}]]];=
>> >>
>> >> ta=Tally[cgraph,IsomorphicQ];
>> >> ta=Sort[ta];
>> >> Print["Tally: Number of Elements: ", Length[ta]];
>> >> Print[GraphicsGrid[Partition[ShowGraph[#]&/@(First/@ta), =
>>
>> >> 3,3,{1,1},{}]]];
>> >>
>> >> Print["Are 5 and 10 isomorphic? ", IsomorphicQ[cgraph[[5]], ==
>>
>> >> cgraph[[10]]]];
>> >>
>> >> ];
>> >>
>> >> rempar[li_,wickli_List,n_Integer,le_]:=Module[{lis, mult, gem, =
pre=
>> , i},
>> >> lis={Take[li,-le]}; pre=Drop[li,-le];
>> >> Do[lis=Join[lis,lis /. {i->i+1, i+1->i}], {i,1,4*n-1,2}];
>> >> lis =Union[lis];
>> >> mult=Length[lis];
>> >> graph=Join[graph,{li*mult}];
>> >> Complement[wickli,pre*lis]
>> >> ];
>> >>
>> >> End[];
>> >> EndPackage[];
>> >>
>> >>
>> >>
>> >>
>> >>
>> >>
>> >>
>> >
>> >
>> >
>>
>>
>>
>> -- =
>>
>> DrMaj...@bigfoot.com
>>
>
>
-- =
DrMajorBob
Daniel Lichtblau said they'd been broken since version 5.1.
Like Szabolcs, I consider the Tally bug harder to forgive, since it's
merely failing to apply a "same" test properly.
Bobby
On Fri, 13 Jun 2008 08:43:32 -0500, Szabolcs Horvát <szho...@gmail.com>
wrote:
> [note: private message, not sent to MathGroup]
>
> That is very unfortunate ... it is not very surprising that Integrate
> does not always return a correct result, but Tally is a very simple
> function. I think that it is outrageous that a broken version was
> included in several versions ...
>
> What about those nasty symbolic eigenvalue-problems that were reported
> a few months ago? Do those work correctly now?
>
> Here is an example:
> http://groups.google.com/group/comp.soft-sys.math.mathematica/browse_thread/thread/6da2b0fcc02f1b04/f1f79e15f20b313a
Michael Weyrauch
Dear Bobby,
Thanks for this information. I do not have 6.0.3 yet, so I cannot see
for myself. (New versions always take a bit longer to swim to Europe...)
Since my original post I have learned a lot, and by now I find it quite
easy to write my own custom Tallies using Sow and Reap, which I
recommend to anyone who finds that Tally is not working properly. (Along
the way there were one or two posts in this group mentioning similar
problems with Tally.)
It is slightly disappointing that such things do not get fixed more
timely, which should not be that difficult in view of the fact that e.g.
Union[] does work correctly.
So, lets hope for the future.
Michael