FYI, Tally is still broken. So are some symbolic eigenvalues

*To*: mathgroup at smc.vnet.net*Subject*: [mg89599] FYI, Tally is still broken. So are some symbolic eigenvalues*From*: DrMajorBob <drmajorbob at att.net>*Date*: Sat, 14 Jun 2008 05:30:09 -0400 (EDT)*References*: <JNEIICAJLELPIHHIMDJDOEIMCEAA.michael.weyrauch@gmx.de> <200806131010.GAA07718@smc.vnet.net> <3786945.1213366358727.JavaMail.root@m08>*Reply-to*: drmajorbob at longhorns.com

Some symbolic eigenvalues are still broken as well, in version 6.0.3. Daniel Lichtblau said they'd been broken since version 5.1. http://groups.google.com/group/comp.soft-sys.math.mathematica/browse_thread/thread/6da2b0fcc02f1b04/f1f79e15f20b313a 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 <szhorvat at 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 > > On Fri, Jun 13, 2008 at 13:10, DrMajorBob <drmajorbob at att.net> wrote: >> For any who might be curious, the Tally failure detailed below (in >> 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.weyrauch at 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" <drmajorbob at bigfoot.com> schrieb im Newsbeitrag >>> news:<fjav9f$rjb$1 at 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 >>>> <drmajorbob at 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.weyrauch at 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[]; >>>> >> >>>> >> >>>> >> >>>> >> >>>> >> >>>> >> >>>> >> >>>> > >>>> > >>>> > >>>> >>>> >>>> >>>> -- = >>>> >>>> DrMajorBob at bigfoot.com >>>> >>> >>> >> >> >> >> -- = >> >> DrMajorBob at longhorns.com >> >> > -- DrMajorBob at longhorns.com

**References**:**FYI, Tally is still broken.***From:*DrMajorBob <drmajorbob@att.net>