Skip to main content

bugs - Factor fails on a simple expression


Bug introduced in 9.0 and fixed in 11.3.0



Consider the following symbolic expression (all the c's are undefined)



exp = (-4*I)*(-1 + c22)*Pi*c1[c7[c12], c7[Glu5], c7[c9[c1312][0]]]*
c13[{c7[Glu5], c7[c9[c1312][0]]}, c10[c25], c10[c24]]*
c8[c11[c15, c6], c5[l, c6]]*
c4[c5[p2, c6], c6].c4[c5[l, c6], c6].c4[c5[p1, c6], c6]*c40[c15]*
c40[c20] - (4*I)*(-1 + c22)*Pi*
c1[c7[c12], c7[Glu5], c7[c9[c1312][0]]]*
c13[{c7[Glu5], c7[c9[c1312][0]]}, c10[c25], c10[c24]]*
c8[c11[c15, c6], c5[p2, c6]]*
c4[c5[p1, c6], c6].c4[c5[p2, c6], c6]*c40[c14]*c40[c15]*
c40[c20] - (4*I)*(-1 + c22)*Pi*

c1[c7[c12], c7[Glu5], c7[c9[c1312][0]]]*
c13[{c7[Glu5], c7[c9[c1312][0]]}, c10[c25], 
 c10[c24]]*(c8[c5[p1, c6], c5[p1, c6]] - 
  2*c8[c5[p1, c6], c5[p2, c6]] + 
  c8[c5[p2, c6], 
   c5[p2, c6]])*(c4[c5[p1, c6], c6].c4[c5[p1, c6], c6].c4[
    c11[c15, c6], c6] - 
  c4[c5[p2, c6], c6].c4[c5[p1, c6], c6].c4[c11[c15, c6], c6] + 
  c4[c5[p1, c6], c6].c4[c11[c15, c6], c6]*c40[c14] - 
  c4[c5[p2, c6], c6].c4[c11[c15, c6], c6]*c40[c14])*c40[c15]*

c40[c20] + (4*I)*(-1 + c22)*Pi*
c1[c7[c12], c7[Glu5], c7[c9[c1312][0]]]*
c13[{c7[Glu5], c7[c9[c1312][0]]}, c10[c25], c10[c24]]*
c8[c11[c15, c6], 
 c5[p1, c6]]*(c4[c5[p1, c6], c6].c4[c5[p1, c6], c6].c4[c5[p1, c6],
     c6] - c4[c5[p1, c6], c6].c4[c5[p1, c6], c6].c4[c5[p2, c6], 
    c6] - c4[c5[p2, c6], c6].c4[c5[p1, c6], c6].c4[c5[p1, c6], 
    c6] + c4[c5[p2, c6], c6].c4[c5[p1, c6], c6].c4[c5[p2, c6], 
    c6] + c4[c5[p1, c6], c6].c4[c5[p1, c6], c6]*c40[c14] - 
  c4[c5[p1, c6], c6].c4[c5[p2, c6], c6]*c40[c14] - 

  c4[c5[p2, c6], c6].c4[c5[p1, c6], c6]*c40[c14] + 
  c4[c5[p2, c6], c6].c4[c5[p2, c6], c6]*c40[c14])*c40[c15]*
c40[c20];

Now try to evaluate the following code


AbsoluteTiming[res1 = Simplify[exp];]
AbsoluteTiming[res2 = Factor[exp];]
Simplify[res1 - res2]

On Mathematica 8 (Linux version) both Simplify and Factor finish in less than 0.1 seconds. However, with all newer versions (9, 10.3, 11.0) that I have, Factor never finishes, while Simplify is still very fast.



To me this looks like a bug/regression, but may be someone has a sensible explanation for this behavior. I have not reported this to WRI so far, but I'm planning to do so.


Edit:


res1 is


(-4*I)*(-1 + c22)*Pi*c1[c7[c12], c7[Glu5], c7[c9[c1312][0]]]*
 c13[{c7[Glu5], c7[c9[c1312][0]]}, c10[c25], c10[c24]]*c40[c15]*c40[c20]*
 (c40[c14]*c8[c11[c15, c6], c5[p2, c6]]*c4[c5[p1, c6], c6] . 
    c4[c5[p2, c6], c6] + c8[c11[c15, c6], c5[l, c6]]*
   c4[c5[p2, c6], c6] . c4[c5[l, c6], c6] . c4[c5[p1, c6], c6] + 
  (c8[c5[p1, c6], c5[p1, c6]] - 2*c8[c5[p1, c6], c5[p2, c6]] + 
    c8[c5[p2, c6], c5[p2, c6]])*

   (c40[c14]*(c4[c5[p1, c6], c6] . c4[c11[c15, c6], c6] - 
      c4[c5[p2, c6], c6] . c4[c11[c15, c6], c6]) + 
    c4[c5[p1, c6], c6] . c4[c5[p1, c6], c6] . c4[c11[c15, c6], c6] - 
    c4[c5[p2, c6], c6] . c4[c5[p1, c6], c6] . c4[c11[c15, c6], c6]) - 
  c8[c11[c15, c6], c5[p1, c6]]*
   (c40[c14]*(c4[c5[p1, c6], c6] . c4[c5[p1, c6], c6] - 
      c4[c5[p1, c6], c6] . c4[c5[p2, c6], c6] - c4[c5[p2, c6], c6] . 
       c4[c5[p1, c6], c6] + c4[c5[p2, c6], c6] . c4[c5[p2, c6], c6]) + 
    c4[c5[p1, c6], c6] . c4[c5[p1, c6], c6] . c4[c5[p1, c6], c6] - 
    c4[c5[p1, c6], c6] . c4[c5[p1, c6], c6] . c4[c5[p2, c6], c6] - 

    c4[c5[p2, c6], c6] . c4[c5[p1, c6], c6] . c4[c5[p1, c6], c6] + 
    c4[c5[p2, c6], c6] . c4[c5[p1, c6], c6] . c4[c5[p2, c6], c6]))

res2 is


(-4*I)*(-1 + c22)*Pi*c1[c7[c12], c7[Glu5], c7[c9[c1312][0]]]*
 c13[{c7[Glu5], c7[c9[c1312][0]]}, c10[c25], c10[c24]]*c40[c15]*c40[c20]*
 (c40[c14]*c8[c5[p1, c6], c5[p1, c6]]*c4[c5[p1, c6], c6] . 
    c4[c11[c15, c6], c6] - 2*c40[c14]*c8[c5[p1, c6], c5[p2, c6]]*
   c4[c5[p1, c6], c6] . c4[c11[c15, c6], c6] + 
  c40[c14]*c8[c5[p2, c6], c5[p2, c6]]*c4[c5[p1, c6], c6] . 

    c4[c11[c15, c6], c6] - c40[c14]*c8[c11[c15, c6], c5[p1, c6]]*
   c4[c5[p1, c6], c6] . c4[c5[p1, c6], c6] + 
  c40[c14]*c8[c11[c15, c6], c5[p1, c6]]*c4[c5[p1, c6], c6] . 
    c4[c5[p2, c6], c6] + c40[c14]*c8[c11[c15, c6], c5[p2, c6]]*
   c4[c5[p1, c6], c6] . c4[c5[p2, c6], c6] - 
  c40[c14]*c8[c5[p1, c6], c5[p1, c6]]*c4[c5[p2, c6], c6] . 
    c4[c11[c15, c6], c6] + 2*c40[c14]*c8[c5[p1, c6], c5[p2, c6]]*
   c4[c5[p2, c6], c6] . c4[c11[c15, c6], c6] - 
  c40[c14]*c8[c5[p2, c6], c5[p2, c6]]*c4[c5[p2, c6], c6] . 
    c4[c11[c15, c6], c6] + c40[c14]*c8[c11[c15, c6], c5[p1, c6]]*

   c4[c5[p2, c6], c6] . c4[c5[p1, c6], c6] - 
  c40[c14]*c8[c11[c15, c6], c5[p1, c6]]*c4[c5[p2, c6], c6] . 
    c4[c5[p2, c6], c6] + c8[c5[p1, c6], c5[p1, c6]]*
   c4[c5[p1, c6], c6] . c4[c5[p1, c6], c6] . c4[c11[c15, c6], c6] - 
  2*c8[c5[p1, c6], c5[p2, c6]]*c4[c5[p1, c6], c6] . c4[c5[p1, c6], c6] . 
    c4[c11[c15, c6], c6] + c8[c5[p2, c6], c5[p2, c6]]*
   c4[c5[p1, c6], c6] . c4[c5[p1, c6], c6] . c4[c11[c15, c6], c6] - 
  c8[c11[c15, c6], c5[p1, c6]]*c4[c5[p1, c6], c6] . c4[c5[p1, c6], c6] . 
    c4[c5[p1, c6], c6] + c8[c11[c15, c6], c5[p1, c6]]*
   c4[c5[p1, c6], c6] . c4[c5[p1, c6], c6] . c4[c5[p2, c6], c6] + 

  c8[c11[c15, c6], c5[l, c6]]*c4[c5[p2, c6], c6] . c4[c5[l, c6], c6] . 
    c4[c5[p1, c6], c6] - c8[c5[p1, c6], c5[p1, c6]]*
   c4[c5[p2, c6], c6] . c4[c5[p1, c6], c6] . c4[c11[c15, c6], c6] + 
  2*c8[c5[p1, c6], c5[p2, c6]]*c4[c5[p2, c6], c6] . c4[c5[p1, c6], c6] . 
    c4[c11[c15, c6], c6] - c8[c5[p2, c6], c5[p2, c6]]*
   c4[c5[p2, c6], c6] . c4[c5[p1, c6], c6] . c4[c11[c15, c6], c6] + 
  c8[c11[c15, c6], c5[p1, c6]]*c4[c5[p2, c6], c6] . c4[c5[p1, c6], c6] . 
    c4[c5[p1, c6], c6] - c8[c11[c15, c6], c5[p1, c6]]*
   c4[c5[p2, c6], c6] . c4[c5[p1, c6], c6] . c4[c5[p2, c6], c6])

Answer




This bug in Factor has been addressed as of version 11.3.0.


While the example may take some seconds to run, it will not hang


AbsoluteTiming[res1 = Simplify[exp];]
AbsoluteTiming[res2 = Factor[exp];]
Simplify[res1 - res2]

(* {0.060817, Null} *)
(* {13.5211, Null} *)
(* 0 *)

Comments

Post a Comment

Popular posts from this blog

front end - keyboard shortcut to invoke Insert new matrix

I frequently need to type in some matrices, and the menu command Insert > Table/Matrix > New... allows matrices with lines drawn between columns and rows, which is very helpful. I would like to make a keyboard shortcut for it, but cannot find the relevant frontend token command (4209405) for it. Since the FullForm[] and InputForm[] of matrices with lines drawn between rows and columns is the same as those without lines, it's hard to do this via 3rd party system-wide text expanders (e.g. autohotkey or atext on mac). How does one assign a keyboard shortcut for the menu item Insert > Table/Matrix > New... , preferably using only mathematica? Thanks! Answer In the MenuSetup.tr (for linux located in the $InstallationDirectory/SystemFiles/FrontEnd/TextResources/X/ directory), I changed the line MenuItem["&New...", "CreateGridBoxDialog"] to read MenuItem["&New...", "CreateGridBoxDialog", MenuKey["m", Modifiers-...
Post a Comment
Read more

How to thread a list

I have data in format data = {{a1, a2}, {b1, b2}, {c1, c2}, {d1, d2}} Tableform: I want to thread it to : tdata = {{{a1, b1}, {a2, b2}}, {{a1, c1}, {a2, c2}}, {{a1, d1}, {a2, d2}}} Tableform: And I would like to do better then pseudofunction[n_] := Transpose[{data2[[1]], data2[[n]]}]; SetAttributes[pseudofunction, Listable]; Range[2, 4] // pseudofunction Here is my benchmark data, where data3 is normal sample of real data. data3 = Drop[ExcelWorkBook[[Column1 ;; Column4]], None, 1]; data2 = {a #, b #, c #, d #} & /@ Range[1, 10^5]; data = RandomReal[{0, 1}, {10^6, 4}]; Here is my benchmark code kptnw[list_] := Transpose[{Table[First@#, {Length@# - 1}], Rest@#}, {3, 1, 2}] &@list kptnw2[list_] := Transpose[{ConstantArray[First@#, Length@# - 1], Rest@#}, {3, 1, 2}] &@list OleksandrR[list_] := Flatten[Outer[List, List@First[list], Rest[list], 1], {{2}, {1, 4}}] paradox2[list_] := Partition[Riffle[list[[1]], #], 2] & /@ Drop[list, 1] RM[list_] := FoldList[Transpose[{First@li...
Post a Comment
Read more

mathematical optimization - Minimizing using indices, error: Part::pkspec1: The expression cannot be used as a part specification

I want to use Minimize where the variables to minimize are indices pointing into an array. Here a MWE that hopefully shows what my problem is. vars = u@# & /@ Range[3]; cons = Flatten@ { Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; Minimize[{Total@((vec1[[#]] - vec2[[u[#]]])^2 & /@ Range[1, 3]), cons}, vars, Integers] The error I get: Part::pkspec1: The expression u[1] cannot be used as a part specification. >> Answer Ok, it seems that one can get around Mathematica trying to evaluate vec2[[u[1]]] too early by using the function Indexed[vec2,u[1]] . The working MWE would then look like the following: vars = u@# & /@ Range[3]; cons = Flatten@{ Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; NMinimize[ {Total@((vec1[[#]] - Indexed[vec2, u[#]])^2 & /@ R...
Post a Comment
Read more