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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 *)

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