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

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

functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...
Post a Comment
Read more

What is and isn't a valid variable specification for Manipulate?

I have an expression whose terms have arguments (representing subscripts), like this: myExpr = A[0] + V[1,T] I would like to put it inside a Manipulate to see its value as I move around the parameters. (The goal is eventually to plot it wrt one of the variables inside.) However, Mathematica complains when I set V[1,T] as a manipulated variable: Manipulate[Evaluate[myExpr], {A[0], 0, 1}, {V[1, T], 0, 1}] (*Manipulate::vsform: Manipulate argument {V[1,T],0,1} does not have the correct form for a variable specification. >> *) As a workaround, if I get rid of the symbol T inside the argument, it works fine: Manipulate[ Evaluate[myExpr /. T -> 15], {A[0], 0, 1}, {V[1, 15], 0, 1}] Why this behavior? Can anyone point me to the documentation that says what counts as a valid variable? And is there a way to get Manpiulate to accept an expression with a symbolic argument as a variable? Investigations I've done so far: I tried using variableQ from this answer , but it says V[1...
Post a Comment
Read more