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Kernel hangs up when evaluating simple expression.

Mario Weitzer
Posted 11 years ago

I'm using Mathematica 8.0.1 and when I try to evaluate the following expression:

FullSimplify[{-(7/9)+1/(3 Sqrt[2 (1+(-89-252 (-(13469/22572)+(31 Sqrt[527/2])/11286)-162 (-(13469/22572)+(31 Sqrt[527/2])/11286)^2)/(162 (4087/22572+(31 Sqrt[527/2])/11286)^2))]),(5 Sqrt[2])/9+Sqrt[(-89-252 (-(13469/22572)+(31 Sqrt[527/2])/11286)-162 (-(13469/22572)+(31 Sqrt[527/2])/11286)^2)/(1+(-89-252 (-(13469/22572)+(31 Sqrt[527/2])/11286)-162 (-(13469/22572)+(31 Sqrt[527/2])/11286)^2)/(162 (4087/22572+(31 Sqrt[527/2])/11286)^2))]/(54 (4087/22572+(31 Sqrt[527/2])/11286))}=={-(8/19)-1/Sqrt[19 (1+(-((31 Sqrt[2])/171)+1/(9 Sqrt[2/(-89-252 (-(13469/22572)+(31 Sqrt[527/2])/11286)-162 (-(13469/22572)+(31 Sqrt[527/2])/11286)^2)]))^2/(-(3965/22572)+(31 Sqrt[527/2])/11286)^2)],(14 Sqrt[2])/19-(-((31 Sqrt[2])/171)+1/(9 Sqrt[2/(-89-252 (-(13469/22572)+(31 Sqrt[527/2])/11286)-162 (-(13469/22572)+(31 Sqrt[527/2])/11286)^2)]))/((-(3965/22572)+(31 Sqrt[527/2])/11286) Sqrt[19 (1+(-((31 Sqrt[2])/171)+1/(9 Sqrt[2/(-89-252 (-(13469/22572)+(31 Sqrt[527/2])/11286)-162 (-(13469/22572)+(31 Sqrt[527/2])/11286)^2)]))^2/(-(3965/22572)+(31 Sqrt[527/2])/11286)^2)])}]

the kernel hangs up. Sometimes I get the correct result true before it hangs up. Does anybody know what the problem is? Does it also occur in newer versions?
POSTED BY: Mario Weitzer
8 Replies
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I am getting a similar problem when I try to simplify a truly simple expression. My entire computer gets hung up in Mathematica 10. More than that, two different computers running two different versions of Windows hang up on it. However, Mathematica 9 handles the expression without problems. I have attached a short notebook which contains the offending expression and which may be helpful in buttressing your case with tech support. Let me know if you have problems with it.

Attachments:
POSTED BY: Douglas Skinner

Bad, with Mathematica 10.0.0 the sequence of evaluation does not matter seemingly, needs investigation. Sometimes the second expression gets through, mostly not. RootApproximant[] works constantly

    In[1]:= FullSimplify[((-3965 + 31 Sqrt[1054]) (-1 + 
           9 Sqrt[1254/(230348 - 1891 Sqrt[1054] + 
                15710428 Sqrt[17/(341575 - 8174 Sqrt[1054])] - 
                10588825 Sqrt[62/(341575 - 8174 Sqrt[1054])])]))/22572 ==  0]
Out[1]= True

done as the second one, works always ... 

In[1]:= FullSimplify[((51250980 Sqrt[2] + 777480 Sqrt[527] + 
        Sqrt[31 (341575 - 8174 Sqrt[1054])] (4087 + 
           31 Sqrt[1054]))/(4087 + 31 Sqrt[1054]) - 
     9 Sqrt[2] (1848 + 
        Sqrt[(627 (-341575 + 8174 Sqrt[1054]))/(-94972831936 + 
             2528782877 Sqrt[1054] - 
             10732578888200 Sqrt[17/(341575 - 8174 Sqrt[1054])] + 
             5799967553399 Sqrt[
               62/(341575 - 8174 Sqrt[1054])])] (-4092 Sqrt[2] + 
           Sqrt[31 (341575 - 8174 Sqrt[1054])])))/22572 == 0]

done first, no result, kernel hangs up, the simpler one on top gets again In[1] ... 

 In[2]:= RootApproximant[((51250980 Sqrt[2] + 777480 Sqrt[527] + 
           Sqrt[31 (341575 - 8174 Sqrt[1054])] (4087 + 
              31 Sqrt[1054]))/(4087 + 31 Sqrt[1054]) - 
        9 Sqrt[2] (1848 + 
           Sqrt[(627 (-341575 + 8174 Sqrt[1054]))/(-94972831936 + 
                2528782877 Sqrt[1054] - 
                10732578888200 Sqrt[17/(341575 - 8174 Sqrt[1054])] + 
                5799967553399 Sqrt[
                  62/(341575 - 8174 Sqrt[1054])])] (-4092 Sqrt[2] + 
              Sqrt[31 (341575 - 8174 Sqrt[1054])])))/22572]

    Out[2]= 0
POSTED BY: Udo Krause
Mario Weitzer
Mario Weitzer
Posted 11 years ago

Unfortunately this is no option to me. This is just one of many similar computations and I need algebraic proof and not just numerical precision in these steps.
POSTED BY: Mario Weitzer

If you replace the FullSimplify[…] by N[…] it appears to work very well.

So

N[{-(7/9) + 
    1/(3 Sqrt[
        2 (1 + (-89 - 252 (-(13469/22572) + (31 Sqrt[527/2])/11286) - 
              162 (-(13469/22572) + (31 Sqrt[527/2])/
                   11286)^2)/(162 (4087/22572 + (31 Sqrt[527/2])/
                  11286)^2))]), (5 Sqrt[2])/9 + 
    Sqrt[(-89 - 252 (-(13469/22572) + (31 Sqrt[527/2])/11286) - 
         162 (-(13469/22572) + (31 Sqrt[527/2])/11286)^2)/(1 + (-89 - 
            252 (-(13469/22572) + (31 Sqrt[527/2])/11286) - 
            162 (-(13469/22572) + (31 Sqrt[527/2])/
                 11286)^2)/(162 (4087/22572 + (31 Sqrt[527/2])/
                11286)^2))]/(54 (4087/22572 + (31 Sqrt[527/2])/
          11286))} == {-(8/19) - 
    1/Sqrt[19 (1 + (-((31 Sqrt[2])/171) + 
             1/(9 Sqrt[
                 2/(-89 - 
                    252 (-(13469/22572) + (31 Sqrt[527/2])/11286) - 
                    162 (-(13469/22572) + (31 Sqrt[527/2])/
                    11286)^2)]))^2/(-(3965/22572) + (31 Sqrt[527/2])/
              11286)^2)], (14 Sqrt[2])/
     19 - (-((31 Sqrt[2])/171) + 
       1/(9 Sqrt[
           2/(-89 - 252 (-(13469/22572) + (31 Sqrt[527/2])/11286) - 
              162 (-(13469/22572) + (31 Sqrt[527/2])/
                   11286)^2)]))/((-(3965/22572) + (31 Sqrt[527/2])/
          11286) Sqrt[
        19 (1 + (-((31 Sqrt[2])/171) + 
               1/(9 Sqrt[
                   2/(-89 - 
                    252 (-(13469/22572) + (31 Sqrt[527/2])/11286) - 
                    162 (-(13469/22572) + (31 Sqrt[527/2])/
                    11286)^2)]))^2/(-(3965/22572) + (31 Sqrt[527/2])/
                11286)^2)])}]

is fast and gives the right result.

Cheers,

M.
POSTED BY: Marco Thiel
Mario Weitzer
Mario Weitzer
Posted 11 years ago

"I wouldn't really call it a "simple" expression."

I meant that it doesn't involve any complicated functions, only the most basic operations.

What you all write about splitting the lists is not true for me. If I only Simplify the expression, so if I evaluate

Simplify[{-(7/9)+1/(3 Sqrt[2 (1+(-89-252 (-(13469/22572)+(31 Sqrt[527/2])/11286)-162 (-(13469/22572)+(31 Sqrt[527/2])/11286)^2)/(162 (4087/22572+(31 Sqrt[527/2])/11286)^2))]),(5 Sqrt[2])/9+Sqrt[(-89-252 (-(13469/22572)+(31 Sqrt[527/2])/11286)-162 (-(13469/22572)+(31 Sqrt[527/2])/11286)^2)/(1+(-89-252 (-(13469/22572)+(31 Sqrt[527/2])/11286)-162 (-(13469/22572)+(31 Sqrt[527/2])/11286)^2)/(162 (4087/22572+(31 Sqrt[527/2])/11286)^2))]/(54 (4087/22572+(31 Sqrt[527/2])/11286))}=={-(8/19)-1/Sqrt[19 (1+(-((31 Sqrt[2])/171)+1/(9 Sqrt[2/(-89-252 (-(13469/22572)+(31 Sqrt[527/2])/11286)-162 (-(13469/22572)+(31 Sqrt[527/2])/11286)^2)]))^2/(-(3965/22572)+(31 Sqrt[527/2])/11286)^2)],(14 Sqrt[2])/19-(-((31 Sqrt[2])/171)+1/(9 Sqrt[2/(-89-252 (-(13469/22572)+(31 Sqrt[527/2])/11286)-162 (-(13469/22572)+(31 Sqrt[527/2])/11286)^2)]))/((-(3965/22572)+(31 Sqrt[527/2])/11286) Sqrt[19 (1+(-((31 Sqrt[2])/171)+1/(9 Sqrt[2/(-89-252 (-(13469/22572)+(31 Sqrt[527/2])/11286)-162 (-(13469/22572)+(31 Sqrt[527/2])/11286)^2)]))^2/(-(3965/22572)+(31 Sqrt[527/2])/11286)^2)])}]

I get

{-(((-3965+31 Sqrt[1054]) (-1+9 Sqrt[1254/(230348-1891 Sqrt[1054]+15710428 Sqrt[17/(341575-8174 Sqrt[1054])]-10588825 Sqrt[62/(341575-8174 Sqrt[1054])])]))/22572),((51250980 Sqrt[2]+777480 Sqrt[527]+Sqrt[31 (341575-8174 Sqrt[1054])] (4087+31 Sqrt[1054]))/(4087+31 Sqrt[1054])-9 Sqrt[2] (1848+Sqrt[(627 (-341575+8174 Sqrt[1054]))/(-94972831936+2528782877 Sqrt[1054]-10732578888200 Sqrt[17/(341575-8174 Sqrt[1054])]+5799967553399 Sqrt[62/(341575-8174 Sqrt[1054])])] (-4092 Sqrt[2]+Sqrt[31 (341575-8174 Sqrt[1054])])))/22572}=={0,0}

If I now split the expression and apply FullSimplify to both of them, different things happen depending of the order of evaluation.

FullSimplify[((-3965+31 Sqrt[1054]) (-1+9 Sqrt[1254/(230348-1891 Sqrt[1054]+15710428 Sqrt[17/(341575-8174 Sqrt[1054])]-10588825 Sqrt[62/(341575-8174 Sqrt[1054])])]))/22572==0]

FullSimplify[((51250980 Sqrt[2]+777480 Sqrt[527]+Sqrt[31 (341575-8174 Sqrt[1054])] (4087+31 Sqrt[1054]))/(4087+31 Sqrt[1054])-9 Sqrt[2] (1848+Sqrt[(627 (-341575+8174 Sqrt[1054]))/(-94972831936+2528782877 Sqrt[1054]-10732578888200 Sqrt[17/(341575-8174 Sqrt[1054])]+5799967553399 Sqrt[62/(341575-8174 Sqrt[1054])])] (-4092 Sqrt[2]+Sqrt[31 (341575-8174 Sqrt[1054])])))/22572==0]

If I evaluate the first expression first and then the second, it hangs up. If I do it the other way around, it usually works, though sometimes it also hangs up. Surprisingly calling

ClearSystemCache[]

between the two doesn't seem to make any difference.
POSTED BY: Mario Weitzer

Part of the problem may be that the left-hand side and the right-hand side of your equality are lists. If set expr = what's inside FullSimplify, I can get a result this way:

In[3]:= FullSimplify[expr /. Equal[a, b] -> a - b]

Out[3]= {0, 0}
POSTED BY: Frank Kampas

Your original expression hung up three times out of three trials (Mathematica 10.0.0 Windows 7 64 Bit); if one skips the Equal[] test of pairs and simply maps FullSimplify[] onto the 4 single expressions, it works seemless

In[1]:= FullSimplify /@ {-(7/9) + 
   1/(3 Sqrt[
       2 (1 + (-89 - 252 (-(13469/22572) + (31 Sqrt[527/2])/11286) - 
             162 (-(13469/22572) + (31 Sqrt[527/2])/
                  11286)^2)/(162 (4087/22572 + (31 Sqrt[527/2])/
                 11286)^2))]), (5 Sqrt[2])/9 + 
   Sqrt[(-89 - 252 (-(13469/22572) + (31 Sqrt[527/2])/11286) - 
        162 (-(13469/22572) + (31 Sqrt[527/2])/11286)^2)/(1 + (-89 - 
           252 (-(13469/22572) + (31 Sqrt[527/2])/11286) - 
           162 (-(13469/22572) + (31 Sqrt[527/2])/
                11286)^2)/(162 (4087/22572 + (31 Sqrt[527/2])/
               11286)^2))]/(54 (4087/22572 + (31 Sqrt[527/2])/
         11286)), -(8/19) - 
   1/Sqrt[19 (1 + (-((31 Sqrt[2])/171) + 
            1/(9 Sqrt[
                2/(-89 - 
                   252 (-(13469/22572) + (31 Sqrt[527/2])/11286) - 
                   162 (-(13469/22572) + (31 Sqrt[527/2])/
                    11286)^2)]))^2/(-(3965/22572) + (31 Sqrt[527/2])/
             11286)^2)], (14 Sqrt[2])/
    19 - (-((31 Sqrt[2])/171) + 
      1/(9 Sqrt[
          2/(-89 - 252 (-(13469/22572) + (31 Sqrt[527/2])/11286) - 
             162 (-(13469/22572) + (31 Sqrt[527/2])/
                  11286)^2)]))/((-(3965/22572) + (31 Sqrt[527/2])/
         11286) Sqrt[
       19 (1 + (-((31 Sqrt[2])/171) + 
              1/(9 Sqrt[
                  2/(-89 - 
                    252 (-(13469/22572) + (31 Sqrt[527/2])/11286) - 
                    162 (-(13469/22572) + (31 Sqrt[527/2])/
                    11286)^2)]))^2/(-(3965/22572) + (31 Sqrt[527/2])/
               11286)^2)])}

Out[1]= {(-13469 + 31 Sqrt[1054])/22572, (14617 Sqrt[2] - 61 Sqrt[527])/22572, 
         (-13469 + 31 Sqrt[1054])/22572, (14617 Sqrt[2] - 61 Sqrt[527])/22572}

the two pairs equal each other and you could restore the intended behavior by partitioning and asking for equality afterwards

In[9]:= Equal @@ 
 Partition[
  FullSimplify /@ {-(7/9) + 
     1/(3 Sqrt[
         2 (1 + (-89 - 
               252 (-(13469/22572) + (31 Sqrt[527/2])/11286) - 
               162 (-(13469/22572) + (31 Sqrt[527/2])/
                    11286)^2)/(162 (4087/22572 + (31 Sqrt[527/2])/
                   11286)^2))]), (5 Sqrt[2])/9 + 
     Sqrt[(-89 - 252 (-(13469/22572) + (31 Sqrt[527/2])/11286) - 
          162 (-(13469/22572) + (31 Sqrt[527/2])/
               11286)^2)/(1 + (-89 - 
             252 (-(13469/22572) + (31 Sqrt[527/2])/11286) - 
             162 (-(13469/22572) + (31 Sqrt[527/2])/
                  11286)^2)/(162 (4087/22572 + (31 Sqrt[527/2])/
                 11286)^2))]/(54 (4087/22572 + (31 Sqrt[527/2])/
           11286)), -(8/19) - 
     1/Sqrt[19 (1 + (-((31 Sqrt[2])/171) + 
              1/(9 Sqrt[
                  2/(-89 - 
                    252 (-(13469/22572) + (31 Sqrt[527/2])/11286) - 
                    162 (-(13469/22572) + (31 Sqrt[527/2])/
                    11286)^2)]))^2/(-(3965/22572) + (31 Sqrt[527/2])/
               11286)^2)], (14 Sqrt[2])/
      19 - (-((31 Sqrt[2])/171) + 
        1/(9 Sqrt[
            2/(-89 - 252 (-(13469/22572) + (31 Sqrt[527/2])/11286) - 
               162 (-(13469/22572) + (31 Sqrt[527/2])/
                    11286)^2)]))/((-(3965/22572) + (31 Sqrt[527/2])/
           11286) Sqrt[
         19 (1 + (-((31 Sqrt[2])/171) + 
                1/(9 Sqrt[
                    2/(-89 - 
                    252 (-(13469/22572) + (31 Sqrt[527/2])/11286) - 
                    162 (-(13469/22572) + (31 Sqrt[527/2])/
                    11286)^2)]))^2/(-(3965/22572) + (31 Sqrt[527/2])/
                 11286)^2)])}, 2]

Out[9]= True
POSTED BY: Udo Krause

It also happens in 10.0. I wouldn't really call it a "simple" expression.
POSTED BY: Frank Kampas
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