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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.

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[Â…] by N[Â…] 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

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

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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