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Kernel hangs up when evaluating simple expression.

Posted 10 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

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
Posted 10 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
Posted 10 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
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
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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