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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?
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Posted 10 years ago
 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 10 years ago
 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 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 10 years ago
 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 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 10 years ago
 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 10 years ago
 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 10 years ago
 It also happens in 10.0. I wouldn't really call it a "simple" expression.