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?
fkampas
July 27, 2014, 3:38pm
2
It also happens in 10.0. I wouldn’t really call it a “simple” expression.
sukrause
July 27, 2014, 3:46pm
3
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
fkampas
July 27, 2014, 3:46pm
4
Part of the problem may be that the left-hand side and the right-hand side of your equality are lists.
In[3]:= FullSimplify[expr /. Equal[a_, b_] → a - b]
Out[3]= {0, 0}
“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.
mthiel
July 27, 2014, 5:07pm
6
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.
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.
sukrause
July 27, 2014, 7:05pm
8
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
skinnerd
September 2, 2014, 4:40pm
9
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.