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MathGroup Archive 2006

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Simplifying equations for Mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg65752] Simplifying equations for Mathematica
  • From: Yaroslav Bulatov <yaroslavvb at gmailnospa.com>
  • Date: Sun, 16 Apr 2006 03:49:30 -0400 (EDT)
  • Organization: Oregon State University
  • Sender: owner-wri-mathgroup at wolfram.com

[This post has been delayed due to email problems - moderator]


I'm trying to solve some likelihood equations, and Mathematica will not

finish in reasonable time. I'm wondering if there is a way I can

rewrite it so that Mathematica can do them



The concrete example is

f[t1,t2,t3,t4,t5]=Log[Exp[0]+Exp[t1]+Exp[t2]+Exp[t1+t2]+Exp[t5]+Exp[t5+t1
+t2]+Exp[t5+t2+t4]+Exp[t1+t2+t3+t4+t5]]



The gradient of f defines a map R^5->R^5, and I need to invert that

map. (This particular example can be solved by hand, but I'm wondering 
about other cases of the same form)



Here's the command I use to solve it (works on Mathematica 5.2 only)

Solve[Map[Apply[Equal,#]&,Thread[{D[Log[Exp[0]+Exp[t1]+Exp[t2]+Exp[t1+t2]
+Exp[t5]+Exp[t5+t1+t2]+Exp[t5+t2+t4]+Exp[t1+t2+t3+t4+t5]],
{{t1,t2,t3,t4,t5},1}],{m1,m2,m3,m4,m5}}]],{t1,t2,t3,t4,t5}]



It's been running for several days on a Pentium 2Ghz. Are there simple

transformations I can do to help Mathematica solve it?


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