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?

**Follow-Ups**:**Re: Simplifying equations for Mathematica***From:*Daniel Lichtblau <danl@wolfram.com>