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Re: Reduce/Solve

• To: mathgroup at smc.vnet.net
• Subject: [mg49997] Re: Reduce/Solve
• From: ab_def at prontomail.com (Maxim)
• Date: Tue, 10 Aug 2004 06:02:54 -0400 (EDT)
• References: <cf7djh$3na$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

An even simpler example:

In[1]:=
Reduce[x == E^(a*x), x]
Reduce[x == E^(y*x), x]

Out[1]=
Reduce[x == E^(a*x), x]

Out[2]=
C[1] \[Element] Integers && y != 0 && x == -(ProductLog[C[1], -y]/y)

What's more, Out[2] is incorrect because it misses the x==1&&y==0 case.

Maxim Rytin
m.r at inbox.ru


"Dana DeLouis" <delouis at bellsouth.net> wrote in message news:<cf7djh$3na$1 at smc.vnet.net>...
> Hello.  It is because of Mathematica's huge bug in variable names.  Reduce
> often doesn't work because of this bug.  The first thing you need to try is
> to change the variable name.  I would first start by changing the "r" to a
> variable name that comes near the beginning of the alphabet, like "a" (at
> least something before the "d" in the equation).
> 
> Taking your equation, and changing r to a:
> 
> eq = J == J0*(1 + r/d)*Exp[-(r/d)] /. r -> a
> 
> J == ((1 + a/d)*J0)/E^(a/d)
> 
> Now it should work:
> 
> tt = Reduce[eq, a]
> 
> d != 0 && J == 0 &&
>    (J0 == 0 || a == -d) ||
>   C[1] ? Integers &&
>    J != 0 && J0 != 0 &&
>    d != 0 && a ==
>     -d - d*ProductLog[C[1],
>        -(J/(E*J0))]
> 
> HTH
> Sad, isn't it!
> 
> Dana
> 
> 
> "Dr A.H. Harker" <a.harker at ucl.ac.uk> wrote in message
> news:cetf3i$6i8$1 at smc.vnet.net...
> > Dear All,
> >          I tend to think of Reduce as a more powerful tool than Solve,
> > yet with
> >
> > eq = J == J0 (1 + r/d) Exp[-r/d]
> > ss = Solve[eq, r]
> > tt = Reduce[eq, r]
> >
> >  I get useful output from Solve, but Reduce returns the expression
> > unevaluated. What am I missing?  Mathematica 5.0.0.0 under Windows XP.
> >
> >        Tony
> >
> >  Dr A.H. Harker
> >  Director of Postgraduate Studies
> >  Deputy Head, Condensed Matter and Materials Physics Group
> >  Department of Physics and Astronomy
> >  University College London
> >  Gower Street
> >  LONDON
> >  WC1E  6BT
> >  (44)(0)207 679 3404
> >  a.harker at ucl.ac.uk
> >
> >
> >