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Re: Solve fails

  • To: mathgroup at
  • Subject: [mg33346] Re: [mg33326] Solve fails
  • From: Andrzej Kozlowski <andrzej at>
  • Date: Sat, 16 Mar 2002 01:40:35 -0500 (EST)
  • Sender: owner-wri-mathgroup at

Solve is not meant to find approximate solutions at all, and is not 
really  intended to be used to solve non-algebraic ones. It does of 
course "solve" some simple non-algebraic equations in terms of "Inverse 
Functions", e,g. it will give some solutions to Solve[Sin[x^3] == 1, x]. 
So, the issue being raised, is, I assume, whether Solve ought to find 
the "trivial" solutions, like x==0,x=1, x=-1 for it clearly cannot be 
expected to find x=+-2.0253909752730426 (this is , a job for FindRoot). 
These "trivial" solutions are "essentially algebraic" since they just 
the solutions x^3==x. In some similar cases Mathematica does get the 
expected answer:

Solve[ArcSin[x] == ArcSin[x^3], x]

{{x -> -1}, {x -> 0}, {x -> 1}}

Solve[Exp[x] == Exp[x^3], x]

 From In[2]:=
Solve::ifun:Inverse functions are being used by Solve, so some solutions 
may \
not be found.

{{x -> -1}, {x -> 0}, {x -> 1}}

Solve[Log[x] == Log[x^3], x]

{{x -> -1}, {x -> 1}}

but it others it does not. Should it? Well, I do not know, and I do not 
think it is terribly important, since all such solutions lie clearly 
"beyond the call of duty" of Solve. However, evaluating

Trace[Solve[x*Sin[x] == x*Sin[x^3], x], TraceInternal -> True]

seems to show that Solve does notice that the equation is equivalent to 
x==0 || Sin[x]-Sin[x^3]==0, so it ought at least to give 0 as a solution 
but then it somehow manages to  "loose" it and returns {{}}.

Andrzej Kozlowski
Toyama International University

On Friday, March 15, 2002, at 12:51  AM, Richard Fateman wrote:

> Solve[x*Sin[x]==x*Sin[x^3],x] gives {{}}
> but
> Solve[Sin[x]==Sin[x^3],x]  returns unchanged
> each gives a warning.
> There are very many solutions, among them x=0, x=+-1,
> x=+-2.0253909752730426 approximately

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