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Re: Problem with Solve and NSolve
*To*: mathgroup at smc.vnet.net
*Subject*: [mg122518] Re: Problem with Solve and NSolve
*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>
*Date*: Sun, 30 Oct 2011 04:25:53 -0500 (EST)
*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com
*References*: <201110280935.FAA20759@smc.vnet.net> <201110291110.HAA05311@smc.vnet.net> <E0EE4F64-F1B0-4B96-8C9D-CF17C9E57B8A@mimuw.edu.pl>
On 29 Oct 2011, at 14:45, Andrzej Kozlowski wrote:
>
> On 29 Oct 2011, at 13:10, Daniel Lichtblau wrote:
>
>> W|A is (probably) using FindRoot in clever ways. You can get solutions
>> in a similar manner.
>
>
> Wolfram Alpha certainly uses Reduce (or Solve) to solve non-algebraic equations, e.g. try
>
> WolframAlpha["Solve[x Exp[x] == 2 Sin[x]&&Abs[x]<=10,x]"] in Mathematica (or directly in a browser).
>
> It will show real roots only but if you ask for more you also get the complex ones. If you do not give a bounding condition it will choose one by itself
>
> WolframAlpha["Solve[x Exp[x] == 2 Sin[x],x]"]
>
> and asssume that you want only real roots. I don't see any evidence that it "is using FindRoot in clever ways".
>
> Andrzej Kozlowski
I forgot the add that unlike Mathematica, Wolfram Alpha does not return exact solutions to any equations whose roots cannot be expressed in radicals, e.g. WolframAlpha["Solve[x^6+3x^2+x +1 == 0,x]"] will give only numerical solutions (however WolframAlpha["Solve[x^6+x^2+ 3 == 0,x]"] will return one exact solution as it can be expressed in terms of radicals). Perhaps this makes it look like FindRoot is being used but undoubtedly it is Solve (or Reduce - they seem to mean the same thing to WolframAlpha).
Andrzej Kozlowski
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