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Re: VerifySolutions setting


>Are there cases witch the default setting fails...?

I came across an interesting counter example recently.
However, it's not an issue w/ Mathematica 5.2 because it gave a valid
warning with the "Solve::verif" message.

Off[Solve::ifun]; 
Off[InverseFunction::ifun]; 
Off[Solve::verif]; 

Equ = (x + 1)^(1/x); 

Solve[equ == E, x, 
  VerifySolutions -> True]

{}

Ok.  No Solutions.  Everything was "obviously extraneous" and removed.

Solve[equ == E, x, 
  VerifySolutions -> False]

{{x -> 0}}

Hmmm.  If we test 0, it does not return E, so it's wrong.

equ /. x -> 0

Indeterminate

However...it is correct after all!

Limit[equ, x -> 0]

E

Try resolving, except turn on message.
On[Solve::verif]; 


Anyway, just thought this was interesting.

Dana
Windows XP, Mathematica 5.2



>Consider the following equation
>
>eq=x^(1/3) + x^(1/2) == a;
>
>With[{a = -3}, Solve[x^(1/3) + x^(1/2) == a, x, VerifySolutions ->
>Automatic]] (*default*)
>{}
>
>With[{a = -3}, Solve[x^(1/3) + x^(1/2) == a, x, VerifySolutions ->
>True]]          (*admissible 1*)
>{}
>
>With[{a = -3}, Solve[x^(1/3) + x^(1/2) == a, x, VerifySolutions ->
>False]]         (*admissible 2*)

<snip>

>Are there cases witch the default setting fails and VerifySolutions ->
>True must be used in order
>to eliminate extraneous roots?


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