Re: VerifySolutions setting
- To: mathgroup at smc.vnet.net
- Subject: [mg71537] Re: VerifySolutions setting
- From: "Dana DeLouis" <dana.del at gmail.com>
- Date: Wed, 22 Nov 2006 05:22:19 -0500 (EST)
>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?