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 ->
>{}
>
>With[{a = -3}, Solve[x^(1/3) + x^(1/2) == a, x, VerifySolutions ->