Re: VerifySolutions setting
- To: mathgroup at smc.vnet.net
- Subject: [mg71423] Re: VerifySolutions setting
- From: "dimitris" <dimmechan at yahoo.com>
- Date: Fri, 17 Nov 2006 04:31:06 -0500 (EST)
- References: <ejgudg$888$1@smc.vnet.net>
In case I was not clear I ask about situations
I ask about cases where the default
Solve[..., VerifySolutions->Automatic] gives extreneous roots
and Solve[...,VerifySolutions->True] must be used.
Thanks a lot
dimitris wrote:
> Information["VerifySolutions", LongForm -> True]
>
> "VerifySolutions is an option to Solve and related functions. With
> VerifySolutions -> True, solutions are verified and extraneous
> solutions are eliminated. With VerifySolutions -> False, they are not.
> Note that only those numerical solutions that are obviously extraneous
> are eliminated."
> Attributes[VerifySolutions] = {Protected}
>
> 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]] (*admissable 1*)
> {}
>
> With[{a = -3}, Solve[x^(1/3) + x^(1/2) == a, x, VerifySolutions ->
> False]] (*admissable 2*)
> {{x -> 46/3 + (1/3)*(136109/2 - (6561*Sqrt[85])/2)^(1/3) +
> (1/3)*((1/2)*(136109 + 6561*Sqrt[85]))^(1/3)}, {x -> 46/3 - (1/6)*(1 +
> I*Sqrt[3])*(136109/2 - (6561*Sqrt[85])/2)^(1/3) -
> (1/6)*(1 - I*Sqrt[3])*((1/2)*(136109 + 6561*Sqrt[85]))^(1/3)},
> {x -> 46/3 - (1/6)*(1 - I*Sqrt[3])*(136109/2 -
> (6561*Sqrt[85])/2)^(1/3) -
> (1/6)*(1 + I*Sqrt[3])*((1/2)*(136109 + 6561*Sqrt[85]))^(1/3)}}
>
> Are there cases witch the default setting fails and VerifySolutions ->
> True must be used in order
> to eliminate extreneous roots?
>
> Thanks a lot,
> Dimitris