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?