VerifySolutions setting

*To*: mathgroup at smc.vnet.net*Subject*: [mg71363] VerifySolutions setting*From*: "dimitris" <dimmechan at yahoo.com>*Date*: Thu, 16 Nov 2006 00:52:37 -0500 (EST)

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

**Follow-Ups**:**Re: VerifySolutions setting***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>