Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2006
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2006

[Date Index] [Thread Index] [Author Index]

Search the Archive

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


  • Prev by Date: Re: List difference using patterns and substitutions.
  • Next by Date: Re: Assumptions for Trigonometry Inequalities
  • Previous by thread: Re: Patterns_ to define linear operators?
  • Next by thread: Re: VerifySolutions setting