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Re: How can I make the NSolve output the roots meeting

• To: mathgroup at smc.vnet.net
• Subject: [mg86462] Re: [mg86446] How can I make the NSolve output the roots meeting
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Wed, 12 Mar 2008 00:09:58 -0500 (EST)
• References: <200803110801.DAA25007@smc.vnet.net>

Elements wrote:
> Hi everyone,
>  I'm dealing with an equation with NSolve, and  there are many roots
> of this equation, but I only need the roots which a real and positive.
> So which function or option should I choose?
> Thanks!

Most reliable would be to post process using, say, Select or maybe Cases.

NSolve has a built in capability, entirely undocumented, that can also 
be used. But there is no guarantee it will remain from one version to 
another. It lives in Internal` context.

SelectCriterion::usage =
"SelectCriterion is an option for NSolve that determines whether
to keep or discard a root in any variable. The value provided
should be a pure function. It will be applied to the pair
{var, candidate value} to determine whether to keep or discard
that value. Hence one can use different criteria for different
variables, provided these criteria are independent of one another."

Quick example:

In[8]:= NSolve[{x^3-2*x*y-4==0,y^3-3*x*y^2-4*x^2+7==0}, {x,y}]
Out[8]= {{x -> 6.23339, y -> 19.1067},
     {x -> -1.35984 - 1.14053 I, y -> 1.13758 + 0.826794 I},
     {x -> -1.35984 + 1.14053 I, y -> 1.13758 - 0.826794 I},
     {x -> -0.18174 + 0.678448 I, y -> 0.52317 + 2.62723 I},
     {x -> -0.18174 - 0.678448 I, y -> 0.52317 - 2.62723 I},
     {x -> 0.0492886 - 1.83995 I, y -> -1.72058 - 1.1769 I},
     {x -> 0.0492886 + 1.83995 I, y -> -1.72058 + 1.1769 I},
     {x -> 1.3756 + 0.240822 I, y -> -0.493535 + 0.578238 I},
     {x -> 1.3756 - 0.240822 I, y -> -0.493535 - 0.578238 I}}

In[9]:= NSolve[{x^3-2*x*y-4==0,y^3-3*x*y^2-4*x^2+7==0}, {x,y},
   Internal`SelectCriterion->(Im[#[[2]]]==0 && Re[#[[2]]]>=0&)]
Out[9]= {{x -> 6.23339, y -> 19.1067}}

 From the way NSolve works, there is almost never any speed advantage to 
be had by using this option. It's just a convenience.

Daniel Lichtblau
Wolfram Research

• References:
  • How can I make the NSolve output the roots meeting the constraint conditions?
    • From: Elements <philyer@gmail.com>