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>