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Re: How to choose real positive solutions only?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg74346] Re: How to choose real positive solutions only?
*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
*Date*: Mon, 19 Mar 2007 02:05:54 -0500 (EST)
*Organization*: The Open University, Milton Keynes, UK
*References*: <etije4$irj$1@smc.vnet.net>
Dix, Manfredo A wrote:
> Hello,
> this question probably came up before, but anyway:
>
> suppose I have a system of 3 equations and 3 unknowns,
> which I want to solve numerically with NSolve.
> They are polynomial of degree "n" so that I get n solutions.
>
> Is there a way to tell Mathematica to just return the
> real positive solutions, and dismiss the imaginary and negative
> ones?
>
> thank you so much for any help,
> cordially,
>
> Manfred
> mdix at tulane.edu
>
>
You cannot. However, you case use Mathematica pattern matching
capabilities to extract whatever you want from the solutions returned by
NSolve. For instance,
In[1]:=
eqns = {x^5 + y^2 + z == 1, 2*x + y - z == 2, x - 3*y + z == 3};
sols = NSolve[eqns, {x, y, z}]
Out[2]=
{{x\[Rule]-1.69511, y\[Rule]-5.04267,z\[Rule]-10.4329},
{x\[Rule]0.24097 + 1.42038 I, y\[Rule] -2.13854 + 2.13058 I, z\[Rule]
-3.6566 + 4.97134 I},
{x\[Rule] 0.24097 - 1.42038 I, y\[Rule] -2.13854 - 2.13058 I, z\[Rule]
-3.6566 - 4.97134 I},
{x\[Rule] 1., y\[Rule] -1., z\[Rule] -1.},
{x\[Rule] 0.213171, y\[Rule] -2.18024, z\[Rule] -3.7539}}
In[3]:=
(* We want the three variables negative *)
Cases[sols, {x_ -> xval_Real /; xval < 0, y_ -> yval_Real /; yval < 0,
z_ -> zval_Real /; zval < 0}]
Out[4]=
{{x\[Rule]-1.69511, y\[Rule]-5.04267, z\[Rule]-10.4329}}
In[5]:=
(* We want the first variable positive and the other two negative *)
Cases[sols, {x_ -> xval_Real /; xval > 0, y_ -> yval_Real /; yval < 0,
z_ -> zval_Real /; zval < 0}]
Out[6]=
{{x\[Rule]1., y\[Rule]-1., z\[Rule]-1.},
{x\[Rule]0.213171, y\[Rule]-2.18024, z\[Rule]-3.7539}}
HTH,
Jean-Marc
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