Re: system of simultaneous equations

• To: mathgroup at smc.vnet.net
• Subject: [mg22923] Re: [mg22895] system of simultaneous equations
• From: Bojan Bistrovic <bojanb at python.physics.odu.edu>
• Date: Thu, 6 Apr 2000 02:04:39 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```> WHile I've got the attention of a Mathematica expert, I am wanting to
> select a single root of a system of simultaneous equations (with
> positive values for all 3 variables) - and (being new to mathematica)
> cannot work out how to do this. I successfully get a list of roots, but
> cannot make the (you would think) easy step to reduce the list to
> only (positive) roots. Any help VERY gratefully received. I have
> searched in Mathgroup at Wolfram without finding anything.
>
> Cheers
>
>
> David Braunholtz
> Department of Public Health & Epidemiology
> Public Health Building
> University of Birmingham
> Birmingham B15 2TT
> E-Mail:  D.A.Braunholtz at bham.ac.uk
> Tel: 0121-414-7495
> FAX: 0121-414-7878
>
Assuming that your results are in the form

results={ {x1,y2,z1}, {x2,y2,z2}, {x3,y3,z3}, ...}
you would select the ones where all {xn,yn,zn} are positive with

Select[results, (And@@Map[Positive,#])& ]

If you are using Solve or something like that to get your results, they would
be in a form

results2={ {x->x1, y->y1,z->z1},{x->x2, y->y2,z->z2},{x->x3, y->y3,z->z3}, ...}

In this case you'd have to modify the line to

Select[results2, (And@@Map[Positive[#[[2]]]&,#])&]

Here's some examples:

In[1]:= results={{1,2,3},{-3,4,5},{4,-5,6},{7,8,9},{2+3I,4,5},{3,5+5I,7}};
In[2]:= results2={ {x->1,y->2,z->3}, {x->-3,y->4,z->5}, {x->7,y->8,z->9},
{x->2+3I,y-> 4,z->5}}

In[3]:= Select[results, (And@@Map[Positive,#])& ]
Out[3]={{1,2,3},{7,8,9}}

In[4]:= Select[results2, (And@@Map[Positive[#[[2]]]&,#])&]
Out[4]={{x -> 1,y -> 2,z -> 3},{x -> 7,y -> 8,z -> 9}}

Bye, Bojan

--
---------------------------------------------------------------------
Bojan Bistrovic,                                      bojanb at jlab.org
Old Dominion University, Norfolk VA & Jefferson Lab, Newport News, VA
---------------------------------------------------------------------

```

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