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From: "Michael Snyder" <sirzerp@mathworks.com>
Newsgroups: comp.soft-sys.matlab
Subject: algebraic problem, no explicit solution
Date: Mon, 18 Feb 2008 17:59:01 +0000 (UTC)
Organization: Murray State Univeristy
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I have a well known physics equation (dipole field) and I&#8217;m
trying to solve for constant values.  I can fill an array
with values and have Matlab plot the constant values very
easily. Wanted to solve the equation for a single constant
value and make it into a function that plots one curve at a
time.

i.e.  k=.002 is a curved line and k=.03 is a different
curved line.

x1 y1 z1, x2 y2 z2 are fixed foci points.

k is a given value, I just want to solve for y in terms of x
and z. 

--------------------------------------

>> syms x x1 x2 y y1 y2 z z1 z2 k K

>>
K=1/((x-x2)^2+(y-y2)^2+(z-z2)^2)^(1/2)-1/((x-x1)^2+(y-y1)^2+(z-z1)^2)^(1/2)-1/k
 
>> solve(K,y)
 
Warning: Explicit solution could not be found.

ans =

[ empty sym ]

--------------------------------------


How can a well known algebraic equation have no explicit
solution?  It is frustrating because I know which parameters
plot which lines.

Also I&#8217;ve tried a log form and got the same results.

--------------------------------------

K =
log(((x-x2)^2+(y-y2)^2+(z-z2)^2)^(1/2)-((x-x1)^2+(y-y1)^2+(z-z1)^2)^(1/2))-1/2*log((x-x1)^2+(y-y1)^2+(z-z1)^2)-1/2*log((x-x2)^2+(y-y2)^2+(z-z2)^2)-log(1/k)
 
>> solve(K,y)

ans =

[ empty sym ]

--------------------------------------