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System of 3 equations in 3 variables with symbolic coefficients

asked 2015-02-09 20:40:02 -0500

dhathri gravatar image

updated 2015-02-10 06:15:40 -0500

Here is my Sage code:

a, b, c, d, e, f, k, l, m, n, x, y, z = var('a, b, c, d, e, f, k, l, m, n, x, y, z')
eq1 = x*k+(a/m)-(x*d/(sqrt(x^2+y^2+z^2)*e*f))==0
eq2 = y*l+(b/m)-(y*d/(sqrt(x^2+y^2+z^2)*e*f))==0
eq3 = z*n+(c/m)-(z*d/(sqrt(x^2+y^2+z^2)*e*f))==0
print solve([eq1,eq2,eq3],x,y,z)

When I evaluate this, all I get are my original input equations, pretty-printed.

I am expecting a solution for x, y and z in terms of the other constant symbols and that's not happening.

How can I get Sage to solve these equations?

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answered 2015-02-10 03:23:06 -0500

I very much doubt that there are closed form solutions for such a system. It looks like this would imply that univariate polynomial equations of arbitrary degrees have a closed form solution, which is well-known not to be the case.

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Asked: 2015-02-09 20:40:02 -0500

Seen: 211 times

Last updated: Feb 10 '15