ASKSAGE: Sage Q&A Forum - Individual question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 10 Feb 2015 03:23:06 -0600System of 3 equations in 3 variables with symbolic coefficientshttp://ask.sagemath.org/question/25786/system-of-3-equations-in-3-variables-with-symbolic-coefficients/ 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?
Mon, 09 Feb 2015 20:40:02 -0600http://ask.sagemath.org/question/25786/system-of-3-equations-in-3-variables-with-symbolic-coefficients/Answer by Dima for <p>Here is my Sage code:</p>
<pre><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)
</code></pre>
<p>When I evaluate this, all I get are my original input equations, pretty-printed.</p>
<p>I am expecting a solution for x, y and z in terms of the other constant symbols and that's not happening.</p>
<p>How can I get Sage to solve these equations?</p>
http://ask.sagemath.org/question/25786/system-of-3-equations-in-3-variables-with-symbolic-coefficients/?answer=25790#post-id-25790I 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. Tue, 10 Feb 2015 03:23:06 -0600http://ask.sagemath.org/question/25786/system-of-3-equations-in-3-variables-with-symbolic-coefficients/?answer=25790#post-id-25790