check_eigvals.tex

%% AMS-LaTeX Created by Wolfram Mathematica 7.0 for Students - Personal Use Only : www.wolfram.com

\documentclass{article}
\usepackage{amsmath, amssymb, graphics}

\newcommand{\mathsym}[1]{{}}
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\begin{document}

\noindent\(\pmb{\text{Clear}[a,b,n]}\\
\pmb{m=\{\{-2a n,a,0\},\{1,-1,1\},\{0,-b,0\}\};}\\
\pmb{m\text{//}\text{MatrixForm}}\\
\pmb{\text{match}=}\\
\pmb{\text{And}\text{@@}}\\
\pmb{(\text{Equal}\text{@@@}}\\
\pmb{\text{Transpose}[\{\text{CoefficientList}[\text{Expand}[k(l-x) (l-y) (l-z)],l],}\\
\pmb{\text{CoefficientList}[\text{CharacteristicPolynomial}[m,l],l]\}])}\\
\pmb{\text{FindInstance}[\text{match}\&\&a>0\&\&b>0\&\&n>0\&\&x<0\&\&y<0\&\&z<0,}\\
\pmb{\{a,b,n,x,y,z,k\}]}\)

\noindent\(\pmb{\text{match}=}\\
\pmb{\text{And}\text{@@}}\\
\pmb{(\text{Equal}\text{@@@}}\\
\pmb{\text{Transpose}[}\\
\pmb{\{\text{CoefficientList}[\text{Expand}[k(l-(x+I y)) (l-(x-I y)) (l-z)],l],}\\
\pmb{\text{CoefficientList}[\text{CharacteristicPolynomial}[m,l],l]\}])}\\
\pmb{\text{FindInstance}[\text{match}\&\&a>0\&\&b>0\&\&n>0\&\&x<0\&\&y\geq 0\&\&z<0,}\\
\pmb{\{a,b,n,x,y,z,k\}]}\\
\pmb{\text{FindInstance}[\text{match}\&\&a>0\&\&b>0\&\&n>0\&\&x>0\&\&y\geq 0\&\&z<0,}\\
\pmb{\{a,b,n,x,y,z,k\}]}\\
\pmb{\text{FindInstance}[\text{match}\&\&a>0\&\&b==14\&\&n\text{==}1/6\&\&x\text{==}0\&\&y\geq 0\&\&z<0,}\\
\pmb{\{a,b,n,x,y,z,k\}]}\\
\pmb{\text{FindInstance}[\text{match}\&\&a>0\&\&b>0\&\&n>0\&\&x>0\&\&y\geq 0\&\&z>0,}\\
\pmb{\{a,b,n,x,y,z,k\}]}\)

\end{document}