

%% 
%% This is a LaTeX document generated by automatic conversion of a
%% Mathematica notebook using Mathematica 5.0.
%% 
%% This document uses special macros that are defined in a LaTeX 
%% package file named notebook2e.sty.  Appropriate commands for 
%% loading the package have been included in this document.
%% 
%% The LaTeX package files can be found in a directory with path:
%% 
%% D:\Programme\Wolfram Research\Mathematica\5.0\SystemFiles\IncludeFiles\TeX\
%% 
%% The LaTeX package used in this document may require that your 
%% LaTeX implementation support fonts other than the standard 
%% Computer Modern fonts that are used by LaTeX.  For more
%% information see the Additional Information under TeXSave
%% in the Help Browser, or at
%% 
%% http://documents.wolfram.com/v5/RefGuide/TeXSave.html
%% 
%% Implementation-specific instructions for installing TeX-related 
%% files can be found at
%% 
%% http://support.wolfram.com/mathematica/interface/export/virtualfonts.html
%% 
%% 

\documentclass{article}
\usepackage{notebook2e, latexsym}


\begin{document}

\dispSFinmath{
G=\{y-x\RawWedge 5,z-x\RawWedge 2,z\RawWedge 2+y\RawWedge 2+x\RawWedge 3\};
}

\dispSFinmath{
\Mfunction{GroebnerBasis}[G,\{x,y,z\},\Mvariable{MonomialOrder}\rightarrow \Mvariable{Lexicographic}]
}

\dispSFoutmath{
\{-{z^9}-2\multsp {z^6}-{z^3}+{z^2},-{z^6}-{z^3}-y,-{z^5}-{z^2}-x\multsp z,z-{x^2}\}
}

\dispSFinmath{
\Mfunction{GroebnerBasis}[G,\{x,y,z\},\Mvariable{MonomialOrder}\rightarrow \Mvariable{DegreeLexicographic}]
}

\dispSFoutmath{
\{-{y^2}-{z^2}-x\multsp z,z-{x^2},{z^3}-x\multsp y,-z\multsp {y^2}-x\multsp y-y,x\multsp {y^2}+y+{z^2},-{y^4}-{y^3}-{z^2}\multsp y+x\multsp y+2\multsp
z\multsp y\}
}

\dispSFinmath{
\MathBegin{MathArray}{l}
\Mfunction{GroebnerBasis}[G,\{x,y,z\},  \\
\noalign{\vspace{0.636364ex}}
\hspace{1.em} \Mvariable{MonomialOrder}\rightarrow \Mvariable{DegreeReverseLexicographic}]\\
\MathEnd{MathArray}
}

\dispSFoutmath{
\{-{y^2}-{z^2}-x\multsp z,z-{x^2},x\multsp y-{z^3},y-x\multsp {z^2}\}
}

\dispSFinmath{
G=\{(1/a\multsp +b)y+x,y\RawWedge 2+1/a\multsp z\}
}

\dispSFoutmath{
\Big\{x+\Big(b+\frac{1}{a}\Big)\multsp y,{y^2}+\frac{z}{a}\Big\}
}

\dispSFinmath{
\MathBegin{MathArray}{l}
\Mfunction{GroebnerBasis}[G,\{x,y,z\},  \\
\noalign{\vspace{0.636364ex}}
\hspace{1.em} \Mvariable{MonomialOrder}\rightarrow \Mvariable{DegreeReverseLexicographic},  \\
\noalign{\vspace{0.636364ex}}
\hspace{1.em} \Mvariable{CoefficientDomain}\rightarrow \Mvariable{RationalFunctions}]\\
\MathEnd{MathArray}
}

\dispSFoutmath{
\Big\{x+\Big(b+\frac{1}{a}\Big)\multsp y,{y^2}+\frac{z}{a}\Big\}
}

\dispSFinmath{
\Mfunction{GroebnerBasis}[\{x,1-x\multsp y\},\{x,y\}]
}

\dispSFoutmath{
\{1\}
}

\dispSFinmath{
\{ \} 
}


\end{document}
