%% Created by Maple 9.5, Linux
%% Source Worksheet: Untitled (1)
%% Generated: Sun May 10 17:38:23 CEST 2009
\documentclass{article}
\usepackage{maplestd2e}
\def\emptyline{\vspace{12pt}}
\DefineParaStyle{Maple Heading 4}
\DefineParaStyle{Maple Heading 2}
\DefineParaStyle{Maple Text Output}
\DefineParaStyle{Maple Bullet Item}
\DefineParaStyle{Maple Warning}
\DefineParaStyle{Maple Error}
\DefineParaStyle{Maple Dash Item}
\DefineParaStyle{Maple Heading 3}
\DefineParaStyle{Maple Heading 1}
\DefineParaStyle{Maple Title}
\DefineParaStyle{Maple Normal}
\DefineCharStyle{Maple 2D Input}
\DefineCharStyle{Maple Maple Input}
\DefineCharStyle{Maple 2D Output}
\DefineCharStyle{Maple 2D Math}
\DefineCharStyle{Maple Hyperlink}
\begin{document}
\pagestyle{empty}
\begin{mapleinput}
\mapleinline{active}{1d}{\begin{Maple Normal}\QTR{Maple Maple Input}{}\QTR{Maple Maple Input}{F:=t*x\symbol{94}2-y\symbol{94}3;}\end{Maple Normal}}{}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\QTR{Maple 2D Output}{\mapleinline{inert}{2d}{F := t*x^2-y^3}{%
\[
F\, := \,t{x}^{2}-{y}^{3}
\]
}
}

\end{maplelatex}
\begin{mapleinput}
\mapleinline{active}{1d}{\begin{Maple Normal}\QTR{Maple Maple Input}{}\QTR{Maple Maple Input}{H:=det(hessian(F,[x,y,t]));}\end{Maple Normal}}{}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\QTR{Maple 2D Output}{\mapleinline{inert}{2d}{H := 24*x^2*y}{%
\[
H\, := \,24\,{x}^{2}y
\]
}
}

\end{maplelatex}
\begin{mapleinput}
\mapleinline{active}{1d}{\begin{Maple Normal}\QTR{Maple Maple Input}{}\QTR{Maple Maple Input}{solve({H=0, F=0}, {x,y,t});}\end{Maple Normal}}{}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\QTR{Maple 2D Output}{\mapleinline{inert}{2d}{{t = 0, y = 0, x = x}, {y = 0, x = 0, t = t}}{%
\[
 \left\{ x=x,y=0,t=0 \right\} ,\, \left\{ t=t,y=0,x=0 \right\} 
\]
}
}

\end{maplelatex}
\begin{mapleinput}
\mapleinline{active}{1d}{\begin{Maple Normal}\QTR{Maple Maple Input}{}\QTR{Maple Maple Input}{X:=(1,0,0); # e' l'unico flesso,  O=(0,0,1) e' un punto doppio, anzi e' l'unica cuspide}\end{Maple Normal}}{}
\end{mapleinput}
\begin{mapleinput}
\mapleinline{active}{1d}{\QTR{Maple Maple Input}{}\QTR{Maple Maple Input}{Cpolare:=(xx,yy,zz)  -\TEXTsymbol{>}  
\quad	multiply(<x|y|t\TEXTsymbol{>}, multiply((subs({x=xx,y=yy,z=zz},hessian(F,[x,y,t])),<x,y,t\TEXTsymbol{>})));}}{}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\QTR{Maple 2D Output}{\mapleinline{inert}{2d}{X := 1, 0, 0}{%
\[
X\, := \,1,\,0,\,0
\]
}
}

\end{maplelatex}
\begin{mapleinput}
\mapleinline{active}{1d}{\begin{Maple Normal}\QTR{Maple Maple Input}{}\QTR{Maple Maple Input}{grad(F,[x,y,t]);}\end{Maple Normal}}{}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\QTR{Maple 2D Output}{\mapleinline{inert}{2d}{vector([2*t*x, -3*y^2, x^2])}{%
\[
[2\,xt,-3\,{y}^{2},{x}^{2}]
\]
}
}

\end{maplelatex}
\begin{mapleinput}
\mapleinline{active}{1d}{\begin{Maple Normal}\QTR{Maple Maple Input}{}\QTR{Maple Maple Input}{Cpolare(X);}\end{Maple Normal}}{}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\QTR{Maple 2D Output}{\mapleinline{inert}{2d}{x*(2*t*x+2*t)+2*t*x}{%
\[
x \left( 2\,xt+2\,t \right) +2\,xt
\]
}
}

\end{maplelatex}
\begin{mapleinput}
\mapleinline{active}{1d}{\begin{Maple Normal}\QTR{Maple Maple Input}{}\QTR{Maple Maple Input}{S:=x*(2*x+2)+2*x; # e' la componente della conica polare che non passa per X}\end{Maple Normal}}{}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\QTR{Maple 2D Output}{\mapleinline{inert}{2d}{S := x*(2*x+2)+2*x}{%
\[
S\, := \,x \left( 2\,x+2 \right) +2\,x
\]
}
}

\end{maplelatex}
\begin{mapleinput}
\mapleinline{active}{1d}{\begin{Maple Normal}\QTR{Maple Maple Input}{}\QTR{Maple Maple Input}{solve({S=0, F=0}, {x,y,t});}\end{Maple Normal}}{}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\QTR{Maple 2D Output}{\mapleinline{inert}{2d}{{t = t, y = 0, x = 0}, {y = y, x = -2, t = 1/4*y^3}}{%
\[
 \left\{ t=t,y=0,x=0 \right\} ,\, \left\{ y=y,x=-2,t=1/4\,{y}^{3} \right\} 
\]
}
}

\end{maplelatex}
\begin{mapleinput}
\mapleinline{active}{1d}{\begin{Maple Normal}\QTR{Maple Maple Input}{}\QTR{Maple Maple Input}{#Quindi abbiamo ottenuto solo un punto Q=(-2,1,1/4) non singolare, (O e' l'unico punto singolare di F)}\end{Maple Normal}}{}
\end{mapleinput}
\begin{mapleinput}
\mapleinline{active}{1d}{\begin{Maple Normal}\QTR{Maple Maple Input}{}\QTR{Maple Maple Input}{#Quindi le rette tangenti, passanti per X sono solo t=0,  e XQ.}\end{Maple Normal}}{}
\end{mapleinput}
\begin{mapleinput}
\mapleinline{active}{1d}{\begin{Maple Normal}\QTR{Maple Maple Input}{}\QTR{Maple Maple Input}{clear;}\end{Maple Normal}}{}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\QTR{Maple 2D Output}{\mapleinline{inert}{2d}{clear}{%
\[
{\it clear}
\]
}
}

\end{maplelatex}
\begin{mapleinput}
\mapleinline{active}{1d}{\begin{Maple Normal}\QTR{Maple Maple Input}{}\QTR{Maple Maple Input}{}\end{Maple Normal}}{}
\end{mapleinput}

\end{document}
%% End of Maple 9.5 Output