2014-12-19 06:59:26 +00:00
|
|
|
\documentclass[a4paper,10pt]{article}
|
|
|
|
\usepackage[utf8x]{inputenc}
|
|
|
|
\usepackage[francais]{babel}
|
|
|
|
\usepackage{amssymb}
|
|
|
|
\usepackage{amsmath}
|
|
|
|
\usepackage{amsfonts}
|
2014-08-29 12:33:04 +00:00
|
|
|
|
|
|
|
% Title Page
|
2014-12-19 06:59:26 +00:00
|
|
|
\title{Jouons avec DS\_géné et pyMath}
|
2014-08-29 12:33:04 +00:00
|
|
|
% \quatreC \quatreD \troisB \troisPro
|
2014-12-19 06:59:26 +00:00
|
|
|
\date{}
|
2014-08-29 12:33:04 +00:00
|
|
|
|
|
|
|
|
|
|
|
\begin{document}
|
|
|
|
\maketitle
|
|
|
|
|
2014-12-19 06:59:26 +00:00
|
|
|
\section{Exercice de simplification de fraction}
|
|
|
|
\Block{do RdExpression.set_form("exp")}
|
|
|
|
\Block{set A = RdExpression("{a}/2+2")()}
|
|
|
|
\Block{set B = RdExpression("{a}/2+2")()}
|
2014-08-29 12:33:04 +00:00
|
|
|
Développer et réduire les expressions suivantes:
|
2014-12-19 06:59:26 +00:00
|
|
|
|
2014-08-29 12:33:04 +00:00
|
|
|
\begin{equation*}
|
2014-12-19 06:59:26 +00:00
|
|
|
A = \Var{ A } \qquad
|
2014-08-29 12:33:04 +00:00
|
|
|
B = \Var{ B }
|
|
|
|
\end{equation*}
|
2014-09-02 09:20:09 +00:00
|
|
|
|
|
|
|
Solutions:
|
|
|
|
\Var{A.simplify() | calculus}
|
|
|
|
\Var{B.simplify() | calculus(name = "B")}
|
2014-12-19 06:59:26 +00:00
|
|
|
|
|
|
|
\section{Mettre sous forme canonique}
|
|
|
|
\Block{set P = RdExpression("{a}x^2 + {b}x + {c}")()}
|
|
|
|
Mettre $\Var{P}$ sous la forme canonique.
|
|
|
|
|
|
|
|
Solution:
|
|
|
|
|
|
|
|
On simplifie le polynôme:
|
|
|
|
\begin{eqnarray*}
|
|
|
|
\Var{P.simplify() | calculus(name = "P(x) = ")}
|
|
|
|
\end{eqnarray*}
|
|
|
|
|
|
|
|
|
|
|
|
Calcul des coordonnées du sommet de la courbe:
|
|
|
|
\begin{eqnarray*}
|
|
|
|
\alpha & = & \frac{-b}{2a} = \\
|
|
|
|
\beta & = & -\frac{b^2 - 4ac}{4a} =
|
|
|
|
\end{eqnarray*}
|
|
|
|
|
2014-08-29 12:33:04 +00:00
|
|
|
|
|
|
|
|
|
|
|
\end{document}
|
|
|
|
|
|
|
|
%%% Local Variables:
|
|
|
|
%%% mode: latex
|
|
|
|
%%% TeX-master: "master"
|
|
|
|
%%% End:
|
|
|
|
|