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DS_gene.py
11
DS_gene.py
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@ -8,7 +8,14 @@ import csv
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from path import path
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from texenv import texenv
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from pymath.random_expression import RdExpression
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from pymath.expression import Expression
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from pymath.polynom import Polynom
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from pymath.fraction import Fraction
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pymath_tools = {"Expression":Expression,\
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"Polynom":Polynom,\
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"Fraction":Fraction,\
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}
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def main(options):
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#template = report_renderer.get_template(options.template)
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@ -45,7 +52,7 @@ def main(options):
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dest = path(str(infos['num']) + output)
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tmp_pdf.append(dest.namebase + ".pdf")
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with open( dest, 'w') as f:
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f.write(template.render( RdExpression = RdExpression , infos = infos))
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f.write(template.render( infos = infos, **pymath_tools ))
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if not options.no_compil:
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os.system("pdflatex " + dest)
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@ -0,0 +1,113 @@
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\documentclass[a4paper,10pt]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classDS}
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\usepackage{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/2013_2014}
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% Title Page
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\titre{Calcul littéral et statistiques}
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% \quatreC \quatreD \troisB \troisPro
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\classe{\troisB}
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\date{26 septemble 2013}
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% DS DSCorr DM DMCorr Corr
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\typedoc{DS}
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\duree{1 heure}
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\sujet{}
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\begin{document}
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\maketitle
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\Calc
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Le barème est donné à titre indicatif, il pourra être modifié.
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\begin{Exo}[4.5]
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Développer et réduire les expressions suivantes:
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\begin{eqnarray*}
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A &=& \frac{ 1 }{ 2 } + 2 \\
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P(x) &=& 6 x - 2 \\
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Q(x) &=& 4 x + 11\\
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R(x) &=& ( 6 x - 2 ) \times ( 4 x + 11 )
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\end{eqnarray*}
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Solutions:
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\begin{eqnarray*}
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A & = & \frac{ 1 }{ 2 } + 2 \\
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A & = & \frac{ 1 \times 1 }{ 2 \times 1 } + \frac{ 2 \times 2 }{ 1 \times 2 } \\
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A & = & \frac{ 1 + 4 }{ 2 } \\
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A & = & \frac{ 5 }{ 2 }
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\end{eqnarray*}
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\begin{eqnarray*}
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P(2) & = & 6 \times 2 - 2 \\
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P(2) & = & 12 - 2 \\
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P(2) & = & 10
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\end{eqnarray*}
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\begin{eqnarray*}
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Q(2) & = & 4 \times 2 + 11 \\
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Q(2) & = & 8 + 11 \\
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Q(2) & = & 19
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\end{eqnarray*}
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\begin{eqnarray*}
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P(x) + Q(X) & = & 6 x + 4 x - 2 + 11 \\
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P(x) + Q(X) & = & ( 6 + 4 ) x + ( -2 ) + 11 \\
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P(x) + Q(X) & = & 10 x + 9
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\end{eqnarray*}
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\begin{eqnarray*}
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P(x) + Q(X) & = & 6 x - 2 + 4 x + 11 \\
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P(x) + Q(X) & = & 4 x + 6 x + 11 - 2 \\
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P(x) + Q(X) & = & ( 4 + 6 ) x + 11 + ( -2 ) \\
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P(x) + Q(X) & = & 10 x + 9
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\end{eqnarray*}
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\begin{eqnarray*}
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R(x) & = & ( 6 x - 2 ) \times ( 4 x + 11 ) \\
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R(x) & = & 6 \times 4 x^{ 2 } + ( -2 ) \times 4 x + 6 \times 11 x + ( -2 ) \times 11 \\
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R(x) & = & 6 \times 4 x^{ 2 } + ( ( -2 ) \times 4 + 6 \times 11 ) x + ( -2 ) \times 11 \\
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R(x) & = & 24 x^{ 2 } + ( ( -8 ) + 66 ) x - 22 \\
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R(x) & = & 24 x^{ 2 } + 58 x - 22
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\end{eqnarray*}
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\end{Exo}
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\begin{Exo}
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Résoudre l'équation suivante
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\begin{eqnarray*}
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3 x^{ 2 } + x + 10 & = & 0
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\end{eqnarray*}
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Solution:
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On commence par calculer le discriminant
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\begin{eqnarray*}
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\Delta & = & b^2-4ac
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\end{eqnarray*}
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\begin{eqnarray*}
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\Delta & = & 1^{ 2 } - 4 \times 3 \times 10 \\
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\Delta & = & 1 - 12 \times 10 \\
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\Delta & = & 1 - 120 \\
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\Delta & = & -119
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\end{eqnarray*}
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Alors $\Delta = -119$
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\end{Exo}
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\end{document}
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%%% Local Variables:
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%%% mode: latex
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%%% TeX-master: "master"
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%%% End:
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@ -19,18 +19,46 @@
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Le barème est donné à titre indicatif, il pourra être modifié.
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\begin{Exo}[4.5]
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\Block{do RdExpression.set_form("exp")}
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\Block{set A = RdExpression("{a} / 2 + 2")()}
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\Block{set B = RdExpression("{a} / 2 + 4")()}
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\Block{set A = Expression.random("{a} / 2 + 2")}
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\Block{set P = Polynom.random(["{b}","{a}"])}
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\Block{set Q = Polynom.random(["{b+2}","{a}"])}
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\Block{set R = P('x')*Q('x') }
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Développer et réduire les expressions suivantes:
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\begin{equation*}
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A = \Var{ A } \\
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B = \Var{ B }
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\end{equation*}
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\begin{eqnarray*}
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A &=& \Var{ A } \\
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P(x) &=& \Var{ P } \\
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Q(x) &=& \Var{ Q }\\
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R(x) &=& \Var{R}
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\end{eqnarray*}
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Solutions:
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\Var{A.simplify() | calculus}
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\Var{B.simplify() | calculus(name = "B")}
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\Var{P(2).simplify() | calculus(name = "P(2)")}
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\Var{Q(2).simplify() | calculus(name = "Q(2)")}
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\Var{(P+Q) | calculus(name = "P(x) + Q(X)")}
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\Var{(P('x')+Q('x')).simplify() | calculus(name = "P(x) + Q(X)")}
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\Var{R.simplify() | calculus(name = "R(x)")}
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\end{Exo}
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\begin{Exo}
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\Block{set P = Polynom.random(["{a}", "{b}", "{c}"])}
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Résoudre l'équation suivante
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\begin{eqnarray*}
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\Var{P} & = & 0
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\end{eqnarray*}
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Solution:
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On commence par calculer le discriminant
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\begin{eqnarray*}
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\Delta & = & b^2-4ac
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\end{eqnarray*}
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\Block{set Delta = Expression("{b}^2 - 4*{a}*{c}".format(a = P._coef[2], b = P._coef[1], c = P._coef[0]))}
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\Var{Delta.simplify()|calculus(name="\\Delta")}
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\Block{set Delta = Delta.simplified()}
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Alors $\Delta = \Var{Delta}$
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\end{Exo}
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