From 33625b36f55afe9ba800201d39199b39fce3ed85 Mon Sep 17 00:00:00 2001 From: Lafrite Date: Sun, 8 Feb 2015 17:04:05 +0100 Subject: [PATCH] Yeah can solve 2nd deg equation! --- DS_gene.py | 11 ++- example/1_example.tex | 159 ++++++++++++++++++++-------------------- example/all_example.pdf | Bin 49822 -> 88159 bytes example/tpl_2ndDeg.tex | 136 ++++++++++++++++++++++++++++++++++ example/tpl_example.tex | 147 ++++++++++++++++++++++++++----------- texenv.py | 11 ++- 6 files changed, 336 insertions(+), 128 deletions(-) create mode 100644 example/tpl_2ndDeg.tex diff --git a/DS_gene.py b/DS_gene.py index d4d958e..81279dd 100755 --- a/DS_gene.py +++ b/DS_gene.py @@ -8,14 +8,19 @@ import csv from path import path from texenv import texenv + +import math as m from pymath.expression import Expression from pymath.polynom import Polynom from pymath.fraction import Fraction -pymath_tools = {"Expression":Expression,\ +export_dict = {} +export_dict.update(m.__dict__) +#export_dict.update(__builtin__.__dict__) +export_dict.update({"Expression":Expression,\ "Polynom":Polynom,\ "Fraction":Fraction,\ - } + }) def main(options): #template = report_renderer.get_template(options.template) @@ -52,7 +57,7 @@ def main(options): dest = path(str(infos['num']) + output) tmp_pdf.append(dest.namebase + ".pdf") with open( dest, 'w') as f: - f.write(template.render( infos = infos, **pymath_tools )) + f.write(template.render( infos = infos, **export_dict )) if not options.no_compil: os.system("pdflatex " + dest) diff --git a/example/1_example.tex b/example/1_example.tex index a48e693..c93b245 100644 --- a/example/1_example.tex +++ b/example/1_example.tex @@ -1,106 +1,107 @@ -\documentclass[a4paper,10pt]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classDS} -\usepackage{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/2013_2014} +\documentclass[a4paper,10pt]{article} +\RequirePackage[utf8x]{inputenc} +\RequirePackage[francais]{babel} +\RequirePackage{amssymb} +\RequirePackage{amsmath} +\RequirePackage{amsfonts} +\RequirePackage{subfig} +\RequirePackage{graphicx} +\RequirePackage{color} % Title Page -\titre{Calcul littéral et statistiques} -% \quatreC \quatreD \troisB \troisPro -\classe{\troisB} -\date{26 septemble 2013} -% DS DSCorr DM DMCorr Corr -\typedoc{DS} -\duree{1 heure} -\sujet{} - +\title{Calcul littéral et statistiques} +\date{\today} \begin{document} \maketitle -\Calc -Le barème est donné à titre indicatif, il pourra être modifié. -\begin{Exo}[4.5] - - - - - Développer et réduire les expressions suivantes: - \begin{eqnarray*} - A &=& \frac{ 1 }{ 2 } + 2 \\ - P(x) &=& 6 x - 2 \\ - Q(x) &=& 4 x + 11\\ - R(x) &=& ( 6 x - 2 ) \times ( 4 x + 11 ) - \end{eqnarray*} - - Solutions: - \begin{eqnarray*} -A & = & \frac{ 1 }{ 2 } + 2 \\ -A & = & \frac{ 1 \times 1 }{ 2 \times 1 } + \frac{ 2 \times 2 }{ 1 \times 2 } \\ -A & = & \frac{ 1 + 4 }{ 2 } \\ -A & = & \frac{ 5 }{ 2 } -\end{eqnarray*} - - \begin{eqnarray*} -P(2) & = & 6 \times 2 - 2 \\ -P(2) & = & 12 - 2 \\ -P(2) & = & 10 -\end{eqnarray*} - - \begin{eqnarray*} -Q(2) & = & 4 \times 2 + 11 \\ -Q(2) & = & 8 + 11 \\ -Q(2) & = & 19 -\end{eqnarray*} - - \begin{eqnarray*} -P(x) + Q(X) & = & 6 x + 4 x - 2 + 11 \\ -P(x) + Q(X) & = & ( 6 + 4 ) x + ( -2 ) + 11 \\ -P(x) + Q(X) & = & 10 x + 9 -\end{eqnarray*} - - \begin{eqnarray*} -P(x) + Q(X) & = & 6 x - 2 + 4 x + 11 \\ -P(x) + Q(X) & = & 4 x + 6 x + 11 - 2 \\ -P(x) + Q(X) & = & ( 4 + 6 ) x + 11 + ( -2 ) \\ -P(x) + Q(X) & = & 10 x + 9 -\end{eqnarray*} - - \begin{eqnarray*} -R(x) & = & ( 6 x - 2 ) \times ( 4 x + 11 ) \\ -R(x) & = & 6 \times 4 x^{ 2 } + ( -2 ) \times 4 x + 6 \times 11 x + ( -2 ) \times 11 \\ -R(x) & = & 6 \times 4 x^{ 2 } + ( ( -2 ) \times 4 + 6 \times 11 ) x + ( -2 ) \times 11 \\ -R(x) & = & 24 x^{ 2 } + ( ( -8 ) + 66 ) x - 22 \\ -R(x) & = & 24 x^{ 2 } + 58 x - 22 -\end{eqnarray*} +\section{Polynômes} -\end{Exo} -\begin{Exo} - Résoudre l'équation suivante \begin{eqnarray*} - 3 x^{ 2 } + x + 10 & = & 0 + - 4 x^{ 2 } + 4 x - 1 & = & 0 \end{eqnarray*} Solution: On commence par calculer le discriminant + \begin{eqnarray*} - \Delta & = & b^2-4ac + \Delta & = & b^2-4ac \\ + \Delta & = & 4^{ 2 } - 4 \times ( -4 ) \times ( -1 ) \\ +\Delta & = & 16 - ( -16 ) \times ( -1 ) \\ +\Delta & = & 16 - 16 \\ +\Delta & = & 0 \end{eqnarray*} - \begin{eqnarray*} -\Delta & = & 1^{ 2 } - 4 \times 3 \times 10 \\ -\Delta & = & 1 - 12 \times 10 \\ -\Delta & = & 1 - 120 \\ -\Delta & = & -119 -\end{eqnarray*} - Alors $\Delta = -119$ + Alors $\Delta = 0 = 0$ donc il y a une solution + + + + \begin{eqnarray*} + x_1 = \frac{-b}{2a} = \frac{ -4 }{ 2 \times ( -4 ) } = \frac{ -4 }{ -8 } = \frac{ 4 }{ 8 } = \frac{ 1 \times 4 }{ 2 \times 4 } = \frac{ 1 }{ 2 } = \frac{ -4 }{ -8 } + \end{eqnarray*} + + Les solutions sont donc $\mathcal{S} = \left\{ \frac{ -4 }{ -8 }\right\}$ + + + + \bigskip + ~\dotfill + \bigskip -\end{Exo} + + + Résoudre l'équation suivante + \begin{eqnarray*} + - 10 x^{ 2 } - 5 x - 5 & = & x^{ 2 } + 5 x - 9 + \end{eqnarray*} + + Solution: + + On commence par se ramener à une équation de la forme $ax^2+bx+c = 0$. + + \begin{eqnarray*} + - 10 x^{ 2 } - 5 x - 5 = x^{ 2 } + 5 x - 9 & \Leftrightarrow & - 10 x^{ 2 } - 5 x - 5 - (x^{ 2 } + 5 x - 9) = 0 \\ + & \Leftrightarrow & - 10 x^{ 2 } - x^{ 2 } - 5 x - 5 x - 5 + 9= 0 \\ + & \Leftrightarrow & ( ( -10 ) + ( -1 ) ) x^{ 2 } + ( ( -5 ) + ( -5 ) ) x + ( -5 ) + 9= 0 \\ + & \Leftrightarrow & - 11 x^{ 2 } - 10 x + 4= 0 + \end{eqnarray*} + + + On cherche maintenant à résoudre l'équation $- 11 x^{ 2 } - 10 x + 4 = 0$. + + On commence par calculer le discriminant + + \begin{eqnarray*} + \Delta & = & b^2-4ac \\ + \Delta & = & ( -10 )^{ 2 } - 4 \times ( -11 ) \times 4 \\ +\Delta & = & 100 - ( -44 ) \times 4 \\ +\Delta & = & 100 - ( -176 ) \\ +\Delta & = & 276 + \end{eqnarray*} + + + + Alors $\Delta = 276 > 0$ donc il y a deux solutions + + + + + \begin{eqnarray*} + x_1 & = & \frac{-b - \sqrt{\Delta}}{2a} = \frac{-10 - \sqrt{276}}{2 \times -11} = 0.3 \\ + x_2 & = & \frac{-b + \sqrt{\Delta}}{2a} = \frac{-10 + \sqrt{276}}{2 \times -11} = -1.21 + \end{eqnarray*} + + Les solutions sont donc $\mathcal{S} = \left\{ 0.3; -1.21 \right\}$ + + \end{document} diff --git a/example/all_example.pdf b/example/all_example.pdf index 847f353057b70ccc6e16be6e6ecf66736dc4b5df..fcb26d1a0e7a9dc516c68353ef14b12244efc3b8 100644 GIT binary patch literal 88159 zcmce-1#BkGmL&R_ncZe)W@ct)=FiN`%x+_wnW4=LZD=zyGcz;W@4qv1pGKOMcAxaL zrBW&KsPZT>kCahIiXvAMlb~m2V2352Sr}Y_P~8lmpsZxLOi%un_&% z1t&ox#xCV+@2ggzKQn5Zcd1 z*!~+CH7`dX5u=u(i8avF6_!!e&BXOTA`%YHcK`7D=lLIRFvBt`sflYb{6iF|U~C5@ zqGEJ6c4l<7b7XWhGq*Ojqu17CkymzPba8NVHU<8(@_)kA|20X;*aE2FW@qxx3jdu) z+TPqj%*xc2h?(ghGAgi)A|ei+M7sYPuyeCBuyAq^aj`KoaB=IyGO7UoGpP&FzjjZ; z!QS;B@XuZ`vlB71{%iKXFbB~;_kUv6f8yN#g}I1WSpNMA8xafpzcDir3)g>PP9j$3 ze}{=!|Ft*&k&u;$^Yj=H4kVA-laG0Fl-#=`*k&2en6&-h8Q(XAzrq9jsj1sZ>idK1P|BX4p2PRU>$4t$a4FFJLR1+W0%U#KrKd$pNkNOFmwtB? 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par calculer le discriminant + \Block{set Delta = Expression("{b}^2 - 4*{a}*{c}".format(a = P._coef[2], b = P._coef[1], c = P._coef[0]))} + \begin{eqnarray*} + \Delta & = & b^2-4ac \\ + \Var{Delta.simplify()|calculus(name="\\Delta")} + \end{eqnarray*} + \Block{set Delta = Delta.simplified()} + + \Block{if Delta > 0} + Alors $\Delta = \Var{Delta} > 0$ donc il y a deux solutions + + \Block{set x1 = (-P._coef[1] - sqrt(Delta))/(2*P._coef[2])} + \Block{set x2 = (-P._coef[1] + sqrt(Delta))/(2*P._coef[2])} + + \begin{eqnarray*} + x_1 & = & \frac{-b - \sqrt{\Delta}}{2a} = \frac{\Var{-P._coef[1]} - \sqrt{\Var{Delta}}}{2 \times \Var{P._coef[2]}} = \Var{x1 | round(2)} \\ + x_2 & = & \frac{-b + \sqrt{\Delta}}{2a} = \frac{\Var{-P._coef[1]} + \sqrt{\Var{Delta}}}{2 \times \Var{P._coef[2]}} = \Var{x2 | round(2)} + \end{eqnarray*} + + Les solutions sont donc $\mathcal{S} = \left\{ \Var{x1|round(2)}; \Var{x2|round(2)} \right\}$ + + \Block{elif Delta == 0} + Alors $\Delta = \Var{Delta} = 0$ donc il y a une solution + + \Block{set x1 = Expression("-{b}/(2*{a})".format(b = P._coef[1], a = P._coef[2]))} + + \begin{eqnarray*} + x_1 = \frac{-b}{2a} = \Var{" = ".join(x1.simplify())} + \end{eqnarray*} + + Les solutions sont donc $\mathcal{S} = \left\{ \Var{x1.simplified()}\right\}$ + + \Block{else} + Alors $\Delta = \Var{Delta} < 0$ donc il n'y a pas de solution. + + \Block{endif} + + \bigskip + ~\dotfill + \bigskip + + + \Block{set P = Polynom.random(["{a}", "{b}", "{c}"])} + \Block{set Q = Polynom.random(["{a}", "{b}", "{c}"])} + Résoudre l'équation suivante + \begin{eqnarray*} + \Var{P} & = & \Var{Q} + \end{eqnarray*} + + Solution: + + On commence par se ramener à une équation de la forme $ax^2+bx+c = 0$. + + \begin{eqnarray*} + \Var{P} = \Var{Q} & \Leftrightarrow & \Var{P} - (\Var{Q}) = 0 \\ + \Var{(P - Q)|calculus(name = "", sep = "\\Leftrightarrow", end = "= 0")} + \end{eqnarray*} + + \Block{set R = (P-Q)[-1]} + On cherche maintenant à résoudre l'équation $\Var{R} = 0$. + + On commence par calculer le discriminant + \Block{set Delta = Expression("{b}^2 - 4*{a}*{c}".format(a = R._coef[2], b = R._coef[1], c = R._coef[0]))} + \begin{eqnarray*} + \Delta & = & b^2-4ac \\ + \Var{Delta.simplify()|calculus(name="\\Delta")} + \end{eqnarray*} + \Block{set Delta = Delta.simplified()} + + \Block{if Delta > 0} + Alors $\Delta = \Var{Delta} > 0$ donc il y a deux solutions + + \Block{set x1 = (-R._coef[1] - sqrt(Delta))/(2*R._coef[2])} + \Block{set x2 = (-R._coef[1] + sqrt(Delta))/(2*R._coef[2])} + + \begin{eqnarray*} + x_1 & = & \frac{-b - \sqrt{\Delta}}{2a} = \frac{\Var{-R._coef[1]} - \sqrt{\Var{Delta}}}{2 \times \Var{R._coef[2]}} = \Var{x1 | round(2)} \\ + x_2 & = & \frac{-b + \sqrt{\Delta}}{2a} = \frac{\Var{-R._coef[1]} + \sqrt{\Var{Delta}}}{2 \times \Var{R._coef[2]}} = \Var{x2 | round(2)} + \end{eqnarray*} + + Les solutions sont donc $\mathcal{S} = \left\{ \Var{x1|round(2)}; \Var{x2|round(2)} \right\}$ + + \Block{elif Delta == 0} + Alors $\Delta = \Var{Delta} = 0$ donc il y a une solution + + \Block{set x1 = Expression("-{b}/(2*{a})".format(b = R._coef[1], a = R._coef[2]))} + + \begin{eqnarray*} + x_1 = \frac{-b}{2a} = \Var{" = ".join(x1.simplify())} + \end{eqnarray*} + + Les solutions sont donc $\mathcal{S} = \left\{ \Var{x1.simplified()}\right\}$ + + \Block{else} + Alors $\Delta = \Var{Delta} < 0$ donc il n'y a pas de solution. + + \Block{endif} + + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "master" +%%% End: + + diff --git a/example/tpl_example.tex b/example/tpl_example.tex index f34bb01..ec5ec91 100644 --- a/example/tpl_example.tex +++ b/example/tpl_example.tex @@ -1,48 +1,25 @@ -\documentclass[a4paper,10pt]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classDS} -\usepackage{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/2013_2014} +\documentclass[a4paper,10pt]{article} +\RequirePackage[utf8x]{inputenc} +\RequirePackage[francais]{babel} +\RequirePackage{amssymb} +\RequirePackage{amsmath} +\RequirePackage{amsfonts} +\RequirePackage{subfig} +\RequirePackage{graphicx} +\RequirePackage{color} % Title Page -\titre{Calcul littéral et statistiques} -% \quatreC \quatreD \troisB \troisPro -\classe{\troisB} -\date{26 septemble 2013} -% DS DSCorr DM DMCorr Corr -\typedoc{DS} -\duree{1 heure} -\sujet{\Var{infos.Nom}} - +\title{Calcul littéral et statistiques} +\date{\today} \begin{document} \maketitle -\Calc -Le barème est donné à titre indicatif, il pourra être modifié. -\begin{Exo}[4.5] - \Block{set A = Expression.random("{a} / 2 + 2")} - \Block{set P = Polynom.random(["{b}","{a}"])} - \Block{set Q = Polynom.random(["{b+2}","{a}"])} - \Block{set R = P('x')*Q('x') } - Développer et réduire les expressions suivantes: - \begin{eqnarray*} - A &=& \Var{ A } \\ - P(x) &=& \Var{ P } \\ - Q(x) &=& \Var{ Q }\\ - R(x) &=& \Var{R} - \end{eqnarray*} +\section{Polynômes} - Solutions: - \Var{A.simplify() | calculus} - \Var{P(2).simplify() | calculus(name = "P(2)")} - \Var{Q(2).simplify() | calculus(name = "Q(2)")} - \Var{(P+Q) | calculus(name = "P(x) + Q(X)")} - \Var{(P('x')+Q('x')).simplify() | calculus(name = "P(x) + Q(X)")} - \Var{R.simplify() | calculus(name = "R(x)")} -\end{Exo} - -\begin{Exo} - \Block{set P = Polynom.random(["{a}", "{b}", "{c}"])} +\Block{set P = Polynom.random(["{a}", "{b}", "{c}"], ["{b}**2 - 4*{a}*{c} == 0"])} Résoudre l'équation suivante \begin{eqnarray*} \Var{P} & = & 0 @@ -51,16 +28,102 @@ Le barème est donné à titre indicatif, il pourra être modifié. Solution: On commence par calculer le discriminant - \begin{eqnarray*} - \Delta & = & b^2-4ac - \end{eqnarray*} \Block{set Delta = Expression("{b}^2 - 4*{a}*{c}".format(a = P._coef[2], b = P._coef[1], c = P._coef[0]))} - \Var{Delta.simplify()|calculus(name="\\Delta")} + \begin{eqnarray*} + \Delta & = & b^2-4ac \\ + \Var{Delta.simplify()|calculus(name="\\Delta")} + \end{eqnarray*} \Block{set Delta = Delta.simplified()} - Alors $\Delta = \Var{Delta}$ + + \Block{if Delta > 0} + Alors $\Delta = \Var{Delta} > 0$ donc il y a deux solutions + + \Block{set x1 = (-P._coef[1] - sqrt(Delta))/(2*P._coef[2])} + \Block{set x2 = (-P._coef[1] + sqrt(Delta))/(2*P._coef[2])} + + \begin{eqnarray*} + x_1 & = & \frac{-b - \sqrt{\Delta}}{2a} = \frac{\Var{-P._coef[1]} - \sqrt{\Var{Delta}}}{2 \times \Var{P._coef[2]}} = \Var{x1 | round(2)} \\ + x_2 & = & \frac{-b + \sqrt{\Delta}}{2a} = \frac{\Var{-P._coef[1]} + \sqrt{\Var{Delta}}}{2 \times \Var{P._coef[2]}} = \Var{x2 | round(2)} + \end{eqnarray*} + + Les solutions sont donc $\mathcal{S} = \left\{ \Var{x1|round(2)}; \Var{x2|round(2)} \right\}$ + + \Block{elif Delta == 0} + Alors $\Delta = \Var{Delta} = 0$ donc il y a une solution + + \Block{set x1 = Expression("-{b}/(2*{a})".format(b = P._coef[1], a = P._coef[2]))} + + \begin{eqnarray*} + x_1 = \frac{-b}{2a} = \Var{" = ".join(x1.simplify())} + \end{eqnarray*} + + Les solutions sont donc $\mathcal{S} = \left\{ \Var{x1.simplified()}\right\}$ + + \Block{else} + Alors $\Delta = \Var{Delta} < 0$ donc il n'y a pas de solution. + + \Block{endif} + + \bigskip + ~\dotfill + \bigskip -\end{Exo} + \Block{set P = Polynom.random(["{a}", "{b}", "{c}"])} + \Block{set Q = Polynom.random(["{a}", "{b}", "{c}"])} + Résoudre l'équation suivante + \begin{eqnarray*} + \Var{P} & = & \Var{Q} + \end{eqnarray*} + + Solution: + + On commence par se ramener à une équation de la forme $ax^2+bx+c = 0$. + + \begin{eqnarray*} + \Var{P} = \Var{Q} & \Leftrightarrow & \Var{P} - (\Var{Q}) = 0 \\ + \Var{(P - Q)|calculus(name = "", sep = "\\Leftrightarrow", end = "= 0")} + \end{eqnarray*} + + \Block{set R = (P-Q)[-1]} + On cherche maintenant à résoudre l'équation $\Var{R} = 0$. + + On commence par calculer le discriminant + \Block{set Delta = Expression("{b}^2 - 4*{a}*{c}".format(a = R._coef[2], b = R._coef[1], c = R._coef[0]))} + \begin{eqnarray*} + \Delta & = & b^2-4ac \\ + \Var{Delta.simplify()|calculus(name="\\Delta")} + \end{eqnarray*} + \Block{set Delta = Delta.simplified()} + + \Block{if Delta > 0} + Alors $\Delta = \Var{Delta} > 0$ donc il y a deux solutions + + \Block{set x1 = (-R._coef[1] - sqrt(Delta))/(2*R._coef[2])} + \Block{set x2 = (-R._coef[1] + sqrt(Delta))/(2*R._coef[2])} + + \begin{eqnarray*} + x_1 & = & \frac{-b - \sqrt{\Delta}}{2a} = \frac{\Var{-R._coef[1]} - \sqrt{\Var{Delta}}}{2 \times \Var{R._coef[2]}} = \Var{x1 | round(2)} \\ + x_2 & = & \frac{-b + \sqrt{\Delta}}{2a} = \frac{\Var{-R._coef[1]} + \sqrt{\Var{Delta}}}{2 \times \Var{R._coef[2]}} = \Var{x2 | round(2)} + \end{eqnarray*} + + Les solutions sont donc $\mathcal{S} = \left\{ \Var{x1|round(2)}; \Var{x2|round(2)} \right\}$ + + \Block{elif Delta == 0} + Alors $\Delta = \Var{Delta} = 0$ donc il y a une solution + + \Block{set x1 = Expression("-{b}/(2*{a})".format(b = R._coef[1], a = R._coef[2]))} + + \begin{eqnarray*} + x_1 = \frac{-b}{2a} = \Var{" = ".join(x1.simplify())} + \end{eqnarray*} + + Les solutions sont donc $\mathcal{S} = \left\{ \Var{x1.simplified()}\right\}$ + + \Block{else} + Alors $\Delta = \Var{Delta} < 0$ donc il n'y a pas de solution. + + \Block{endif} \end{document} diff --git a/texenv.py b/texenv.py index e2b3008..6df7ba7 100644 --- a/texenv.py +++ b/texenv.py @@ -16,17 +16,20 @@ texenv = jinja2.Environment( # Filters -def do_calculus(steps, name = "A"): +def do_calculus(steps, name = "A", sep = "=", end = "", joining = " \\\\ \n"): """Display properly the calculus + Generate this form string: + "name & sep & a_step end joining" + :param steps: list of steps :returns: latex string ready to be endbeded """ - ans = "\\begin{eqnarray*}\n" + #ans = "\\begin{eqnarray*}\n" - ans += " \\\\ \n".join([name + " & = & " + str(s) for s in steps]) - ans += "\n\\end{eqnarray*}\n" + ans = joining.join([name + " & " + sep + " & " + str(s) + end for s in steps]) + #ans += "\n\\end{eqnarray*}\n" return ans