88 lines
3.0 KiB
TeX
88 lines
3.0 KiB
TeX
% vim:ft=tex:
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%
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\documentclass[12pt]{article}
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\usepackage[utf8x]{inputenc}
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\usepackage[francais]{babel}
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\usepackage[T1]{fontenc}
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\usepackage{amssymb}
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\usepackage{amsmath}
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\usepackage{amsfonts}
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\title{
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Snippets pour Opytex \\
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Suites
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}
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\author{
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Benjamin Bertrand
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}
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\begin{document}
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\maketitle
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\section{Calculs de termes}
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\begin{enumerate}
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\item Calculer les termes $u_0$, $u_1$, $u_2$, $u_{10}$ et $u_{100}$ pour les suites suivantes
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\begin{enumerate}
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%-set u = Expression.random("{a}*n+{b}")
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\item $\forall n \in \mathbb{N} \qquad u_n = \Var{u}$
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Solution:
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\begin{align*}
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u_0 &= \Var{u(0).explain() | join('=')} \\
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u_1 &= \Var{u(1).explain() | join('=')} \\
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u_2 &= \Var{u(2).explain() | join('=')} \\
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u_{10} &= \Var{u(10).explain() | join('=')} \\
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u_{100} &= \Var{u(100).explain() | join('=')}
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\end{align*}
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%-set v = Expression.random("({a}*n+{b})/{c}", ["c>1"])
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\item $\forall n \in \mathbb{N} \qquad v_n = \Var{v|replace("frac","dfrac")}$
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Solution:
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\begin{align*}
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v_0 &= \Var{v(0).explain() | join('=')} \\
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v_1 &= \Var{v(1).explain() | join('=')} \\
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v_2 &= \Var{v(2).explain() | join('=')} \\
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v_{10} &= \Var{v(10).explain() | join('=')} \\
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v_{100} &= \Var{v(100).explain() | join('=')}
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\end{align*}
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%-set v = Expression.random("({a}*n+{b})/{c}", ["c>1"])
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\item $\forall n \in \mathbb{N} \qquad v_n = \Var{v}$
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Solution:
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\begin{align*}
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%- for j in [0, 1, 2, 10, 100]
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v_{\Var{j}} &= \Var{v(j).explain() | join('=')} \\
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%- endfor
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\end{align*}
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%-set f = Expression.random("{a}*x")
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%-set v0 = randint(0, 10)
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\item $\forall n \in \mathbb{N} \qquad v_{n+1} = \Var{f("v_n")} \mbox{ et } v_0 = \Var{v0}$
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Solution:
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\begin{align*}
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v_0 &= \Var{v0} \\
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%-set v = f(v0)
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v_1 &= \Var{v.explain() | join('=')} \\
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%-set v = f(v)
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v_2 &= \Var{v.explain() | join('=')} \\
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\end{align*}
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Pour le terme 10, il faut calculer tous les autres avant!
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\begin{align*}
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%#- Trick to move around scoping rules
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%#- https://stackoverflow.com/a/49699589
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%- set v = namespace(val = v)
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%- for i in range(8)
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%- set v.val = f(v.val)
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v_{\Var{i+3}} &= \Var{v.val.explain() | join('=')} \\
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%- endfor
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\end{align*}
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\end{enumerate}
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\end{enumerate}
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\end{document}
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