bopytex_snippets/snippets/tpl_suite.tex

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