Fórmulas no [;\LaTeXe;] - Modo Matemático


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No \LaTeXe, fórmulas são introduzidas dentro do ambiente matemático (ou o modo matemático). Há duas formas básicas de se incluir o ambiente matemático no arquivo tex. A primeira é com o par de dólar:

$ fórmula a ser escrita $

O início do modo matemático começa com o primeiro '$' e termina com o próximo '$'. Em geral, usamos o modo matemático incluindo no preâmbulo os pacotes da AMS. Para isto, basta introduzir os comandos:

\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}

Exemplo de preâmbulo:

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Classe de documento
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\documentclass[10pt,a4paper]{article}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Pacotes de língua e fontes
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage[utf8]{inputenc}
\usepackage[portuguese]{babel}
\usepackage[T1]{fontenc}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%pacotes matemáticos
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Dados
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\title{Modo Matemático}
\author{Alessandro Duarte}

O comando da fórmula a ser escrita deve ser introduzida dentro do ambiente matemático. Por exemplo, se quisermos produzir a fórmula:

(2^4>5)\supset (3^2<10)

temos que introduzir o comando

(2^4>5)\supset (3^2<10)

dentro do ambiente matemático

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Classe de documento
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\documentclass[10pt,a4paper]{article}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Pacotes de língua e fontes
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage[utf8]{inputenc}
\usepackage[portuguese]{babel}
\usepackage[T1]{fontenc}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%pacotes matemáticos
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Dados
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\title{Modo Matemático}
\author{Alessandro Duarte}
\begin{document}
\maketitle

$(2^4>5)\supset (3^2<10)$
\end{document}

Compilando

imagem5

O mesmo resultado é obtido se, ao invés de "$ fórmula $", usarmos

Exemplo:

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Classe de documento
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\documentclass[10pt,a4paper]{article}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Pacotes de língua e fontes
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage[utf8]{inputenc}
\usepackage[portuguese]{babel}
\usepackage[T1]{fontenc}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%pacotes matemáticos
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Dados
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\title{Modo Matemático}
\author{Alessandro Duarte}
\begin{document}
\maketitle

$(2^4>5)\supset (3^2<10)$


\end{document}

Ou seja,

$.... $

é equivalente a

A outra forma básica de modo matemático é obtida com o uso de duas "duplas" de dólar:

Exemplo de código

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Classe de documento
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\documentclass[10pt,a4paper]{article}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Pacotes de língua e fontes
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage[utf8]{inputenc}
\usepackage[portuguese]{babel}
\usepackage[T1]{fontenc}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%pacotes matemáticos
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Dados
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\title{Modo Matemático}
\author{Alessandro Duarte}
\begin{document}
\maketitle



\end{document}

Compilando

imagem6

O mesmo resultado é obtido substituindo-se "" por

 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Classe de documento
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\documentclass[10pt,a4paper]{article}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Pacotes de língua e fontes
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage[utf8]{inputenc}
\usepackage[portuguese]{babel}
\usepackage[T1]{fontenc}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%pacotes matemáticos
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Dados
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\title{Modo Matemático}
\author{Alessandro Duarte}
\begin{document}
\maketitle






\end{document}

Compilando

imagem7

Ou seja,

e

são equivalentes.

Observação: note que esses dois modos matemáticos básicos não são iguais. Usamos o primeiro - $ fórmula $ - quando queremos introduzir a fórmula dentro de um parágrafo, enquanto o segundo é usado quando desejamos introduzir a fórmula centralizada e em linha separada.

Exemplo:

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Classe de documento
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\documentclass[10pt,a4paper]{article}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Pacotes de língua e fontes
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage[utf8]{inputenc}
\usepackage[portuguese]{babel}
\usepackage[T1]{fontenc}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%pacotes matemáticos
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Dados
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\title{Modo Matemático}
\author{Alessandro Duarte}
\begin{document}
\maketitle

Dada a tabela de verdade da implicação, a fórmula $(2^4>5)\supset (3^2<10)$ é verdadeira

\end{document}

Compilando

imagem8

Veja o que acontece se, ao invés de "$...$", colocarmos ":

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Classe de documento
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\documentclass[10pt,a4paper]{article}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Pacotes de língua e fontes
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage[utf8]{inputenc}
\usepackage[portuguese]{babel}
\usepackage[T1]{fontenc}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%pacotes matemáticos
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Dados
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\title{Modo Matemático}
\author{Alessandro Duarte}
\begin{document}
\maketitle

Dada a tabela de verdade da implicação, a fórmula  é verdadeira

\end{document}

Compilando

imagem9

Observação2: a primeira forma do modo matemático é chamado de math environment; o segundo, displaymath environment.

No \LaTeXe, é possível introduzir fórmulas numeradas, que são obtidas por meio do ambiente equation. Este ambiente começa com o comando \begin{equation} e termina com o comando \end{equation}.

Exemplo de código:

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Classe de documento
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\documentclass[10pt,a4paper]{article}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Pacotes de língua e fontes
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage[utf8]{inputenc}
\usepackage[portuguese]{babel}
\usepackage[T1]{fontenc}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%pacotes matemáticos
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Dados
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\title{Modo Matemático}
\author{Alessandro Duarte}
\begin{document}
\maketitle

Seja a fórmula:

\begin{equation}
p\supset(q\supset p)
\end{equation}

\end{document}

Compilando

imagem10

Por padrão, a numeração segue de 1 em diante. Mas é possível modificá-la. Para isso, usamos o comando \tag{nome}. Por exemplo, se quiséssemos chamar a fórmula do exemplo de Axioma 1, bastaria introduzir o comando

\tag{Axioma 1}

logo depois da fórmula dentro do ambiente equation.

Exemplo:

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Classe de documento
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\documentclass[10pt,a4paper]{article}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Pacotes de língua e fontes
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage[utf8]{inputenc}
\usepackage[portuguese]{babel}
\usepackage[T1]{fontenc}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%pacotes matemáticos
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Dados
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\title{Modo Matemático}
\author{Alessandro Duarte}
\begin{document}
\maketitle

Seja a fórmula:

\begin{equation}
p\supset(q\supset p)\tag{Axioma 1}
\end{equation}

\end{document}

Compilando

imagem11

Abaixo há uma série de links de comandos para símbolos matemáticos, lógicos, etc..

http://web.ift.uib.no/Teori/KURS/WRK/TeX/symALL.html

http://en.wikibooks.org/wiki/LaTeX/Mathematics

Pdf com muitos comandos: http://www.tex.ac.uk/tex-archive/info/symbols/comprehensive/symbols-a4.pdf

Nesse link a seguir você pode desenhar o símbolo e o programa tenta adivinhá-lo: http://detexify.kirelabs.org/classify.html