Comment déclarer de nouveaux opérateurs mathématiques ?#

1.  Avec l’extension mathtools#

Pour cela, vous pouvez utiliser la commande \mathop. Par exemple :

Exemple compilable et éditable
\documentclass{article}
  \usepackage[T1]{fontenc}    % Encodage T1 (adapté au français)
  \usepackage{lmodern}        % Caractères plus lisibles
  \pagestyle{empty}           % N'affiche pas de numéro de page
  \usepackage{mathtools}
\begin{document}
\newcommand{\diag}{\mathop{\mathrm{diag}}}
\[  \diag_1^n  \]
\end{document}
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
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Compilation... . . .

Les indices et les exposants associés à \diag seront placés en dessous et au-dessus du nom de la fonction, comme ils le sont pour la commande \sum. Si vous voulez que vos indices et exposants soient toujours placés à droite, utilisez la commande \nolimits. Pour plus d’information, vous pouvez consulter la question « Comment positionner les limites des grands opérateurs ? ».

Exemple compilable et éditable
\documentclass{article}
  \usepackage[T1]{fontenc}    % Encodage T1 (adapté au français)
  \usepackage{lmodern}        % Caractères plus lisibles
  \pagestyle{empty}           % N'affiche pas de numéro de page
  \usepackage{mathtools}
\begin{document}
\newcommand{\diag}{\mathop{\mathrm{diag}}\nolimits}
\[  \diag_1^n  \]
\end{document}
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
Compilation... . . .

L’extension mathtools charge l’extension amsmath qui, elle-même, charge l’extension amsopn. Cette dernière fournit une commande \DeclareMathOperator qui effectue le même travail que la deuxième définition ci-dessus :

Exemple compilable et éditable
\documentclass{article}
  \usepackage[T1]{fontenc}    % Encodage T1 (adapté au français)
  \usepackage{lmodern}        % Caractères plus lisibles
  \pagestyle{empty}           % N'affiche pas de numéro de page
  \usepackage{mathtools}
  \DeclareMathOperator{\diag}{diag}
\begin{document}
\[  \diag_1^n  \]
\end{document}
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
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Compilation... . . .

Pour créer notre commande \diag originale, il faut utiliser la commande étoilée \DeclareMathOperator* qui génère un opérateur qui a toujours ses exposants et exposants.

Exemple compilable et éditable
\documentclass{article}
  \usepackage[T1]{fontenc}    % Encodage T1 (adapté au français)
  \usepackage{lmodern}        % Caractères plus lisibles
  \pagestyle{empty}           % N'affiche pas de numéro de page
  \usepackage{mathtools}
  \DeclareMathOperator*{\diag}{diag}
\begin{document}
\[  \diag_1^n  \]
\end{document}
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
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Compilation... . . .

La commande \operatorname de l’extension amsopn vous permet d’introduire des opérateurs ad hoc directement dans vos mathématiques. Vous pouvez donc saisir :

\[  \operatorname{truc}(bidule)  \]

Ceci sera équivalent à :

% Dans le préambule
\DeclareMathOperator{\truc}{truc}
% (...)
% Dans le document
\[  \truc(bidule)  \]

Comme pour \DeclareMathOperator, il existe une version étoilée \operatorname* pour gérer la position des indices et exposants.