Math Symbols – Adjusting Font Size for \mathcal(O)

fontsize

I use the following mystic TeX so as to display the Landau's notations for big and small O.

There is one partial solution to improve the scriptscriptstyle so as to not use a small o : see the secund answer below. The problemen with \smallOBis is the wrong spacing, contrary to \smallO. How can I do this ?

% Sources :
%     1) http://forum.mathematex.net/latex-f6/bonnes-commandes-de-base-t12278.html
%     2) http://tex.stackexchange.com/questions/30944/mathcalo-and-font-size

\documentclass{article}
    \usepackage{amsmath}
    \usepackage{amsfonts}
    \usepackage{amssymb}

    \usepackage{graphicx}

    \newcommand{\bigO}[1]{\ensuremath{\mathop{}\mathopen{}\mathcal{O}\mathopen{}\left(#1\right)}}

    \newcommand\smallO[1]{
        \mathchoice
            {% \displaystyle
                \ensuremath{\mathop{}\mathopen{}{\scriptstyle\mathcal{O}}\mathopen{}\left(#1\right)}
            }
            {% \textstyle
                \ensuremath{\mathop{}\mathopen{}{\scriptstyle\mathcal{O}}\mathopen{}\left(#1\right)}
            }
            {% \scriptstyle
                \ensuremath{\mathop{}\mathopen{}{\scriptscriptstyle\mathcal{O}}\mathopen{}\left(#1\right)}
            }
            {% \scriptscriptstyle  
                \ensuremath{\mathop{}\mathopen{}{o}\mathopen{}\left(#1\right)}
            }
    }

    \newcommand\smallOBis[1]{
        \mathchoice
        {% \displaystyle
            \scriptstyle\mathcal{O}\left(#1\right)
        }
        {% \textstyle
        \scriptstyle\mathcal{O}\left(#1\right)
        }
        {% \scriptstyle
        \scriptscriptstyle\mathcal{O}\left(#1\right)
        }
        {% \scriptscriptstyle
        \scalebox{0.8}{$\scriptscriptstyle\mathcal{O}$}\left(#1\right)
        }
    }


\begin{document}

\[
    \renewcommand{\arraystretch}{1.2}%
    \begin{array}{llll} 
        \textbf{Style}            & \verb!\bigO!
        & \verb!\smallO!                          & \verb!\smallOBis!
        \\ \hline
        \verb!\displaystyle!      & \displaystyle      \bigO{\frac{1}{n}}
        & \displaystyle      1 + \smallO{\frac{1}{n}} - 2 & \displaystyle      1 + \smallOBis{\frac{1}{n}} - 2
        \\
        \verb!\textstyle!         & \textstyle         \bigO{\frac{1}{n}}
        & \textstyle         1 + \smallO{\frac{1}{n}} - 2 & \textstyle         1 + \smallOBis{\frac{1}{n}} - 2
        \\
        \verb!\scriptstyle!       & \scriptstyle       \bigO{\frac{1}{n}}
        & \scriptstyle       1 + \smallO{\frac{1}{n}} - 2 & \scriptstyle       1 + \smallOBis{\frac{1}{n}} - 2
        \\
        \verb!\scriptscriptstyle! & \scriptscriptstyle \bigO{\frac{1}{n}}
        & \scriptscriptstyle 1 + \smallO{\frac{1}{n}} - 2 & \scriptscriptstyle 1 + \smallOBis{\frac{1}{n}} - 2
    \end{array}
\]

\end{document}

Best Answer

One problem here is the available font sizes at that small-a-size. Using a scaling factor supported by graphicx by means of \scalebox{<factor>}{<stuff>}:

\documentclass{article}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
%\usepackage{amsfonts}% http://ctan.org/pkg/amsfonts
%\usepackage{amssymb}% http://ctan.org/pkg/amssymb
\usepackage{graphicx}% http://ctan.org/pkg/graphicx

\newcommand{\bigO}[1]{\ensuremath{\mathop{}\mathopen{}\mathcal{O}\mathopen{}\left(#1\right)}}

\newcommand\smallO[1]{
    \mathchoice
    {% mode \displaystyle
      \scriptstyle\mathcal{O}\left(#1\right)
    }
    {% mode \textstyle
      \scriptstyle\mathcal{O}\left(#1\right)
    }
    {% mode \scriptstyle
      \scriptscriptstyle\mathcal{O}\left(#1\right)
    }
    {% mode \scriptscriptstyle
      \scalebox{0.8}{$\scriptscriptstyle\mathcal{O}$}\left(#1\right)
    }
}

\begin{document}

\[
\renewcommand{\arraystretch}{1.2}%
\begin{array}{lll}
\textbf{Style} & \verb!\bigO! & \verb!\smallO! \\ \hline
\verb!\displaystyle! & \displaystyle\bigO{n} & \displaystyle\smallO{n} \\  \verb!\textstyle! & \textstyle\bigO{n} & \textstyle\smallO{n} \\ \verb!\scriptstyle! & \scriptstyle\bigO{n} & \scriptstyle\smallO{n} \\ \verb!\scriptscriptstyle! & \scriptscriptstyle\bigO{n} & \scriptscriptstyle\smallO{n}
\end{array}
\]

\end{document}

Different sizes of bigO and smallO

The choice was made to scale a \scriptscriptstyle\mathcal{O} by 80%, since the shape of \mathcal{O} at larger font sizes looks different from that of \scriptscriptstyle. I'm sure that playing around with larger size and smaller scale factors would provide a suitable solution.

Edit: An update to the definition of \smallOBis, as defined in @projetmbc's updated question:

\documentclass{article}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\usepackage{graphicx}% http://ctan.org/pkg/graphicx

\newcommand{\bigO}[1]{\ensuremath{\mathop{}\mathopen{}\mathcal{O}\mathopen{}\left(#1\right)}}

\newcommand\smallO[1]{
  \mathchoice
  {% \displaystyle
    \mathop{}\mathopen{}{\scriptstyle\mathcal{O}}\mathopen{}\left(#1\right)
  }
  {% \textstyle
    \mathop{}\mathopen{}{\scriptstyle\mathcal{O}}\mathopen{}\left(#1\right)
  }
  {% \scriptstyle
    \mathop{}\mathopen{}{\scriptscriptstyle\mathcal{O}}\mathopen{}\left(#1\right)
  }
  {% \scriptscriptstyle  
    \mathop{}\mathopen{}{o}\mathopen{}\left(#1\right)
  }
}

\newcommand\smallOBis[1]{
  \mathchoice
  {% \displaystyle
    \operatorname{\scriptstyle\mathcal{O}}\!\left(#1\right)
  }
  {% \textstyle
      \operatorname{\scriptstyle\mathcal{O}}\!\left(#1\right)
  }
  {% \scriptstyle
      \operatorname{\scriptscriptstyle\mathcal{O}}\left(#1\right)
  }
  {% \scriptscriptstyle
      \operatorname{\scalebox{0.8}{$\scriptscriptstyle\mathcal{O}$}}\left(#1\right)
  }
}

\begin{document}

\[
\renewcommand{\arraystretch}{1.2}%
\begin{array}{llll} 
\textbf{Style}            & \verb!\bigO!
& \verb!\smallO!                          & \verb!\smallOBis!
\\ \hline
\verb!\displaystyle!      & \displaystyle      \bigO{\frac{1}{n}}
& \displaystyle      1 + \smallO{\frac{1}{n}} - 2 & \displaystyle      1 + \smallOBis{\frac{1}{n}} - 2
\\ \verb!\textstyle!         & \textstyle         \bigO{\frac{1}{n}}
& \textstyle         1 + \smallO{\frac{1}{n}} - 2 & \textstyle         1 + \smallOBis{\frac{1}{n}} - 2
\\ \verb!\scriptstyle!       & \scriptstyle       \bigO{\frac{1}{n}}
& \scriptstyle       1 + \smallO{\frac{1}{n}} - 2 & \scriptstyle       1 + \smallOBis{\frac{1}{n}} - 2
\\ \verb!\scriptscriptstyle! & \scriptscriptstyle \bigO{\frac{1}{n}}
& \scriptscriptstyle 1 + \smallO{\frac{1}{n}} - 2 & \scriptscriptstyle 1 + \smallOBis{\frac{1}{n}} - 2
\end{array}
\]
\end{document}

enter image description here

Two changes were made to \smallOBis:

Declared the resized \mathcal{O} as an operator via \operatorname{..}, therefore correcting the spacing with other relational/binary operators on the left side; and
Corrected for spacing between new operator and brackets on the right side with \!.

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I'd use one environment, with an optional argument; the environment does not change the font size if no optional argument is specified.

However, since the size declaration has to be given before the tabbing environment starts, because tabbing cells form groups, we need to terminate the current paragraph.

\documentclass[11pt,a4paper]{article}

\newenvironment{sftabbing}[1][]
  {\par\sffamily#1\tabbing}
  {\endtabbing}

\newcommand{\blah}{blah blah blah blah blah blah blah blah blah blah blah blah 
blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah 
blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah}


\begin{document}

First paragraph \blah
\begin{sftabbing}
some code some code some code some code some code some code \\
some code some code some code some code some code some code \\
some code some code some code some code some code some code \\
some code some code some code some code some code some code \\
some code some code some code some code some code some code \\
some code some code some code some code some code some text
\end{sftabbing}
first paragraph continues here \blah

Second paragraph \blah
\begin{sftabbing}[\small]
some code some code some code some code some code some code \\
some code some code some code some code some code some code \\
some code some code some code some code some code some code \\
some code some code some code some code some code some code \\
some code some code some code some code some code some code \\
some code some code some code some code some code some text
\end{sftabbing}
second paragraph continues here \blah
blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah 

Third paragraph \blah
\begin{sftabbing}[\scriptsize]
some code some code some code some code some code some code \\
some code some code some code some code some code some code \\
some code some code some code some code some code some code \\
some code some code some code some code some code some code \\
some code some code some code some code some code some code \\
some code some code some code some code some code some text
\end{sftabbing}
third paragraph continues here \blah 

\end{document}

enter image description here

Best Answer

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