How to define ReDeclareLargeMathOperator

Question

I want alter an existing math operator by applying a macro to it. In the MWE the \ReDeclareLargeMathOperator applies the \ProcessSymbol macro which in this example changes the color of the symbol as well make a hyperlink to a Wikipedia page.

However, my attempt to adapt the first reference listed below required a few a hack to get the smallest size to be correct for the \sum operator. But, this macro does work properly for the integral as the style is altered.

So, what is the best way to define \ReDeclareLargeMathOperator so that I can tweak the symbol yet have the same spacing as the default?

Notes:

• The black text below is the default operator and the red text is the one that is the one defined with the \ReDeclareLargeMathOperator macro.

---

Sum: The horizontal spacing does not align with the default symbol. Even in inline mode there seems to be some additional horizontal spacing added prior to the symbol.

---

Integral: The spacing of the limits of integration are incorrect and the style of the integral symbol does not match.

References:

• How to create my own math operator with limits?
• How to redefine a command using \DeclareMathOperator

Code:

\documentclass{article}
\usepackage{xcolor}
\usepackage{amsmath}
\usepackage{etoolbox}
\usepackage[colorlinks=false, pdfborder={0 0 1}, allbordercolors=magenta]{hyperref}

\newcommand*{\ProcessSymbol}[2]{%
    \color{red}\href{#2}{#1}%
}%


%% Adapted from https://tex.stackexchange.com/questions/23432/how-to-create-my-own-math-operator-with-limits
\newcommand*{\ReDeclareLargeMathOperator}[3]{%
    % #1 = name of operator
    % #2 = symbol 
    % #3 = web link
    % ---------------------
    \renewcommand#1{%
        \vphantom{\OldSum}%
        \mathop{\mathchoice%
            {\vcenter{\hbox{\ProcessSymbol{\huge$#2$}{#3}}}}%
            {\vcenter{\hbox{\ProcessSymbol{\Large$#2$}{#3}}}}%
            {\vcenter{\hbox{\ProcessSymbol{$#2$}{#3}}}}%
            {\vcenter{\hbox{\ProcessSymbol{$\scriptstyle#2$}{#3}}}}%
        }\displaylimits%
    }%
}%

%% So that we can test things and also ensure that limit placement matches
%%  the height of where the original definition of \sum placed things.
\let\OldSum\sum
\let\OldInt\int

\ReDeclareLargeMathOperator{\sum}{\Sigma}{https://en.wikipedia.org/wiki/Summation}
\ReDeclareLargeMathOperator{\int}{\intop}{https://en.wikipedia.org/wiki/Integral}

\newcommand{\dx}{\mathrm{d}x}%

\begin{document}  
\section{Sum}
In inline math $\OldSum_{i=0}^n i$, and in display math it is:
\begin{flalign*}
    &\displaystyle\OldSum_{i=0}^n i
    \textstyle\OldSum_{i=0}^n i
    \scriptstyle\OldSum_{i=0}^n i
    \scriptscriptstyle\OldSum_{i=0}^n i
    \quad%% so that we can view vertical spacing.
    \displaystyle\sum_{i=0}^n i
    \textstyle\sum_{i=0}^n i
    \scriptstyle\sum_{i=0}^n i
    \scriptscriptstyle\sum_{i=0}^n i &
\end{flalign*}
\noindent
In inline math $\sum_{i=0}^n i$, and in display math it is:
\begin{flalign*}
    &\displaystyle\sum_{i=0}^n i
    \textstyle\sum_{i=0}^n i
    \scriptstyle\sum_{i=0}^n i
    \scriptscriptstyle\sum_{i=0}^n i
    &
\end{flalign*}


% ----------------------------------------------------------------

\section{Integral}
In inline math $\OldInt_a^b y\dx$, and in display math it is:
\begin{flalign*}
    &\displaystyle\OldInt_a^b  y\dx
    \textstyle\OldInt_a^b  y\dx
    \scriptstyle\OldInt_a^b  y\dx
    \scriptscriptstyle\OldInt_a^b  y\dx
    \quad%% so that we can view vertical spacing.
    \displaystyle\int_a^b  y\dx
    \textstyle\int_a^b  y\dx
    \scriptstyle\int_a^b  y\dx
    \scriptscriptstyle\int_a^b  y\dx &
    &
\end{flalign*}
\noindent
In inline math $\int_a^b  y\dx$, and in display math it is:
\begin{flalign*}
    &\displaystyle\int_a^b  y\dx
    \textstyle\int_a^b  y\dx
    \scriptstyle\int_a^b  y\dx
    \scriptscriptstyle\int_a^b  y\dx
    &
\end{flalign*}

\end{document}

Answer 1

Why changing the symbol for \sum into \Sigma? It's surely wrong.

Operators such as \sum or \bigcup can be dealt with in a simpler way; for the integral some more work is needed, if you want to preserve the kerning. Thus the new \int command must absorb the possible \limits token and then the (optional) limits. Then a red integral is typeset as part of \href, with the limits added in the current color.

\documentclass{article}
\usepackage{xcolor}
\usepackage{amsmath}
\usepackage{etoolbox}
\usepackage[colorlinks=false, pdfborder={0 0 1}, allbordercolors=magenta]{hyperref}

%% Adapted from http://tex.stackexchange.com/questions/23432/how-to-create-my-own-math-operator-with-limits
\newcommand*{\ReDeclareLargeMathOperator}[2]{%
  % #1 = name of operator
  % #2 = web link
  % ---------------------
  \cslet{\string#1}#1%
  \renewcommand#1{%
    \mathop{%
      \mathpalette{\ProcessSymbol}{{\csuse{\string#1}}{#2}}%
    }\displaylimits
  }%
}
\newcommand*{\ProcessSymbol}[2]{\doProcessSymbol{#1}#2}
\newcommand*{\doProcessSymbol}[3]{%
  \vcenter{\hbox{\color{red}\href{#3}{$#1#2$}}}%
}
%% for integrals the above can't work
\makeatletter
\let\linkedint@int\intop
\DeclareRobustCommand{\linkedint}{%
  \let\linkedint@limits\nolimits % default
  \let\linkedint@lower\@empty
  \let\linkedint@upper\@empty
  \colorlet{linkedint@color}{.}%
  \@ifnextchar\limits{\let\linkedint@limits\limits\linkedint@checksub}{\linkedint@checksub}%
}
\newcommand{\linkedint@checksub}{%
  \@ifnextchar_{\linkedint@sub}{\linkedint@checksup}%
}
\newcommand{\linkedint@checksup}{%
  \@ifnextchar^{\linkedint@sup}{\linkedint@do}%
}
\newcommand\linkedint@sub[2]{%
  \def\linkedint@lower{#2}\linkedint@checksup
}
\newcommand\linkedint@sup[2]{%
  \def\linkedint@upper{#2}\linkedint@do
}
\newcommand{\linkedint@do}{%
  \mathop{\mathpalette\linkedint@final{https://en.wikipedia.org/wiki/Integral}}%
}
\newcommand\linkedint@final[2]{%
  \vcenter{\hbox{\color{red}%
    \href{#2}{$#1%
      \linkedint@int\linkedint@limits
        _{\textcolor{linkedint@color}{\linkedint@lower}}%
        ^{\textcolor{linkedint@color}{\linkedint@upper}}%
    $}%
  }}%
}
\makeatother

%% So that we can test things and also ensure that limit placement matches
%%  the height of where the original definition of \sum placed things.
\let\OldSum\sum
\let\OldIntop\intop
\def\OldInt{\OldIntop\nolimits}

\ReDeclareLargeMathOperator{\sum}{https://en.wikipedia.org/wiki/Summation}
%\ReDeclareLargeMathOperator{\intop}{https://en.wikipedia.org/wiki/Integral}
\let\int\linkedint

\newcommand{\dx}{\mathrm{d}x}%

\begin{document}  

\section{Sum}
In inline math $\OldSum_{i=0}^n i$, and in display math it is:
\begin{flalign*}
    &\displaystyle\OldSum_{i=0}^n i
    \textstyle\OldSum_{i=0}^n i
    \scriptstyle\OldSum_{i=0}^n i
    \scriptscriptstyle\OldSum_{i=0}^n i
    \quad%% so that we can view vertical spacing.
    \displaystyle\sum_{i=0}^n i
    \textstyle\sum_{i=0}^n i
    \scriptstyle\sum_{i=0}^n i
    \scriptscriptstyle\sum_{i=0}^n i &
\end{flalign*}
\noindent
In inline math $\sum_{i=0}^n i$, and in display math it is:
\begin{flalign*}
    &\displaystyle\sum_{i=0}^n i
    \textstyle\sum_{i=0}^n i
    \scriptstyle\sum_{i=0}^n i
    \scriptscriptstyle\sum_{i=0}^n i
    &
\end{flalign*}


% ----------------------------------------------------------------

\section{Integral}
In inline math $\OldInt_a^b y\dx$, and in display math it is:
\begin{flalign*}
    &\displaystyle\OldInt_a^b  y\dx
    \textstyle\OldInt_a^b  y\dx
    \scriptstyle\OldInt_a^b  y\dx
    \scriptscriptstyle\OldInt_a^b  y\dx
    \quad%% so that we can view vertical spacing.
    \displaystyle\int_a^b  y\dx
    \textstyle\int_a^b  y\dx
    \scriptstyle\int_a^b  y\dx
    \scriptscriptstyle\int_a^b  y\dx &
    &
\end{flalign*}
\noindent
In inline math $\int_a^b  y\dx$, and in display math it is:
\begin{flalign*}
    &\displaystyle\int^b_a  y\dx
    \textstyle\int_a^b  y\dx
    \scriptstyle\int_a^b  y\dx
    \scriptscriptstyle\int_a^b  y\dx
    &
\end{flalign*}

\end{document}