\frac command: height of the numerator vs height of denominator

Question

I have the following code:

\begin{equation}
 \underline{W}^1_{\,q,\rho} =  \left\lceil
 \frac{\sum\limits_{v \in
Q, v \neq q}\underline{C}_{\,v} + \sum\limits_{i=\rho+1}^{|\Omega^{(U)}_q|}p_i+
\sum\limits_{i \in U \backslash \Omega^{(U)}_q}p_i%
+\underline{TT}_{\,q, \rho} }{m-1}
 \right\rceil\,,
\end{equation}

that is rendered as:

As you may see, the numerator height is the same as the denominator. I don't need all this waste of empty space. How can I avoid this situation?

Answer 1

Not a real answer to your question, see below.

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\begin{equation}
\underline{W}^1_{\,q,\rho} =
\biggl\lceil \frac{1}{m-1}
  \biggl(\,
  \sum_{v \in Q, v \neq q}\underline{C}_{\,v} +
  \sum_{i=\rho+1}^{|\Omega^{(U)}_q|}p_i +
  \sum_{i \in U \setminus \Omega^{(U)}_q}p_i +
  \underline{TT}_{\,q, \rho}
  \biggr)
\biggr\rceil,
\end{equation}
\end{document}

Note that you don't need \limits when in a display; also \backslash should be \setminus. Note also that \left and \right would give an inferior result, because they would cover also the big upper limit, which is not necessary.

You can easily adapt this for a two column format:

\documentclass[twocolumn]{article}
\usepackage{amsmath}

\begin{document}

\begin{multline}
\underline{W}^1_{\,q,\rho} =
\biggl\lceil \frac{1}{m-1}
  \biggl(\,
  \sum_{v \in Q, v \neq q}\underline{C}_{\,v} + {}\\
  \sum_{i=\rho+1}^{|\Omega^{(U)}_q|}p_i +
  \sum_{i \in U \setminus \Omega^{(U)}_q}p_i +
  \underline{TT}_{\,q, \rho}
  \biggr)
\biggr\rceil,
\end{multline}
\end{document}

Why does that horrible result appear? Because the main fraction line is set on the “formula axis” and fences are set to cover the material and be centered on the axis.

Answer 2

While the other answers may be preferable alternatives to answer your question, you did mention "I don't need all this waste of empty space." Here is a different way to avoid the empty space, while preserving your original intent. The \stretchleftright macro of scalerel package using glyph stretching to simulate a \left\...\right effect, but only as far as necessary to match the vertical extent of the middle argument. In this case, the optional argument of [300] tells the macro to not let the aspect ratio of the stretch exceed 300%, increasing the width as necessary to maintain it.

\documentclass{article}
\usepackage{scalerel}
\begin{document}
\begin{equation}
 \underline{W}^1_{\,q,\rho} =  \stretchleftright[300]{\lceil}{%
 \frac{\sum\limits_{v \in
Q, v \neq q}\underline{C}_{\,v} + \sum\limits_{i=\rho+1}^{|\Omega^{(U)}_q|}p_i+
\sum\limits_{i \in U \backslash \Omega^{(U)}_q}p_i%
+\underline{TT}_{\,q, \rho} }{m-1}
}{\rceil}\,,
\end{equation}
\end{document}

Answer 3

I think this is easier to read than the fraction you're trying to write:

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\begin{equation}
 \underline{W}^1_{\,q,\rho} =  \left\lceil
\frac{1}{m-1} \left(
\sum\limits_{v \in
Q, v \neq q}\underline{C}_{\,v} + \sum\limits_{i=\rho+1}^{|\Omega^{(U)}_q|}p_i+
\sum\limits_{i \in U \backslash \Omega^{(U)}_q}p_i%
+\underline{TT}_{\,q, \rho} \right)
 \right\rceil\,,
\end{equation}

\end{document}