Mathematical Expression Optimization: Combining Equations for Enhanced Readability

This article focuses on optimizing the presentation of mathematical expressions. We start with two separate equations, each within its own \begin{equation*}\begin{cases}...\end{cases}\end{equation*} structure. Our goal is to combine these two equations into a single, unified expression, enhancing readability and potentially simplifying further mathematical analysis.

Initially, the equations are presented as:

\begin{equation*} \begin{cases}L^=116(\frac{Y}{Y_0})^{1/3}-16\a^=500[(\frac{X}{X_0})^{1/3}-(\frac{Y}{Y_0})^{1/3}]\b^=200[(\frac{Y}{Y_0})^{1/3}-(\frac{Z}{Z_0})^{1/3}]\end{cases}\end{equation}

\begin{equation*} \begin{cases}L^=903.3(\frac{Y}{Y_0})\a^=3893.5(\frac{X}{X_0}-\frac{Y}{Y_0})\b^=1557.4(\frac{Y}{Y_0}-\frac{Z}{Z_0})\end{cases}\end{equation}

To achieve a more compact representation, we can merge these two expressions into a single case statement. This results in the following combined expression:

\begin{equation*} \begin{cases}L^=116(\frac{Y}{Y_0})^{1/3}-16, \quad a^=500[(\frac{X}{X_0})^{1/3}-(\frac{Y}{Y_0})^{1/3}], \quad b^=200[(\frac{Y}{Y_0})^{1/3}-(\frac{Z}{Z_0})^{1/3}]\L^=903.3(\frac{Y}{Y_0}), \quad a^=3893.5(\frac{X}{X_0}-\frac{Y}{Y_0}), \quad b^=1557.4(\frac{Y}{Y_0}-\frac{Z}{Z_0})\end{cases}\end{equation*}

This combined expression provides a more efficient representation, potentially facilitating further mathematical operations or analysis. The use of \quad ensures proper spacing between the equations within the case statement, enhancing readability.