# Aligning and line-breaking a set of long equations in both single- and two-column modes with proportional vertical spacing

For the following set of long equations, how to

1- aesthetically align and line-break them in a single- and two-column modes without crossing the single column dedicated space and

2- separately control the vertical spacing inside both align and aligned in order to enhance the readability since, for instance ,I need \begin{spreadlines}{1em} to only affect align while having another setting for aligned (e.g. \begin{spreadlines}{0.5em} without manually using \\[<spacing>]?

\documentclass{article}
\usepackage{mathtools,multicol,lipsum}
\usepackage[bold-style=TeX]{unicode-math}
\setmathfont[math-style=ISO]{Cambria Math}
\usepackage[showframe]{geometry}
\begin{document}
\begin{align}
&\frac{1}{\sigma(1-\alpha)} \sum_{j=0}^{k-1} \frac{T^{j+1}-T^j}{\tau_{j+1}} \left(1-\exp\left(-\sigma\tau_{j+1}\right)\right)\cdot\exp\left(-\sigma(k-j-1)\tau_{j+1}\right) = \nabla^2 T^{k}\\
%
&\frac{1}{\sigma(1-\alpha)} \begin{bmatrix*}[l] \left(T^k-T^{k-1}\right) \frac{1-\exp\left(-\sigma\tau_k\right)}{\tau_k} \\
+ \sum_{j=0}^{k-2} \left( T^{j+1} - T^j \right) \cdot (1-\exp\left(-\sigma\tau_{j+1}\right)) \cdot \exp \left( - \sigma (k-j-1) \tau_{j+1} \right)\end{bmatrix*} = \nabla^2 T^{k}\\
%
& \begin{aligned} &\left(T^k-T^{k-1}\right) \frac{1-\exp\left(-\sigma\tau_k\right)}{\tau_k} - [\sigma(1-\alpha)]\nabla^2 T^{k} \\
&= - \sum_{j=0}^{k-2} \left( T^{j+1} - T^j \right) \cdot (1-\exp\left(-\sigma\tau_{j+1}\right)) \cdot \exp \left( - \sigma (k-j-1) \tau_{j+1} \right) \end{aligned}\\
%
&\begin{aligned} &T^k \frac{1-\exp\left(-\sigma\tau_k\right)}{\tau_k} - [\sigma(1-\alpha)]\nabla^2 T^{k} = \\
&T^{k-1} \frac{1-\exp\left(-\sigma\tau_k\right)}{\tau_k} - \sum_{j=0}^{k-2} \left( T^{j+1} - T^j \right) \cdot (1-\exp\left(-\sigma\tau_{j+1}\right)) \cdot \exp \left( - \sigma (k-j-1) \tau_{j+1} \right) \end{aligned}
\end{align}

\newpage

\begin{multicols}{2}
the above set of equations is needed to be typeset here again in a two-column mode.
\end{multicols}
\end{document}

• I've used an interesting system to get two columns, but I don't know how to control the spacing... Commented May 1, 2020 at 13:31

This is still a bit overfull but might give you a start

Main changes:

• don't use spreadlines, just use \\[\jot] on outer level line breaks and \\ on inner ones.
• don't use bmatrix for displayed equations (it uses textstyle math for matrices)
• use multlined (or similar) not align when there is no alignment.
\documentclass{article}
\usepackage{mathtools,multicol,lipsum}
\usepackage[bold-style=TeX]{unicode-math}
\setmathfont[math-style=ISO]{Cambria Math}
\usepackage[showframe]{geometry}
\allowdisplaybreaks
\begin{document}
\begin{gather}
\frac{1}{\sigma(1-\alpha)} \sum_{j=0}^{k-1} \frac{T^{j+1}-T^j}{\tau_{j+1}} \left(1-\exp\left(-\sigma\tau_{j+1}\right)\right)\cdot\exp\left(-\sigma(k-j-1)\tau_{j+1}\right) = \nabla^2 T^{k}\\[\jot]
%
\frac{1}{\sigma(1-\alpha)} \left[\begin{multlined} \left(T^k-T^{k-1}\right) \frac{1-\exp\left(-\sigma\tau_k\right)}{\tau_k} \\
+ \sum_{j=0}^{k-2} \left( T^{j+1} - T^j \right) \cdot (1-\exp\left(-\sigma\tau_{j+1}\right)) \cdot \exp \left( - \sigma (k-j-1) \tau_{j+1} \right)\end{multlined}\right] = \nabla^2 T^{k}\\[\jot]
%
\begin{multlined} \left(T^k-T^{k-1}\right) \frac{1-\exp\left(-\sigma\tau_k\right)}{\tau_k} - [\sigma(1-\alpha)]\nabla^2 T^{k} \\
= - \sum_{j=0}^{k-2} \left( T^{j+1} - T^j \right) \cdot (1-\exp\left(-\sigma\tau_{j+1}\right)) \cdot \exp \left( - \sigma (k-j-1) \tau_{j+1} \right) \end{multlined}\\[\jot]
%
\begin{multlined} T^k \frac{1-\exp\left(-\sigma\tau_k\right)}{\tau_k} - [\sigma(1-\alpha)]\nabla^2 T^{k} = \\
T^{k-1} \frac{1-\exp\left(-\sigma\tau_k\right)}{\tau_k} - \sum_{j=0}^{k-2} \left( T^{j+1} - T^j \right) \cdot (1-\exp\left(-\sigma\tau_{j+1}\right)) \cdot \exp \left( - \sigma (k-j-1) \tau_{j+1} \right) \end{multlined}
\end{gather}

\begin{multicols}{2}
the above set of equations is needed to be typeset here again in a two-column mode.
\begin{gather}
\begin{multlined}
\frac{1}{\sigma(1-\alpha)} \sum_{j=0}^{k-1} \frac{T^{j+1}-T^j}{\tau_{j+1}} \left(1-\exp\left(-\sigma\tau_{j+1}\right)\right)\cdot\\\exp\left(-\sigma(k-j-1)\tau_{j+1}\right)\\  = \nabla^2 T^{k}
\end{multlined}\\[\jot]
%
\begin{multlined}
\frac{1}{\sigma(1-\alpha)} \bigl[ \left(T^k-T^{k-1}\right) \frac{1-\exp\left(-\sigma\tau_k\right)}{\tau_k} \\
+ \sum_{j=0}^{k-2} \left( T^{j+1} - T^j \right) \cdot (1-\exp\left(-\sigma\tau_{j+1}\right)) \cdot\\
\exp \left( - \sigma (k-j-1) \tau_{j+1} \right)\bigr]\\ = \nabla^2 T^{k}
\end{multlined}\\[\jot]
%
\begin{multlined} \left(T^k-T^{k-1}\right) \frac{1-\exp\left(-\sigma\tau_k\right)}{\tau_k} - [\sigma(1-\alpha)]\nabla^2 T^{k} \\
= - \sum_{j=0}^{k-2} \left( T^{j+1} - T^j \right) \cdot (1-\exp\left(-\sigma\tau_{j+1}\right)) \cdot\\
\exp \left( - \sigma (k-j-1) \tau_{j+1} \right) \end{multlined}\\[\jot]
%
\begin{multlined} T^k \frac{1-\exp\left(-\sigma\tau_k\right)}{\tau_k} - [\sigma(1-\alpha)]\nabla^2 T^{k} = \\
T^{k-1} \frac{1-\exp\left(-\sigma\tau_k\right)}{\tau_k}\\ - \sum_{j=0}^{k-2} \left( T^{j+1} - T^j \right) \cdot (1-\exp\left(-\sigma\tau_{j+1}\right)) \cdot\\ \exp \left( - \sigma (k-j-1) \tau_{j+1} \right) \end{multlined}
\end{gather}

\end{multicols}
\end{document}

• For the set of equations in the single-column mode, I needed to left align them, so I used the align environment. Is there another recommendation?
– Diaa
Commented May 1, 2020 at 23:48
• How to make the second line in multilined left-aligned with the first one? Additionally, what are the other alternatives to multilined in this example? Thanks
– Diaa
Commented May 2, 2020 at 10:22
• @Diaa I would say if you want left aligned equations you should use fleqn as a document option and left align them all, but nothing bad actually happens if you use align and and empty first cell as you did originally. I think if you are splitting a long equation the multilined layout with left aligned first line centred middle and right aligned last line is clearer and distinguishes it from a normal align where you are aligning on &= for semantic reasons not just for space. But there are lots of possibilities.... Commented May 2, 2020 at 11:58

A small variation of nice @DavidCarlisle answer (+1):

• instead of \exp(...) are used e^{-....}
• in multicolum are used \medmath defined in the nccmath package
\documentclass{article}
\usepackage[showframe]{geometry}
\usepackage[bold-style=TeX]{unicode-math}
\setmathfont[math-style=ISO]{Cambria Math}

\usepackage{nccmath, mathtools}
\makeatletter
\let\origexp\exp
\DeclareRobustCommand{\exp}{\@ifnextchar^{\Exp^{}}{\origexp }}
\def\Exp^#1{\,\mathop{\mathrm{\mathstrut e}\!\!}\nolimits^{#1}\,}
\makeatother
\allowdisplaybreaks
\usepackage{multicol,lipsum}

\begin{document}

\begin{gather}
\frac{1}{\sigma(1-\alpha)}
\sum_{j=0}^{k-1}\frac{T^{j+1} - T^j}{\tau_{j+1}}
\bigl(1-\exp^{-\sigma\tau_{j+1}}\bigr)
\cdot\exp^{(-\sigma(k-j-1)\tau_{j+1})}
= \nabla^2 T^{k}      \\
%
\frac{1}{\sigma(1-\alpha)}
\left[
\left(T^k-T^{k-1}\right)
\frac{1-\exp^{-\sigma\tau_k}}{\tau_k} +
\displaystyle\sum_{j=0}^{k-2} \bigl( T^{j+1} - T^j \bigr)
\cdot \bigl(1-\exp^{-\sigma\tau_{j+1}}\bigr)
\cdot \exp^{-\sigma(k-j-1)\tau_{j+1}}
\right]
= \nabla^2 T^{k}  \\
%
\bigl(T^k-T^{k-1}\bigr) \frac{1-\exp^{-\sigma\tau_k}}{\tau_k}
- \bigl[\sigma(1-\alpha)\bigr]\nabla^2 T^{k}
= - \sum_{j=0}^{k-2} \bigl( T^{j+1} - T^j \bigr)
\cdot \bigl(1-\exp^{-\sigma\tau_{j+1}}\bigr)
\cdot \exp^{- \sigma(k-j-1)\tau_{j+1}} \\
%
\begin{multlined}[0.75\linewidth]
T^k \frac{1-\exp^{-\sigma\tau_k}}{\tau_k}
- \bigl[\sigma(1-\alpha)\bigr]\nabla^2 T^{k} = \\[-1ex]
T^{k-1} \frac{1-\exp^{-\sigma\tau_k}}{\tau_k}
- \sum_{j=0}^{k-2} \left( T^{j+1} - T^j \right)
\cdot \bigl(1-\exp^{-\sigma\tau_{j+1}}\bigr)
\cdot \exp^{- \sigma (k-j-1) \tau_{j+1}}
\end{multlined}
\end{gather}
%%%%
\hrule
%%%%
\begin{multicols}{2}
The above set of equations is needed to be typeset here again in a two-column mode.
\begin{gather}
%\begin{gathered}
\medmath{\begin{multlined}[0.8\linewidth]
\frac{1}{\sigma(1-\alpha)}
\sum_{j=0}^{k-1}\frac{T^{j+1} - T^j}{\tau_{j+1}}=  \\[-1ex]
\left(1-\exp^{-\sigma\tau_{j+1}}\right)
\cdot\exp^{-\sigma(k-j-1)\tau_{j+1}}
= \nabla^2 T^{k}
\end{multlined}}     \\[2ex]
%
\medmath{\begin{multlined}[0.8\linewidth]
\frac{1}{\sigma(1-\alpha)}
\Biggl[
\bigl(T^k - T^{k-1}\bigr)
\frac{1-\exp^{-\sigma\tau_k}}{\tau_k} +   \\[-1ex]
\sum_{j=0}^{k-2} \bigl( T^{j+1} - T^j \bigr)
\cdot \bigl(1-\exp^{-\sigma\tau_{j+1}}\bigr) \\[-1ex]
\cdot \exp^{-\sigma(k-j-1)\tau_{j+1}}
\Biggr]
= \nabla^2 T^{k}
\end{multlined}}     \\[2ex]
%
\medmath{\begin{multlined}[0.8\linewidth]
\bigl(T^k-T^{k-1}\bigr) \frac{1-\exp^{-\sigma\tau_k}}{\tau_k}
- \bigl[\sigma(1-\alpha)\bigr]\nabla^2 T^{k} =      \\[-1ex]
- \sum_{j=0}^{k-2} \bigl( T^{j+1} - T^j \bigr)
\cdot \bigl(1-\exp^{-\sigma\tau_{j+1}}\bigr)
\cdot \exp^{- \sigma(k-j-1)\tau_{j+1}}
\end{multlined}}     \\[2ex]
%
\medmath{\begin{multlined}[0.8\linewidth]
T^k \frac{1-\exp^{-\sigma\tau_k}}{\tau_k} - \bigl[\sigma(1-\alpha)\bigr]\nabla^2
= T^{k-1} \frac{1-\exp^{-\sigma\tau_k}}{\tau_k}     \\[-1ex]
- \sum_{j=0}^{k-2} \bigl( T^{j+1} - T^j \bigr)
\cdot \bigl(1-\exp^{-\sigma\tau_{j+1}}\bigr)
\cdot \exp^{- \sigma (k-j-1) \tau_{j+1}}
\end{multlined}}
\end{gather}
\end{multicols}
\end{document}