[Tex/LaTex] Aligning multiple equations on multiple points

alignequations

I'm trying to generate the following output in LaTeX:

However I am failing pretty hard at aligning those correctly, this is what I've tried so far:

\begin{align*}
&(a)\hspace{20pt}\lfloor{n/2}\rfloor &< p &\leq\hspace{19pt} n &\Rightarrow {l}_{p}(n\wr)&=1 \\
&(b)\hspace{20pt}\lfloor{n/3}\rfloor &< p &\leq \lfloor{n/2}\rfloor &\Rightarrow {l}_{p}(n\wr)&=0 \\
&(c)\hspace{20pt}\sqrt{n} &< p &\leq \lfloor{n/3}\rfloor &\Rightarrow {l}_{p}(n\wr)&=\lfloor{n/p}\rfloor\mod 2\\
&(d)\hspace{20pt}2 &< p &\leq \sqrt{n} &\Rightarrow {l}_{p}(n\wr)&<\log_2(n)\\
&(d)\hspace{20pt}{} p &= 2 &\Rightarrow {l}_{p}(n\wr)={\sigma}_{2}(\lfloor{n/2}\rfloor)
\end{align*}

How can I do this alignment the right way as presented in the example?

Best Answer

For multiple points (and no big spacing between the blocks) there is alignat. Let's examine your problem, recalling that alignat makes pairs of “right aligned/left aligned” columns.

You have: left aligned column (for the item labels); right aligned column (for the lower bounds); left aligned column (for the relations); right aligned column (for the variable); left aligned column (for the upper bounds); column that can be either left or right aligned (the arrows); left aligned column (for the final conditions).

So we should have

&\text{(a)}\qquad
&\lfloor n/2\rfloor
&<{}
&p
&&\le n
&\implies
&l_p(n\wr)=1
\\

and we should repeat the pattern. We have a total of eight &, which makes for five pairs. The empty group after the relation is to ensure correct spacing. I use \implies that adds some space at either end by itself. I took advantage from the fact that the final condition all have the same structure, so the alignment is automatic; otherwise, follow the same pattern analysis.

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\begin{alignat*}{5}
&\text{(a)}\qquad &\lfloor n/2\rfloor &<{} &p &\leq n                  &\implies &l_{p}(n\wr)=1 \\
&\text{(b)}\qquad &\lfloor n/3\rfloor &<{} &p &\leq \lfloor n/2\rfloor &\implies &l_{p}(n\wr)=0 \\
&\text{(c)}\qquad &\sqrt{n}           &<{} &p &\leq \lfloor n/3\rfloor &\implies &l_{p}(n\wr)=\lfloor n/p\rfloor \bmod 2\\
&\text{(d)}\qquad &2                  &<{} &p &\leq \sqrt{n}           &\implies &l_{p}(n\wr)<\log_2(n)\\
&\text{(e)}\qquad &                   &    &p &= 2                     &\implies &l_{p}(n\wr)=\sigma_{2}(\lfloor n/2\rfloor)
\end{alignat*}

\end{document}

I removed all the useless braces (none is needed for \lfloor x\rfloor). Note that “mod” as a binary operation should be \bmod, not \mod.

You may want to consider a space saving macro \floor:

\documentclass{article}
\usepackage{amsmath,mathtools}

\DeclarePairedDelimiter{\floor}{\lfloor}{\rfloor}

\begin{document}

\begin{alignat*}{5}
&\text{(a)}\qquad &\floor{n/2} &<{} &p &\leq n           &\implies &l_{p}(n\wr)=1 \\
&\text{(b)}\qquad &\floor{n/3} &<{} &p &\leq \floor{n/2} &\implies &l_{p}(n\wr)=0 \\
&\text{(c)}\qquad &\sqrt{n}    &<{} &p &\leq \floor{n/3} &\implies &l_{p}(n\wr)=\floor{n/p} \bmod 2\\
&\text{(d)}\qquad &2           &<{} &p &\leq \sqrt{n}    &\implies &l_{p}(n\wr)<\log_2(n)\\
&\text{(e)}\qquad &            &    &p &= 2              &\implies &l_{p}(n\wr)=\sigma_{2}(\floor{n/2})
\end{alignat*}

\end{document}

Related Solutions

[Tex/LaTex] Left-aligning equations

Don't use align*.

De raaklijn aan $(x_{0},f(x_{0}))$ wordt algemeen bepaald met:
\begin{flushleft}
\colorbox{vanillegeel}{%
$\displaystyle
\begin{cases}
z=f(x) \text{ is continu in } x_{0}.
\\
f'(x_{0})=0 \text{ : } z=f(x_{0}) \text{ is de horizontale raaklijn.}
\\
\lim_{x\to x_{0}} f'(x)=\pm\infty \text{ : } x=x_{0} \text{ is de verticale raaklijn.}
\\
f'(x_{0})\in\mathbb{R}_{0} \text{ : } z-f(x_{0})=f'(x_{0})\cdot(x-x_{0})
  \text{ is de raaklijn.}
\end{cases}
$\kern-\nulldelimiterspace\kern-2\arraycolsep}
\end{flushleft}

enter image description here

[Tex/LaTex] Multiple align points and multiple equations

I believe you're using a two column format.

The environment split only accepts one alignment point; you can use \mathmakebox from mathtools (that also loads amsmath) and calc:

\documentclass[twocolumn]{article}
\usepackage{mathtools}
\usepackage{calc}

\begin{document}
\begin{align}
\begin{split}
z_1^{i,j}
    & = a_1^{} x_1^{i,j} + b_1^{} \delta_1^{i,j} \\
    & \qquad+ \sum_k y_k^{i,j}
      \qquad \forall i,j
\end{split}
\\
\begin{split}
z_2^{i,j}
    & = a_2^{} x_2^{i,j} + b_2^{} \delta_2^{i,j} + c_2^{} \\
    & \qquad + \mathmakebox[\widthof{$\displaystyle\sum_k y_k^{i,j}$}][l]{z_1^{i,j}}
      \qquad \forall i,j
\end{split}
\end{align}
\end{document}

Note that \, between factors is not used, while ^{} is recommended in order to push subscripts at the same level. The + on the second line shouldn't be under the equals sign, as it belongs to the right hand side of the expression.

enter image description here

However, the subscripts are not really level, because of j at the exponent, so you might want a slightly more complex adjustment:

\documentclass[twocolumn]{article}
\usepackage{mathtools}
\usepackage{calc}

\newcommand{\adjs}[1]{^{\vphantom{#1}}}

\begin{document}
\begin{align}
\begin{split}
z_1^{i,j}
    & = a_1\adjs{j} x_1^{i,j} + b_1\adjs{j} \delta_1^{i,j} \\
    & \qquad+ \sum_k y_k^{i,j}
      \qquad \forall i,j
\end{split}
\\
\begin{split}
z_2^{i,j}
    & = a_2\adjs{j} x_2^{i,j} + b_2\adjs{j} \delta_2^{i,j} + c_2\adjs{j} \\
    & \qquad + \mathmakebox[\widthof{$\displaystyle\sum_k y_k^{i,j}$}][l]{z_1^{i,j}}
      \qquad \forall i,j
\end{split}
\end{align}
\end{document}

enter image description here

Best Answer

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[Tex/LaTex] Left-aligning equations

[Tex/LaTex] Multiple align points and multiple equations

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