[Tex/LaTex] Box or [ around multiple lines inside align

alignboxesequations

I have the following code

\documentclass{article}
\usepackage{amsmath}

\begin{document}
\begin{alignat*}{4}
        \begin{minipage}[h!]{0\linewidth}
            \text{Let:} \end{minipage}
        && G_{\delta_r}^{\beta} &= \frac{n_1 s + n_0}{s^2 + d_1 s + d_0} = \frac{0.01956 s + 7.01}{s^2 + 0.802 s + 6.489} \\
        && step \left(G_{\delta_r}^{\beta}(s) \right) = \frac{G_{\delta_r}^{\beta}(s)}{s} &= \frac{1}{s} \cdot \frac{n_1 s + n_0}{s^2 + d_1 s + d_0} \\ 
        \\ 
        % \left[ 
        % \makebox[0\linewidth][s] {
        %   \begin{dcases}
                \makebox[0\linewidth][s]{Expanding with partial fractions:} \\
                && \frac{x_1}{s} + \frac{x_{21}s + x_{20}}{s^2 + d_1 s + d_0} &= \frac{1}{s} \cdot \frac{n_1 s + n_0}{s^2 + d_1 s + d_0} \\
                \\
                \makebox[0\linewidth][s]{Removing denominator:} \\
                && x_1(s^2 + d_1 s + d_0) + s(x_{21} s + x_{20}) &= n_1 s + n_0 \\
                \\
                \makebox[0\linewidth][s]{Has solutions:} \\
                \makebox[0\linewidth][s]{
                \begin{minipage}[h!]{0.3\linewidth} \centering
                    $x_{21} = \frac{-n_0}{d_0} = -1.08$ \end{minipage}
                \begin{minipage}[h!]{0.3\linewidth} \centering
                    $x_1 = \frac{n_0}{d_0} = 1.08$ \end{minipage} 
                \begin{minipage}[h!]{0.3\linewidth} \centering
                    $x_{20} = n_1 - \frac{n_0 d_1}{d_0} = -0.847$ \end{minipage} }
            % \end{dcases}
            % }
        \\
        \begin{minipage}[h!]{0\linewidth}
            \text{Hence:} \end{minipage} 
        && \frac{G_{\delta_r}^{\beta}(s)}{s} &= \frac{1.08}{s} - \frac{1.08s + 0.847}{s^2 + 0.8-2s + 6.489} \\
        \\
        \makebox[0\linewidth][s]{Completing the square:} \\
        && \frac{G_{\delta_r}^{\beta}(s)}{s} &= \frac{1.08}{s} - \frac{1.08s + 0.847}{(s + 0.401)^2 + 6.328} \\
        \makebox[0\linewidth][s]{Inverse Laplace:} \\
        && \mathcal{L}^{-1}\left\{ \frac{G_{\delta_r}^{\beta}(s)}{s} \right\} &=  1.08 - e^{-.401t} \left(1.08 \cos(t\sqrt{6.328}) + \frac{0.847}{\sqrt{6.328}} \sin(t\sqrt{6.328}) \right) 
    \end{alignat*}
\end{document}

Which produces:

I would like to put a box (or some kind of a bracket) like the one shown in the picture to denote "sub working out". The complications are that the box will need to span many lines of equations and many columns of the alignat environment.

I have tried many things including \makebox, \minipage, \bcases, \matrix

Any suggestions?

Best Answer

An option using a \parbox inside a \fcolorbox inside a \makebox, and the whole construct inside \intertext; some changes to the original mark-up were done (in particular, the code was greatly simplified), but the original alignment of expressions before and after the box was preserved:

\documentclass{article}
\usepackage{mathtools}
\usepackage{tikzpagenodes}
\usetikzlibrary{tikzmark}

\begin{document}

Let:
\begin{align*}
G_{\delta_r}^{\beta} &= \frac{n_1 s + n_0}{s^2 + d_1 s + d_0} = \frac{0.01956 s + 7.01}{s^2 + 0.802 s + 6.489} \\
\text{step} \left(G_{\delta_r}^{\beta}(s) \right) = \frac{G_{\delta_r}^{\beta}(s)}{s} &= \frac{1}{s} \cdot \frac{n_1 s + n_0}{s^2 + d_1 s + d_0}
\intertext{%
\makebox[\linewidth][c]{\fcolorbox{blue}{white}{\parbox{\linewidth}{%
Expanding with partial fractions:
\[
\frac{x_1}{s} + \frac{x_{21}s + x_{20}}{s^2 + d_1 s + d_0} = 
\frac{1}{s} \cdot \frac{n_1 s + n_0}{s^2 + d_1 s + d_0}
\]
Removing denominator:
\[
x_1(s^2 + d_1 s + d_0) + s(x_{21} s + x_{20}) = n_1 s + n_0 
\]
Has solutions:
\[
x_{21} = \frac{-n_0}{d_0} = -1.08\qquad
x_1 = \frac{n_0}{d_0} = 1.08\qquad
x_{20} = n_1 - \frac{n_0 d_1}{d_0} = -0.847
\]
Hence:}}}
}
\frac{G_{\delta_r}^{\beta}(s)}{s} &= \frac{1.08}{s} - \frac{1.08s + 0.847}{s^2 + 0.8-2s + 6.489} \\
\shortintertext{Completing the square:}
\frac{G_{\delta_r}^{\beta}(s)}{s} &= \frac{1.08}{s} - \frac{1.08s + 0.847}{(s + 0.401)^2 + 6.328} \\
\shortintertext{Inverse Laplace:}
\mathcal{L}^{-1}\left\{ \frac{G_{\delta_r}^{\beta}(s)}{s} \right\} &=  1.08 - e^{-.401t} \left(1.08 \cos\alpha + \frac{0.847}{\sqrt{6.328}} \sin\alpha \right), 
\end{align*}
where $\alpha=t\sqrt{6.328}$.

\end{document}

enter image description here

Another option would be to use the tikzmark library; the idea is to use \tikzmark to place marks at the appropriate locations and then to use those marks to draw the blue rectangle. Below I show this approach and also illustrate another option for the mark-up (of course, this approach will also work with the above approach or with any other variation):

\documentclass{article}
\usepackage{mathtools}
\usepackage{tikzpagenodes}
\usetikzlibrary{tikzmark}

\begin{document}

Let:
\begin{align*}
G_{\delta_r}^{\beta} &= \frac{n_1 s + n_0}{s^2 + d_1 s + d_0} = \frac{0.01956 s + 7.01}{s^2 + 0.802 s + 6.489} \\
\text{step} \left(G_{\delta_r}^{\beta}(s) \right) = \frac{G_{\delta_r}^{\beta}(s)}{s} &= \frac{1}{s} \cdot \frac{n_1 s + n_0}{s^2 + d_1 s + d_0}
\end{align*}         
\tikzmark{start}Expanding with partial fractions:
\[
\frac{x_1}{s} + \frac{x_{21}s + x_{20}}{s^2 + d_1 s + d_0} = 
\frac{1}{s} \cdot \frac{n_1 s + n_0}{s^2 + d_1 s + d_0}
\]
Removing denominator:
\[
x_1(s^2 + d_1 s + d_0) + s(x_{21} s + x_{20}) = n_1 s + n_0 
\]
Has solutions:
\[
x_{21} = \frac{-n_0}{d_0} = -1.08\qquad
x_1 = \frac{n_0}{d_0} = 1.08\qquad
x_{20} = n_1 - \frac{n_0 d_1}{d_0} = -0.847\tikzmark{end}
\]
Hence:
\begin{align*} 
\frac{G_{\delta_r}^{\beta}(s)}{s} &= \frac{1.08}{s} - \frac{1.08s + 0.847}{s^2 + 0.8-2s + 6.489} \\
\shortintertext{Completing the square:}
\frac{G_{\delta_r}^{\beta}(s)}{s} &= \frac{1.08}{s} - \frac{1.08s + 0.847}{(s + 0.401)^2 + 6.328} \\
\shortintertext{Inverse Laplace:}
\mathcal{L}^{-1}\left\{ \frac{G_{\delta_r}^{\beta}(s)}{s} \right\} &=  1.08 - e^{-.401t} \left(1.08 \cos(t\sqrt{6.328}) + \frac{0.847}{\sqrt{6.328}} \sin(t\sqrt{6.328}) \right) 
\end{align*}

\begin{tikzpicture}[remember picture,overlay]
\draw[line width=1.5pt,blue]
  ([xshift=-1ex,yshift=2.5ex]current page text area.west|-{pic cs:start})
  rectangle
  ([yshift=-2.5ex]current page text area.east|-{pic cs:end});
\end{tikzpicture}

\end{document}

enter image description here

Related Solutions

[Tex/LaTex] How to box two lines inside align*

Here an inspiration with tikz

(everyone is welcome to modify the example -- i am not familiar with tikz)

\documentclass{article}
\usepackage{mathtools}
\usepackage{mhchem}
\usepackage{siunitx}

\usepackage{tikz}
\newcounter{markeq}
\setcounter{markeq}{0}
\newcommand*\bmarkeq{%
   \stepcounter{markeq}%
   \tikz[remember picture]\node(startframe-\themarkeq){\strut};}
\newcommand*\emarkeq{%
   \begin{tikzpicture}[remember picture,overlay]
     \node (endframe-\themarkeq){\strut};
     \draw[,red,opacity=0.8] (startframe-\themarkeq.north) rectangle (endframe-\themarkeq.south);
   \end{tikzpicture}%
}

\begin{document}


\begin{align*}
\ce{K_a $\times$ K_b} &= \ce{K_w}\\
-\log(\ce{K_a $\times$ K_b}) &= -\log\ce{K_w}\\
 -( \log(\ce{K_a}) + \log(\ce{K_b}) ) &= -\log\ce{K_w} & \text{(Using log law for LHS.)} \\
 - \log(\ce{K_a}) - \log(\ce{K_b}) &= -\log\ce{K_w}\\
\bmarkeq\ce{pK_a} + \ce{pK_b} &= \ce{pK_w}\\
&=14.00 \text{ (at \SI{25}{\celsius})}\emarkeq
\end{align*}


\end{document}

EDIT

With the very great idea of egreg you get:

\documentclass{article}
\usepackage{mathtools}
\usepackage{mhchem}
\usepackage{siunitx}

\usepackage{tikz}
\newcounter{markeq}
\setcounter{markeq}{0}

\newcommand{\pstrut}[1]{\vrule height0pt depth0pt width0pt #1 \fboxsep}
\newcommand*\bmarkeq{\stepcounter{markeq}%
  \tikz[remember picture]\node(startframe-\themarkeq){\pstrut{height}};%
  \kern\fboxsep}
\newcommand*\emarkeq{\kern\fboxsep
  \begin{tikzpicture}[remember picture,overlay]
    \node (endframe-\themarkeq){\pstrut{depth}};
    \draw[,red,opacity=0.8] (startframe-\themarkeq.north) 
      rectangle (endframe-\themarkeq.south);
  \end{tikzpicture}%
}


\begin{document}


\begin{align*}
\ce{K_a $\times$ K_b} &= \ce{K_w}\\
-\log(\ce{K_a $\times$ K_b}) &= -\log\ce{K_w}\\
 -( \log(\ce{K_a}) + \log(\ce{K_b}) ) &= -\log\ce{K_w} & \text{(Using log law for LHS.)} \\
 - \log(\ce{K_a}) - \log(\ce{K_b}) &= -\log\ce{K_w}\\
\bmarkeq\ce{pK_a} + \ce{pK_b} &= \ce{pK_w}\\
&=14.00 \text{ (at \SI{25}{\celsius})}\emarkeq
\end{align*}


\end{document}

enter image description here

[Tex/LaTex] Box for multiple lines and automatic width

How about a simple tabular?

% arara: pdflatex
\documentclass{article}
\begin{document}

I like \begin{tabular}{l}A\\B\\C2\end{tabular} but who cares?
\end{document}

screenshot

Best Answer

Related Solutions

[Tex/LaTex] How to box two lines inside align*

[Tex/LaTex] Box for multiple lines and automatic width

Related Question