Multiple alignments within align environment

Question

My minimum working example:

\documentclass{report}

\usepackage{amsmath}

\begin{document}

\begin{align}
\dot{x}_2 =  \dot{x}_{2,0}&+\frac{\partial f_2(x_1)}{\partial x_1} \bigg|_{x_1=x_{1,0}}       (x_1-x_{1,0})+\\
&+ \frac{1}{2}\frac{\partial {f_2}^2(x_1)}{\partial {x_1}^2} \bigg|_{x_1=x_{1,0}}       (x_1-x_{1,0})^2+ \\
&+ \frac{1}{6}\frac{\partial {f_2}^3(x_1)}{\partial {x_1}^3} \bigg|_{x_1=x_{1,0}}       (x_1-x_{1,0})^3+ \\
&+   g_2  (u-u_0) 
\end{align}

\end{document}

The result:

Now I would like to obtain the following result instead:

Any ideas?

Answer 1

Yep! alignat

\documentclass{report}

\usepackage{amsmath}

\begin{document}

\begin{alignat}{3}
\dot{x}_2 =  \dot{x}_{2,0} \,& + \,& \,\frac{\partial f_2(x_1)}{\partial x_1} \bigg|_{x_1=x_{1,0}} &       (x_1-x_{1,0}) &+\\
&+& \,\frac{1}{2}\frac{\partial {f_2}^2(x_1)}{\partial {x_1}^2} \bigg|_{x_1=x_{1,0}}  &     (x_1-x_{1,0})^2 &+ \\
&+& \,\frac{1}{6}\frac{\partial {f_2}^3(x_1)}{\partial {x_1}^3} \bigg|_{x_1=x_{1,0}}  &     (x_1-x_{1,0})^3 &+ \\
&+ \protect\makebox[0pt][l]{\,\,$g_2  (u-u_0)$}\, 
\end{alignat}

\end{document}

Note: you should take care with the number in curly brackets - it's to do with the total number of ampersands. I think it's supposed to be total + 1 divided by 2, but I have four... I had just copied and pasted from a bit of my own code. Perhaps someone will explain the number of ampersands thing better! The first ampersand marks an alignment point, and the next column will be right aligned. If you put in another, it will then be left aligned for the subsequent column so you can put && in if you want to immediately left align.

Note I put a few \, spacing commands in to line stuff up with slightly bigger gaps to match what you were looking for.

Now tell me, I'm confused: since you have uploaded exactly what you wanted - how did you generate that?

Answer 2

Use alignat and \mathrlap from the mathtools package for the last line.

The alignat environment has an implicit {rlrl...rlrl} alignment. The argument is the number of the r columns.

The command \mathrlap puts its argument in a zero width box and aligns it left.

\documentclass{report}

\usepackage{mathtools}% loads amsmath

\begin{document}
\begin{alignat}{3}
\dot{x}_2 =  \dot{x}_{2,0}&+{}&\frac{\partial f_2(x_1)}{\partial x_1} \bigg|_{x_1=x_{1,0}}
       &(x_1-x_{1,0})&{}+{}\\
&+{}& \frac{1}{2}\frac{\partial {f_2}^2(x_1)}{\partial {x_1}^2} \bigg|_{x_1=x_{1,0}}       &(x_1-x_{1,0})^2&{}+{} \\
&+{}& \frac{1}{6}\frac{\partial {f_2}^3(x_1)}{\partial {x_1}^3} \bigg|_{x_1=x_{1,0}}       &(x_1-x_{1,0})^3&{}+{} \\
&+\mathrlap{g_2(u-u_0)}
\end{alignat}
\end{document}

I have used &+{}& and &{}+{} to get the right spacing around the +.

Answer 3

Here, I did it with a tabular stack. Note, however, that it will only allow a single equation number to be applied to the result. However, since it is a single equation, I thought that might be okay (if you want the vertical position of the number to be adjusted, that can be done).

The only real quirk to the solution was getting the g_2 term left aligned in a right-aligned column. For that, I just grafted it to the right side of the preceding + sign.

\documentclass{report}
\usepackage{tabstackengine}
\stackMath
\usepackage{amsmath}
\begin{document}
\begin{equation}
\setstackgap{S}{6pt}
\TABbinary
\setstacktabulargap{0pt}
\tabularShortstack{rcrlc}{
\dot{x}_2 =  \dot{x}_{2,0}&+&\dfrac{\partial f_2(x_1)}{\partial x_1} \bigg|_{x_1=x_{1,0}}&       (x_1-x_{1,0})&+\\
&+& \dfrac{1}{2}\dfrac{\partial {f_2}^2(x_1)}{\partial {x_1}^2} \bigg|_{x_1=x_{1,0}}&       (x_1-x_{1,0})^2&+ \\
&+& \dfrac{1}{6}\dfrac{\partial {f_2}^3(x_1)}{\partial {x_1}^3} \bigg|_{x_1=x_{1,0}}&       (x_1-x_{1,0})^3&+ \\
&+ \protect\makebox[0pt][l]{$g_2  (u-u_0)$}& &&&
}
\end{equation}
\end{document}

Answer 4

You can keep the alignment points in the align environment as they are now, and just insert a couple of \phantom instructions in the first row to achieve the needed spacing adjustments.

By the way, I would recommend you omit the + symbols at the ends of rows 1, 2, and 3 since they're made redundant by the + symbols at the start of rows 2, 3, and 4.

\documentclass{report}
\usepackage{amsmath}
\begin{document}
\begin{align}
\dot{x}_2 =  \dot{x}_{2,0}&+\phantom{\frac{1}{2}}\frac{\partial {f_2}\phantom{^1}(x_1)}{\partial x_1} \bigg|_{x_1=x_{1,0}}       (x_1-x_{1,0})\\
&+ \frac{1}{2}\frac{\partial {f_2}^2(x_1)}{\partial {x_1}^2} \bigg|_{x_1=x_{1,0}}       (x_1-x_{1,0})^2\\
&+ \frac{1}{6}\frac{\partial {f_2}^3(x_1)}{\partial {x_1}^3} \bigg|_{x_1=x_{1,0}}       (x_1-x_{1,0})^3\\
&+   g_2  (u-u_0)
\end{align}
\end{document} 

However, if these + symbols must be there, I would recommend you (a) write +{} instead of just + for these symbols to get proper spacing and (b) append \phantom{^1} to (x_1-x_{1,0}) in the first row to further fine-tune the spacing.

Finally, if you wanted the vertical space between the third and fourth row to be the same as between the other rows, you could add the instruction \phantom{\bigg|} after g_2 (u-u_0). With this adjustment made, and the + symbols at the ends of the first three rows not deleted, your equations would look like this:

\documentclass{report}
\usepackage{amsmath,}
\begin{document}
\begin{align}
\dot{x}_2 =  \dot{x}_{2,0}&+\phantom{\frac{1}{2}}\frac{\partial {f_2}\phantom{^1}(x_1)}{\partial x_1} \bigg|_{x_1=x_{1,0}}       (x_1-x_{1,0})\phantom{^1} +{}\\
&+ \frac{1}{2}\frac{\partial {f_2}^2(x_1)}{\partial {x_1}^2} \bigg|_{x_1=x_{1,0}}       (x_1-x_{1,0})^2 +{}\\
&+ \frac{1}{6}\frac{\partial {f_2}^3(x_1)}{\partial {x_1}^3} \bigg|_{x_1=x_{1,0}}       (x_1-x_{1,0})^3 +{}\\
&+   g_2  (u-u_0)\phantom{\bigg|}
\end{align}
\end{document}