How can I align math in table across regular and multirow cells?

Question

I'm trying to create a table with math that is properly aligned horizontally but can also be centred across multiple rows. I've tried two different methods (one using a solution from this answer) and both result in slight alignment errors, as shown.

I've previously tried using an aligned environment as in this example but as far as I can tell there is no way to align math across multiple such environments or insert a cmidrule into one.

Is there a way to modify either of these solutions to fix the errors shown? What's the best solution to align math in this way?

\documentclass{report}
\usepackage{amsmath,array,booktabs,multirow}

% From https://tex.stackexchange.com/questions/78788/align-equations-over-multiple-tabular-rows/78839#78839
\newcolumntype{A}{ >{$} r <{$} @{} >{${}} l <{$} } % A for "align"

\begin{document}

%   FIXED COLUMN DIVIDER
\begin{table}[ht]
    \centering
    \caption{Fixed column divider}
    \begin{tabular}{ l r@{ = } l r@{ $\leftarrow$ } l }
        \toprule
        \textbf{Name}
        &   \multicolumn{2}{l}{\textbf{Math}}   
        &   \multicolumn{2}{l}{\textbf{More Math}}      \\
        \midrule
        \multirow{2}{*}{Foo}
        &   $A$
        &   $x^2 + y^3$
        &   $x$
        &   $x(1 - \alpha)$                         \\
        &   $BC$
        &   $x^3 - y^2$         
        &   $y$
        &   $y(1 + \beta)$                          \\
        \cmidrule{4-5}
        \multirow{2}{*}{Bar}
        &   $D$
        &   $xy + w_z$
        &   \multirow{2}{*}{$w_z$}
        &   \multirow{2}{*}{$w_z(1 + q)$}           \\  
        &   \multicolumn{2}{l}{Note: if $A > D \text{ then } D \leftarrow AB + C$}
        &   \multicolumn{2}{l}{}                    \\
        \bottomrule
    \end{tabular}   
\end{table}

%   NEW COLUMN TYPE
\begin{table}[ht]
    \centering
    \caption{New column type}
    \begin{tabular}{ l A A }
        \toprule
        \textbf{Name}
        &   \multicolumn{2}{l}{\textbf{Math}}   
        &   \multicolumn{2}{l}{\textbf{More Math}}      \\
        \midrule
        \multirow{2}{*}{Foo}
        &   A   &= x^2 + y^3
        &   x   &\leftarrow x(1 - \alpha)           \\
        &   BC  &= x^3 - y^2            
        &   y   &\leftarrow y(1 + \beta)            \\
        \cmidrule{4-5}
        \multirow{2}{*}{Bar}
        &   D   &= xy + w_z
        &   \multirow{2}{*}{$w_z$}
        &   \multirow{2}{*}{$\leftarrow w_z(1 + q)$}\\  
        &   \multicolumn{2}{l}{Note: if $A > D \text{ then } D \leftarrow AB + C$}
        &   \multicolumn{2}{l}{}                    \\
        \bottomrule
    \end{tabular}   
\end{table}

\end{document}

Answer 1

You can place the LHS of each equation inside a box that's measurable and then adjust it so that all those in the second [third] column have the same-width LHS. This approach is made easy using eqparbox which uses a \label-\ref-like approach to store the maximum box width (requires two compilation on the first go or any subsequent changes).

\eqmathbox is similar to \eqparbox, retaining the math context. The syntax \eqmathbox[<tag>][<align>]{<stuff>} aligns <stuff> with the same <tag> based on the preferred <align>ment specified. This is ultimately done where <stuff> is placed inside a box of maximum width across all <stuff>s with the same <tag>.

\documentclass{article}

\usepackage{amsmath,eqparbox,booktabs,xparse}

% https://tex.stackexchange.com/a/34412/5764
\makeatletter
\NewDocumentCommand{\eqmathbox}{o O{c} m}{%
  \IfValueTF{#1}
    {\def\eqmathbox@##1##2{\eqmakebox[#1][#2]{$##1##2$}}}
    {\def\eqmathbox@##1##2{\eqmakebox{$##1##2$}}}
  \mathpalette\eqmathbox@{#3}
}
\begin{document}

\begin{tabular}{ *{3}{l} }
  \toprule
  \textbf{Name} & \textbf{Math} & \textbf{More Math} \\
  \midrule
  \raisebox{-.5\normalbaselineskip}[0pt][0pt]{Foo} &
    $\eqmathbox[L][r]{A} = x^2 + y^3$ &
    $\eqmathbox[R][r]{x} \leftarrow x (1 - \alpha)$ \\
  &
    $\eqmathbox[L][r]{BC} = x^3 - y^2$ &
    $ \eqmathbox[R][r]{y} \leftarrow y (1 + \beta)$ \\
  \cmidrule{3-3}
  \raisebox{-.5\normalbaselineskip}[0pt][0pt]{Bar} &
    $ \eqmathbox[L][r]{D} = x y + w_z$ &
    \raisebox{-.5\normalbaselineskip}[0pt][0pt]{%
      $\eqmathbox[R][r]{w_z} \leftarrow w_z (1 + q)$%
    } \\
  & Note: if $A > D$ then $D \leftarrow AB + C$ \\
  \bottomrule
\end{tabular}

\end{document}

Above I used \raisebox{<len>}[0pt][0pt]{<stuff>} in lieu of \multirow since it's not really part of the question, nor needed.

Answer 2

I wasn't sure it would work, but you can put \multirow inside a \multicolumn (just like \raisebox) and let it compute the offsets.

Note the phantom entries (including a phantom \leftarrow) in the last line to set up the alignment. Both cells are the widest for any row, so placement of the \multicolumn version is simple.

\documentclass{report}
\usepackage{amsmath,array,booktabs,multirow}

\begin{document}

%   FIXED COLUMN DIVIDER
\begin{table}[ht]
    \centering
    \caption{Fixed column divider}
    \begin{tabular}{ l r@{ = } l r@{ $\leftarrow$ } l }
        \toprule
        \textbf{Name}
        &   \multicolumn{2}{l}{\textbf{Math}}   
        &   \multicolumn{2}{l}{\textbf{More Math}}      \\
        \midrule
        \multirow{2}{*}{Foo}
        &   $A$
        &   $x^2 + y^3$
        &   $x$
        &   $x(1 - \alpha)$                         \\
        &   $BC$
        &   $x^3 - y^2$         
        &   $y$
        &   $y(1 + \beta)$                          \\
        \cmidrule{4-5}
        \multirow{2}{*}{Bar}
        &   $D$
        &   $xy + w_z$
        &   \multicolumn{2}{c}{\multirow{2}{*}{$w_z \leftarrow w_z(1 + q)$}}\\
        &   \multicolumn{2}{l}{Note: if $A > D \text{ then } D \leftarrow AB + C$}
        &   \multicolumn{1}{r@{ \phantom{$\leftarrow$} }}{\phantom{$w_z$}}% remove \leftarrowy
        &   \phantom{$w_z(1 + q)$}\\

        \bottomrule
    \end{tabular}   
\end{table}

\end{document}

Answer 3

It is better to use math environments directly rather than adjust column properties. You may have noticed that in align environments, the spacing between entries is large for a table. In this case you can use \\[-1.5mm] just to reduce the spacing. You can replace 1.5 with whatever number you want, , but you must always be sure not to separate \\ from [-1.5mm].

The >{\hsize=scale\hsize} specification in tabularx environment can be used to specify the column width in terms of another, a very desirable feature. For instance, in the table above, the second row is set to be 70% larger than the third one. Here is the source code for the table shown above:

\documentclass{report}
\usepackage{amsmath,array,booktabs,multirow}
\usepackage{ragged2e}
\usepackage{tabularx}
\usepackage{makecell}

\newcolumntype{C}{ >{ \arraybackslash \Centering } X }
\renewcommand \tabularxcolumn [1] { >{ \centering } m{#1} }
\newcommand {\scalelinespace} [1] {\rule{0pt}{#1\normalbaselineskip}}

\begin{document}


\begin{table*}[h]


    \centering
    \begin{tabularx}{1\textwidth}{>{\hsize=0.5\hsize}C| >{\hsize=1.45\hsize}C| >{\hsize=1.05\hsize}C}

        \toprule

        \textbf{Name} & \textbf{Math} & \textbf{More Math} \\

        \midrule

        Foo
        & 
            $\begin{aligned}
                A &= x^{2} + y^{3} \\[-1.5mm]
                BC &= x^{3} - y^{2}
            \end{aligned}$
        &
            $\begin{aligned}
            x &\leftarrow x \thinspace (1 - \alpha)  \\[-1.5mm]
            y &\leftarrow y \thinspace (1 + \beta) 
            \end{aligned}$
        \\
        \Xcline{3-3}{0.2mm}
        \scalelinespace{1}
        Bar
        & 
        \scalelinespace{1}
            \hspace{4.1mm} $D = x y + w_{z}$
            \text{Note if } $A>D \text{ then } D \leftarrow AB+C$
        &
        \scalelinespace{1}
            $w_{z} \leftarrow w_{z} \thinspace (1 + q)$
        \\ 
        \bottomrule

    \end{tabularx}

\end{table*}




\end{document}