Multiple align points with a single equation number

Question

I have the following equation:

\begin{align}
\begin{split}
     &\phantom{{}={}} [ (1,1,1) : (1,1) : (1,2) : (1) : (2,2,2) : (2,2) : (2) :  (3) ] \\
     \textsc{one} &= [ 0 : 3 : 0 : 0 : 0 : 0 : 0 : 0 ] \\
     \textsc{two} &= [ 1 : 0 : 3 : 0 : -1 : 0 : 0 : 0 ] \\
     \textsc{three} &= [ 0  : 0 : 3 : 0 : -1 : 0 : 0 : 0 ] \\
\end{split}
\end{align}
\end{document}

I would like to have the opening [, each :, and closing ] aligned vertically to match the top row.

I have tried various combinations of align, alignat, equation, alignedat, but I am unable to find anything that works.

Any pointer would be appreciated.

I tried the alignedat from other answers:

\begin{equation}
    \begin{alignedat}{9}
     &[ (1,1,1) &: (1,1) &: (1,2) &: (1) &: (2,2,2) &: (2,2) &: (2) &:  (3) & & ] \\
     \textsc{one} = &[ 0 &: 3 &: 0 &: 0 &: 0 &: 0 &: 0 &: 0 & &] \\
     \textsc{two} = &[ 1 &: 0 &: 3 &: 0 &: -1 &: 0 &: 0 &: 0 & & ] \\
     \textsc{three} = &[ 0  &: 0 &: 3 &: 0 &: -1 &: 0 &: 0 &: 0 & &] \\
\end{alignedat}
\end{equation}

but it doesn't actually seem to do the alignment (only aligns some :'s).

Answer 1

You can use autoaligne:

\documentclass{article}
\usepackage{amsmath}
\usepackage{autoaligne}

\begin{document}

\begin{equation}
\definirseparateurs{\\}{}{:||[||]}
\autoaligne[*d]{
                  [\, (1,1,1) : (1,1) : (1,2) : (1) : (2,2,2) : (2,2) : (2) :  (3) \,] \\
\textsc{one}={}   [\, 0 : 3 : 0 : 0 : 0 : 0 : 0 : 0 \,] \\
\textsc{two}={}   [\, 1 : 0 : 3 : 0 : -1 : 0 : 0 : 0 \,] \\
\textsc{three}={} [\, 0  : 0 : 3 : 0 : -1 : 0 : 0 : 0 \,]
}
\end{equation}

\begin{equation}
\definirseparateurs{\\}{}{:||[||]}
\autoaligne[*c]{
                        [\, (1,1,1) : (1,1) : (1,2) : (1) : (2,2,2) : (2,2) : (2) :  (3) \,] \\
\hfill\textsc{one}={}   [\, 0 : 3 : 0 : 0 : 0 : 0 : 0 : 0 \,] \\
\hfill\textsc{two}={}   [\, 1 : 0 : 3 : 0 : -1 : 0 : 0 : 0 \,] \\
\hfill\textsc{three}={} [\, 0  : 0 : 3 : 0 : -1 : 0 : 0 : 0 \,]
}
\end{equation}

\end{document}

Answer 2

I'd use an array

\documentclass{article}

\usepackage{amsmath,array}


\begin{document}

\begin{equation}
    \begin{array}{r<{{}}@{[}r@{:}r@{:}r@{:}r@{:}r@{:}r@{:}r@{:}r@{]}}
     & (1,1,1) & (1,1) & (1,2) & (1) & (2,2,2) & (2,2) & (2) &  (3) \\
     \textsc{one} = & 0 & 3 & 0 & 0 & 0 & 0 & 0 & 0   \\
     \textsc{two} = & 1 & 0 & 3 & 0 & -1 & 0 & 0 & 0   \\
     \textsc{three} = & 0  & 0 & 3 & 0 & -1 & 0 & 0 & 0  \\
\end{array}
\end{equation}
\end{document}

Answer 3

Here is a correct code with alignedat:

\documentclass[]{article}
\usepackage{mathtools}
\begin{document}

\begin{equation}
    \begin{alignedat}{9}
     &[ (1,1,1) & & : (1,1) & & : (1,2) & & : (1) & & : (2,2,2) & & : (2,2) & & : (2) & & : (3) & & ] \\
     \textsc{one} = {}&[ 0 & & : 3 & & : 0 & & : 0 & & : 0 & & : 0 & & : 0 & & : 0 & &] \\
     \textsc{two} = {}&[ 1 & & : 0 & & : 3 & & : 0 & & : -1 & & : 0 & & : 0 & & : 0 & & ] \\
     \textsc{three} = {}&[ 0 & & : 0 & & : 3 & & : 0 & &: -1 & & : 0 & & : 0 & & : 0 & &] \\
\end{alignedat}
\end{equation}

\end{document} 

Answer 4

Here is a TABstack.

\documentclass[12pt]{article}
\usepackage{tabstackengine,amsmath}
\begin{document}
\begin{equation}
    \setstacktabbedgap{3pt}
    \tabbedCenterstack[r]{
     [& (1,1,1) :& (1,1) :& (1,2) :& (1) :& (2,2,2) :& (2,2) :& (2) :&  (3) & ] \\
     \textsc{one} = [& 0 :& 3 :& 0 :& 0 :& 0 :& 0 :& 0 :& 0 &] \\
     \textsc{two} = [& 1 :& 0 :& 3 :& 0 :& -1 :& 0 :& 0 :& 0 & ] \\
     \textsc{three} = [& 0  :& 0 :& 3 :& 0 :& -1 :& 0 :& 0 :& 0 &]
}
\end{equation}
\end{document}