Alignment at equals signs in two columns of an array environment

Question

I would like to make a table of two columns of the squares of all the digits. With the following code, there is no proper spacing between the equals sign and the numbers in the first column, and the equals sign is not typeset in the second column.

\documentclass{amsart}
\usepackage{amsmath}

\begin{document}

$$
\begin{array}{r@{${}={}$}lc@{\qquad\qquad}cr@{${}={}$}l}
0^2&0, & 5^2&25, \\
1^2&1, & 6^2&36, \\
2^2&4, & 7^2&49, \\
3^2&9, & 8^2&64, \\
4^2&16, & 9^2&81.
\end{array}
$$

\end{document}

I would appreciate tips on how to do this only using the array environment.

Answer 1

You have declared a fifth column in between the two groups. In my opinion, it's unnecessary. Here is a simpler code:

\documentclass{amsart}
\usepackage{amsmath}
\usepackage{array}

\begin{document}

\[
\begin{array}{r@{{}²={}}l!{\qquad}r@{{}²={}}l}
0&0, & 5&25, \\
1&1, & 6&36, \\
2&4, & 7&49, \\
3&9, & 8&64, \\
4&16, &9&81.
\end{array}
\]

\end{document} 

Answer 2

You can ask TeX to do the computations itself in whatever radix you like (up to 36).

\documentclass{article}
\usepackage{xparse,array,booktabs}

\ExplSyntaxOn

\NewDocumentCommand{\digitsquares}{sO{c}m}
 {% #1 * option for the header, #2 = alignment, #3 = radix
  \IfBooleanTF { #1 }
   {
    \tl_set:Nn \l_tmpa_tl { \multicolumn{6}{c}{\mbox{Base ~ $#3$}} \\ \midrule }
   }
   {
    \tl_clear:N \l_tmpa_tl
   }
  \int_step_inline:nnn { 0 } { \int_div_round:nn { #3 } { 2 } - 1 }
   {
    \tl_put_right:Nx \l_tmpa_tl
     {
      \int_to_Base:nn { ##1 } { #3 } ^2 & = & \int_to_Base:nn { (##1)*(##1) } { #3 } &
      \int_compare:nT { ##1 + \int_div_round:nn { #3 } { 2 } < #3 }
       {
        \int_to_Base:nn { ##1 + \int_div_round:nn { #3 } { 2 } } { #3 }^2 & = &
        \int_to_Base:nn
         {
          (##1 + \int_div_round:nn { #3 } { 2 })*
          (##1 + \int_div_round:nn { #3 } { 2 })
         } { #3 }
        \exp_not:N \\
       }
     }
   }
  \begin{array}[#2]{@{} r @{} >{{}}c<{{}} @{} l @{\qquad} r @{} >{{}}c<{{}} @{} l @{}}
  \l_tmpa_tl
  \end{array}
 }

\ExplSyntaxOff

\begin{document}

\[
\digitsquares*[t]{10} \qquad \digitsquares*[t]{7}
\]
\[
\digitsquares{16}
\]

\end{document}

The * means that we want the header; the optional argument is for passing the alignment option to array. The mandatory argument is the radix.

The array preamble consists of two sets

r @{} >{{}}c<{{}} @{} l

that is: right aligned column, no space, a centered column with {} on either side of the item (it will be the = sign), left aligned column; in between a \qquad separation. The leading and trailing @{} nullify the padding on either side of the array.

Answer 3

I am using a platform that apparently does not allow all the options for an array environment. It may only allow l, r, c, and @{\qquad}. I have modified my code so that it gives me exactly what I want.

\documentclass{amsart}
\usepackage{amsmath}

\begin{document}

$$\begin{array}{r@{}l @{\qquad\qquad} r@{}l}
0^2 &{}={} 0, & 5^2 &{}={} 25, \\
1^2 &{}={} 1, & 6^2 &{}={} 36, \\
2^2 &{}={} 4, & 7^2 &{}={} 49, \\
3^2 &{}={} 9, & 8^2 &{}={} 64, \\
4^2 &{}={} 16, & 9^2 &{}={} 81.
\end{array}$$

\end{document}