Aligning polynomial terms

Question

In LaTeX align, I'm struggling to align polynomial terms and assume there's an easy way to do it. But I cannot find the simple/elegant solution. What I would like is something like this:

x1 + x2 ______ = 3

x1_______+ x3 = 4

etc with more lines and variables (the underlines are just for space/alignment). Any help appreciated.

UPDATE Here is the solution I found:

\begin{alignat*}{7}
8x_1 &{}+ 4x_2 &{}+ y_1   &        &        &        &= 160     \\
4x_1 &{}+ 6x_2 &          &{}+ y_2 &        &        &= 120     \\
x_1  &         &          &        &{}+ y_3 &        &= 34      \\
\phantom{{}+{}x_1}&{}+x_2&&        &        &{}+ y_4 &= 14      \\
x_1\geq0&x_2\geq0&y_1\geq0&y_2\geq0&y_3\geq0& y_4\geq0
\end{alignat*}

with result:

Answer 1

A fairly intuitive way would be to use \phantom to hide away components of the equations that you don't want to typeset, but have the space left for it. Additionally, since \phantom causes some spacing issues if used untouched, you need to (re-)specify the binary relation of + using \mathrel or a combination of atom-related use of {}.

\documentclass{article}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\begin{document}
\begin{align*}
  x_1+x_2\phantom{{}+{}x_3} &= 3 \\
  x_1\phantom{{}+{}x_2}{}+x_3 &= 4 \\
  x_1+x_2+x_3 &= 5
\end{align*}
\end{document}

Alternatively, one can also typeset this using an array environment. However, in terms of elegance, I don't think this ranks very high. It reduces the code readability somewhat.

Answer 2

This is probably not the elegant solution you look for, but the following code works for me:

\usepackage{mathtools}

...

\[\begin{matrix*}[r]
        x1 & +x2 &  & = & 3 \\
        x1 &  & +x3 & = & 4 \\
         & -x2 & x3 & = & 5 \\
\end{matrix*}\]

Answer 3

You could also use the alignat* environment from the amsmath package- see page 5 of the documentation for details and other examples.

Note that without the {} you don't get correct spacing after the + sign.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{alignat*}{4} % 4 is the number of equation columns
  x_1&+x_2&     & =3\\
  x_1&    &{}+x_3 &= 4
\end{alignat*}
\end{document}

EDIT Following mforbes' comment, and a few extra test cases, it is probably more robust to make extra columns for the + and =. For example, say that you wanted to put some coefficients in front of some of the terms.

\begin{alignat*}{4}
     x_1 &{}+{}&x_2    &      &     &{}={}&3\\
     x_1 &     &       &{}+{} & x_3 &{}={}&4
\end{alignat*}

As mforbes pointed out, the amsmath documentation says 'count the maximum number of &s in any row, add 1 and divide by 2'; I've found that if you get a fraction, then you should round up, hence {4} and not {3}.

Answer 4

This requires array, and has the advantage that spacing is taken care of automatically; the disadvantage is the number of & symbols.

\usepackage{array}
\newenvironment{polyalign}[1][9]
  {\array{c*{#1}{@{}>{{}}c<{{}}@{}r@{}}}}
  {\endarray}

\[
\begin{polyalign}
x_1 & + &  x_2 &   &     & = & 3 \\
x_1 &   &      & + & x_3 & = & 4 \\
    &   & 2x_2 & + & x_3 & = & 5
\end{polyalign}
\]

The optional argument to the environment (default is 9) is intended for helping when very big systems are needed: it can be seen as the maximum number of monomials in the left hand side.

Answer 5

The systeme package easily enables such alignments:

\documentclass{minimal}
\usepackage{systeme}
\begin{document}
\sysdelim..
\systeme{x_1+x_3=6,x_2-x_3=7,x_1-x_2=4}
\end{document}

Answer 6

I am so going to get flak for this. Oh well :-D

\documentclass{minimal}
\begin{document}
\[
  \vcenter{\halign{&${}#$\hfil\cr
    8x_1 & +4x_2 &    +y_1 &&&& = 160 \cr
    4x_1 & +6x_2 &&   +y_2 &&&  = 120 \cr
    x_1  &       &&&  +y_3 &&   = 34 \cr
         & +x_2  &&&& +y_4 &    = 14 \cr }}
  \qquad
  x_1 \ge 0x_2 \ge 0y_1 \ge 0y_2 \ge 0y_3 \ge 0y_4 \ge 0
\]
\end{document}

Answer 7

Ok, here is my final solution, thanks to everyone's suggestions and guidance. Everything is now clean and well aligned :

\begin{alignat*}
8x_1  &{}+{}&    &4x_2  &{}+{}& y_1                     &&&&&& &{}={}&160\\
4x_1  &{}+{}&    &6x_2  &&       &{}+{}& y_2              &&&& &{}={}&120\\
x_1   &&         &      &&       &&       &{}+{}& y_3       && &{}={}& 34\\
\phantom{{}+{}x_1}
      &&         &x_2   &&       &&          &&    &{}+{}& y_4 &{}={}&14
\end{alignat*}

I've split the inequalities line from the alignat because it was messing with the columns width.

I learned:

• surround the operators in ${}+{}$
• use the exact same number of & on each line
• use \phantom{{}+{}x_1} for missing terms at the head of the polynomial
• don't put anything else (text) in the structure. That will mess thing up
• there are many many ways of doing the same thing and I have a lot to learn

Here's the output: