How to align displayed, multi-line computations

Question

I work in a field of mathematics where long, multi-line computations are bread and butter, and I mostly use align* (and its siblings) from the amsmath package to display them. However, I have not found a simple, foolproof way of typesetting such expressions. What is the easiest way of correctly aligning lines horizontally in multi-line expressions?

Ideally, the solution should not be overly technical, lest my coauthors resort to easier, but incorrect, solutions.

Take the following caricature of a multi-line computation: x = -y [newline] -y. If I have understood Knuth and Swanson1 correctly, then the above should be typeset as

that is, something like

x [thickspace] = [thickspace] - [no space] y
                              - [medium space] y

(where the minuses are horizontally aligned). (There should be no space after the first minus, since it's a unary operator, and a medium space after the second, since it's a binary operator.)

I have searched StackExchange for solutions, but in vain. Below are the solutions I have found so far, with MWEs at the bottom.

1. The correct, but overly complicated way:

   \documentclass{article}
   \usepackage{amsmath}
   \begin{document}
   \begin{align*}
   x &= -y \\
   &\mathrel{\phantom{=}} -\:y
   \end{align*}
   \end{document}
   

2. Do nothing. The minuses are incorrectly aligned.

   x &= -y \\
   &-y
   

   (I'm only changing the contents of align* here.)

3. Indent arbitrarily using e.g. \quad or \qquad. The minuses are incorrectly aligned.

   x &= -y \\
   &\quad -y
   

4. Use \phantom. The minuses are incorrectly aligned.

   x &= -y \\
   &\phantom{=} -y
   

5. Use \mathrel{\phantom}. The minuses are incorrectly aligned, and there is no medium space after the second minus.

   x &= -y \\
   &\mathrel{\phantom{=}} -y
   

6. Use {}&. There seems to be a thin and a thick space after the equals sign, and a thin space after the first minus.

   x ={}& -y \\
   & -y
   

7. Use aligned. Produces the same as in (6).

   x &= \begin{aligned}[t]
   &-y \\ &-y
   \end{aligned}
   

1: Donald Knuth: The TeXbook, page 170 and Ellen Swanson: Mathematics into Type, Section 3.3.5.

Edit 29 January: I misread Knuth's table; there should be a medspace after the second minus. Also, turned the fragments into a full document.

Answer 1

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align}
  x ={}& {-}y \
   & {-}:y
\end{align}
\end{document}

This produces the spacing that you ask for as clarified in comments:

x={} gives standard thickmuspace around =

{-}y then forces the prefix - with no space added,

and {-}\: produces a medmuspace between - and y as you would get automatically in x-y

---

The above however is not the layout I would use as there is no real semantic reason to align the - and (as can better be seen with a more typical alignment involving a second = or inequality) it makes it harder to distinguish a wrapped continuation line from a second aligned equation.

Compare the first form using the spacing given above with the second which has much simpler markup and I would say much clearer layout.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align}
  x ={}& {-}y \
   & {-}:y \
   ={}&{-}2y
\end{align}
\begin{align}
  x &= -y \
   &  \qquad - y \
   & =-2y
\end{align}
\end{document}

Answer 2

Something like this:

\def\n{\mathrel{\phantom{=}}\mskip-\thinmuskip{}}
$$\eqalign{
  x &= -y \cr
    &\n -y
}
$$
\bye