# `Expresso.Element.Math.Rewrite`
[🔗](https://github.com/rellen/expresso/blob/main/lib/expresso/element/math/rewrite.ex#L1)

The lines of a derivation that a substitution makes

A `rewrite` entity makes the LaTeX of a new line from the LaTeX of an old
line. `expand/1` reads the old line with `Expresso.Element.Math.Latex` and
walks its atoms:

  * An occurrence of `replace` becomes the new content: `\from{name}{…}`
    with the LaTeX of the part `by`, or the LaTeX of `by_tex`.
  * A part of `drop` goes away.
  * A run of other atoms in one group becomes `\part{keep-k-n}{…}` in the
    old line and `\from{keep-k-n}{…}` in the new line, so it moves down at
    the step of the new line. `k` is the number of the new line.
  * A group or a command that holds an occurrence or a part of `drop` stays,
    and the walk goes into it. In the new line, it fades in.

Each occurrence also gets `\class{hit-k}{…}` in the old line. The new line
has 3 steps by default, one for each phase: at `:occurrences`, the
occurrences and the source of `by` get a color; at `:kept`, the kept runs
move; at `:copies`, the copies of `by` move. The `steps` option puts phases
together in one step. Without `why`, the reason is `replace := by` in LaTeX.

The links of `Expresso.Element.Math.Links` and the copies of
`Expresso.Element.Copy` then move the symbols. `docs/line-rewrites.md` gives
the design.

# `expand`

```elixir
@spec expand([Expresso.Element.MathLine.t() | Expresso.Element.MathRewrite.t()]) ::
  {:ok, [Expresso.Element.MathLine.t()]} | {:error, String.t()}
```

Turn each rewrite of a list of lines into a line

The function returns the lines in order. A rewrite also changes its old
line, because each kept run of the old line gets a `\part`. It returns an
error for a rewrite with no line before it, for a name that the old line or
an earlier line does not have, and for a rewrite with no occurrence.

---

*Consult [api-reference.md](api-reference.md) for complete listing*