Expresso.Element.Math.Latex (expresso v0.1.0)

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A parser of the LaTeX of a formula into a tree of atoms

A rewrite entity of a derivation makes the LaTeX of a new line from the LaTeX of an old line, so it must find the parts, the symbols and the groups of the old line. parse/1 reads LaTeX into a list of atoms, and write/1 writes the list back. write(parse(tex)) returns tex, except for the white space between a command and its brace groups. docs/line-rewrites.md gives the design.

An atom is one of these tuples:

  • {:symbol, text}, a letter, a number, an operator or a parenthesis. A number is a run of digits, with a point in it.
  • {:command, name, groups}, a command such as \lambda or \frac, with the brace groups that follow it. A command with no group, such as \alpha, is a symbol for a rewrite.
  • {:group, atoms}, a brace group.
  • {:script, mark}, the mark ^ or _ of an index.
  • {:space, text}, white space or a command of space, such as \,.

\part{name}{…} is a command with two groups, and part/2 finds its body.

Summary

Types

atom_t()

An atom of a formula

Functions

name_of(arg1)

Return the name of a command that gives a name to its second group, such as \part, or nil for each other atom

parse(tex)

Read LaTeX into a list of atoms

part(atoms, name)

Return the body of the \part or \id with a name, or nil

write(atoms)

Write a list of atoms as LaTeX

Types

atom_t()

@type atom_t() ::
  {:symbol, String.t()}
  | {:command, String.t(), [{:group, [atom_t()]}]}
  | {:group, [atom_t()]}
  | {:script, String.t()}
  | {:space, String.t()}

An atom of a formula

Functions

name_of(arg1)

@spec name_of(atom_t()) :: String.t() | nil

Return the name of a command that gives a name to its second group, such as \part, or nil for each other atom

parse(tex)

@spec parse(String.t()) :: {:ok, [atom_t()]} | {:error, String.t()}

Read LaTeX into a list of atoms

The function returns an error for a brace that has no partner.

iex> Expresso.Element.Math.Latex.parse(~S"\lambda x.\,x^{2}")
{:ok,
 [
   {:command, "\\lambda", []},
   {:space, " "},
   {:symbol, "x"},
   {:symbol, "."},
   {:space, "\\,"},
   {:symbol, "x"},
   {:script, "^"},
   {:group, [{:symbol, "2"}]}
 ]}

part(atoms, name)

@spec part([atom_t()], String.t()) :: [atom_t()] | nil

Return the body of the \part or \id with a name, or nil

The function looks at each depth of the tree.

iex> {:ok, atoms} = Expresso.Element.Math.Latex.parse(~S"a + \part{b}{c\,d}")
iex> Expresso.Element.Math.Latex.part(atoms, "b")
[{:symbol, "c"}, {:space, "\\,"}, {:symbol, "d"}]

write(atoms)

@spec write([atom_t()]) :: String.t()

Write a list of atoms as LaTeX

iex> {:ok, atoms} = Expresso.Element.Math.Latex.parse(~S"\frac{a}{b} + \part{x}{y}")
iex> Expresso.Element.Math.Latex.write(atoms)
~S"\frac{a}{b} + \part{x}{y}"