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VerTeX: a pre-filter for easier LaTeX

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VerTeX: a prefilter for easier LaTeX

Do you find anything cumbersome about TeX syntax? For example,

If instead of this... you'd prefer to type this...
a_0, a_1, \ldots, a_{n-1} a0, a1, ddd, an-1
\alpha, \beta, \gamma, ... alpha, beta, gamma, ...
\mathfrak{p} \in \mathbb{Z} frp in bbZ
n^\mathrm{th} n eth
\frac{2}{3} frac 2 over 3;
\left| x \right| abs x;
f^{(n)} f supp n;
f^{-1} f inv
\sum_{n=0}^\infty a_n sum over n from 0 to infty; an

...then VerTeX may be for you!

VerTeX is pronounced "ver-tech," and stands for "Verbal TeX," i.e. TeX in which what you type is often much closer to what you say when you read mathematics aloud.

I developed VerTeX while I was translating German mathematics into English, and I wanted to be able to type symbolic expressions as quickly as I could type words.

Therefore one of the goals of VerTeX is to help you keep your fingers over the home row. This leads to some verbal equivalents that may appeal to some, but not to others. Hey, suit yourself!

Usage

There are just two main functions that you'll make use of: translate_snippet, and translate_document.

Apply translate_snippet directly to math mode contents written in VerTeX, in order to translate them into plain TeX:

>>> from vertex2tex import *
>>> translate_snippet('bbQ(alp)')
'\\mathbb{Q}(\\alpha)'

When working on an entire document, use translate_document. The default behavior of translate_document is to translate the contents of math modes only if they begin immediately with @. (The @ char is then omitted from the output.) This allows you to be selective about where VerTeX is used, and where it isn't.

For example in the following application the text contains three occurrences of math mode, but only in the last do we use VerTeX (we use the built-in keyword times), so only there do we begin the math mode with @.

>>> text = 'Find integers $a, b, c$ such that the sum $a+b+c$ and the product $@a times b times c$ are equal.'
>>> translate_document(text)
'Find integers $a, b, c$ such that the sum $a+b+c$ and the product $a\\times b\\times c$ are equal.'

This behavior can be controlled by using the translate_document function's keyword argument keychar. Setting keychar=None means that VerTeX translation will be applied in all math modes. However, this requires some adaptation in our text. If we try this with precisely the same text from the previous example, there will be two problems:

>>> translate_document(text, keychar=None)
'Find integers $a, b, c$ such that the sum $a_{+ b+ c}$ and the product $@ a\\times b\\times c$ are equal.'

The first problem is that now VerTeX is being applied to $a+b+c$, which engages the auto-subscripting mechanism. We must put spaces, as in $a + b + c$ in order to avoid this. The second problem is that now the character @ at the beginning of the third math mode is no longer being interpreted as a keychar, and so simply passes through. Adapting for these two problems, we would have

>>> text2 = 'Find integers $a, b, c$ such that the sum $a + b + c$ and the product $a times b times c$ are equal.'
>>> translate_document(text2, keychar=None)
'Find integers $a, b, c$ such that the sum $a+ b+ c$ and the product $a\\times b\\times c$ are equal.'

again producing the desired result.

As a third possibility, you may even use a different "key character" instead of @, by setting the keyword argument keychar equal to that character. However, this pattern is discouraged, for the sake of interoperability. It is better that @ be standard.

The VerTeX Language

Slash the Backslashes!

When you are writing mathematics, how often do you want a Greek letter alpha, and how often do you want to multiply the variables a, l, p, h, and a together, in that order? Why then should $alpha$ give you a sequence of Roman letters, while the Greek letter requires a backslash?

In VerTeX, $alpha$ yields the Greek letter, and if you really want the product of variables, simply put spaces between the letters, as in $a l p h a$.

In general, VerTeX keywords are not strings of letters preceded by a backslash, but simply strings of letters uninterrupted by whitespace. Conceptually, the keywords in VerTeX may be divided into the following four kinds, according to the role they play in avoiding backslashes.

Types of VerTeX keywords:

  1. bsme
  2. built-in
  3. bracket word
  4. font prefix

If you want to see (and perhaps alter locally) the lists of keywords, just consult the config.py module in the vertex package.

bsmes

"bsme" stands for "backslash me," and a bsme keyword is one that is exactly the same as a keyword in TeX, except without the backslash. It produces the exact same result as the corresponding TeX keyword. For the list of all bsme keywords, consult the config.py module.

built-ins

The so-called “built-in” keywords do not correspond to any existing TeX keywords. They do not take any arguments, but simply translate directly into some string of TeX, and their purpose is to in one way or another give an easier way to type certain commonly used TeX strings.

In particular, one of the goals of VerTeX is to give you the option to keep your fingers over the home row while typing, and for this reason the built-in keywords provide many alphabetical equivalents to TeX strings that ordinarily involve non-alphabetical characters. For example, inv (for “inverse”) produces ^{-1}, and squ (for “squared”) produces ^2.

For the list of all built-ins, consult the config.py module.

Going Greek

Greek letters are near and dear to our heart in mathematics. They should be easy to type. In VerTeX, every Greek letter -- including the variants -- has a three-letter name. And yes, this even includes the letters whose names are ordinarily only two-letters long, like pi and mu!

For example, you may type alp for alpha, lam for lambda, or Lam for capital Lambda.

You may type vep for varepsilon (everybody's favorite epsilon), and vph for varphi.

As for pi, xi, mu, and nu, these letters have funny three-letter spellings (anyone for pie?) in order to get around the auto-subscripting mechanism discussed below.

As usual, consult config.py for the full lists.

You do not have to use these abbreviations if you don't want to. Every Greek letter whose name is ordinarily more than two letters long is also a bsme keyword, so just go right ahead and spell it out if you want to, whether it's alpha, lambda, or Omega.

bracket words

In TeX there are many constructions in which a keyword takes arguments surrounded by braces { }. For example,

\frac{\pi}{4}

yields the sum of the Bhaskara-Leibniz Series. In VerTex, the same construction is achieved by

frac pie over 4;

In this example, frac, over, and the final semicolon ; serve as bracket words.

In general, when a construction takes arguments, then the arguments are to be surrounded by the appropriate bracket words. For the most part, the final bracket word will be a semicolon.

The list of all such constructions in VerTeX can be found in config.py, under the unarynodes, binarynodes, tertiarynodes, and rangenodes definitions. It includes many popular constructions, such as sets, sequences, floors, ceilings, absolute values, "mod" expressions, Legendre symbols, binomial coefficients, sums, products, and more.

font (and decorator) prefixes

Technically font prefixes are not “keywords” in and of themselves. They are two- or three-character prefixes which, when followed by a letter of the alphabet, produce that letter in the appropriate font. The prefixes and the fonts that they correspond to can be found in config.py.

For example, instead of

\mathfrak{p} \mathsf{M} \mathbf{v} \mathbb{Q} \mathcal{O} \mathscr{B}

you may type

frp sfM bfv bbQ calO scrB

to achieve the same thing.

You can also use prefixes to get things like hats and tildes. For example, instead of \hat{x} just type hatx.

Auto-Subscripts (and Superscripts)

In mathematics, subscripted variables are the coin of the realm, and therefore it ought to be easy to type them. VerTeX makes it fast and easy to get subscripts and superscripts. For example,

Cumbersome TeX... ...is easy in VerTeX
a_1, a_2, \ldots, a_{n+1} a1, a2, ddd, an+1
x_{i_1}, x_{i_2}, \ldots, x_{i_m} xivv1, xivv2, ddd, xivvm
a_{i j}^2 aijuu2

The semiautomatic subscripting and superscripting (henceforth SSS) mechanism of VerTeX is very handy, and, as the examples in the table show, makes it much easier to type certain common kinds of subscripts and superscripts.

While many subscript and superscript combinations can be achieved through SSS, some things are not possible. In such cases, you can use the sub and sup bracket words, or can even fall back on standard TeX syntax.

The complete description of the SSS process is a bit complex, but for most common purposes it is quite simple. Therefore before we give a detailed specification of the process, we consider the main ideas.

First we need some terminology. We all know what subscripts and superscripts are, but what do we call the letter they get attached to? Let's call it the "base".

In most cases, the process is simple: VerTeX will take a word w and split it as w = bs, where b is the longest initial segment of w that matches as a letter name, and s is everything that remains. Then b will be the base, and s will be the subscript.

Examples (and one non-example):

VerTeX TeX
pi p_i
alphan \alpha_n
bbZm \mathbb{Z}_m
cn+1 c_{n+1}
ai,j a_{i,j}
zeta \zeta

There are several things to note about these examples:

  1. It was so that pi could be available for automatic subscripting that we gave the Greek letter pi the (admittedly somewhat silly) spelling pie. Writing p_i is a perhaps daily occurrence for anyone who works with prime numbers, and this includes a lot of mathematicians.

  2. Letters with extended names, like alpha, and letters with a font prefix in front of them, like bbZ, will indeed be counted as initial letters.

  3. Commas, as well as plus and minus signs, are considered part of the word.

  4. What happened with zeta? Perhaps we were hoping this would translate to z_\eta, but of course VerTeX instead matched the entire word zeta as the base. There is a way to get around this, which we discuss below. Preview: You may type zvveta in order to get z_\eta.

The Details

To the VerTeX parser, a "word" consists of alphanumeric characters, as well as commas and the plus and minus symbols. It must begin with an alphabetical character. (In other words a “letter,” but this means one of the ASCII letters in the character class [A-Za-z], and is not to be confused with all things that may be considered "letters" in VerTeX, which includes, for example, Greek letters, and letters with font prefixes.)

For those familiar with regular expressions, this means that words are built on the character class

[A-Za-z0-9+-,]

The last three symbols are included in the character class because they are common in subscripts. (However, this means that if you do not want to accidentally trigger a subscript, you need to put whitespace on at least one side of these characters!)

Now suppose that w is the next word that VerTeX has to process. If w fails to match as any kind of keyword – bsme, built-in, bracket word, or font-prefix-letter combination -- then w is submitted to the SSS process.

VerTeX first matches the longest possible letter name at the beginning of w, as discussed above. Let the word w consist of initial letter b followed by remainder s, that is, w = bs. Then b will be the base, and s will give one or more subscripts and/or superscripts.

In the simplest case, s simply represents a subscript. It is possible however to switch between subscripts and superscripts using the special character sequences vv, uu, and UU.

A few examples illustrate all of the ways to use these control sequences:

VerTeX TeX
auur a^r
aiuur a_i^r
auurvvk a^{r_k}
aivvj a_{i_j}
aivvjuur a_{i^r_j}
aivvjUUr a_{i_j}^r
zvveta z_\eta

The rules are:

  • Sequence vv opens a deeper subscript. In TeX it is as though you typed _{.
  • Sequence uu closes a subscript and opens a superscript. In TeX it is as though you typed }^{.
  • Seuqnece UU closes two subscripts and opens a superscript. In TeX it is as though you typed }}^{.
  • One special exception is that if vv is used at the very beginning of s, it merely keeps you at the first subscript level. Thus, zvveta provides a way to produce z_\eta, while zeta simply gives \zeta.

Again, use of these special control sequences may appeal to some, while to others the above examples may just look like so much Icelandic (kinda does to me -- but then, I have no idea what Icelandic actually looks like). Suit yourself...which is the subject of the next section.

Use only what you want

VerTeX is 99% transparent to ordinary TeX. That means you can type (almost) any ordinary TeX you want, and it will pass through the VerTeX filter unaltered. So, use as many or as few of the features of VerTex as you wish.

What are the gotchas?

The main gotchas are keywords and automatic subscripting; but the solution is always very simple: Add spaces!

If a sequence of characters has been matched as a VerTeX keyword but this is not what you wanted, just put one or more spaces between those characters.

Likewise, if automatic subscripting is taking place when you don't want it, the solution is the same: separate the characters with spaces.

Safety net

As a “safety net,” any word whatsoever may be prefixed with a double backslash \\ in order to allow that word to pass through VerTeX unaltered. To be precise, if there is any remainder w to the word, then this, minus the two backslashes, is what will pass through. If just two backslashes alone are typed, they will pass though unaltered (which is useful in TeX table environments). Meanwhile, any word beginning with a single backslash is passed through VerTeX completely unaltered, i.e. with the leading backslash still intact. In summary:

\\w  -->  w
\\   -->  \\
\w   -->  \w

where w is a word at least one character long.

But you probably won't need to use this anyway.

Enjoy!

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