Automatic delimiter sizes in LaTeX

I recently read a math book in which delimiters never adjusted to the size of their content or the level of nesting. This isn’t unusual in articles, but books usually pay more attention to typography.

Here’s a part of an equation from the book:

\varphi^{-1} (\int \varphi(f+g) ,d\mu)

Larger outer parentheses make the equation much easier to read, especially as part of a complex equation. It’s clear at a glance that the function φ-1 applies to the result of the integral.

\varphi^{-1} \left(\int \varphi(f+g) ,d\mu\right)

The first equation was typeset using

\varphi^{-1} ( \int \varphi(f+g) ,dmu )

The latter used left and right to tell LaTeX that the parentheses should grow to match the size of the content between them.

\varphi^{-1} \left( \int \varphi(f+g) ,d\mu \right)

You can use \left and \right with more delimiters than just parentheses: braces, brackets, ceiling, floor, etc. And the left and right delimiters do not need to match. You could make a half-open interval, for example, with \left( on one side and \right] on the other.

For every \left delimiter there must be a corresponding \right delimiter. However, you can make one of the pair empty by using a period as its mate. For example, you could start an expression with \left[ and end it with \right. which would create a left bracket as tall as the tallest thing between that bracket and the corresponding \right. command. Note that \right. causes nothing to be displayed, not even a period.

The most common example of a delimiter with no mate may be a curly brace on the left with no matching brace on the right. In that case you’d need to open with \left\{. The backslash in front of the brace is necessary to tell LaTeX that you want a literal brace and that you’re not just using the brace for grouping.

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The paper is too big

In response to the question “Why are default LaTeX margins so big?” Paul Stanley answers

It’s not that the margins are too wide. It’s that the paper is too big!

This sounds flippant, but he gives a compelling argument that paper really is too big for how it is now used.

As is surely by now well-known, the real question is the size of the text block. That is a really important factor in legibility. As others have noted, the optimum line length is broadly somewhere between 60 characters and 75 characters.

Given reasonable sizes of font which are comfortable for reading at the distance we want to read at (roughly 9 to 12 point), there are only so many line lengths that make sense. If you take a book off your shelf, especially a book that you would actually read for a prolonged period of time, and compare it to a LaTeX document in one of the standard classes, you’ll probably notice that the line length is pretty similar.

The real problem is with paper size. As it happens, we have ended up with paper sizes that were never designed or adapted for printing with 10-12 point proportionally spaced type. They were designed for handwriting (which is usually much bigger) or for typewriters. Typewriters produced 10 or 12 characters per inch: so on (say) 8.5 inch wide paper, with 1 inch margins, you had 6.5 inches of type, giving … around 65 to 78 characters: in other words something pretty close to ideal. But if you type in a standard proportionally spaced font (worse, in Times—which is rather condensed because it was designed to be used in narrow columns) at 12 point, you will get about 90 to 100 characters in the line.

He then gives six suggestions for what to do about this. You can see his answer for a full explanation. Here I’ll just summarize his points.

  1. Use smaller paper.
  2. Use long lines of text but extra space between lines.
  3. Use wide margins.
  4. Use margins for notes and illustrations.
  5. Use a two column format.
  6. Use large type.

Given these options, wide margins (as in #3 and #4) sound reasonable.

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Gutenberg + Readability

Here’s a very simple idea: Use Project Gutenberg for content and Readability for style.

Project Gutenberg has a large collection of public domain books in digital form. The books are available in several formats, none of which are ideal for reading. Project Gutenberg provides text without much styling in order to make it easier for people to use the content as they please.

You can go to the HTML version of a book on Gutenberg and use Readability (or Instapaper) to format it for easier reading. Importing the HTML page to a Kindle similarly improves the formatting.

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Has anyone made a style sheet to approximate the look of Readability or Instapaper? I’d like to use something like that to improve the appearance of the static HTML pages on my site.

Readability

The Readability bookmarklet lets you reformat any web to make it easier to read. It strips out flashing ads and other distractions. It uses black text on a white background, wide margins, a moderate-sized font, etc. I use Readability fairly often. (Instapaper is a similar service. I discuss it at the end of this post.)

Yesterday I used it to reformat an article on literate programming. For some inexplicable reason, the author chose to use a lemon yellow background. It’s ironic that the article is about making source code easier to read. The content of the article is easy to read, but the format is not.

Readability to the rescue! Here are before and after screen shots.

Before:

After:

I recommend the article, Example of Literate Programming in HTML [Update: link went away], and I also recommend using reformatting the page unless you enjoy reading black text on a yellow background.

Readability did a good job until about half way through the article. The article has C and HTML code examples, and perhaps these confused Readability. (Readability usually handles code samples well. It correctly formats the first few code samples in this article.) The last half of the article renders like source code, and the font gets smaller and smaller.

I ran the page through an HTML validator to see whether some malformed HTML could be the source of the problem. The validator found numerous problems, so perhaps that was the issue.

I haven’t seen Readability fail like this before. I’ve been surprised how well it has handled some pages I thought might trip it up.

I ended up saving the article and editing its source, changing the bgcolor value to white. It’s a nice article on literate programming once you get past the formatting. The best part of the article is the first section, and that much Readability formats correctly.

Instapaper

Instapaper reformats web pages similarly. It produces a narrower column of text, but otherwise the output looks quite similar.

Instapaper did not discover the title of the literate programming article. (The title of the article was not in an <h1> tag as software might expect but was only in a <title> tag in the page header.) However, it did format the entire body of the article correctly.

I find it slightly more convenient to use the Readability bookmarklet than to submit a link to Instapaper. I imagine there are browser plug-ins that make Instapaper just as easy to use, though I haven’t looked into this because I’m usually satisfied with Readability.

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Draw a symbol, look it up

LaTeX users may know about Detexify, a web site that lets you draw a character then looks up its TeX command. Now there’s a new site Shapecatcher that does the same thing for Unicode. According to the site, “Currently, there are 10,007 Unicode character glyphs in the database.” It does not yet support Chinese, Japanese, or Korean.

For example, I drew a treble clef on the page:

The site came back with a list of possible matches, and the first one was what I was hoping for:

Interestingly, the sixth possible match on the list was a symbol for contour integration:

Notice the treble clef response has a funny little box on the right side. That’s because my browser did not have a glyph to display that Unicode character. The browser did have a glyph for the contour integration symbol and displayed it.

Another Unicode resource I recommend is this Unicode Codepoint Chart. It is organized by code point value, in blocks of 256. If you were looking for the contour integration symbol above, for example, you could click on a link “U+2200 to U+22FF: Mathematical Operators” and see a grid of 256 symbols and click on the one you’re looking for. This site gives more detail about each character than does Shapecatcher. So you might use Shapecatcher to find where to start looking, then go to the Unicode Codepoint Chart to find related symbols or more details.

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Typesetting “C#” in LaTeX

How do you refer to the C# programming language in LaTeX? Simply typing C# doesn’t work because # is a special character in LaTeX. You could type C#. That works, but it looks a little odd. The number sign is too big and too low.

What about using a musical sharp sign, i.e. C$\sharp$? That also looks a little odd. Even though the language is pronounced “C sharp,” it’s usually written with a number sign, not a sharp.

Let’s look at recommended ways of typesetting C++ to see whether that helps. The top answer to this question on TeX Stack Exchange is to define a new command as follows:

\newcommand{\CC}{C\nolinebreak\hspace{-.05em}\raisebox{.4ex}{\tiny\bf +}\nolinebreak\hspace{-.10em}\raisebox{.4ex}{\tiny\bf +}}

This does several things. First, it prevents line breaks between the constituent characters. It also does several things to the plus signs:

  • Draws them in closer
  • Makes them smaller
  • Raises them
  • Makes them bold

The result is what we’re subconsciously accustomed to seeing in print.

Here’s an analogous command for C#.

\newcommand{\CS}{C\nolinebreak\hspace{-.05em}\raisebox{.6ex}{\tiny\bf \#}}

And here’s the output. The number sign is a little too small.

To make a little larger number sign, replace \tiny with \scriptsize.

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Typesetting chemistry in LaTeX

Yesterday I gave the following tip on TeXtip:

Set chemical formulas with math Roman. Example: sulfate is $mathrm{SO_4^{2-}}$

TorbjoernT and scmbradley let me know there’s a better way: use Martin Hansel’s package mhchem. The package is simpler to use and it correctly handles subtle typographical details.

Using the mhchem package, sulfate would be written ce{SO4^2-}. In addition to chemical compounds, mhchem has support for bonds, arrows, and related chemical notation.

Example:

Source:

\documentclass{article}
\usepackage[version=3]{mhchem}
\parskip=0.1in
\begin{document}

\ce{SO4^2-}

\ce{^{227}_{90}Th+}

\ce{A\bond{-}B\bond{=}C\bond{#}D}

\ce{CO2 + C -> 2CO}

\ce{SO4^2- + Ba^2+ -> BaSO4 v}

\end{document}

 

For more information, see the mhchem package documentation.

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Complexity of HTML and LaTeX

Sometime around 1994, my office mate introduced me to HTML by saying it was 10 times simpler than LaTeX. At the time I thought he was right. Now I’m not so sure. Maybe he was right in 1994 when the expectations for HTML were very low.

It is easier to bang out a simple, ugly HTML page than to write your first LaTeX document. When you compare the time required to make an attractive document, the effort becomes more comparable. The more sophisticated you get, the simpler LaTeX becomes by comparison.

Of course the two languages are not exactly comparable. HTML targets a web browser while LaTeX targets paper. HTML would be much simpler if people only used it to create documents to print out on their own printer. A major challenge with HTML is not knowing how someone else will use your document. You don’t know what browser they will view it with, at what resolution, etc. For that matter, you don’t know whether they’re even going to view it at all — they may use a screen reader to listen to the document.

Writing HTML is much more complicated than writing LaTeX if you take a broad view of all that is required to do it well: learning about accessibility and internationalization, keeping track of browser capabilities and market shares, adapting to evolving standards, etc. The closer you look into it, the less HTML has in common with LaTeX. The two languages are not simply two systems of markup; they address different problems.

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Top four LaTeX mistakes

Here are four of the most common typesetting errors I see in books and articles created with LaTeX.

1) Quotes

Quotation marks in LaTeX files begin with two back ticks, ``, and end with two single quotes, ''.

The first “Yes” was written as

``Yes.''

in LaTeX while the one with the backward opening quote was written as

"Yes."

2) Differentials

Differentials, most commonly the dx at the end of an integer, should have a little space separating them from other elements. The “dx” is a unit and so it needs a little space to keep from looking like the product of “d” and “x.” You can do this in LaTeX by inserting \, before and between differentials.

The first integral was written as

 \int_0^1 f(x) \, dx

while the second forgot the , and was written as

 \int_0^1 f(x)  dx

The need for a little extra space around differentials becomes more obvious in multiple integrals.

The first was written as

dx \, dy = r \, dr \, d\theta

while the second was written as

dx  dy = r  dr  d\theta

3) Multi-letter function names

The LaTeX commands for typesetting functions like sin, cos, log, max, etc. begin with a backslash. The command log keeps “log,” for example, from looking like the product of variables “l”, “o”, and “g.”

The first example above was written as

\log e^x = x

and the second as

log e^x = x

The double angle identity for sine is readable when properly typeset and a jumbled mess when the necessary backslashes are left out.

The first example was written

\sin 2u = 2 \sin u \cos u

and the second as

sin 2u = 2 sin u cos u

4) Failure to use math mode

LaTeX uses math mode to distinguish variables from ordinary letters. Variables are typeset in math italic, a special style that is not the same as ordinary italic prose.

The first sentence was written as

Given a matrix $A$ and vector $b$, solve $Ax = b$.

and the second as

Given a matrix A and vector b, solve Ax = b.

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The disappointing state of Unicode fonts

Modern operating systems understand Unicode internally, but font support for Unicode is spotty. For an example of the problems this can cause, take a look at these screen shots of how the same Twitter message appears differently depending on what program is used to read it.

No font can display all Unicode characters. According to Wikipedia

… it would be impossible to create such a font in any common font format, as Unicode includes over 100,000 characters, while no widely-used font format supports more than 65,535 glyphs.

However, the biggest problem isn’t the number of characters a font can display. Most Unicode characters are quite rare. About 30,000 characters are enough to display the vast majority of characters in use in all the world’s languages as well as a generous selection of symbols. However Unicode fonts vary greatly in their support even for the more commonly used ranges of characters. See this comparison chart. The only range completely covered by all Unicode fonts in the chart is the 128 characters of Latin Extended-A.

Unifont supports all printable characters in the basic multilingual plane, characters U+0000 through U+FFFF. This includes the 30,000 characters mentioned above plus many more. Unifont isn’t pretty, but it’s complete. As far as I know, it’s the only font that covers the characters below U+FFFF.

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