TeX

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TeX
Developer(s)	Donald Knuth
Initial release	1978; 47 years ago (1978)
Stable release	TeX Live 2024[1] / 13 March 2024; 16 months ago (2024-03-13)
Repository	www.tug.org/svn/texlive/
Written in	Permissive free software
Website	tug.org

TeX (

TeX was designed with two main goals in mind: to allow anybody to produce high-quality books with minimal effort, and to provide a system that would give exactly the same results on all computers, at any point in time (together with the Metafont language for font description and the Computer Modern family of typefaces).^[4] TeX is free software, which made it accessible to a wide range of users.

When the first paper volume of Knuth's The Art of Computer Programming was published in 1968,^[5] it was typeset using hot metal typesetting on a Monotype machine. This method, dating back to the 19th century, produced a "classic style" appreciated by Knuth.^[6] When the second edition was published, in 1976, the whole book had to be typeset again because the Monotype technology had been largely replaced by phototypesetting, and the original fonts were no longer available. When Knuth received the galley proofs of the new book on 30 March 1977, he found them inferior. Disappointed, Knuth set out to design his own typesetting system.

Knuth saw for the first time the output of a high-quality digital typesetting system, and became interested in digital typography. On 13 May 1977, he wrote a memo to himself describing the basic features of TeX.

Since the primary goal of the TeX language is high-quality typesetting for publishers of books, Knuth gave a lot of attention to the spacing rules for mathematical formulae.^[23][24] He took three bodies of work that he considered to be standards of excellence for mathematical typography: the books typeset by the Addison-Wesley Publishing house (the publisher of The Art of Computer Programming) under the supervision of Hans Wolf; editions of the mathematical journal Acta Mathematica dating from around 1910; and a copy of Indagationes Mathematicae, a Dutch mathematics journal. Knuth looked closely at these printed papers to sort out and look for a set of rules for spacing.^[25][26] While TeX provides some basic rules and the tools needed to specify proper spacing, the exact parameters depend on the font used to typeset the formula. For example, the spacing for Knuth's Computer Modern fonts has been precisely fine-tuned over the years and is now set; but when other fonts, such as AMS Euler, were used by Knuth for the first time, new spacing parameters had to be defined.^[27]

The typesetting of math in TeX is not without criticism, particularly with respect to technical details of the font metrics, which were designed in an era when significant attention was paid to storage requirements. This resulted in some "hacks" overloading some fields, which in turn required other "hacks". On an aesthetics level, the rendering of radicals has also been criticized.

Formally, the algorithm defines a value called badness associated with each possible line break; the badness is increased if the spaces on the line must stretch or shrink too much to make the line the correct width. Penalties are added if a breakpoint is particularly undesirable: for example, if a word must be hyphenated, if two lines in a row are hyphenated, or if a very loose line is immediately followed by a very tight line. The algorithm will then find the breakpoints that will minimize the sum of squares of the badness (including penalties) of the resulting lines. If the paragraph contains ${\displaystyle n}$ possible breakpoints, the number of situations that must be evaluated naively is ${\displaystyle 2^{n}}$. However, by using the method of dynamic programming, the complexity of the algorithm can be brought down to ${\displaystyle O(n^{2})}$ (see Big O notation). Further simplifications (for example, not testing extremely unlikely breakpoints such as a hyphenation in the first word of a paragraph, or very overfull lines) lead to an efficient algorithm whose running time is ${\displaystyle O(nw)}$, where ${\displaystyle w}$ is the width of a line. A similar algorithm is used to determine the best way to break paragraphs across two pages, in order to avoid

Metafont, not strictly part of TeX, is a font description system which allows the designer to describe characters algorithmically. It uses Bézier curves in a fairly standard way to generate the actual characters to be displayed, but Knuth devotes substantial attention to the rasterizing problem on bitmapped displays. Another thesis, by John Hobby, further explores this problem of digitizing "brush trajectories". This term derives from the fact that Metafont describes characters as having been drawn by abstract brushes (and erasers). It is commonly believed that TeX is based on bitmap fonts but, in fact, these programs "know" nothing about the fonts that they are using other than their dimensions. It is the responsibility of the device driver to appropriately handle fonts of other types, including PostScript Type 1 and TrueType. Computer Modern (commonly known as "the TeX font") is freely available in Type 1 format, as are the AMS math fonts. Users of TeX systems that output directly to PDF, such as pdfTeX, XeTeX, or LuaTeX, generally never use Metafont output at all.

TeX documents are written and programmed using an unusual macro language. Broadly speaking, the running of this macro language involves expansion and execution stages which do not interact directly. Expansion includes both literal expansion of macro definitions as well as conditional branching, and execution involves such tasks as setting variables/registers and the actual typesetting process of adding glyphs to boxes.

The definition of a macro not only includes a list of commands but also the syntax of the call. It differs with most widely used

A sample

Hello, World
\bye          % marks the end of the file; not shown in the final output

This might be in a file myfile.tex, as .tex is a common

TeX provides a different text syntax specifically for mathematical formulas. For example, the quadratic formula (which is the solution of the quadratic equation) appears as:

Source code	Renders as
The quadratic formula is $-b \pm \sqrt{b^2 - 4ac} \over 2a$ \bye	${\displaystyle {\hbox{The quadratic formula is }}\textstyle {-b\pm {\sqrt {b^{2}-4ac}} \over 2a}}$

The formula is printed in a way a person would write by hand, or typeset the equation. In a document, entering mathematics mode is done by starting with a $ symbol, then entering a formula in TeX syntax, and closing again with another of the same symbol. Knuth explained in jest that he chose the dollar sign to indicate the beginning and end of mathematical mode in plain TeX because typesetting mathematics was traditionally supposed to be expensive.^[40] Display mathematics (mathematics presented centred on a new line) is similar but uses $$ instead of a single $ symbol. For example, the above with the quadratic formula in display math:

Source code	Renders as
The quadratic formula is $$-b \pm \sqrt{b^2 - 4ac} \over 2a$$ \bye	${\displaystyle {\begin{matrix}{\text{The quadratic formula is}}\\\displaystyle {\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}\end{matrix}}}$

In several technical fields such as computer science, mathematics, engineering and physics, TeX has become a de facto standard. Many thousands of books have been published using TeX, including books published by Addison-Wesley, Cambridge University Press, Elsevier, Oxford University Press, and Springer. Numerous journals in these fields are produced using TeX or LaTeX, allowing authors to submit their raw manuscript written in TeX.^[41] While many publications in other fields, including dictionaries and legal publications, have been produced using TeX, it has not been as successful as in the more technical fields, as TeX was primarily designed to typeset mathematics.

When he designed TeX, Donald Knuth did not believe that a single typesetting system would fit everyone's needs; instead, he designed many hooks inside the program so that it would be possible to write extensions, and released the source code, hoping that the publishers would design versions tailoring to their own needs. While such extensions have been created (including some by Knuth himself),^[42] most people have extended TeX only using macros and it has remained a system associated with technical typesetting.^[43][44][26]

Packages like mhchem, XyMTeX, chemfig, and chemmacros for typesetting chemical equations, structures, and reactions in LaTeX.^[45]

It is possible to use TeX for automatic generation of sophisticated layout for XML data. The differences in syntax between the two description languages can be overcome with the help of TeXML. In the context of XML publication, TeX can thus be considered an alternative to XSL-FO. TeX allowed scientific papers in mathematical disciplines to be reduced to relatively small files that could be rendered client-side, allowing fully typeset scientific papers to be exchanged over the early Internet and emerging World Wide Web, even when sending large files was difficult. This paved the way for the creation of repositories of scientific papers such as arXiv, through which papers could be 'published' without an intermediary publisher.^[46]

The original source code for the current TeX software is written in

Due to scammers finding scanned copies of his checks on the internet and using them to try to drain his bank account, Knuth no longer sends out real checks, but those who submit bug reports can get credit at The Bank of San Serriffe instead.^[52]

TeX is usually provided in the form of an easy-to-install bundle of TeX itself along with

Numerous extensions and companion programs for TeX exist, among them BibTeX for bibliographies (distributed with LaTeX); pdfTeX, a TeX-compatible engine which can directly produce PDF output (as well as continuing to support the original DVI output); XeTeX, a TeX-compatible engine that supports Unicode and OpenType; and LuaTeX, a Unicode-aware extension to TeX that includes a Lua runtime with extensive hooks into the underlying TeX routines and algorithms. Most TeX extensions are available for free from CTAN, the Comprehensive TeX Archive Network.

Donald Knuth has indicated several times^{[53][54][55][26]} that the source code of TeX has been placed into the "public domain", and he strongly encourages modifications or experimentations with this source code. However, since Knuth highly values the reproducibility of the output of all versions of TeX, any changed version must not be called TeX, or anything confusingly similar. To enforce this rule, any implementation of the system must pass a test suite called the TRIP test^[56] before being allowed to be called TeX. The question of licence is somewhat confused by the statements included at the beginning of the TeX source code,^[57] which indicate that "all rights are reserved. Copying of this file is authorized only if ... you make absolutely no changes to your copy". This restriction should be interpreted as a prohibition to change the source code as long as the file is called tex.web. The copyright note at the beginning of tex.web (and mf.web) was changed in 2021 to explicitly state this. This interpretation is confirmed later in the source code when the TRIP test is mentioned ("If this program is changed, the resulting system should not be called 'TeX'").^[58] The American Mathematical Society tried in the early 1980s to claim a trademark for TeX. This was rejected because at the time "TEX" (all caps) was registered by Honeywell for the "Text EXecutive" text processing system.^{[citation needed]}

Since the source code of TeX is essentially in the

Notable entities in the TeX community include the TeX Users Group (TUG), which currently publishes