TeX

TeX, stylized as TEX{displaystyle mathbf {T!_{displaystyle E}!X} }, is a typography system written by Donald E. Knuth, very popular in the academic environment, especially among the communities of mathematicians, physical and computer. He has managed to replace troff with more, another standard typography program in Unix.

TeX is generally considered the best way to compose complex mathematical formulas but, especially in the form of LaTeX and other macro packages, it can be used for other composition tasks.

History

Knuth started writing TeX because he was upset with the declining quality of typography in volumes I to III of his work The Art of Computer Programming. He therefore began to design his own language of typography. He thought he could finish it in his sabbatical, 1978; he was wrong by only eight years. The language was finalized and frozen (no further modifications made) around 1985.

Guy Steele happened to be at Stanford in the summer of 1978, when Knuth was developing his first version of TeX. When he returned to MIT at the end of the year, he rewrote TeX input/output to run on the ITS.

The first version of TeX was written using the SAIL programming language running on a PDP-10 on Stanford University's WAITS operating system. For later versions of TeX, Knuth invented the concept of literary programming, a way of producing high-quality compilable source code and referenced documentation (written in TeX, of course) from the same original file. The language used is called WEB and produces programs in Pascal.

TeX has a peculiar version numbering system. Since version 3, updates are indicated by adding an extra decimal place at the end, so that the version number approaches π asymptotically. The most recent version is 3.14159265 and because it is very stable, only small updates are expected.

Knuth has indicated that the "last final change (made after my death)" will be to change the version number to π, at which point all remaining bugs will be considered features.

The typographic system

TeX commands begin with a backslash ("") and their arguments are indicated by braces ("{}"). However, almost all syntactic properties TeX can be changed on the fly, so TeX input is somewhat difficult to parse except for TeX itself. TeX is a language based on basic commands and macros: many commands, including the most of which are defined by users, are replaced on the fly until that only basic commands remain, which are then executed. The substitution itself itself is free of side effects. Macro recursion does not consume memory and if-then-else constructs are also available. All this does from TeX a Turing complete language even at the replacement level.

The TeX system has precise knowledge of character sizes and symbols, and using this information calculates the optimal alignment of letters per line and lines on each page. It then produces a DVI (device independent) file containing the final position of all characters. The dvi file can be printed directly using a driver suitable printer, or can be converted to other formats. At the moment, pdfTeX is used to generate PDF files bypassing DVI generation.

Most of the functionality is provided by various macros: the Knuth's originals included in what is called plainTeX, LaTeX (mostly in technical sciences) and ConTeXt (mainly used for publications).

The main reference for TeX is the first two volumes of Knuth's Computers and Typesetting: `The TeXbook'´ and `TeX: The Program´ (this includes the complete and documented TeX source code).

The organization of directories in a TeX installation is standardized in a tree called texmf.

License

The TeX license allows free distribution and modification, but requires that any modified version not be called T_EX, TeX, or something similar that might be confused with the original version. The license gives rights similar to those of a registered trademark.

Quality

Although well written, TeX is so large (and so packed with advanced technique) that it is said to have discovered at least one bug in every Pascal system it has been compiled on, since TeX runs on most systems. operating systems.

Knuth offers monetary rewards for people who find and report a bug in the program. The mistake prize started at one penny and doubled every year until it was frozen at its current value of $327.68. This, however, has not ruined Knuth, because very few errors have been found and in any case the check that proves that the owner found a bug in TeX is often framed rather than cashed.

About the name

Donald Knuth explains in his work The TeXbook that the word technology ("technology") has a Greek root and it begins with the letters τεχ. Therefore, the name TeX in Spanish must be pronounced [tej], and not [teks]. This is because TeX does not mean TEX but τεχ, ending in the Greek letter χ [chi]. The very Greek word τέχνη (ΤΕΧΝΗ – technē) means "art", a reference to the fact that technique is not at odds with art or elegant presentation.

When you are writing a file in TeX and you want to reference the name the TeX command is available, defined as follows:

 hbox{Tkern- 1667emlower.5exhbox{E!kern-125ex X!

Or so. LATEX{displaystyle mathbf {L!!^{{{}_{scriptstyle A}!!!!!;T!_{displaystyle E}!X} }:

 TeX()

and which was created by Knuth to demonstrate what is possible to do with TeX. The letter "E" remains below baseline and closer to T; in the other systems it is written using the "TeX" approach.

Derivative works

Several document processing systems are based on TeX; stand out among them:

• LaTeX (its name comes from Leslie Lamport, its creator), which incorporates document styles for books, letters, transparencies, etc., and adds cross reference features and automatic numbering of sections and equations.
• WithTeXt, created mostly by Hans Hagen in Pragma, is a professional document design tool based on TeX. It is more recent than LaTeX and therefore perhaps less popular.
• AMS-TeX, produced by the American Mathematical Society, has many more comfortable orders for the user, which can be modified by journals to accommodate in editorial style. Most of the AMS-TeX features can be used in LaTeX using the different AMS "packages" and referenced to AMS-LaTeX. The main AMS-TeX manual is entitled The Joy of TeX.
• jadeTeX that uses TeX as a basis for printing from James Clark's DSSSL system.
• Texinfo, the GNU project documentation preparation system.

All of these systems are written in the TeX programming language (some with plugins in other programming languages). In addition, there are programs that extend the programming language with new commands and capabilities:

• pdfTeX allows you to create PDF files and add new font functions, such as marginal score.
• Omega allows you to use Unicode and writing in several ways (right to left or above).
• NTS reimplements TeX in Java and allows you to extend it with new classes.
• LuaTeX combines pdfTeX, Omega and Lua programming language.

In addition, there are associated programs such as BibTeX for handling bibliographies, MakeIndex and xindy for alphabetical indexes and Metafont for graphics.

All extensions are available in the CTAN, (Comprehensive TeX Archive Network).

Supported Tools

On Unix-compatible systems, TeX is distributed as teTeX. On Windows systems there are MiKTeX and fpTeX. On Mac OS X systems there is MacTeX with utilities like TeXShop.

The TeXmacs text editor is a WYSIWYG scientific text editor that claims to be TeX compatible. It uses Knuth's fonts and can generate a TeX file. Another similar tool is LyX.

Examples

A simple example in TeX: Create a file called myprimer.tex that contains the following:

 Hello.
 ♪

Open a shell and type

tex miprimer.tex

TeX will create a file called myprimer.dvi. Use a suitable program to visualize it. For example, MiKTeX includes the yap viewer

yap miprimer.dvi

The viewer displays hello on a page. bye is the Tex command that marks the end of a file and is not shown in the final output.

The dvi file can be printed directly from the viewer or converted to a more common format such as PostScript using the dvips program.

It is possible to directly create PDF files using pdfTeX:

 pdftex miprimer.tex

pdfTeX was originally created because converting generated PostScript to PDF resulted in poor-quality font display, but good printing. This is because TeX natively uses bitmapped Type 3 fonts, which don't display as well as scalable Type 1 fonts.

It's currently possible to make dvips use the scalable fonts with a bit of configuration (recent versions of Ghostscript allow it), but a direct conversion to PDF has other benefits: it's a one-time process. step, instead of two, and pdfTeX includes such things as bookmarks and hyperlinks, which are absent from PostScript.

Mathematical Examples

To see TeX in action, try typing the well-known quadratic equation formula:

 The f'ormula square'Atica is $x_1,2!={-bpmsqrt{b^2-4times atimes c. over {2 times Aah!$ ♪

With the text above you should get something that looks like this

The quadratic formula is x1,2=− − b± ± b2− − 4× × a× × c2× × a{displaystyle x_{1,2}={-bpm {sqrt {b^{2}-4times atimes c}} over {2times a}}}}

In a document, to enter mathematical mode, write a sign $, then the formula so that TeX understands it and close it with another sign $. Another display mode, which leaves the formula centered on a new line, is achieved by using $$. For example, the above formula would be written

 The f'ormula square'Atica is $x_1,2!={-bpmsqrt{b^2-4times atimes c. over {2times Aah!$ ♪

and it would look like

The quadratic formula is

x1,2=− − b± ± b2− − 4× × a× × c2× × a{displaystyle x_{1,2}={-bpm {sqrt {b^{2}-4times atimes c}} over {2times a},!}

Examples for roots, derivatives and limits

Algebraic equation of the first degree

: backwardmathsqrt[3]{x+5+2x! = sqrt[3]{3x+7x+12!≤2
: backwardmath-givex+5+2x = 3x+7x+12

x+5+2x3=3x+7x+123{displaystyle {sqrt[{3}]{x+5+2x}}}}{{sqrt[{3}{3x+7x+12}}}{,}

x+5+2x=3x+7x+12{displaystyle x+5+2x=3x+7x+12,}

Derivative of a quotient

: backwardmathleft ({x^2 over x^3 +1! right) ^ = { left (xx)^3 +1 right)
left (xx)^2 right)^ - left (xx)^2 right) left (xx)^3 +1 right) ^ over left (xx)^3 +1 right)^2 ! ≤2
quotient formula application

(x2x3+1)♫ ♫ =(x3+1)(x2)♫ ♫ − − (x2)(x3+1)♫ ♫ (x3+1)2{displaystyle left({x^{2} over x^{3}+1}right)^{prim}={left(x^{3}+1right)left(x^{2}{2}{2}{right)^{prim }-left(x^{2}{2}{3+1bright}{bright}{cH00FFFFFFFFFFFFFFFFFF}{cH00}{cH00}{cH00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00}{cH00}{cH00}{cH00}{cHFFFFFFFFFFFFFFFFFFFF00}{cH00}{cH00}{cH00FFFFFFFFFFFFFFFF}{cH00FFFFFFFFFFFFFFFFFF00}{cH00FFFF00}{cH00}{cH00FFFFFF

Application of Quotient Formula

Limits

: backwardmathlim_x  1^+! {1 over x - 1! = ? Δ/math
Solution
: ` {1 over 1,001 - 1! ≤2
: ` {1 over 0.001! ≤2
: backwardmathlim_x  1^+! {1 over x - 1! =infty Rightarrow  ≤2 This means that it tends to ≤3000infty≤2

limx→ → 1+1x− − 1=?{displaystyle lim _{xto 1^{+}{1 over x-1}=?

Solution

=11,001− − 1{displaystyle ={1 over 1,001-1}}

=10,001{displaystyle ={1 over 0.001}}

limx→ → 1+1x− − 1=+∞ ∞ ⇒ ⇒ {displaystyle lim _{xto 1^{+}{1 over x-1}=+infty Rightarrow } This means it tends to +∞ ∞ {displaystyle +infty }