Subscript and superscript

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Example of subscript and superscript. In each example the first "2" is professionally designed, and is included as part of the glyph set; the second "2" is a manual approximation using a small version of the standard "2." The visual weight of the first "2" matches the other characters better. (The top typeface is Adobe Garamond Pro; the size of the subscript is about 62% of the original characters, dropped below the baseline by about 16%. The second typeface is Myriad Pro; the superscript is about 60% of the original characters, raised by about 44% above the baseline.) Subscript superscript expert.png
Example of subscript and superscript. In each example the first "2" is professionally designed, and is included as part of the glyph set; the second "2" is a manual approximation using a small version of the standard "2." The visual weight of the first "2" matches the other characters better. (The top typeface is Adobe Garamond Pro; the size of the subscript is about 62% of the original characters, dropped below the baseline by about 16%. The second typeface is Myriad Pro; the superscript is about 60% of the original characters, raised by about 44% above the baseline.)

A subscript or superscript is a character (number, letter or symbol) that is (respectively) set slightly below or above the normal line of type. It is usually smaller than the rest of the text. Subscripts appear at or below the baseline, while superscripts are above. Subscripts and superscripts are perhaps most often used in formulas, mathematical expressions, and specifications of chemical compounds and isotopes, but have many other uses as well.

Symbol something that represents an idea, a process, or a physical entity

A symbol is a mark, sign or word that indicates, signifies, or is understood as representing an idea, object, or relationship. Symbols allow people to go beyond what is known or seen by creating linkages between otherwise very different concepts and experiences. All communication is achieved through the use of symbols. Symbols take the form of words, sounds, gestures, ideas or visual images and are used to convey other ideas and beliefs. For example, a red octagon may be a symbol for "STOP". On a map, a blue line might represent a river. Numerals are symbols for numbers. Alphabetic letters may be symbols for sounds. Personal names are symbols representing individuals. A red rose may symbolize love and compassion. The variable 'x', in a mathematical equation, may symbolize the position of a particle in space.

In European and West Asian typography and penmanship, the baseline is the line upon which most letters "sit" and below which descenders extend.

Formula equation using mathematical or scientific notation

In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a chemical formula. The informal use of the term formula in science refers to the general construct of a relationship between given quantities.

Contents

In professional typography, subscript and superscript characters are not simply ordinary characters reduced in size; to keep them visually consistent with the rest of the font, typeface designers make them slightly heavier (i.e. medium or bold typography) than a reduced-size character would be. The vertical distance that sub- or superscripted text is moved from the original baseline varies by typeface and by use.

Typography Art and the craft of printing and the arranging of layouts

Typography is the art and technique of arranging type to make written language legible, readable, and appealing when displayed. The arrangement of type involves selecting typefaces, point sizes, line lengths, line-spacing (leading), and letter-spacing (tracking), and adjusting the space between pairs of letters (kerning). The term typography is also applied to the style, arrangement, and appearance of the letters, numbers, and symbols created by the process. Type design is a closely related craft, sometimes considered part of typography; most typographers do not design typefaces, and some type designers do not consider themselves typographers. Typography also may be used as a decorative device, unrelated to communication of information.

In typesetting, such types are traditionally called "superior" and "inferior" letters, figures, etc., or just "superiors" and "inferiors". In English, most nontechnical use of superiors is archaic. [1] Superior and inferior figures on the baseline are used for fractions and most other purposes, while lowered inferior figures are needed for chemical and mathematical subscripts. [2]

In typography and handwriting, a superior letter is a lower-case letter placed above the baseline and made smaller than ordinary script. The style has traditionally been distinct from superscript. Formerly quite common in abbreviations, the original purpose was to make handwritten abbreviations clearly distinct from normal words. These could also be used to enable the important words on signs to be larger. In technical terms, the superior letter can also be called the superscripted minuscule letter. In modern usage, with word processors and text entry interfaces, superscript and superior letters are produced in the same way and look identical, and their distinction would refer to their usage and not to their form.

Uses

The four common locations of subscripts and superscripts. The typeface is Myriad Pro. Sub super num dem.svg
The four common locations of subscripts and superscripts. The typeface is Myriad Pro.

A single typeface may contain sub- and superscript glyphs at different positions for different uses. The four most common positions are listed here. Because each position is used in different contexts, not all alphanumerics may be available in all positions. For example, subscript letters on the baseline are quite rare, and many typefaces provide only a limited number of superscripted letters. Despite these differences, all reduced-size glyphs go by the same generic terms subscript and superscript, which are synonymous with the terms inferior letter (or number) and superior letter (or number), respectively. Most fonts that contain superscript/subscript will have predetermined size and orientation that is dependent on the design of the font.

Subscripts that are dropped below the baseline

Perhaps the most familiar example of subscripts is in chemical formulas. For example, the molecular formula for glucose is C 6 H 12 O 6 (meaning that it is a molecule with 6 carbon atoms, 12 hydrogen atoms and 6 oxygen atoms). Or the most famous molecule in the world, water, known almost universally by its chemical formula, H2O (meaning it has 2 hydrogen atoms and 1 oxygen atom.)

A chemical formula is a way of presenting information about the chemical proportions of atoms that constitute a particular chemical compound or molecule, using chemical element symbols, numbers, and sometimes also other symbols, such as parentheses, dashes, brackets, commas and plus (+) and minus (−) signs. These are limited to a single typographic line of symbols, which may include subscripts and superscripts. A chemical formula is not a chemical name, and it contains no words. Although a chemical formula may imply certain simple chemical structures, it is not the same as a full chemical structural formula. Chemical formulas can fully specify the structure of only the simplest of molecules and chemical substances, and are generally more limited in power than are chemical names and structural formulas.

Glucose A simple form of sugar

Glucose is a simple sugar with the molecular formula C6H12O6. Glucose is the most abundant monosaccharide, a subcategory of carbohydrates. Glucose is mainly made by plants and most algae during photosynthesis from water and carbon dioxide, using energy from sunlight. There it is used to make cellulose in cell walls, which is the most abundant carbohydrate. In energy metabolism, glucose is the most important source of energy in all organisms. Glucose for metabolism is partially stored as a polymer, in plants mainly as starch and amylopectin and in animals as glycogen. Glucose circulates in the blood of animals as blood sugar. The naturally occurring form of glucose is d-glucose, while l-glucose is produced synthetically in comparatively small amounts and is of lesser importance. Glucose is a monosaccharide containing six carbon atoms and an aldehyde group and is therefore referred to as an aldohexose. The glucose molecule can exist in an open-chain (acyclic) and ring (cyclic) form, the latter being the result of an intramolecular reaction between the aldehyde C atom and the C-5 hydroxyl group to form an intramolecular hemiacetal. In water solution both forms are in equilibrium and at pH 7 the cyclic one is the predominant. Glucose is a primary source of energy for living organisms. It is naturally occurring and is found in fruits and other parts of plants in its free state. In animals glucose arises from the breakdown of glycogen in a process known as glycogenolysis.

Carbon Chemical element with atomic number 6

Carbon is a chemical element with the symbol C and atomic number 6. It is nonmetallic and tetravalent—making four electrons available to form covalent chemical bonds. It belongs to group 14 of the periodic table. Three isotopes occur naturally, 12C and 13C being stable, while 14C is a radionuclide, decaying with a half-life of about 5,730 years. Carbon is one of the few elements known since antiquity.

A subscript is also used to distinguish between different versions of a subatomic particle. Thus electron, muon, and tau neutrinos are denoted
ν
e

ν
μ
and
ν
τ
. A particle may be distinguished by multiple subscripts, such as
Ω
bbb
for the triple bottom omega particle.

Subatomic particle Particle whose size or mass is less than that of the atom, or of which the atom is composed; small quantum particle

In the physical sciences, subatomic particles are particles much smaller than atoms. The two types of subatomic particles are: elementary particles, which according to current theories are not made of other particles; and composite particles. Particle physics and nuclear physics study these particles and how they interact. The idea of a particle underwent serious rethinking when experiments showed that light could behave like a stream of particles as well as exhibiting wave-like properties. This led to the new concept of wave–particle duality to reflect that quantum-scale "particles" behave like both particles and waves. Another new concept, the uncertainty principle, states that some of their properties taken together, such as their simultaneous position and momentum, cannot be measured exactly. In more recent times, wave–particle duality has been shown to apply not only to photons but to increasingly massive particles as well.

Neutrino Elementary particle with extremely low mass that interacts only via the weak force and gravity

A neutrino is a fermion that interacts only via the weak subatomic force and gravity. The neutrino is so named because it is electrically neutral and because its rest mass is so small (-ino) that it was long thought to be zero. The mass of the neutrino is much smaller than that of the other known elementary particles. The weak force has a very short range, the gravitational interaction is extremely weak, and neutrinos, as leptons, do not participate in the strong interaction. Thus, neutrinos typically pass through normal matter unimpeded and undetected.

Omega baryon subatomic hadron particle

The omega baryons are a family of subatomic hadron particles that are represented by the symbol
Ω
and are either neutral or have a +2, +1 or −1 elementary charge. They are baryons containing no up or down quarks. Omega baryons containing top quarks are not expected to be observed. This is because the Standard Model predicts the mean lifetime of top quarks to be roughly 5×10−25 s, which is about a twentieth of the timescale for strong interactions, and therefore that they do not form hadrons.

Similarly, subscripts are also used frequently in mathematics to define different versions of the same variable: for example, in an equation x0 and xf might indicate the initial and final value of x, while vrocket and vobserver would stand for the velocities of a rocket and an observer. Commonly, variables with a zero in the subscript are referred to as the variable name followed by "naught" (e.g. v0 would be read, "v-naught").

Subscripts are often used to refer to members of a mathematical sequence or set or elements of a vector. For example, in the sequence O = (45, 2, 800), O3 refers to the third member of sequence O, which is 800.

Also in mathematics and computing, a subscript can be used to represent the radix, or base, of a written number, especially where multiple bases are used alongside each other. For example, comparing values in hexadecimal, denary, and octal one might write Chex = 12dec = 14oct.

Subscripted numbers dropped below the baseline are also used for the denominators of stacked fractions, like this: .

Subscripts that are aligned with the baseline

The only common use of these subscripts is for the denominators of diagonal fractions, like ½ or the signs for percent %, permille ‰, and basis point ‱. Certain standard abbreviations are also composed as diagonal fractions, such as (care of), (account of), (addressed to the subject), or in Spanish (cada uno/una, "each one").

Superscripts that typically do not extend above the ascender line

These superscripts typically share a baseline with numerator digits, the top of which are aligned with the top of the full-height numerals of the base font; lowercase ascenders may extend above.

Ordinal indicators are sometimes written as superscripts (1st, 2nd, 3rd, 4th, rather than 1st, 2nd, 3rd, 4th), although many English-language style guides recommend against this use. [3] Other languages use a similar convention, such as 1er or 2e in French, or and in Spanish, Portuguese, Galician and Italian.

In medieval manuscripts, many superscript as well as subscript signs were used to abbreviate text. From these developed modern diacritical marks (glyphs, or "accents" placed above or below the letter). Also, in early Middle High German, umlauts and other modifications to pronunciation would be indicated by superscript letters placed directly above the letter they modified. Thus the modern umlaut ü was written as . Both vowels and consonants were used in this way, as in ſheͨzze and boͮsen. [4] In modern typefaces, these letters are usually smaller than other superscripts, and their baseline is slightly above the base font's midline, making them extend no higher than a typical ordinal indicator.

Superscripts are used for the standard abbreviations for service mark and trademark . The signs for copyright © and registered trademark ® are also sometimes superscripted, depending on the typeface or house style.

On handwritten documents and signs, a monetary amount may be written with the cents value superscripted, as in $8⁰⁰ or 8€⁵⁰. Often the superscripted numbers are underlined: $8⁰⁰, 8€⁵⁰. The currency symbol itself may also be superscripted, as in $80 or 6¢.

Superscripted numerals are used for the numerators of diagonal fractions, like ¾ or the signs for percent %, permille ‰, and basis point ‱. Certain standard abbreviations are also composed as diagonal fractions, such as ℅ (care of), ℀ (account of), ℁ (addressed to the subject), or in Spanish ℆ (cada uno/a, "each one").

Superscripts that typically extend above the ascender line

Both low and high superscripts can be used to indicate the presence of a footnote in a document, like this5 or thisxi. Any combination of characters can be used for this purpose; in technical writing footnotes are sometimes composed of letters and numbers together, like this.A.2 The choice of low or high alignment depends on taste, but high-set footnotes tend to be more common, as they stand out more from the text.

In mathematics, high superscripts are used for exponentiation to indicate that one number or variable is raised to the power of another number or variable. Thus y4 is y raised to the fourth power, 2x is 2 raised to the power of x, and the famous equation E=mc² includes a term for the speed of light squared. This led over time to an "abuse of notation" whereby superscripts indicate iterative function composition, including derivatives. In an unrelated use, superscripts also indicate contravariant tensors in Ricci calculus.

The charges of ions and subatomic particles are also denoted by superscripts.
Cl-
is a negatively charged chlorine atom,
Pb4+
is an atom of lead with a positive charge of four,
e
is an electron,
e+
is a positron, and
μ+
is an antimuon.

Atomic isotopes are written using superscripts. In symbolic form, the number of nucleons is denoted as a superscripted prefix to the chemical symbol (for example 3
He
, 12
C
, 13
C
, 131
I
, and 238
U
). The letters m or f may follow the number to indicate metastable or fission isomers, as in 58m
Co
or 240f
Pu
.

Subscripts and superscripts can also be used together to give more specific information about nuclides. For example, 235
92
U
denotes an atom of uranium with 235 nucleons, 92 of which are protons. A chemical symbol can be completely surrounded: 14
6
C2+
2
is an ion of carbon with 14 nucleons, of which six are protons and 8 are neutrons, there are two atoms a chemical compound.

The numerators of stacked fractions (such as ) usually use high-set superscripts, although some specially designed glyphs keep the top of the numerator aligned with the top of the full-height numerals.

Alignment examples

Subscript superscript examples.png

This image shows the four common locations for subscripts and superscripts, according to their typical uses. The typeface is Minion Pro, set in Adobe Illustrator. Note that the default superscripting algorithms of most word processors would set the "th" and "lle" too high, and the weight of all the subscript and superscript glyphs would be too light.

HTML subscripts and superscripts
X6
O8M
X6
O8M
Default subscript and superscript rendered in HTML for fonts in normal styles.Example of possible collision of italic styles in HTML.

Another minor adjustment that is often omitted by renderers is the control of the direction of movement[ clarification needed ] for superscripts and subscripts, when they do not lie on the baseline. Ideally this should allow for the font, e.g. italics are slanting; most renderers adjust the position only vertically and do not also shift it horizontally. This may create a collision with surrounding letters in the same italic font size. One can see an example of such collision on the right side when rendered in HTML (see the figure on the right). To avoid this, it is often desirable to insert a small positive horizontal margin (or a thin space) (on the left side of the first superscript character), or a negative margin (or a tiny backspace) before a subscript. It is more critical with glyphs from fonts in Oblique styles that are more slanted than those from fonts in Italic style, and some fonts reverse the direction of slanting, so there is no general solution except when the renderer takes into account the font metrics properties that specifies the angle of slanting,

However the same problem occurs more generally between spans of normal glyphs (non-superscript and non-subscript) when slanting styles are mixed.

Software support

Desktop publishing

Many text editing and word processing programs have automatic subscripting and superscripting features, although these programs usually simply use ordinary characters reduced in size and moved up or down rather than separately designed subscript or superscript glyphs. Professional typesetting programs such as QuarkXPress or Adobe InDesign also have similar features for automatically converting regular type to subscript or superscript. These programs, however, may also offer native OpenType support for the special subscript and superscript glyphs included in many professional typeface packages (such as those shown in the image above).

Comparison of software support
SoftwareOpenType support for
professional glyphs?
Default values for glyph transformation (non-professional glyphs)Keyboard shortcuts
SizeSubscript positionSuperscript positionUser-modifiable settings?SuperscriptSubscript
OpenOffice.org 3.3No58%−33%+33%YesCtrl+⇧ Shift+PCtrl+⇧ Shift+B
LibreOffice 5.3Yes [lower-alpha 1] 58%−33%+33%YesCtrl+⇧ Shift+PCtrl+⇧ Shift+B
Microsoft Word 2015Yes50%−14.1%+40%Manual [lower-alpha 2] Ctrl+⇧ Shift+=Ctrl+=
Adobe Illustrator CS3Yes58.3%−33.3%+33.3%Yes
Adobe Photoshop CS3 Ordinal indicators only[ citation needed ]58.3%−33.3%+33.3%Manual [lower-alpha 2] Alt+Ctrl+⇧ Shift+=Ctrl+⇧ Shift+=
LaTeX Yes (using XeLaTeX or LuaTeX only)≈70% [lower-alpha 3] −14% [lower-alpha 4] +25% [lower-alpha 4] Manual [lower-alpha 5] math: ^ (caret)
text: \textsuperscript{stuff}
math: _ (underscore)
text: \textsubscript{stuff} [lower-alpha 6]
Notes:
  1. Availably by typing a syntax consisting font name, feature tag and its value into Font Name area. [5]
  2. 1 2 Default subscript and superscript options can be overcome by manually changing the font size and raising/lowering text.
  3. Dependent on math mode; differs for subsub- and supersuper-scripts.
  4. 1 2 Nominal values; dependent on fontdimen parameters (16 and 17).
  5. Changing fontdimen values requires some skill the textual commands can be modified to use the \raisebox command.
  6. Requires package.

HTML

In HTML and Wiki syntax, subscript text is produced by putting it inside the tags <sub> and </sub>. Similarly, superscripts are produced with <sup> and </sup>. [6] The exact size and position of the resulting characters will vary by font and browser, but are usually reduced to around 75% original size. Note that superscripts are usually placed too high for many typographic purposes.[ citation needed ][ clarification needed ]

TeX

In TeX's mathematics mode (as used in MediaWiki), subscripts are typeset with the underscore, while superscripts are made with the caret. Thus $X_{ab}$ produces , and $X^{ab}$ produces .

In LaTeX text mode the math method above is inappropriate, as letters will be in math italic, so the command n\textsuperscript{th} will give nth and A\textsubscript{base} will give Abase (textual subscripts are rare, so \textsubscript is not built-in, but requires the fixltx2e package). As in other systems, when using UTF-8 encoding, the masculine º and feminine ª ordinal indicators can be used as characters, with no need to use a command.

Superscripts and subscripts of arbitrary height can be done with the \raisebox{<dimen>}{<text>} command: the first argument is the amount to raise, and the second is the text; a negative first argument will lower the text. In this case the text is not resized automatically, so a sizing command can be included, e.g. go\raisebox{1ex}{\large home}.

Unicode

Unicode defines subscript and superscript characters in several areas; in particular, it has a full set of superscript and subscript digits. Owing to the popularity of using these characters to make fractions, most modern fonts render most or all of these as cap height superscripts and baseline subscripts. The same font may align letters and numbers in different ways. Other than numbers, the set of super- and subscript letters and other symbols is incomplete and somewhat random, and many fonts do not contain them. Because of these inconsistencies, these glyphs may not be suitable for some purposes (see Uses, above).

OpenType

Several advanced features of OpenType typefaces are support for professionally designed subscript and superscript glyphs. Exactly which glyphs are included varies by typeface; some have only basic support for numerals, while others contain a full set of letters, numerals, and punctuation. They can be available via activating subs or sups tag. Since many of these glyphs are not included in Unicode, they can be turned on if software environment support optional features, while other typefaces placed them in the Unicode Private Use Area.

See also

Related Research Articles

Typeface Set of characters that share common design features

In typography, a typeface is a set of one or more fonts each composed of glyphs that share common design features. Each font of a typeface has a specific weight, style, condensation, width, slant, italicization, ornamentation, and designer or foundry. For example, "ITC Garamond Bold Condensed Italic" means the bold, condensed-width, italic version of ITC Garamond. It is a different font from "ITC Garamond Condensed Italic" and "ITC Garamond Bold Condensed", but all are fonts within the same typeface, "ITC Garamond". ITC Garamond is a different typeface from "Adobe Garamond" or "Monotype Garamond". There are thousands of different typefaces in existence, with new ones being developed constantly.

Phi is the 21st letter of the Greek alphabet.

Frutiger (typeface) typeface

Frutiger is a series of typefaces named after its Swiss designer, Adrian Frutiger. Frutiger is a humanist sans-serif typeface, intended to be clear and highly legible at a distance or at small text sizes. A very popular design worldwide, type designer Steve Matteson described its structure as "the best choice for legibility in pretty much any situation" at small text sizes, while Erik Spiekermann named it as "the best general typeface ever".

In typography, a descender is the portion of a letter that extends below the baseline of a font. The line that descenders reach down to is known as the beard line.

Text figures

Text figures are numerals typeset with varying heights in a fashion that resembles a typical line of running text, hence the name. They are contrasted with lining figures, which are the same height as upper-case letters.

Zapfino typeface

Zapfino is a calligraphic typeface designed for Linotype by typeface designer Hermann Zapf in 1998. It is based on an alphabet Zapf originally penned in 1944. As a font, it makes extensive use of ligatures and character variations.

Typographical conventions in mathematical formulae provide uniformity across mathematical texts and help the readers of those texts to grasp new concepts quickly.

Unicode has subscripted and superscripted versions of a number of characters including a full set of Arabic numerals. These characters allow any polynomial, chemical and certain other equations to be represented in plain text without using any form of markup like HTML or TeX.

Font Particular size, weight and style of a typeface

In metal typesetting, a font was a particular size, weight and style of a typeface. Each font was a matched set of type, one piece for each glyph, and a typeface consisting of a range of fonts that shared an overall design.

Rotis typeface

Rotis is a typeface developed in 1988 by Otl Aicher, a German graphic designer and typographer. In Rotis, Aicher explores an attempt at maximum legibility through a highly unified yet varied typeface family that ranges from full serif, glyphic, and sans-serif. The four basic Rotis variants are:

Parisine

Parisine is a typeface created by Jean-François Porchez. Distributed by Typofonderie.

Apple's Macintosh computer supports a wide variety of fonts. This support was one of the features that initially distinguished it from other systems.

FF DIN font

FF DIN is a realist sans-serif typeface. It was designed in 1995 by Albert-Jan Pool, based on DIN-Mittelschrift and DIN-Engschrift, as defined in the German standard DIN 1451. DIN is an acronym for Deutsches Institut für Normung. It was published by FontShop in its FontFont library of typefaces.

Unicode equivalence is the specification by the Unicode character encoding standard that some sequences of code points represent essentially the same character. This feature was introduced in the standard to allow compatibility with preexisting standard character sets, which often included similar or identical characters.

Avenir (typeface) Typeface

Avenir is a sans-serif typeface designed by Adrian Frutiger and released in 1988 by Linotype GmbH.

In Unicode and the UCS, a compatibility character is a character that is encoded solely to maintain round trip convertibility with other, often older, standards. As the Unicode Glossary says:

A character that would not have been encoded except for compatibility and round-trip convertibility with other standards

Numerals are characters or sequences of characters that denote a number. The Hindu-Arabic numeral system (base-10) is used widely in various writing systems throughout the world and all share the same semantics for denoting numbers. However, the graphemes representing the numerals differ widely from one writing system to another. To support these grapheme differences, Unicode includes encodings of these numerals within many of the script blocks. The decimal digits are repeated in 22 separate blocks. In addition to many forms of the Hindu-Arabic numerals, Unicode also includes several less common numerals such as: Aegean numerals, Roman numerals, counting rod numerals, Cuneiform numerals and ancient Greek numerals. There is also a large number of typographical variations of the Arabic numerals provided for specialized mathematical use and for compatibility with earlier character sets, and also composite characters containing Arabic numerals such as ½.

Superscripts and Subscripts is a Unicode block containing superscript and subscript numerals, mathematical operators, and letters used in mathematics and phonetics. The use of Unicode subscripts and superscripts allows any polynomial, chemical and certain other equations to be represented in plain text without using any form of markup like HTML or TeX. Other superscript letters can be found in the Spacing Modifier Letters, Phonetic Extensions and Phonetic Extensions Supplement blocks, while the superscript 1, 2, and 3, inherited from ISO 8859-1, were included in the Latin-1 Supplement block.

References

  1. Bringhurst 2005, pp 311–12.
  2. Bringhurst 2005, p 309.
  3. "UCC EPU: Editing Word files for publication: Making the best of what Word provides". Publish.ucc.ie. 2011-07-03. Archived from the original on 2014-01-03. Retrieved 2014-01-03.Cite uses deprecated parameter |deadurl= (help)
  4. "Archived copy" (PDF). Archived (PDF) from the original on 2007-06-12. Retrieved 2008-03-31.Cite uses deprecated parameter |deadurl= (help)CS1 maint: archived copy as title (link)
  5. "Opentype features now enabled? Documentation?". Ask LibreOffice. Archived from the original on 30 December 2016. Retrieved 18 May 2017.Cite uses deprecated parameter |deadurl= (help)
  6. "Math Unicode Entities". Tlt.its.psu.edu. 2013-06-04.Missing or empty |url= (help)

Bibliography