Square-free polynomial: Difference between revisions

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en>William JJ
m grammar
en>MvH
do not write that separable is the same as square-free
 
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{{for2|the sound change|[[Umlaut (linguistics)]]. For other uses of "trema", see [[Trema (disambiguation)]]}}
== der udgør vores ansigter Polo Ralph Lauren Skjorte ==
{{Refimprove|date=July 2010}}
{{diacritical marks|¨|caption=Diaeresis}}
{{Letters with umlaut}}
The '''diaeresis''' ({{IPAc-en|d|aɪ|ˈ|ɛr|ɨ|s|ɨ|s}} {{respell|dy|ERR|ə-səs}}) (also spelled '''diæresis''' or '''dieresis'''; plural: ''-es''), '''trema''' or '''umlaut''' is a [[diacritic]] that consists of two dots ( '''¨''' ) placed over a letter, most commonly a [[vowel]]. When that letter is an ''i'' or a ''j'', the diacritic replaces the [[tittle]]: ''ï''.<ref name=Unicode5.0>{{cite book|title=The Unicode Standard v 5.0|year=1991-2007|publisher=Addison-Wesley|location=San Francisco, etc.|isbn=0-321-48091-0|pages=228}}</ref>


The ''diaeresis'' and the ''umlaut'' are diacritics marking two distinct [[Phonology|phonological]] phenomena. The diaeresis represents the phenomenon also known as ''diaeresis'', or ''[[Hiatus (linguistics)|hiatus]]'', in which a vowel letter is ''not'' pronounced as part of a [[digraph (orthography)|digraph]] or [[diphthong]]. The ''[[Umlaut_(linguistics)|umlaut]]'' ({{IPAc-en|ˈ|ʊ|m|l|aʊ|t}} {{respell|UUM|lowt}}), in contrast, indicates a [[sound shift]]. These two diacritics originated separately; the diaeresis is considerably older. Nevertheless, in modern computer systems using [[Unicode]], the umlaut and diaeresis diacritics are identical: {{angle bracket|'''ä'''}} (code point E4<sub>16</sub>, 228<sub>10</sub>) represents both a-umlaut and a-diaeresis.  
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The same symbol is also used as a diacritic in other cases, distinct from both diaeresis and umlaut. For example, in [[Albanian language|Albanian]], ''ë'' represents a [[schwa]].
  <li>[http://lab.nqnwebs.com/lavoz_bak/spip.php?article5818/ http://lab.nqnwebs.com/lavoz_bak/spip.php?article5818/]</li>
 
 
==Etymologies==
  <li>[http://hlr.k275.com/forum.php?mod=viewthread&tid=252316&fromuid=57777 http://hlr.k275.com/forum.php?mod=viewthread&tid=252316&fromuid=57777]</li>
The word ''diaeresis'' is from {{lang-grc|διαίρεσις}}, meaning ''division'', ''separation'', ''distinction''.<ref>{{LSJ|diai/resis|διαίρεσις|ref}}</ref>
 
 
  <li>[http://annuncianimali.altervista.org/index.php?page=item&id=133821 http://annuncianimali.altervista.org/index.php?page=item&id=133821]</li>
''Umlaut'' is German for "around/changed" (''um-'') "sound" (''Laut'').  
 
 
  <li>[http://www.wnrjmc.com/news/html/?55904.html http://www.wnrjmc.com/news/html/?55904.html]</li>
The word ''trema'' (plural ''tremas'' or ''tremata''), a term generally used in the context of the French language and also occasionally used in [[classical scholarship]], is from {{lang-grc|τρῆμα}}, meaning a ''perforation'', ''orifice'', or ''pip'' (as on dice),<ref>{{LSJ|trh{{=}}ma|τρῆμα|ref}}</ref> and is derived from the form of the diacritic rather than its function.
 
 
  <li>[http://cgi.www5c.biglobe.ne.jp/~kk_aoi/bbs/apeboard_plus.cgi/ http://cgi.www5c.biglobe.ne.jp/~kk_aoi/bbs/apeboard_plus.cgi/]</li>
==Diaeresis==
 
The diaeresis indicates that two adjoining letters that would normally form a [[digraph (orthography)|digraph]] and be pronounced as one are instead to be read as separate vowels in two syllables. The diaeresis indicates that a vowel should be pronounced apart from the letter that precedes it. For example, in the spelling ''coöperate'', the diaeresis reminds the reader that the word has four syllables ''co-op-er-ate'', not three, ''*coop-er-ate''. In British English this usage has been obsolete for many years, and in US English, although it persisted for longer, it is also now considered archaic.<ref>Harry Shaw, 1964. ''Punctuate It Right''. [http://books.google.co.nz/books?id=kjisFLQK8-cC&pg=PT43 p. 43, ''Accent Marks'': Dieresis]: "...it is much less used than formerly, having been largely replaced by the hyphen..."</ref> Nevertheless, it is still used by the US magazine ''[[The New Yorker]]''. In English language texts it is perhaps most familiar in the spellings ''naïve'', ''Noël'', and ''Chloë''. Languages such as [[Dutch language|Dutch]], [[Catalan language|Catalan]], [[French language|French]], and [[Spanish language|Spanish]] make regular use of the diaeresis.
</ul>
 
===History===
Two dots, called a ''trema'', were used in the [[Hellenistic period]] on the letters ι and υ, most often at the beginning of a word, as in ϊδων, ϋιος, and ϋβριν, to separate them from a preceding vowel, as writing was ''[[scriptio continua]]'', where spacing was not yet used as a [[word divider]]. (See [[Coptic alphabet]], for example.) However, it was also used to indicate that a vowel formed its own syllable (in [[hiatus (linguistics)|phonological hiatus]]), as in ηϋ and Αϊδι.<ref>William Johnson, 2004. ''Bookrolls and scribes in Oxyrhynchus'', p 343; examples on pp 259, 315, 334, etc.</ref><ref>Roger Bagnall, 2009:262. ''The Oxford handbook of papyrology''</ref> In [[Modern Greek]], αϊ and οϊ represent the diphthongs {{IPA|/ai̯/}} and {{IPA|/oi̯/}}, and εϊ the disyllabic sequence {{IPA|/e.i/}}, whereas αι, οι, and ει transcribe the simple vowels {{IPA|/e/}}, {{IPA|/i/}}, and {{IPA|/i/}}. The diacritic can be the only one on a vowel, as in ακαδημαϊκός ''akadēmaïkos'' "academic", or in combination with an [[acute accent]], as in πρωτεΐνη ''prōteïnē'' "protein".
 
The diaeresis was borrowed for this purpose in several languages of western and southern Europe, among them [[Occitan language|Occitan]], [[Catalan language|Catalan]], [[French language|French]], [[Dutch language|Dutch]], [[Welsh language|Welsh]], and (rarely) in [[English language|English]].
 
When a vowel in Greek was stressed, it did not assimilate to a preceding vowel but remained as a separate syllable. Such vowels were marked with an accent such as the [[acute accent|acute]], a tradition that has also been adopted by other languages, such as [[Spanish language|Spanish]] and [[Portuguese language|Portuguese]]. For example, the Portuguese words ''saia'' {{IPA|[ˈsajɐ]}} "skirt" and the imperfect ''saía'' {{IPA|[saˈi.ɐ]}} "I used to leave" differ in that the sequence {{IPA|/ai/}} forms a diphthong in the former ([[synaeresis]]), but is a [[hiatus (linguistics)|hiatus]] in the latter (diaeresis).
 
===Hiatus===
In [[Catalan language|Catalan]], the digraphs ''ai'', ''ei'', ''oi'', ''au'', ''eu'', and ''iu'' are normally read as [[diphthong]]s. To indicate exceptions to this rule ([[Hiatus (linguistics)|hiatus]]), a diaeresis mark is placed on the second vowel: without this the words ''raïm'' {{IPA|[rəˈim]}} ("grape") and ''diürn'' {{IPA|[diˈurn]}} ("diurnal") would be read *{{IPA|[ˈrajm]}} and *{{IPA|[ˈdiwrn]}}, respectively. The [[Occitan language|Occitan]] use of diaeresis is very similar to Catalan: ''ai, ei, oi, au, eu, ou'' are [[diphthong]]s consisting of one syllable but ''aï, eï, oï, aü, eü, oü'' are groups consisting of two distinct syllables.
 
In [[Welsh language|Welsh]], where the diaeresis appears, it is usually on the stressed vowel, and this is most often on the first of the two adjacent vowels; a typical example is ''copïo'' {{IPA|[kɔ.ˈpi.ɔ]}} (to copy), cf. ''mopio'' {{IPA|[ˈmɔ.pjɔ]}} (to mop).
In Dutch, spellings such as ''coëfficiënt'' are necessary because the digraphs ''oe'' and ''ie'' normally represent the simple vowels {{IPA|[u]}} and {{IPA|[i]}}, respectively. However, hyphenation is now preferred for compound words so that ''zeeëend'' (sea duck) is now spelled ''zee-eend''.<ref>[http://woordenlijst.org/zoek/?q=zee-eend&w=w Woordenlijst Nederlandse taal]</ref>
 
In German, diaeresis occurs in a few proper names, such as [[Ferdinand Piëch]] and [[Bernhard Hoëcker]].
 
===Non-silent vowels===
As a further extension, some languages began to use a diaeresis whenever a vowel letter was to be pronounced separately. This included vowels that would otherwise form digraphs with consonants or simply be silent.
 
In the orthographies of [[Spanish language|Spanish]], [[Catalan language|Catalan]], [[French language|French]], [[Galician language|Galician]] and [[Occitan language|Occitan]], the graphemes ''gu'', and ''qu'' normally represent a single sound, {{IPA|[ɡ]}} or {{IPA|[k]}}, before the front vowels ''e'' and ''i'' (or before nearly all vowels in Occitan). In the few exceptions where the ''u'' is pronounced, a diaeresis is added to it. Before the [[Portuguese Language Orthographic Agreement of 1990|1990 Orthographic Agreement]], a diaeresis was also used in [[Portuguese language|Portuguese]] in this manner, in words like ''sangüíneo'' {{IPA-pt|sɐ̃ˈɡwiniu|}} “sanguineous”. In French, in such cases the diaeresis is usually written over the following vowel.
 
Examples:
*Spanish ''pingüino'' {{IPA-es|piŋˈɣwino|}} "penguin"
*Catalan ''aigües'' {{IPA-ca|ˈajɣwəs|}} "waters", ''qüestió'' {{IPA-ca|kwəstiˈo|}} "matter, question"
*Occitan ''lingüista'' {{IPA-oc|liŋˈɡwistɔ|}} "linguist", ''aqüatic'' {{IPA-oc|aˈkwatik|}} "aquatic"
*French ''aiguë'' or ''aigüe'' {{IPA-fr|eɡy|}} "acute (fem.)" (note that the ''e'' is silent; without the diacritic, both it and the ''u'' would be silent)
*Galician ''mingüei'' {{IPA-gl|miŋˈɡwei|}} "I shrank"
*[[Luxembourgish language|Luxembourgish]] ''chance'' {{IPA-all|ˈʃãːs|}} "opportunity", ''chancë'' {{IPA-all|ˈʃãːsə|}} (before a consonant) "opportunities"
*English ''Brontë'' {{IPAc-en|ˈ|b|r|ɒ|n|t|iː}} (see [[Brontë family]])
 
This has been extended to [[Luganda|Ganda]], where a diaeresis separates ''y'' from ''n'': ''anya'' {{IPA-all|aɲa|}}, ''anÿa'' {{IPA-all|aɲja|}}.
 
===French===
{{anchor|In French}}
In [[French language|French]], some diphthongs that were written with pairs of vowel letters were later reduced to [[monophthong]]s, which led to an extension of the value of this diacritic. It often now indicates that the second vowel letter is to be pronounced separately from the first, rather than merge with it into a single sound. For example, the French words ''maïs'' {{IPA|[ma.is]}} and ''naïve'' {{IPA|[na.iv]}} would be pronounced {{IPA|*[mɛ]}} and {{IPA|*[nɛv]}}, respectively, without the diaeresis mark, since the [[Digraph (orthography)|digraph]] ''ai'' is pronounced {{IPA|[ɛ]}}. The English spelling of ''Noël'' "Christmas" (French {{IPA|[nɔ.ɛl]}}) comes from this use. ''Ÿ'' occurs in French as a variant of ''ï'' in a few proper nouns, as in the name of the [[Paris]]ian suburb of [[L'Haÿ-les-Roses]] {{IPA|[la.i le ʁoz]}}.
 
The diaeresis is also used when a silent ''e'' is added to the sequence ''gu'', to show that it is to be pronounced {{IPA|[ɡy]}} rather than as a digraph for {{IPA|[ɡ]}}. For example, when the feminine ''-e'' is added to ''aigu'' {{IPA|[eɡy]}} "sharp", the pronunciation does not change: ''aiguë'' {{IPA|[eɡy]}}. Similar is the feminine noun ''ciguë'' {{IPA|[siɡy]}} "hemlock"; compare ''figue'' {{IPA|[fiɡ]}} "fig". In the ongoing [[Reforms of French orthography|French spelling reform]] of 1990, this was moved to the ''u'' (''aigüe, cigüe''), though the earlier orthography continues to be widely used. (In ''canoë'' {{IPA|[kanɔ.e]}} the ''e'' is not silent, and so is not affected by the spelling reform.)
 
In some names, a diaeresis is used to show what ''used to be'' two vowels in hiatus, although the second vowel has since fallen silent, as in [[Camille Saint-Saëns|Saint-Saëns]] {{IPA|[sɛ̃sɑ̃s]}} and [[Anne Louise Germaine de Staël|de Staël]] {{IPA|[də stal]}}.
 
===English===
{{anchor|In English}}
Along with the [[grave accent]], the diaeresis is [[English terms with diacritical marks|the only]] [[diacritic]] native to [[Modern English]] (apart from diacritics used in [[loanword]]s, such as the [[acute accent]], the [[cedilla]], or the [[tilde]]). The use of both, however, is considered to be largely [[archaism|archaic]].<ref name="Fowler">{{cite book | last= Burchfield| first = R.W. | title = Fowlers's Modern English Usage |edition=3| year = 1996 | publisher = Oxford University Press | isbn = 0-19-869126-2|page=210  }}</ref><ref>[http://www.flakery.org/search/show/251 On Diacritics and Archaïsm]. Flakery.org, June 18, 2006.</ref>
 
The diaeresis mark is sometimes used in English personal first and last names to indicate that two adjacent vowels should be pronounced separately, rather than as a [[diphthong]]. Examples include the given names ''Chloë'' and ''Zoë'', which otherwise might be pronounced with a silent ''e''. To discourage a similar mispronunciation, the mark is also used in the surname ''Brontë''. It may be used optionally for words that do not have a morphological break at the diaeresis point, such as ''[[naïve]]'', ''[[Boötes]]'', and ''Noël''. However, its use in words such as ''coöperate'' and ''reënter'' has been dropped or replaced by the use of a hyphen except in a very few publications&mdash;notably ''[[The New Yorker]]''.<ref>[http://www.randomhouse.com/wotd/index.pperl?date=19981209 diaeresis: December 9, 1998]. The Mavens' Word of the Day. [[Random House]].</ref><ref>[http://boards.straightdope.com/sdmb/showthread.php?t=302254 Umlauts in English?]. General Questions. Straight Dope Message Board.</ref>
 
''Ÿ'' is sometimes used in transcribed [[Greek language|Greek]], where it represents the Greek letter [[υ]] (upsilon) in hiatus with [[α]]. For example, it can be seen in the transcription ''Artaÿctes'' of the Persian name {{lang|grc|Ἀρταΰκτης}} at the very end of [[Herodotus]], or the name of Mount [[Taygetus|Taÿgetus]] on the southern Peloponnesus peninsula, which in modern Greek is spelled Ταΰγετος.
 
==Umlaut==
"Umlaut" refers to a [[Germanic umlaut|historical sound shift]] in [[German language|German]]. In German, umlauts are found as ''[[ä]]'', ''[[ö]]'' and ''[[ü]]''. The name is used in some other languages that share these symbols with German or where the Latin spelling was introduced in the 19th century, replacing marks that had been used previously. The phonological phenomenon of umlaut occurred historically in English as well (''man ~ men; full ~ fill; goose ~ geese'') in a way cognately parallel with German, but English orthography does not write the sound shift using the umlaut diacritic. Instead, a different letter is used.
 
===History===
{{anchor|Umlaut history}}
{{further2|[[Germanic umlaut]]}}
[[Image:Umlaut forms.png|thumb|100px|New and old forms of umlaut]]
Historically, the umlaut mark is far younger than the diaeresis mark, and has unrelated origins, though it has been speculated that the diaeresis mark might have influenced the final written form of the umlaut.
 
[[File:Umlaut Development.png|thumb|right|220px|Development of the umlaut in Sütterlin: ''schoen'' becomes ''schön'' via ''{{Unicode|schoͤn}}'' 'beautiful']]
Originally, [[Germanic umlaut|phonological umlaut]] was denoted in written German by adding an ''e'' to the affected vowel, either after the vowel or, in small form, above it. This can still be seen in some names, e.g. Goethe, Goebbels, Staedtler. (In medieval German manuscripts, other [[Digraph (orthography)|digraphs]] could also be written using superscripts: in ''bluome'' 'flower', for example, the {{angle bracket|o}} was frequently placed above the {{angle bracket|u}}, although this letter survives now only in [[Czech alphabet|Czech]]. Compare also the [[Tilde#Diacritical use|development of the tilde]] as a superscript ''n''.) In [[blackletter]] handwriting as used in German manuscripts of the later Middle Ages, and also in many printed texts of the early modern period, the superscript {{angle bracket|e}} still had a form that would be recognisable to us as an {{angle bracket|e}}. However, in the [[Kurrent|forms of handwriting]] that emerged in the [[early modern period]] (of which [[Sütterlin]] is the latest and best-known example) the letter {{angle bracket|e}} was composed of two short vertical lines very close together, and the superscript {{angle bracket|e}} looked like two tiny strokes. Gradually these strokes were reduced to dots in some handwriting, and as early as the 16th century we find this handwritten form being transferred sporadically to printed texts too.
 
In modern handwriting, the umlaut sometimes resembles a <!-- RWE: a breve (˘), is not used since it is used to distinguish a "u" from an "n", especially by elderly people who have learned to write in or before WWII -->[[tilde]], [[quotation mark]], [[dash]], miniature u or other small mark.
 
===Printing conventions in German===<!-- This section is linked from [[Nürburgring]] -->
When typing German, if umlaut letters are not available, it is usual to replace them with the underlying vowel and a following {{angle bracket|e}}. So, for example, "Schröder" becomes "Schroeder". As the pronunciation differs greatly between the normal letter and the umlaut, simply omitting the dots is incorrect; this also applies to other Germanic languages and Finnish. The result might often be a different word, as in ''schon'' 'already', ''schön'' 'beautiful'; ''schwul'' 'gay', ''schwül'' 'humid'; or a different grammatic form, e.g. ''Mutter'' 'mother', ''Mütter'' 'mothers' (similarly in Swedish: ''broder'' 'brother', ''bröder'' 'brothers'). Thus, the omission of the umlaut in a printed text can cause confusion, e.g. in Swedish personal and geographic names like Mollberg/Möllberg, Marta/Märta or Hallaryd/Hällaryd, and Finnish Makkonen/Mäkkönen, Sakajärvi/Säkäjärvi.
 
Despite this, the umlauted letters are not considered as separate letters of the alphabet proper in German, in contrast to other Germanic languages. When [[Collation|alphabetically sorting]] German words, the umlaut is usually not distinguished from the underlying vowel, although if two words differ only by an umlaut, the umlauted one comes second – the same treatment as the [[dakuten]] diacritic in Japanese, for instance – for example:
# Schon
# Schön
# Schonen
 
There is a second system in limited use, mostly for sorting names (colloquially called "telephone directory sorting"), which treats ü like ue, and so on.
# Schön
# Schon
# Schonen
 
[[Austria]]n telephone directories insert ö after oz.
# Schon
# Schonen
# Schön
 
In [[Switzerland]], capital umlauts are sometimes printed as [[Digraph (orthography)|digraph]]s, in other words, {{angle bracket|Ae}}, {{angle bracket|Oe}}, {{angle bracket|Ue}}, instead of {{angle bracket|Ä}}, {{angle bracket|Ö}}, {{angle bracket|Ü}} (see ''[[German alphabet]]'' for an elaboration.) This is because the Swiss typewriter keyboard contains the French accents on the same keys as the umlauts (selected by Shift). To write capital umlauts the ¨-key is pressed followed by the capital letter to which the umlaut should apply.
 
===Borrowing of German umlaut notation===
Some languages have borrowed some of the forms of the German letters [[Ä]], [[Ö]], or [[Ü]], including [[Azerbaijani language|Azerbaijani]], [[Estonian language|Estonian]], [[Finnish language|Finnish]], [[Hungarian language|Hungarian]], [[Karelian language|Karelian]], some of the [[Sami languages]], [[Slovak language|Slovak]], [[Swedish language|Swedish]], and [[Turkish language|Turkish]]. This indicates sounds similar to the corresponding umlauted letters in German. In spoken Scandinavian languages the grammatical umlaut change is used (singular to plural, derivations etc.) but the character used differs between languages. In Finnish, a/ä and o/ö change systematically in suffixes according to the rules of [[vowel harmony]]. In Hungarian, where long vowels are indicated with an acute accent, the umlaut notation has been expanded with a version of the umlaut which looks like [[double acute accent]]s, indicating a blend of umlaut and acute. Contrast: short ö; long ő.
The Estonian alphabet has borrowed {{angle bracket|ä}}, {{angle bracket|ö}}, and {{angle bracket|ü}} from German; Swedish and Finnish have {{angle bracket|ä}} and {{angle bracket|ö}}; and Slovak has {{angle bracket|ä}}. In Estonian, Swedish, Finnish, and Sami {{angle bracket|ä}} and {{angle bracket|ö}} denote {{IPA|[æ]}} and {{IPA|[ø]}}, respectively. Hungarian has {{angle bracket|ö}} and {{angle bracket|ü}}. The Slovak language uses the letter {{angle bracket|ä}} to denote {{IPA|[ɛ]}} (or a bit archaic but still correct {{IPA|[æ]}}) – the sign is called ''dve bodky'' ("two dots"), and the full name of the letter ''ä'' is ''a s dvomi bodkami'' ("a with two dots"). In these languages, with the exception of Hungarian, the replacement rule for situations where the umlaut character is not available, is to simply use the underlying unaccented character instead. Hungarian follows the German rules and replaces {{angle bracket|ö}} and {{angle bracket|ü}} with {{angle bracket|oe}} and {{angle bracket|ue}} respectively &ndash; at least for telegrams and telex messages. The same rule is followed for the near-lookalikes {{angle bracket|ő}} and {{angle bracket|ű}}.
 
In [[Luxembourgish language|Luxembourgish]] (''Lëtzebuergesch''), the umlaut diacritic in {{angle bracket|ä}} and {{angle bracket|ë}} represents a stressed [[schwa]]. Since the Luxembourgish language uses the mark to show stress, it cannot be used to modify the ''u'', which therefore has to be {{angle bracket|ue}}.
 
When Turkish switched from the Arabic to the Latin alphabet in 1928, it adopted a number of diacritics borrowed from various languages, including {{angle bracket|ü}}, which was taken from German (Turkey had a close relationship with Germany) and {{angle bracket|ö}} from Swedish, which in turn had borrowed this symbol from German.  These Turkish graphemes represent similar sounds to their values in German (see ''[[Turkish alphabet]]'').
 
As the borrowed diacritic has lost its relationship to Germanic i-mutation, they are in some languages considered independent graphemes, and cannot be replaced with {{angle bracket|ae}}, {{angle bracket|oe}}, or {{angle bracket|ue}} as in German. In Estonian and Finnish, for example, these latter diphthongs have independent meanings. Even some Germanic languages, such as Swedish (which ''does'' have a transformation analogous to the German umlaut, called ''omljud''), treat them always as independent letters. In [[collation]], this means they have their own positions in the alphabet, for example at the end ("A&ndash;Ö" or "A&ndash;Ü", not "A&ndash;Z") as in Swedish, Estonian and Finnish, which means that the dictionary order is different from German. The transformations ''ä'' → ''ae'' and ''ö'' → ''oe'' can therefore be considered less appropriate for these languages, although Swedish passports use the transformation to render ö and ä (and ''å'' as ''aa'') in the [[Machine-readable passport|machine-readable zone]]. In contexts of technological limitation e.g. in English based systems, Swedes can either be forced to omit the diacritics or use the two letter system.
 
When typing in [[Norwegian language|Norwegian]], the letters [[Æ]] and [[Ø]] might be replaced with [[Ä]] and [[Ö]] respectively if the former are not available. If ''ä'' is not available either, it is appropriate to use ''ae''. The same goes for ''ö'' and ''oe''. While ''ae'' has a great resemblance to the letter ''æ'' and therefore does not impede legibility, the digraph ''oe'' is likely to reduce the legibility of a Norwegian text. This especially applies to the digraph ''[[øy]]'', which would be rendered in the more cryptic form ''oey''. Also in [[Danish language|Danish]], Ö has been used in place of Ø in some older texts and to distinguish between open and closed ö-sounds and when confusion with other symbols could occur, e.g. on maps. The Danish/Norwegian Ø is like the German Ö a development of OE, to be compared with the French [[Œ]].  
 
Early [[Volapük]] used [[Fraktur (typeface sub-classification)|Fraktur]] ''a'', ''o'' and ''u'' as different from [[Antiqua (typeface class)|Antiqua]] ones. Later, the Fraktur forms were replaced with umlauted vowels.
 
The usage of umlaut-like diacritic vowels, particularly ''ü'', occurs in the transcription of languages that do not use the Roman alphabet, such as [[Chinese language|Chinese]]. For example, 女 (''female'') is transcribed as ''nǚ'' in proper [[Standard Mandarin|Mandarin Chinese]] [[pinyin]], while ''nv'' is sometimes used as a replacement for convenience since the letter v is not used in pinyin. [[Tibetan pinyin]] uses ''ä, ö, ü'' with approximately their German values.
 
The [[Cyrillic script|Cyrillic]] letters [[ӓ]], [[ӧ]], [[ӱ]] are used in [[Mari language|Mari]], [[Khanty language|Khanty]], and other languages for approximately {{IPA|[æ]}}, {{IPA|[ø]}}, and {{IPA|[y]}}. These directly parallel the German umlaut ''ä, ö, ü.'' Other vowels using a double dot to modify their values in various minority languages of Russia are [[ӛ]], [[ӫ]], and [[ӹ]].
 
===Use of the umlaut for special effect===
{{See also|Metal umlaut}}
The umlaut diacritic can be used in "[[sensational spelling]]s" or [[foreign branding]], for example in advertising, or for other special effects. [[Häagen-Dazs]] is an example of such usage.
 
As the German short {{IPA|/a/}} is more open than the equivalent sound in English, {{IPA|/æ/}}, Germans sometimes use the diacritic {{angle bracket|ä}} to imitate the English sound in writing, giving an English (chiefly American MTV style English) "feel" to words used in advertising; in a McDonald's restaurant in Germany one could buy a "[[Big Mac|Big Mäc]]" (McDonald's renamed Fishmäc and Big Mäc in 2007).
 
Since the letter {{angbr|ü}} is very common in Turkish, its inappropriate use can make a text in another language look "turkified", a purely visual mimicry. Because of the large number of Turks living in Germany, this again is a phenomenon familiar in German. The Turkish-German satirist [[Osman Engin]], for example, wrote a book entitled ''Dütschlünd, Dütschlünd übür üllüs'' – the opening line of the first stanza from ''[[Das Lied der Deutschen]]'', but turkified.
 
In the [[Heavy metal music|heavy metal]] scene, the umlaut diacritic can frequently be observed as a mere decoration (with no significance for the pronunciation) on the names of bands such as [[Blue Öyster Cult]], [[Motörhead]], [[Mötley Crüe]], [[Mägo de Oz]], [[Queensrÿche]], [[Moxy Früvous]], or [[Leftöver Crack]]. The group [[Spinal Tap (band)|{{Unicode|Sp&#305;n&#776;al Tap}}]] places an umlaut over the {{angle bracket|n}}. A self-referential example is the Finnish group Ümlaut.
 
[[Jason Derülo]] is proof that even R&B artists are not immune to this type of usage.
 
==Other uses==
A double dot is also used as a diacritic in cases where it functions as neither a diaeresis nor an umlaut. In the [[International Phonetic Alphabet]], a double dot is used for a [[Centralization (phonetics)|centralized vowel]], a situation more similar to umlaut than to diaeresis. In other languages it is used for vowel length, nasalization, tone, and various other uses where diaeresis or umlaut was available typographically.
 
===Vowels===
* In [[Albanian language|Albanian]] and [[Kashubian language|Kashubian]], {{angbr|ë}} represents a [[schwa]] [ə].
* In [[Aymara language|Aymara]], a double dot is used on {{angbr|ä}} {{angbr|ï}} {{angbr|ü}} for [[vowel length]].
* In the Basque dialect of Soule, {{angbr|ü}} represents another vowel —the main phonetic characteristic of those areas—, pronounced as in French "u" or German "ü".
* In [[Ligurian (Romance language)|Ligurian]] official orthography, {{angbr|ö}} is used to represent the sound {{IPA|[oː]}}.
* In [[Māori language|Māori]] a diaeresis (e.g. ''Mäori'') was often used on computers in the past instead of the [[macron]] to indicate long vowels, as the diaeresis was relatively easy to produce on many systems, and the macron difficult or impossible.<ref name="macrons">[http://www.tetaurawhiri.govt.nz/english/pub_e/conventions3.shtml#Part_One_ Māori Orthographic Conventions], Māori Language Commission, accessed 11 June 2010.</ref><ref>[http://www.teara.govt.nz/en/matauranga-hangarau-information-technology/3 "Māori language on the internet"], Te Ara</ref>
* In [[Seneca language|Seneca]], {{angbr|ë}} {{angbr|ö}} are [[nasal vowel]]s, though {{angbr|ä}} is {{IPA|[ɛ]}}, as in German umlaut.
* In [[Vurës language|Vurës]] (Vanuatu), {{angbr|ë}} {{angbr|ö}} encode respectively {{IPA|[œ]}} and {{IPA|[ø]}}.
* In the [[Pahawh Hmong]] script, a double dot is used as one of several tone marks.
* The double dot was used in the [[early Cyrillic alphabet]], which was used to write [[Old Church Slavonic]]. The modern [[Cyrillic]] [[Belarusian alphabet|Belarusian]] and [[Russian alphabet|Russian]] alphabets include the letter ''[[Yo (Cyrillic)|yo]]'' {{angbr|ё}}, although replacing it with the letter {{angbr|[[е]]}} without the diacritic is allowed in Russian unless doing so would create ambiguity. Since the 1870s, the letter ''[[Yi (Cyrillic)|yi]]'' (Ї, ї) has been used in the [[Ukrainian alphabet]] for [[iotated]] {{IPA|[ji]}}; plain [[і]] is not iotated {{IPA|[i]}}. In [[Udmurt language|Udmurt]], [[ӥ]] is used for uniotated {{IPA|[i]}}, with [[и]] for iotated {{IPA|[ji]}}.
* The form ''ÿ'' is common in [[Dutch orthography|Dutch]] handwriting and also occasionally used in printed text – but is a form of [[IJ (digraph)|the digraph "ij"]] rather than a modification of the letter "y".
* [[Komi language]] uses {{angbr|ӧ}} (Cyrillic [[о]] with diaeresis) for {{IPA|[ə]}}. This letter is not present in most languages that use Cyrillic alphabet and may cause compatibility problems although it has a code point in Unicode.
 
===Consonants=== <!-- this section is linked from [[Template:Letters with umlaut]] -->
[[Jacaltec]] (a [[Mayan languages|Mayan]] language) and [[Malagasy language|Malagasy]] are among the very few languages with a diaeresis on the letter "n"; in both, {{Unicode|[[n̈]]}} is the [[velar nasal]] {{IPA|[ŋ]}}.
 
In [[Udmurt language|Udmurt]], a double dot is also used with the consonant letters [[ӝ]] {{IPA|[dʒ]}} (from ж {{IPA|[ʒ]}}) and [[ӟ]] {{IPA|[dʑ]}} (from з {{IPA|[z] ~ [ʑ]}}).
 
[[Ḧ]] and [[ẍ]] are used for {{IPA|[ħ]}} and {{IPA|[ʁ]}} in the unified [[Kurdish alphabet]]. These are foreign sounds borrowed from Arabic.
 
[[Ẅ]] and [[ÿ]]: ''Ÿ'' is generally a vowel, but it's used as the (semi-vowel) consonant {{IPA|[ɰ]}} (a {{IPA|[w]}} without the use of the lips) in [[Tlingit language|Tlingit]]. This sound is also found in [[Coast Tsimshian]], where it's written [[ẅ]].
 
A number of languages in [[Vanuatu]] use double dots on consonants, to represent [[Linguolabial consonant|linguolabial]] (or ''apicolabial'') phonemes in their orthography. Thus [[Araki language#Consonants|Araki]] contrasts bilabial ''p'' {{IPA|[p]}} with linguolabial ''p̈'' {{IPA|[t̼]}}; bilabial ''m'' {{IPA|[m]}} with linguolabial ''m̈'' {{IPA|[n̼]}}; and bilabial ''v'' {{IPA|[β]}} with linguolabial ''v̈'' {{IPA|[ð̼]}}.
 
The letter [[ẗ]] is not used in any alphabet, but is sometimes seen for [[tāʾ marbūṭa]] ة in Arabic transliteration.
 
[[Syriac]] uses a two dots above a letter, called [[Siyame]], to indicate that the word should be understood as plural. For instance, ܒܝܬܐ (''bayta'') means 'house', while ܒܝ̈ܬܐ (''bayte'') means 'houses'. The sign is used especially when no vowel marks are present, which could differentiate between the two forms. Although the origin of the [[Siyame]] is different from that of the Diaeresis sign, in modern computer systems both are represented by the same Unicode character. This, however, often leads to wrong rendering of the Syriac text.
 
===Calculus===
The [[derivative]] with respect to time (using [[Newton's notation]]) is often represented as a dot above a variable. Two dots represents the second derivative.
 
:<math>{\dot{a}} = {\mathrm{d}a \over \mathrm{d}t}</math>
 
:<math>{\ddot{a}} = {\mathrm{d} ^2 a \over \mathrm{d} t^2}</math>
 
This may be contrasted with the more general notation for a derivative using a [[prime (symbol)|prime]], which may also be used to refer specifically to the derivative with respect to space:
 
:<math>f'(x) = {\mathrm{d} \over \mathrm{d}x} f(x)</math>
 
:<math>f''(x) = {\mathrm{d}^2 \over \mathrm{d} x^2} f(x)</math>
 
==Computer usage==
Character encoding generally treats the umlaut and the diaeresis as the same diacritic mark.
 
=== Keyboard input ===
[[Image:Tastatur-Umlaute-deutsch.jpg|thumb|right|Letters with umlaut on a [[German keyboard|German computer keyboard]].]]
If letters with double dots are not present on the keyboard (or if they are not recognized by the operating system), there are a number of ways to input them into a computer system.
 
Using [[Microsoft Word]] for [[Windows]]<!--only the windows version-->, a letter with double dots can be produced by pressing ''Ctrl-Shift-:'', then the letter.
 
Using [[Mac OS]] or [[OS X]], a letter with double dots can be produced by pressing {{key press|Option|U}}, then the letter. This works on English and other keyboards and is documented further in the supplied manuals.
 
[[X Window System|X-based systems]] with a [[Compose key]] set in the system can usually insert characters with double dots by typing {{key press|Compose}}, {{key press|quotedbl}} (i.e. <tt>"</tt>) followed by the letter. {{key press|Compose|Shift}}, {{key press|letter}} may also work, depending on the system's set-up. However, most modern UNIX-like systems also accept the sequence {{key press|Compose|Shift|U}} to initiate the direct input of a Unicode value. Thus, typing {{key press|Compose|Shift|U}}, <tt>00F6</tt>, finishing with {{key press|Space}} or {{key press|Enter}}, will insert <tt>ö</tt> into the document.
 
[[Microsoft Windows]] allows users to set their US layout keyboard language to ''International'', which allows for something similar, by turning keys (rather characters) into [[dead key]]s. If the user enters ", nothing will appear on screen, until the user types another character, after which the characters will be merged if possible, or added independently at once if not.
 
On several operating systems, double-dotted letters can be written  by entering [[Alt codes]]. On Microsoft Windows [[keyboard layout]]s that do not have double dotted characters, one can especially use [[Windows Alt keycodes]]. Double dots are then entered by pressing the left Alt key, and entering the full decimal value of the character's position in the [[Windows code page]] on the numeric keypad, provided that the compatible code page is used as a system code page. One can also use numbers from [[Code page 850]]; these lack a leading 0. On a Swedish/Finnish keyboard both letters å, ä and ö are present, as well as ¨ to combine with any vowel character, in the same way as ´`^ and ~ accentuation signs.
 
{| class="wikitable"
! Character !! Windows Code Page Code !! CP850 Code
|-
| ä || Alt+0228 || Alt+132
|-
| ë || Alt+0235 || Alt+137
|-
| ï || Alt+0239 || Alt+139
|-
| ö || Alt+0246 || Alt+148
|-
| ü || Alt+0252 || Alt+129
|-
| ÿ || Alt+0255 || Alt+152
|-
| Ä || Alt+0196 || Alt+142
|-
| Ë || Alt+0203 || Alt+211
|-
| Ï || Alt+0207, Alt+02255 || Alt+651
|-
| Ö || Alt+0214 || Alt+153
|-
| Ü || Alt+0220 || Alt+154
|-
| Ÿ || Alt+0159 || N/A
|}
 
=== Character encodings ===
The [[ISO 8859-1]] character encoding includes the letters ''ä'', ''ë'', ''ï'', ''ö'', ''ü'', and their respective [[majuscule|capital]] forms, as well as ''ÿ'' in [[lower case]] only, with ''Ÿ'' added in the revised edition [[ISO 8859-15]].
 
[[Unicode]] includes all of ISO-8859, and also provides the double dot as a [[Combining diacritical mark|combining character]] '''U+0308'''. Mainly for compatibility with older character encodings, dozens of codepoints with letters with double dots are available.
 
Both the combining character U+0308 and the precombined codepoints can be used as umlaut or diaeresis.
 
Sometimes, there's a need to distinguish between the umlaut sign and the diaeresis sign. ISO/IEC JTC 1/SC 2/WG 2 recommends the following for these cases:
* To represent the '''umlaut''' use Combining Diaeresis (U+0308)
* To represent the '''diaeresis''' use Combining Grapheme Joiner (CGJ, U+034F) + Combining Diaeresis (U+0308)
 
As of version 3.2.0, Unicode also provides "COMBINING LATIN SMALL LETTER E" at U+0364 which can produce the older umlaut typography.
 
=== HTML ===
In [[HTML]], vowels with double dots can be entered with an entity reference of the form <code>&amp;?uml;</code>, where <code>?</code> can be any of <code>a</code>, <code>e</code>, <code>i</code>, <code>o</code>, <code>u</code>, <code>y</code> or their [[majuscule]] counterparts. With the exception of the uppercase ''Ÿ'', these characters are also available in all of the [[ISO 8859]] character sets and thus have the same codepoints in [[ISO-8859-1]] ([[ISO 8859-2|-2]], [[ISO 8859-3|-3]], [[ISO 8859-4|-4]], [[ISO 8859-9|-9]], [[ISO 8859-10|-10]], [[ISO 8859-13|-13]], [[ISO 8859-14|-14]], [[ISO 8859-15|-15]], [[ISO 8859-16|-16]]) and [[Unicode]]. The uppercase ''Ÿ'' is available in ISO 8859-15 and Unicode, and Unicode provides a number of other letters with double dots as well.
 
<div style="float: left">
{| class="wikitable"
|-
|+ '''Umlauts <br>'''
|-
! Character !! Replacement !! HTML !! Unicode
|-
| ä || a ''or'' ae || <code>&amp;auml;</code> || U+00E4
|-
| ö || o ''or'' oe || <code>&amp;ouml;</code> || U+00F6
|-
| ü || u ''or'' ue || <code>&amp;uuml;</code> || U+00FC
|-
| Ä || A ''or'' Ae || <code>&amp;Auml;</code> || U+00C4
|-
| Ö || O ''or'' Oe || <code>&amp;Ouml;</code> || U+00D6
|-
| Ü || U ''or'' Ue || <code>&amp;Uuml;</code> || U+00DC
|-
|}
</div>
 
<div style="float: left; margin-left: 1em">
{| class="wikitable"
|-
|+ '''Other double dots'''
|-
! Character !! HTML !! Unicode
|-
| ë || <code>&amp;euml;</code> || U+00EB
|-
| ḧ ||  || U+1E27
|-
| ï || <code>&amp;iuml;</code> || U+00EF
|-
| ẅ ||  || U+1E85
|-
| ẍ ||  || U+1E8D
|-
| ÿ || <code>&amp;yuml;</code> || U+00FF
|-
| Ë || <code>&amp;Euml;</code> || U+00CB
|-
| Ḧ ||  || U+1E26
|-
| Ï || <code>&amp;Iuml;</code> || U+00CF
|-
| Ẅ ||  || U+1E84
|-
| Ẍ ||  || U+1E8C
|-
| Ÿ || <code>&amp;Yuml;</code> || U+0178
|-
|}
</div>
<br style="clear: both">
Note: when replacing umlaut characters with plain [[ASCII]], use ''ae, oe,'' etc. for German language, and the simple character replacements for all other languages.
<br style="clear: both">
 
=== TeX and LaTeX ===
[[TeX]] (and its derivatives, most notably [[LaTeX]]) also allows double dots to be placed over letters. The standard way is to use the control sequence <tt>\"</tt> followed by the relevant letter, e.g. <tt>\"u</tt>. It is good practice to set the sequence off with curly braces: <tt>{\"u}</tt> or <tt>\"{u}</tt>.
 
[[TeX]]'s "German" package can be used: it adds the <tt>"</tt> control sequence (without the backslash) to produce the Umlaut. However, this can cause conflicts if the main language of the document is not German. Since the integration of Unicode through the development of [[XeTeX]] and [[XeLaTeX]], it is also possible to input the Unicode character directly into the document, using one of the recognized methods such as [[Compose key]] or direct [[Unicode input]].
 
[[TeX]]'s traditional control sequences can still be used and will produce the same output (in very early versions of [[TeX]] these sequences would produce double dots that were too far above the letter's body).
 
All these methods can be used with all available font variations (italic, bold etc.).
 
The use of the diaeresis in mathematics is of course different (see above). To produce the diaeresis in math mode, use "<tt>\ddot{}</tt>".
 
== See also ==
*[[Diaeresis (disambiguation)|Diaeresis]]
*[[Umlaut (disambiguation)|Umlaut]]
*[[Alt code]]
*[[Dot (diacritic)]]
*[[Double acute accent]], a similar-looking diacritic
*[[Metal umlaut]]
*[[Macron]]
*[[Tittle]]
 
{{Latin alphabet||diaeresis}}
 
==References==
{{Reflist}}
 
== External links ==
{{Wiktionary|ä|Ë|ë|ö}}
*[http://diacritics.typo.cz Diacritics Project – All you need to design a font with correct accents]
*[http://www.starr.net/is/type/kbh.html Keyboard Help] – Learn how to create world language accent marks and other diacriticals on a computer
 
[[Category:Alphabetic diacritics]]
[[Category:Latin alphabet ligatures]]
[[Category:Greek alphabet]]

Latest revision as of 20:45, 7 February 2014

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