text:
Talk:Mode (music)

Mystic nonclassical mode (it has 3 submodes)
Please include it, make all proper files (if you have a different Mystic mode, name that one Sigil mode, otherwise keep it Mystic)
 * do, re#, mi, sol, sol#, ti
 * do, do#, mi, fa, sol#, la
 * do#, re, fa, fa# la, la#

mood: mysterious

Evil Shaolin nonclassical mode (it has 2 submodes)
Please include it, make all proper files
 * do, re, re#, fa, fa#, sol#, la, ti
 * do#, re, mi, fa, sol, sol#, la#, ti

mood: horrorish (not pure horror; to horrorize it add chromatic ornaments and off-scale the semitonal intervals: 0-13, 0-11, 0-1, 0-6, 0-3, 0-4 (zero means starting note, and number means semitonal steps backwards or forwards)

Lock Fridge Door Mix Lid
In order Locrian (weird), then Phrygian ('heavy minor'), Minor, Dorian ('light minor'), then Mixolydian ('folky major'), Major, Lydian ('spacey major'). Mnemonic: Lock fridge (min) door, mix (maj) lid. Lock fridge - door, mix + lid. Acorrector (talk) 18:27, 2 February 2021 (UTC)

Modifications to the article
I begin modifications to the article. These I think must be justified here. But any comment about all this will be welcome. — Hucbald.SaintAmand (talk) 16:32, 24 July 2021 (UTC)
 * I added a mention of medieval rhythmic modes. These would deserve a section in the article, but that will be for later. I also indicated that the term had denoted intervals, or qualities of notes.
 * I removed the phrase saying that musical modes "were inspired by the theory of ancient Greek music", because that is not true (even if it has at times been believed).
 * I also removed the mention of "ancient Greek octave species called tonos (τόνος) or harmonia (ἁρμονία)" which, unless I am mistaken, are not in Powers 2001.
 * And I reworded the rest of the phrase: "Harold S. Powers proposed mode as a general term but limited for melody types [...], with "most of the area between ... being in the domain of mode" seemed somehow incomplete. I completed Powers' quotation.
 * I removed "This synthesis between tonus as a church tone and the older meaning associated with an octave species was made by medieval theorists for the Western monodic plainchant tradition (see Hucbald and Aurelian)" because I don't understand which synthesis was alluded to (certainly not that of Powers just mentioned), nor what "older meaning" (of "mode"?) is meant, nor why Hucbald and Aurelian are mentioned in this context.
 * I remain puzzled by the following mention and the reference to Wellesz (and by the idea that musicologists "generally assume"...). Wellesz may have had an ideological position in all this. I have first to check that and I'll stop there for the time being.
 * I continue my rereading and rewriting of the article, this time of the section "Mode as a general concept."
 * I removed this sentence: "Musicologists generally assume that Carolingian theorists imported monastic Octoechos propagated in the patriarchates of Jerusalem (Mar Saba) and Constantinople (Stoudios Monastery), which meant the eight echoi they used for the composition of hymns" and the reference to Wellesz that followed. After verification, Wellesz' article in vol 2 of the New Oxford History of Music never mentions Carolingian theorists. In addition, neither Mar Saba nor the Stoudios Monastery are mentioned in the whole volume.
 * I modified the phrase "Since the end of the 18th century, the term "mode" has also applied to pitch structures in non-European musical cultures, sometimes with doubtful compatibility" in order to better reflect what is said by Powers in the New Grove.
 * I added precisions to the early mention of mode in polyphony.
 * And I moved from the lede the references for rhythmic modes, mode denoting intervals and mode denoting quality of notes.
 * I am not sure that this section must survive, under this name at least. But that is for later. — Hucbald.SaintAmand (talk) 13:42, 26 July 2021 (UTC)

 * Thanks for the improvements!
 * The lede is really inadequate as it now stands. It might be rewritten to take account of tonoi and distinguish diatonic modes ("a type of musical scale") gregorian modes ("with characteristic … behaviours"), rhythmic mode, modus in mensural notation. Or, the article might be renamed diatonic modes with mode (music) more of a disambiguation page. Sparafucil (talk) 21:28, 26 July 2021 (UTC)
 * Ah, I see a fork already: Diatonic scale. Sparafucil (talk) 21:32, 26 July 2021 (UTC)

, you are right that the lede is inadequate as it stands, and I should perhaps not have begun there. It seems to me however that the title "Mode (music)" is the most general: the article deserves more than being reduced to a disambiguation page because it has to say things that concern modes in general – and, on the other hand, the matter of "mode" may perhaps not deserve being distributed in many different articles.

It would seem to me more reasonable that sections be devoted to "Rhythmic modes", to "Modes as intervals" or "Modes as qualities of notes", also to non European modes (which are only alluded to in the section on Analogues in different musical traditions), and should link to other articles only if these already exist. For instance, there are general things to be said about non European modes, which hardly could be said in separate articles concerning any of them.

You write that the lede should take account of tonoi: don't you mean tonus, which is not the same? Modes have little if anything to do with Greek tonoi, while the Latin tonus has been used as a name for modes (but this is not for the lede). Diatonic modes are but a special case of modes. Etc. There's a lot of work to be done on this article. — Hucbald.SaintAmand (talk) 10:27, 27 July 2021 (UTC)
 * I at first took your tonus for the singular of tonoi rather than psalm tone. I don't think it can be excluded from lede, and wish I had worked in Octave species as well. Sparafucil (talk) 23:02, 27 July 2021 (UTC)

Jumping Images
Even with autoplay disabled, the list of example modes jumps about as the page loads in Firefox. 138.88.18.245 (talk) 21:36, 22 November 2021 (UTC)
 * This behaviour happens when a page has both sound output from  and from mw:Extension:TimedMediaHandler. There's a discussion at T245377. A resolution might be some time off. -- Michael Bednarek (talk) 01:34, 23 November 2021 (UTC)

title: Talk:Mode (music)


text:
Eddie Blazonczyk

Eddie Blazonczyk, Sr. (July 12, 1941 – May 21, 2012) was an American polka musician and founder of the band The Versatones. He was inducted into the International Polka Hall of Fame in 1970, and was a 1998 National Heritage Fellowship recipient. He has been called "one of the most important figures in the creation of the contemporary Polish-American polka sound." He released more than 60 albums.

History
Eddie Blazonczyk was born in Chicago, Illinois, to Polish immigrant parents of Goral heritage.

Before becoming a polka artist, and founding Chicago-based Bel-Aire Records in 1963, Eddie Blazonczyk recorded under the name Eddy Bell for Mercury Records, Versa Records, and Lucky Four Records, all three labels based in Chicago. During this period Blazonczyk toured with Buddy Holly, Gene Vincent and Brenda Lee. The records he made for these labels were rockabilly sides, and novelty songs. "The Great Great Pumpkin", released on Lucky Four #1012, is probably the most noteworthy of these recordings. This recording is still occasionally heard around Halloween and is highly sought by record collectors. Lenny LaCour, the owner of Lucky Four Records, encouraged Blazonczyk, at the age of 22, to specialize in polka music, rather than to continue as a rockabilly singer. Blazonczyk has said, "I took his advice, and never regretted it."

He is credited with inventing the rhythmic polka subgenre known as "Chicago push," although ironically the name given to the style comes from bands who came after and were inspired by Blazonczyk, notably the Chicago Push. Musicologist Norm Cohen wrote that "in his illustrious career, Blazonczyk and his Versatones were the primary ambassadors of Polish-American polka, touring constantly and playing well over 200 road gigs per year."

The Versatones played a mix of both traditional and original tunes, with Blazonczyk singing in both Polish and English. The band consisted of a fiddler and concertina player, two trumpeter/clarinetists, a drummer and Blazonczyk himself on vocals and electric bass. Though his focus remained on the polka genre, Blazonczyk was a fan of rock, country, bluegrass and Cajun music and liked to incorporate those styles into his music when he felt it was appropriate.

Blazonczyk retired from performing in 2002. At that time, he turned over responsibility for his band, The Versatones, to his son, Eddie Blazonczyk Jr. The Versatones played their last performance on New Year's Eve, 2011.

Death
Blazonczyk died of multiple organ dysfunction syndrome on May 21, 2012.

Awards and honors
Blazonczyk was nominated for 11 Grammy Awards, and his album Another Polka Celebration won the 1986 Grammy for Best Polka Recording. He was a recipient of the 1998 National Heritage Fellowship awarded by the National Endowment for the Arts, which is the highest honor in the folk and traditional arts in the United States.

Discography

 * Live and Kickin'  2001
 * Another Day At The Office 2000
 * Smokin' Polkas	 	1999
 * Shakin' not Stirred	 	1998
 * Holiday Favorites 	 1997
 * Greatest Hits-Vol 2 	 	1997
 * Music, Music, Music	 	1996
 * Polkatime-20 Of The Greatest Hits	 	1996
 * Better Than Ever 	 	1995
 * Always, Forever And A Day	 1994
 * A New Batch Of Polkas 	1993
 * All American Polkas 	 1992
 * All Around The World	 1991
 * Everybody Polka 	 1990
 * Good Ol' Days 1989
 * 25th Anniversary Album	 1988
 * Let's Celebrate Again	 1987
 * Another Polka Celebration 1985   (1986 Grammy Winner)
 * Polka Fireworks	 1984
 * Polka Thriller 	 1983
 * Custom Made Polkas	 1982
 * Polka Medley Album	 1982
 * Polka Music's Here To Stay 	 1981
 * Polka Festival 	 1981
 * Hawaiian Polka Tour 	 1980
 * Polka Cruise 	 1980
 * More Honky Style Polkas Vol 3	 1979
 * Roaring Polkas	 1978
 * Wide World Of Polkas 	 1977
 * Award Winning Polkas	 	1977
 * Polka Jamboree	 	1976
 * We Were Made For Each Other	 	1976
 * Polka Spotlite 	 1976
 * A Polka Christmas	 1975
 * Polka Concert 	 1975
 * More Honky Style Polkas Vol 2 	 1974
 * More Country Flavored Polkas Vol 2	 	1974
 * Polka Hits	 1973
 * Langer Sisters Meet Eddie Blazonczyk's Versatones 	 	1972
 * Country Flavored Polkas	 1972
 * Honkey Style Polkas 	 1971
 * Polka Music Hall Of Fame 	 1971
 * Something A Little Bit Different 	 1970
 * America's Most Wanted Polka Band	 1969
 * Polkas A Plenty	 1969
 * Poland European Tour 1968
 * Let's Hear A Polka	 1967
 * Polish Party 	 1967
 * Christmas Time 	 1966
 * Happy Polka Music 	 1966
 * Po Staro Krajsku- Old Country Style Vol 2 	 1966
 * Polka Tour 	 1965
 * Musically Yours 	 1965
 * Po Staro Krajsku- Old Country Style	 1964
 * Something New Just For You 	 1964
 * Here Come The Versatones	 1963
 * Polka Parade 	 1963

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Eddie Blazonczyk


text:
Frankie Yankovic

Frank John Yankovic (July 28, 1915 – October 14, 1998) was an American accordion player and polka musician. Known as "America's Polka King", Yankovic was considered the premier artist to play in the Slovenian style during his long career. He was not related to fellow accordionist "Weird Al" Yankovic, although the two collaborated.

Background
Yankovic was born in Davis (West Virginia) to Slovene immigrant parents: Andrew Yankovic (Andrej Jankovič, 1879–1949) from Kal and Rose T. Yankovic (née Terezija Mele, 1886–1968) from Cerknica, who married in 1910. Yankovic was raised in the Collinwood neighborhood on Cleveland's East Side. He recorded over 200 songs and sold over 30 million records in his career. In 1986, he was awarded the first-ever Grammy in the Best Polka Recording category. He rarely strayed from Slovenian-style polka, but did record with country guitarist Chet Atkins and pop singer Don Everly. He also recorded a version of the "Too Fat Polka" with comedian Drew Carey.

History
Yankovic's father, a blacksmith, and his mother, a cook, met in a lumber camp in West Virginia where they both worked. When Yankovic was young, his father moved to Cleveland to escape authorities who learned of his bootlegging, and the rest of the family followed shortly thereafter. While living in Cleveland, he became enthralled by the brass bands that played at Slovenian social functions. His mother took on boarders to help with the family finances, including a man named Max Zelodec who performed Slovenian tunes on a button box. Yankovic acquired an accordion at age 9, and received a few lessons from Zelodec. By the late 1920s, in his early teenage years, he was a working musician, playing for community events. In the 1930s, he formed a business relationship with Joe Trolli and began making radio appearances on stations such as WJAY and WGAR. As his reputation spread, he sought opportunities to make records, but the major labels turned him down. His first records were made for the Yankee and Joliet labels operated by Fred Wolf, and the expenses were paid for by Yankovic himself.

In 1940, he married his first wife June, and they began to raise a family. However, the expenses of family life quickly overcame the incoming money from his music career, so he opened a tavern, calling it the Yankovic Bar. It became a popular hangout for local musicians, and he continued to run it until he sold it in 1948, dedicating himself to the accordion.

Yankovic enlisted in the armed forces in 1943 and cut numerous records while on leave, prior to his departure for Europe. Yankovic was assigned duty in 1943 in the infantry as a flame-thrower operator. He fought in the Battle of the Bulge where a severe case of frostbite nearly required the amputation of his hands and feet. Fortunately, he was able to beat the resulting gangrene before that became necessary, and was awarded a Purple Heart. The doctors urged him to have his fingers amputated, but he refused, as that would have ended his music career. After getting out of the hospital, he and four other musicians were assigned to special services to entertain the troops, including General George Patton and his Third United States Army.

Yankovic hit the national scene when he earned two platinum singles for "Just Because" (1947) and "Blue Skirt Waltz" (1949). Others who recorded the Blue Skirt Waltz were the Tunemixers and Guy Lombardo both in 1949, Lawrence Welk (Myron Floren) in 1958, Jim Ed Brown and the Browns in 1960, Hank Thompson in 1962, and Bobby Vinton in 1976. Yankovic found a Bohemian Waltz called "Cervenou Sukynku," (written by Vaclav Blaha) or loosely translated, "Red Skirt Waltz." Yankovic asked Mitchell Parrish ("Stardust", "Sleighride") to write new lyrics to the melody. Parrish changed "red" to "blue". Yankovic sold over 2.5 million records and with the Tunemixers version and Guy Lombardo's version, it sold over 4 million records total in 1949. It was the second Cleveland-style song to sell over one million recordings. Columbia Records initially refused to record "Just Because", because other versions of the song had been around for years without much success; only allowing it when Yankovic said that he would buy the first 10,000 records. Yankovic obtained the title of America's Polka King after beating Louis Bashell, Romy Gosz, Harold Loeffelmacher and the Six Fat Dutchmen, Whoopee John Wilfahrt, and Lawrence Duchow in a battle of the bands in Milwaukee at the Milwaukee Arena on June 9, 1948.

In 1950, he made his Hollywood debut and collaborated with Doris Day as a singer.

In 1970, a house fire destroyed the gold records for "Just Because" and "Blue Skirt Waltz".

Yankovic also hosted the television series Polka Time for Buffalo, New York-based WKBW-TV for 26 weeks in 1962. He commuted from Cleveland to host each episode, which aired live. He also hosted a similar show at WGN-TV Chicago at about the same time.

He won a Grammy Award in 1986 for his album 70 Years of Hits. He was the first winner in the Polka category. The NARAS (Grammy) organization dropped the category in 2008.

He performed with musical comedian and fellow accordionist "Weird Al" Yankovic, although the two are not related. Al, who also performs polka music among many other styles, has jokingly hypothesized that he was given accordion lessons as a child because his parents thought that "there should be at least one more accordion-playing Yankovic in the world." Al performed accordion on "Who Stole the Kishka?" on one of Frankie's final records, Songs of the Polka King, Vol. 1. A portion of Frankie's "The Tick Tock Polka" is included in the song "Polka Face" on Weird Al's Alpocalypse; it was used as a lead-in for Weird Al's take on "Tik Tok" by Ke$ha.

Death
Yankovic died on October 14, 1998, in New Port Richey, Florida, from heart failure, at the age of 83. He is buried in Cleveland's Calvary Cemetery. Hundreds of friends, family, his loyal fans and fellow musicians attended his memorial service. At his peak, Yankovic traveled extensively and performed 325 shows a year. He sold 30 million records during his lifetime.

Honors
Frankie Yankovich visited Cerknica, the hometown of his parents, in 1952 or 1953 and again in 1995. On the second occasion, a special reception was organized in his honor in Rakov Škocjan. He was presented with a commemorative certificate in recognition of his significant contributions to promoting Slovene culture worldwide. Additionally, he received an oil painting by the academic painter Tomaž Perko to remember his time in Cerknica.

In Bob Dolgan's 2006 biography of Yankovic, Frankie's longtime drummer Dave Wolnik observed that "Yankovic didn't have a street named for him in his own hometown". This launched a campaign by the National Cleveland-Style Polka Hall of Fame and Museum and City Councilman Michael Polensek, and in a ceremony on August 21, 2007, the square at the intersection of Waterloo Rd. and East 152nd St. in Cleveland (41.569°N, -81.5752°W), not far from where Yankovic grew up, was named in his honor.

Former band members

 * Denny Boneck (Milwaukee, Wisconsin), stand-up bass and back-up vocals. Played, toured and recorded with Frank as one of the "Yanks" from 1970 to 1981.
 * Joseph A. Godec (upright 3/4 bass) and Frank Godec (guitar) toured Ely and range 1940-44 and 1951.
 * Johnny Pecon - Button Box and Piano Accordion with the original "Frankie Yankovic and His Yanks" from 1946 through 1949.
 * Henry "Hank The Yank" Bokal - Drummer with the original "Frankie Yankovic and His Yanks" from 1941 through 1949.
 * Anthony "Tops" Cardone was a member of the popular Yankovic Show band that toured in the early 1950s, playing in Hollywood, Las Vegas, and top nightclubs in the United States. Tops played second accordion with Frank's band.
 * Georgie Cook - Banjo player, who helped Yankovic establish the "Cleveland Sound".
 * Joey Miskulin - Began playing with Yankovic in 1962 at the age of 13. This was the start of a relationship that lasted for the next 35 years. Joey developed his skill with the accordion and music while touring with the band. Joey began writing and arranging songs for Yankovic, eventually arranging and producing some of Yankovic's albums, including the Grammy Award-winning album "70 Years of Hits".
 * Jeff Winard - Accomplished accordionist from Milwaukee; traveled with Yankovic in later years.
 * Rod Verette - played bass on Yankovic's west coast tour in late '80s.
 * Marian "Lefty" Bell - played bass with Yankovic.
 * Steve Kucenski - played 2nd accordion in the late 70s to early 90s.
 * Adolph "Church" Srnick - long time bass player with Yankovic. Played the stand up 3/4 bass and also the "baby" electric bass from 1945 until he died in 1968
 * Eddie "Teener" - played banjo with Yankovic off and on from 1953 until his death in 1970. Co-wrote with Yankovic on "Happy Polka", which was originally written as a commercial for the TV show.

title: Frankie Yankovic


text:
Talk:Idiolect

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This article was the subject of a Wiki Education Foundation-supported course assignment, between 26 January 2021 and 19 May 2021. Further details are available on the course page. Student editor(s): Garzaju. Peer reviewers: Vivmm13, Leilakinson, Anthro Lover, Jessemerodio.

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Wiki Education Foundation-supported course assignment
This article was the subject of a Wiki Education Foundation-supported course assignment, between 21 January 2020 and 4 May 2020. Further details are available on the course page. Student editor(s): Hjw38, Manar.m2733, Jas1075, Yomna1013, VeronicaCard.

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Dictionary entry/stub
This is a dictionary entry which does not belong here. I am adding it to the list of pages to be deleted.

 * I think of it as more of a stub...

Oi, i think that this really is to do with wibbilance!

Multi-lingual?
What if somebody speaks several languages? Are they different idiolects or are they one idiolect? -- Error
 * I'd guess several, but I think multilingualism and code-switching generally could complicate matters a lot. 惑乱 分からん 14:37, 10 February 2006 (UTC)

Che Guevara
To my knowledge, Che Guevara's use of "Che" is not an idiolect, but rather Argentine slang. Or was there more to it? --Bletch 19:17, 8 August 2005 (UTC)

I also understood that Che Guevara's name originated from Argentine slang, and is a word for 'hey' but became a nickname used by other South American nationalities for Argentinians because they said it so much. That last part might just be legend... -- Danceparadox 13:40, 12 December 2005

I'm confused
The article che explains that it is an expression common to many countries of South America. But it also refers to Guevara's use of the word as part of his idiolect. However, the definition of idiolect we read in this article is: "An idiolect is a variety of a language unique to an individual." To me, it seems that the use of "che" by Guevara denotes only his dialect, which is defined as "a variety of a language used by people from a particular geographic area."

Revision - July 2009
I have revised the section Idiolect and language to bring it closer to the understanding of the relationship between idiolect and language in linguistics. This is not my primary area of expertise, though, so attention from other linguists or students of linguistics is welcome. I've also tried to remove some of the more technical jargon, but if the article is still too technical, say so. Cnilep (talk) 21:11, 8 July 2009 (UTC)

What is special about North Americans?
IP user 71.111.229.19 added a clarify tag to the assertion, "This view contrasts with a common view among non-linguists, especially in North America...." His/Her edit summary asked, "what is special about north americans? what do other people believe about language?" [sic] She/He then rewrote the sentence as follows: "According to research done in the United States, this contrasts with a common view..." etc.

The rewrite refers to the place where the research was done. I think the real issue (at least, the one I had in mind when I wrote that sentence in 2009), though, is that the researchers studied attitudes of English speakers in North America, primarily in Ypsilanti, Michigan, near Eastern Michigan University. To suggest that this view is true of all non-linguists or all English speakers is to go beyond the claims of the source material. Highlighting the place where the research is done is slightly better, but I'm not sure it quite reaches the actual issue.

I suspect the editor objected to the apparent neglect of language attitudes outside of North America, but I'm not quite sure if that is the extent of the problem. Perhaps the editor could clarify the clarify, so to speak? Cnilep (talk) 19:59, 17 May 2010 (UTC)

 * For the sake of discussion, here is an attempted rewrite of the problematic paragraph. Does this seem acceptable?

"This contrasts with a view among non-linguists that languages as ideal systems exist outside the actual practice of language users. Based on work done in the United States, Nancy Niedzielski and Dennis Preston describe a language ideology that appears to be common among American English speakers. According to Niedzielski and Preston, many of their subjects believe that there is one 'correct' pattern of grammar and vocabulary that underlies Standard English, and that individual usage derives from this external system."
 * Cnilep (talk) 20:26, 17 May 2010 (UTC)
 * Cnilep, first off, thanks for being so sensitive to my concerns and polite/professional in your communication. I heartily embrace your re-write above and endorse it for placement in the main article. I just have one question, should the sentence, "This contrasts with a view among non-linguists that languages as ideal systems exist outside the actual practice of language users" be rewritten as This contrasts with a view among non-linguists, at least in the United States, that languages as ideal systems exist outside the actual practice of language users? Thanks so much--71.111.229.19 (talk) 21:20, 17 May 2010 (UTC)
 * I think that's an excellent suggestion. I'll revise the article accordingly. Cnilep (talk) 21:51, 17 May 2010 (UTC)

Disambiguation with "Eye Dialect" near intro?
I think it's odd that neither Wikipedia for Idiolect nor Eye Dialect comment on the other. Is this needed? ButterSoda (talk) 03:21, 3 March 2011 (UTC)

 * It's not obvious to me why you think the two pages need to comment on one another. The concepts are not closely related. Idiolect is (a theoretical model of) an individual's language ability, especially the ability to speak or sign, or an individual's pattern of language output. Eye dialect is a literary technique for representing non-standard dialects via non-standard spelling. Cnilep (talk) 04:35, 3 March 2011 (UTC)

 * To me it's obvious that ButterSoda is referring to a possible confusion of /aɪˈdaɪəlɛkt/ and /ˈɪdiəlɛkt/. Fridek (talk) 19:21, 8 July 2013 (UTC)

First Paragraph Issues
This is a suggested edit to help this article as per the following:

 * Manual_of_Style, " Plain English works best; avoid ambiguity, jargon, and vague or unnecessarily complex wording."
 * Writing_better_articles, "The opening paragraph summarizes the most important points of the article..."
 * Manual_of_Style, "Avoid excessive wikilinking (linking within Wikipedia) as a substitute for parenthetic explanations such as the one in this sentence.  Do not introduce new and specialized words simply to teach them to the reader when more common alternatives will do."

The first couple sentences are too wordy, such as "as manifested by the patterns of", so that text was tightened as copyediting.

The entire second sentence referring to language production moves away from the fundamental concept of an idiolect as a concept of observable phenomena... it moves in an oblique direction towards uncertain and debatable "underlying" language processes. This line is off track for a lead-paragraph-summary of a simple concept. This concept is not addressed more in-depth in the article, so while it might be suitable to discuss, it is not suitable for the lead paragraph. It would be more fundamental to the term "idiolect", for example, to introduce that the meaning of it refers to a spectrum of meaning: as a self-contained totality of an individual's language or as a differential relative to the person's dialect. Or that it's usefulness as a term is itself questionable. These ideas could then be expanded in the article.

Per the reference to Variety_(linguistics). As per above, this is wikilinking as a substitute for a specialized definition which a general audience member would not be familiar with. It's too easy for a general audience to confuse this term with standard english. Furthermore, as a lead paragraph which summarizes a topic, the concept of "variety" should be expanded in the main article but it is not. I kept "variety" in article, but it could arguably be put back into the lead paragraph.

Finally, describing "linguists disagree.." or "mathematicians disagree..." is often a misrepresentation. Scratch any concept and surely one will eventually find disagreement. But is it disagreement or more like different perspectives, as in Variety_(linguistics):
 * Scholars "disagree" on the definition of idiolect. OR
 * For scholars who view language from the perspective of linguistic competence, essentially the knowledge of language and grammar that exists in the mind of an individual language user, the idiolect is a way of referring to this specific knowledge. For scholars who regard language as a shared social practice, idiolect is more like a dialect with a speech community of one individual

The article still needs some work, for sure. I hope these changes can be seen not as an absolute final, but rather as a step in a good direction toward some stylistic and content ideas for balancing the first paragraph with the rest of the text. — Preceding unsigned comment added by CoolHandLouis (talk • contribs) 18:44, 11 March 2014

 * (, you may want to check out BOLD, revert, discuss cycle. In a nutshell: if another editor reverts your additions, do not re-add them until discussion on the talk page reaches some consensus. The text you added at 18:32 on 11 March was the exact same text that I removed at 5:43. Oh, and please sign your talk page comments by typing ~ .)

 * To the substance: I agree with the main point suggested, that the article needs work and the descriptions should be made more easily understandable. This is, after all, an encyclopedia for general readers, not a text for students of linguistics. That said, the changes suggested some things that, I think, are inconsistent with general consensus or state of the art in linguistics. For example, the prose suggested that an individual as "a dialect" and (separately?) "an idiolect". That is simply not correct. (It also said that dialects are either regional or class-based, ignoring sociolinguistic studies of age, gender, ethnicity, or other variables, but that's a bit beyond the scope of this discussion.)

 * The article is at present incomplete. A better way forward may be to seek out treatments of idiolect in tertiary sources such as text books and to summarize those facts in the body of the article. Then the lead section could be written to summarize the information in the article's sections. It is important for a good article to be readable, certainly, but also factually accurate, broad in coverage, and verifiable in all specifics. Cnilep (talk) 23:46, 11 March 2014 (UTC)

title: Talk:Idiolect


text:
Whigs (British political party)

The Whigs were a political party in the Parliaments of England, Scotland, Ireland, Great Britain and the United Kingdom. Between the 1680s and the 1850s, the Whigs contested power with their rivals, the Tories. The Whigs became the Liberal Party when it merged with the Peelites and Radicals in the 1850s. Many Whigs left the Liberal Party in 1886 over the issue of Irish Home Rule to form the Liberal Unionist Party, which merged into the Conservative Party in 1912.

The Whigs began as a political faction that opposed absolute monarchy and Catholic emancipation, supporting constitutional monarchism and parliamentary government, but also Protestant supremacy. They played a central role in the Glorious Revolution of 1688 and were the standing enemies of the Roman Catholic Stuart kings and pretenders. The period known as the Whig Supremacy (1714–1760) was enabled by the Hanoverian succession of George I in 1714 and the failure of the Jacobite rising of 1715 by Tory rebels. The Whigs took full control of the government in 1715 and thoroughly purged the Tories from all major positions in government, the army, the Church of England, the legal profession, and local political offices. The first great leader of the Whigs was Robert Walpole, who maintained control of the government from 1721 to 1742, and whose protégé, Henry Pelham, led the government from 1743 to 1754. Great Britain approximated a one-party state under the Whigs until King George III came to the throne in 1760 and allowed Tories back in. But the Whig Party's hold on power remained strong for many years thereafter. Thus historians have called the period from roughly 1714 to 1783 the "long period of Whig oligarchy". During the American Revolution, the Whigs were the party more sympathetic to American independence and the creation of a democracy in the United States.

By 1784, both the Whigs and Tories had become formal political parties, with Charles James Fox becoming the leader of a reorganized Whig Party arrayed against William Pitt the Younger's new Tories. The foundation of both parties depended more on the support of wealthy politicians than on popular votes. Although there were elections to the House of Commons, only a few men controlled most of the voters.

Both parties slowly evolved during the 18th century. In the beginning, the Whig Party generally tended to support the aristocratic families, the continued disenfranchisement of Catholics and toleration of nonconformist Protestants (dissenters such as the Presbyterians), while the Tories generally favoured the minor gentry and people who were (relatively speaking) smallholders; they also supported the legitimacy of a strongly established Church of England. (The so-called High Tories preferred high church Anglicanism, or Anglo-Catholicism. Some, particularly adherents of the non-juring schism, openly or covertly supported the exiled House of Stuart's claim to the throne—a position known as Jacobitism.) Later, the Whigs came to draw support from the emerging industrial reformists and the mercantile class while the Tories came to draw support from farmers, landowners, royalists and (relatedly) those who favoured imperial military spending.

By the first half of the 19th century, the Whig manifesto had come to encompass the supremacy of parliament, the abolition of slavery, the expansion of the franchise (suffrage) and an acceleration of the move toward complete equal rights for Catholics (a reversal of the party's late-17th-century position, which had been militantly anti-Catholic).

Name
The Whigs were originally referred to as the Country Party and even earlier as "Roundheads".

The term Whig began as a short form of whiggamore, a term originally used by people in the north of England to refer to (cattle) drovers from western Scotland who came to Leith to buy corn (the Scottish cattle drivers would call out "Chuig" or "Chuig an bothar"—meaning "away" or "to the road"—this sounded to the English like "Whig", and they came to use the word "Whig" or "Whiggamore" derisively to refer to these people). During the English Civil Wars, when Charles I reigned, the term "Whig" was picked up and used by the English to refer derisively to a radical faction of the Scottish Covenanters who called themselves the Kirk Party (see the Whiggamore Raid). It was later applied to Scottish Presbyterian rebels who were against the king's Episcopalian order in Scotland.

The word Whig entered English political discourse during the Exclusion Bill crisis of 1679–1681: there was controversy about whether King Charles II's brother, James, Duke of York, should be allowed to succeed to the throne on Charles's death, and Whig became a term of abuse for members of the Country Party, which sought to remove James from the line of succession on the grounds that he was a Roman Catholic (Samuel Johnson, a fervent Tory, often joked that "the first Whig was the Devil".).

Eventually, Country Party politicians themselves would start describing their own faction as the "Whigs".

In his six-volume history of England, c. 1760, David Hume wrote: "The court party reproached their antagonists with their affinity to the fanatical conventiclers in Scotland, who were known by the name of Whigs: The country party found a resemblance between the courtiers and the popish banditti in Ireland, to whom the appellation of Tory was affixed. And after this manner, these foolish terms of reproach came into public and general use; and even at present seem not nearer their end than when they were first invented."

The parliamentarian faction
The precursor to the Whigs was Denzil Holles' parliamentarian faction, which was characterised by its opposition to absolute monarchism.

Exclusion Crisis
Under Lord Shaftesbury's leadership, the Whigs (also known as the Country Party) sought to exclude the Duke of York (who later became King James II) from the throne due to his Roman Catholicism, his favouring of monarchical absolutism, and his connections to France. They believed the heir presumptive, if allowed to inherit the throne, would endanger the Protestant religion, liberty and property.

The first Exclusion Bill was supported by a substantial majority on its second reading in May 1679. In response, King Charles prorogued Parliament and then dissolved it, but the subsequent elections in August and September saw the Whigs' strength increase. This new parliament did not meet for thirteen months, because Charles wanted to give passions a chance to die down. When it met in October 1680, an Exclusion Bill was introduced and passed in the Commons without major resistance, but was rejected in the Lords. Charles dissolved Parliament in January 1681, but the Whigs did not suffer serious losses in the ensuing election. The next Parliament first met in March at Oxford, but Charles dissolved it after only a few days, when he made an appeal to the country against the Whigs and determined to rule without Parliament. In February, Charles had made a deal with the French King Louis XIV, who promised to support him against the Whigs. Without Parliament, the Whigs gradually crumbled, mainly due to government repression following the discovery of the Rye House Plot. The Whig peers, the Earl of Melville, the Earl of Leven, and Lord Shaftesbury, and Charles II's illegitimate son the Duke of Monmouth, being implicated, fled to and regrouped in the United Provinces. Algernon Sidney, Sir Thomas Armstrong and William Russell, Lord Russell, were executed for treason. The Earl of Essex committed suicide in the Tower of London over his arrest for treason, whilst Lord Grey of Werke escaped from the Tower.

Glorious Revolution
After the Glorious Revolution of 1688, Queen Mary II and King William III governed with both Whigs and Tories, despite the fact that many of the Tories still supported the deposed Roman Catholic James II. William saw that the Tories were generally friendlier to royal authority than the Whigs and he employed both groups in his government. His early ministry was largely Tory, but gradually the government came to be dominated by the so-called Junto Whigs, a group of younger Whig politicians who led a tightly organised political grouping. The increasing dominance of the Junto led to a split among the Whigs, with the so-called Country Whigs seeing the Junto as betraying their principles for office. The Country Whigs, led by Robert Harley, gradually merged with the Tory opposition in the later 1690s.

18th century
Although William's successor Anne had considerable Tory sympathies and excluded the Junto Whigs from power, after a brief and unsuccessful experiment with an exclusively Tory government she generally continued William's policy of balancing the parties, supported by her moderate Tory ministers, the Duke of Marlborough and Lord Godolphin. However, as the War of the Spanish Succession went on and became less and less popular with the Tories, Marlborough and Godolphin were forced to rely more and more on the Junto Whigs, so that by 1708 they headed an administration of the Parliament of Great Britain dominated by the Junto. Anne herself grew increasingly uncomfortable with this dependence on the Whigs, especially as her personal relationship with the Duchess of Marlborough deteriorated. This situation also became increasingly uncomfortable to many of the non-Junto Whigs, led by the Duke of Somerset and the Duke of Shrewsbury, who began to intrigue with Robert Harley's Tories. In the spring of 1710, Anne dismissed Godolphin and the Junto ministers, replacing them with Tories.

The Whigs now moved into opposition and particularly decried the 1713 Treaty of Utrecht, which they attempted to block through their majority in the House of Lords. The Tory administration led by Harley and the Viscount Bolingbroke persuaded the Queen to create twelve new Tory peers to force the treaty through.

Liberal ideals
The Whigs primarily advocated the supremacy of Parliament, while calling for toleration for Protestant dissenters. They adamantly opposed a Catholic as king. They opposed the Catholic Church because they saw it as a threat to liberty, or as Pitt the Elder stated: "The errors of Rome are rank idolatry, a subversion of all civil as well as religious liberty, and the utter disgrace of reason and of human nature".

Ashcraft and Goldsmith (1983) have traced in detail, in the period 1689 to 1710, the major influence of the liberal political ideas of John Locke on Whig political values, as expressed in widely cited manifestos such as "Political Aphorisms: or, the True Maxims of Government Displayed", an anonymous pamphlet that appeared in 1690 and was widely cited by Whigs. The 18th-century Whigs borrowed the concepts and language of universal rights employed by political theorists Locke and Algernon Sidney (1622–1682). By the 1770s the ideas of Adam Smith, a founder of classical liberalism became important. As Wilson and Reill (2004) note: "Adam Smith's theory melded nicely with the liberal political stance of the Whig Party and its middle-class constituents".

Samuel Johnson (1709–1784), a leading London intellectual, repeatedly denigrated the "vile" Whigs and praised the Tories, even during times of Whig political supremacy. In his great Dictionary (1755), Johnson defined a Tory as "one who adheres to the ancient Constitution of the state and the apostolical hierarchy of the Church of England, opposed to a Whig". He linked 18th-century Whiggism with 17th-century revolutionary Puritanism, arguing that the Whigs of his day were similarly inimical to the established order of church and state. Johnson recommended that strict uniformity in religious externals was the best antidote to the objectionable religious traits that he linked to Whiggism.

Protectionism
At their inception, the Whigs were protectionist in economic policy, with free trade policies being advocated by Tories. The Whigs were opposed to the pro-French policies of the Stuart kings Charles II and James II as they believed that such an alliance with the Catholic absolute monarchy of France endangered liberty and Protestantism. The Whigs claimed that trade with France was bad for England and developed an economic theory of overbalance, that is a deficit of trade with France was bad because it would enrich France at England's expense.

In 1678, the Whigs passed the Prohibition of 1678 that banned certain French goods from being imported into England. The economic historian William Ashley claimed that this Act witnessed the "real starting-point in the history of Whig policy in the matter of trade". It was repealed upon the accession of James II by a Tory-dominated House of Commons but upon the accession of William III in 1688 a new Act was passed that prohibited the importation of French goods. In 1704, the Whigs passed the Trade with France Act that renewed protectionism against France. In 1710, Queen Anne appointed the predominantly Tory Harley Ministry, which favoured free trade. When the Tory minister Lord Bolingbroke proposed a commercial treaty with France in 1713 that would have led to freer trade, the Whigs were vehemently against it and it had to be abandoned.

In 1786, Pitt's government negotiated the Eden Agreement, a commercial treaty with France which led to freer trade between the two countries. All of the Whig leaders attacked this on traditional Whig anti-French and protectionist grounds. Fox claimed that France was England's natural enemy and that it was only at Britain's expense that she could grow. Edmund Burke, Richard Sheridan, William Windham and Charles Grey all spoke out against the trade agreement on the same grounds.

Ashley claimed that "[t]he traditional policy of the Whig party from before the Revolution [of 1688] down to the time of Fox was an extreme form of Protectionism". The Whigs' protectionism of this period is today increasingly cited with approval by heterodox economists such as Ha-Joon Chang, who wish to challenge contemporary prevailing free trade orthodoxies via precedents from the past.

Later on, several members from the Whig party came to oppose the protectionism of the Corn Laws, but trade restrictions were not repealed even after the Whigs returned to power in the 1830s.

Whig Supremacy
With the succession of Elector George Louis of Hanover as king in 1714, the Whigs returned to government with the support of some Hanoverian Tories. The Jacobite rising of 1715 discredited much of the Tory party as treasonous Jacobites, and the Septennial Act ensured that the Whigs became the dominant party, establishing the Whig oligarchy. Between 1717 and 1720 the Whig Split led to a division in the party. Government Whigs led by the former soldier James Stanhope were opposed by Robert Walpole and his allies. While Stanhope was backed by George I, Walpole and his supporters were closer to the Prince of Wales. Following his success in defeating the government over the Peerage Bill in 1719, Walpole was invited back into government the following year. He was able to defend the government in the Commons when the South Sea Bubble collapsed. When Stanhope died unexpectedly in 1721, Walpole replaced him as leader of the government and became known as the first Prime Minister. In the 1722 general election the Whigs swept to a decisive victory.

Between 1714 and 1760, the Tories struggled as an active political force, but always retained a considerable presence in the House of Commons. The governments of Walpole, Henry Pelham and his older brother the Duke of Newcastle dominated between 1721 and 1757 (with a brief break during the also-Whig Carteret ministry). The leading entities in these governments consistently referred to themselves as "Whigs".

George III's accession
This arrangement changed during the reign of George III, who hoped to restore his own power by freeing himself from the great Whig magnates. Thus George promoted his old tutor Lord Bute to power and broke with the old Whig leadership surrounding the Duke of Newcastle. After a decade of factional chaos, with distinct Bedfordite, Chathamite, Grenvillite and Rockinghamite factions successively in power and all referring to themselves as "Whigs", a new system emerged with two separate opposition groups. The Rockingham Whigs claimed the mantle of Old Whigs as the purported successors of the party of the Pelhams and the great Whig families. With such noted intellectuals as Edmund Burke behind them, the Rockingham Whigs laid out a philosophy which for the first time extolled the virtues of faction, or at least their faction. The other group were the followers of Lord Chatham, who as the great political hero of the Seven Years' War generally took a stance of opposition to party and faction.

The Whigs were opposed by the government of Lord North which they accused of being a Tory administration. While it largely consisted of individuals previously associated with the Whigs, many old Pelhamites as well as the Bedfordite Whig faction formerly led by the Duke of Bedford and elements of that which had been led by George Grenville, it also contained elements of the Kings' Men, the group formerly associated with Lord Bute and which was generally seen as Tory-leaning.

American impact
The association of Toryism with Lord North's government was also influential in the American colonies and writings of British political commentators known as the Radical Whigs did much to stimulate colonial republican sentiment. Early activists in the colonies called themselves Whigs, seeing themselves as in alliance with the political opposition in Britain, until they turned to independence and started emphasising the label Patriots. In contrast, the American Loyalists, who supported the monarchy, were consistently also referred to as Tories.

Later, the United States Whig Party was founded in 1833 on the basis of opposition to a strong presidency, initially the presidency of Andrew Jackson, analogous to the British Whig opposition to a strong monarchy. The True Whig Party, which for a century dominated Liberia, was named for the American party rather than directly for the British one.

Two-party system
Dickinson reports the following: "All historians are agreed that the Tory party declined sharply in the late 1740s and 1750s and that it ceased to be an organized party by 1760. The research of Sir Lewis Namier and his disciples [...] has convinced all historians that there were no organized political parties in Parliament between the late 1750s and the early 1780s. Even the Whigs ceased to be an identifiable party, and Parliament was dominated by competing political connections, which all proclaimed Whiggish political views, or by independent backbenchers unattached to any particular group."

The North administration left power in March 1782 following the American Revolution and a coalition of the Rockingham Whigs and the former Chathamites, now led by the Earl of Shelburne, took its place. After Rockingham's unexpected death in July 1782, this uneasy coalition fell apart, with Charles James Fox, Rockingham's successor as faction leader, quarrelling with Shelburne and withdrawing his supporters from the government. The following Shelburne administration was short-lived and Fox returned to power in April 1783, this time in an unexpected coalition with his old enemy Lord North. Although this pairing seemed unnatural to many at the time, it was to last beyond the demise of the coalition in December 1783. The coalition's untimely fall was brought about by George III in league with the House of Lords and the King now brought in Chatham's son William Pitt the Younger as his prime minister.

It was only now that a genuine two-party system can be seen to emerge, with Pitt and the government on the one side, and the ousted Fox-North coalition on the other. On 17 December 1783, Fox stated in the House of Commons that "[i]f [...] a change must take place, and a new ministry is to be formed and supported, not by the confidence of this House or the public, but the sole authority of the Crown, I, for one, shall not envy that hon. gentleman his situation. From that moment I put in my claim for a monopoly of Whig principles". Although Pitt is often referred to as a Tory and Fox as a Whig, Pitt always considered himself to be an independent Whig and generally opposed the development of a strict partisan political system. Fox's supporters saw themselves as legitimate heirs of the Whig tradition and they strongly opposed Pitt in his early years in office, notably during the regency crisis revolving around the King's temporary insanity in 1788–1789, when Fox and his allies supported full powers as regent for their ally, the Prince of Wales.

The opposition Whigs were split by the onset of the French Revolution. While Fox and some younger members of the party such as Charles Grey and Richard Brinsley Sheridan were sympathetic to the French revolutionaries, others led by Edmund Burke were strongly opposed. Although Burke himself was largely alone in defecting to Pitt in 1791, much of the rest of the party, including the influential House of Lords leader the Duke of Portland, Rockingham's nephew Lord Fitzwilliam and William Windham, were increasingly uncomfortable with the flirtations of Fox and his allies with radicalism and the French Revolution. They split in early 1793 with Fox over the question of support for the war with France and by the end of the year they had openly broken with Fox. By the summer of the next year, large portions of the opposition had defected and joined Pitt's government.

19th century
Many of the Whigs who had joined with Pitt would eventually return to the fold, joining again with Fox in the Ministry of All the Talents following Pitt's death in 1806. The followers of Pitt—led until 1809 by Fox's old colleague the Duke of Portland—rejected the label of Tories and preferred to call themselves The Friends of Mr. Pitt. After the fall of the Talents ministry in 1807, the Foxite Whigs remained out of power for the better part of 25 years. The accession of Fox's old ally, the Prince of Wales, to the regency in 1811 did not change the situation, as the Prince had broken entirely with his old Foxite Whig companions. The members of the government of Lord Liverpool from 1812 to 1827 called themselves Whigs.

Structure and appeal
By 1815, the Whigs were still far from being a "party" in the modern sense. They had no definite programme or policy and were by no means even united. Generally, they stood for reducing crown patronage, sympathy towards nonconformists, support for the interests of merchants and bankers and a leaning towards the idea of a limited reform of the voting system. Most Whig leaders, such as Lord Grey, Lord Grenville, Lord Althorp, William Lamb (later Lord Melbourne) and Lord John Russell, were still rich landowners. The most prominent exception was Henry Brougham, the talented lawyer, who had a relatively modest background.

Hay argues that Whig leaders welcomed the increasing political participation of the English middle classes in the two decades after the defeat of Napoleon in 1815. The fresh support strengthened their position in Parliament. Whigs rejected the Tory appeals to governmental authority and social discipline and extended political discussion beyond Parliament. Whigs used a national network of newspapers and magazines as well as local clubs to deliver their message. The press organised petitions and debates and reported to the public on government policy, while leaders such as Henry Brougham (1778–1868) built alliances with men who lacked direct representation. This new approach to the grass roots helped to define Whiggism and opened the way for later success. Whigs thereby forced the government to recognise the role of public opinion in parliamentary debate and influenced views of representation and reform throughout the 19th century.

Return to power
Whigs restored their unity by supporting moral reforms, especially the abolition of slavery. They triumphed in 1830 as champions of Parliamentary reform. They made Lord Grey prime minister 1830–1834 and the Reform Act 1832 championed by Grey became their signature measure. It broadened the franchise and ended the system of "rotten and pocket boroughs" (where elections were controlled by powerful families) and instead redistributed power on the basis of population. It added 217,000 voters to an electorate of 435,000 in England and Wales. Only the upper and middle classes voted, so this shifted power away from the landed aristocracy to the urban middle classes. In 1832, the party abolished enslavement in the British Empire with the Slavery Abolition Act 1833. It purchased and freed the slaves, especially those in the Caribbean sugar islands. After parliamentary investigations demonstrated the horrors of child labour, limited reforms were passed in 1833. The Whigs also passed the Poor Law Amendment Act 1834 that reformed the administration of relief to the poor.

It was around this time that the great Whig historian Thomas Babington Macaulay began to promulgate what would later be coined the Whig view of history, in which all of English history was seen as leading up to the culminating moment of the passage of Lord Grey's reform bill. This view led to serious distortions in later portrayals of 17th-century and 18th-century history, as Macaulay and his followers attempted to fit the complex and changing factional politics of the Restoration into the neat categories of 19th-century political divisions.

In 1836, a private gentleman's Club was constructed in Pall Mall, Piccadilly as a consequence of the successful Reform Act 1832. The Reform Club was founded by Edward Ellice Sr., MP for Coventry and Whig Whip, whose riches came from the Hudson's Bay Company but whose zeal was chiefly devoted to securing the passage of the Reform Act 1832. This new club, for members of both Houses of Parliament, was intended to be a forum for the radical ideas which the First Reform Bill represented: a bastion of liberal and progressive thought that became closely associated with the Liberal Party, who largely succeeded the Whigs in the second half of the 19th century.

Until the decline of the Liberal Party in the early 20th century, it was de rigueur for Liberal MPs and peers to be members of the Reform Club, being regarded as an unofficial party headquarters. However, in 1882 the National Liberal Club was established under William Ewart Gladstone's chairmanship, designed to be more "inclusive" towards Liberal grandees and activists throughout the United Kingdom.

Transition to the Liberal Party
The Liberal Party (the term was first used officially in 1868, but had been used colloquially for decades beforehand) arose from a coalition of Whigs, free trade Tory followers of Robert Peel and free trade Radicals, first created, tenuously under the Peelite Earl of Aberdeen in 1852 and put together more permanently under the former Canningite Tory Lord Palmerston in 1859. Although the Whigs at first formed the most important part of the coalition, the Whiggish elements of the new party progressively lost influence during the long leadership of former Peelite William Ewart Gladstone. Subsequently the majority of the old Whig aristocracy broke from the party over the issue of Irish home rule in 1886 to help form the Liberal Unionist Party, which in turn would merge with the Conservative Party by 1912. However, the Unionist support for trade protection in the early twentieth century under Joseph Chamberlain (probably the least Whiggish character in the Liberal Unionist party) further alienated the more orthodox Whigs. By the early twentieth century "Whiggery" was largely irrelevant and without a natural political home. One of the last active politicians to celebrate his Whiggish roots was the Liberal Unionist statesman Henry James.

In popular culture
The colours of the Whig Party (blue and buff, a yellow-brown colour named after buff leather) were particularly associated with Charles James Fox.

Poet Robert Burns in "Here's a health to them that's awa" wrote:

"The British Whig March" for piano was written by Oscar Telgmann in Kingston, Ontario, c. 1900.

Punk band The Men That Will Not Be Blamed for Nothing have a song named "Doing It for the Whigs".

Historiography

 * Hill, Brain W. "II. Executive Monarchy and the Challenge of Parties, 1689–1832: Two Concepts of Government and Two Historiographical Interpretations." The Historical Journal (1970) 13#3 pp: 379–401. abstract.
 * Hone, Joseph. "John Darby and the Whig Canon." Historical Journal 1-24. online
 * Loades, David ed. Readers Guide to British History (2003) 2:1353–56.
 * Thomas, Peter D. G. "Party Politics in Eighteenth‐Century Britain: Some Myths and a Touch of Reality." Journal for Eighteenth‐Century Studies (1987) 10#2 pp. 201–210.
 * Thomas, Peter D. G. "Party Politics in Eighteenth‐Century Britain: Some Myths and a Touch of Reality." Journal for Eighteenth‐Century Studies (1987) 10#2 pp. 201–210.

title: Whigs (British political party)


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Linear programming

Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements and objective are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization).

More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints. Its feasible region is a convex polytope, which is a set defined as the intersection of finitely many half spaces, each of which is defined by a linear inequality. Its objective function is a real-valued affine (linear) function defined on this polytope. A linear programming algorithm finds a point in the polytope where this function has the largest (or smallest) value if such a point exists.

Linear programs are problems that can be expressed in standard form as
 * $$ \begin{align}

& \text{Find a vector} && \mathbf{x} \\ & \text{that maximizes}  && \mathbf{c}^\mathsf{T} \mathbf{x}\\ & \text{subject to} && A \mathbf{x} \le \mathbf{b} \\ & \text{and} && \mathbf{x} \ge \mathbf{0}. \end{align} $$ Here the components of $$\mathbf{x}$$ are the variables to be determined, $$\mathbf{c}$$ and $$\mathbf{b}$$ are given vectors, and $$A$$ is a given matrix. The function whose value is to be maximized ($$\mathbf x\mapsto\mathbf{c}^\mathsf{T}\mathbf{x}$$ in this case) is called the objective function. The constraints $$A \mathbf{x} \le \mathbf{b}$$ and $$\mathbf{x} \geq \mathbf{0}$$ specify a convex polytope over which the objective function is to be optimized.

Linear programming can be applied to various fields of study. It is widely used in mathematics and, to a lesser extent, in business, economics, and some engineering problems. There is a close connection between linear programs, eigenequations, John von Neumann's general equilibrium model, and structural equilibrium models (see dual linear program for details). Industries that use linear programming models include transportation, energy, telecommunications, and manufacturing. It has proven useful in modeling diverse types of problems in planning, routing, scheduling, assignment, and design.

History

The problem of solving a system of linear inequalities dates back at least as far as Fourier, who in 1827 published a method for solving them, and after whom the method of Fourier–Motzkin elimination is named.

In the late 1930s, Soviet mathematician Leonid Kantorovich and American economist Wassily Leontief independently delved into the practical applications of linear programming. Kantorovich focused on manufacturing schedules, while Leontief explored economic applications. Their groundbreaking work was largely overlooked for decades.

The turning point came during World War II when linear programming emerged as a vital tool. It found extensive use in addressing complex wartime challenges, including transportation logistics, scheduling, and resource allocation. Linear programming proved invaluable in optimizing these processes while considering critical constraints such as costs and resource availability.

Despite its initial obscurity, the wartime successes propelled linear programming into the spotlight. Post-WWII, the method gained widespread recognition and became a cornerstone in various fields, from operations research to economics. The overlooked contributions of Kantorovich and Leontief in the late 1930s eventually became foundational to the broader acceptance and utilization of linear programming in optimizing decision-making processes.

Kantorovich's work was initially neglected in the USSR. About the same time as Kantorovich, the Dutch-American economist T. C. Koopmans formulated classical economic problems as linear programs. Kantorovich and Koopmans later shared the 1975 Nobel Memorial Prize in Economic Sciences. In 1941, Frank Lauren Hitchcock also formulated transportation problems as linear programs and gave a solution very similar to the later simplex method. Hitchcock had died in 1957, and the Nobel Memorial Prize is not awarded posthumously.

From 1946 to 1947 George B. Dantzig independently developed general linear programming formulation to use for planning problems in the US Air Force. In 1947, Dantzig also invented the simplex method that, for the first time efficiently, tackled the linear programming problem in most cases. When Dantzig arranged a meeting with John von Neumann to discuss his simplex method, Neumann immediately conjectured the theory of duality by realizing that the problem he had been working in game theory was equivalent. Dantzig provided formal proof in an unpublished report "A Theorem on Linear Inequalities" on January 5, 1948. Dantzig's work was made available to public in 1951. In the post-war years, many industries applied it in their daily planning.

Dantzig's original example was to find the best assignment of 70 people to 70 jobs. The computing power required to test all the permutations to select the best assignment is vast; the number of possible configurations exceeds the number of particles in the observable universe. However, it takes only a moment to find the optimum solution by posing the problem as a linear program and applying the simplex algorithm. The theory behind linear programming drastically reduces the number of possible solutions that must be checked.

The linear programming problem was first shown to be solvable in polynomial time by Leonid Khachiyan in 1979, but a larger theoretical and practical breakthrough in the field came in 1984 when Narendra Karmarkar introduced a new interior-point method for solving linear-programming problems.

Uses
Linear programming is a widely used field of optimization for several reasons. Many practical problems in operations research can be expressed as linear programming problems. Certain special cases of linear programming, such as network flow problems and multicommodity flow problems, are considered important enough to have much research on specialized algorithms. A number of algorithms for other types of optimization problems work by solving linear programming problems as sub-problems. Historically, ideas from linear programming have inspired many of the central concepts of optimization theory, such as duality, decomposition, and the importance of convexity and its generalizations. Likewise, linear programming was heavily used in the early formation of microeconomics, and it is currently utilized in company management, such as planning, production, transportation, and technology. Although the modern management issues are ever-changing, most companies would like to maximize profits and minimize costs with limited resources. Google also uses linear programming to stabilize YouTube videos.

Standard form
Standard form is the usual and most intuitive form of describing a linear programming problem. It consists of the following three parts:
 * A linear (or affine) function to be maximized
 * e.g. $$ f(x_{1},x_{2}) = c_1 x_1 + c_2 x_2$$

 * Problem constraints of the following form
 * e.g.
 * $$\begin{matrix}

a_{11} x_1 + a_{12} x_2 &\leq b_1 \\ a_{21} x_1 + a_{22} x_2 &\leq b_2 \\ a_{31} x_1 + a_{32} x_2 &\leq b_3 \\ \end{matrix}$$
 * Non-negative variables
 * e.g.
 * $$\begin{matrix}

x_1 \geq 0 \\ x_2 \geq 0 \end{matrix}$$

The problem is usually expressed in matrix form, and then becomes:
 * $$\max \{\, \mathbf{c}^\mathsf{T} \mathbf{x} \mid \mathbf{x}\in\mathbb{R}^n\land A \mathbf{x} \leq \mathbf{b} \land \mathbf{x} \geq 0 \,\}$$

Other forms, such as minimization problems, problems with constraints on alternative forms, and problems involving negative variables can always be rewritten into an equivalent problem in standard form.

Example
Suppose that a farmer has a piece of farm land, say L km2, to be planted with either wheat or barley or some combination of the two. The farmer has a limited amount of fertilizer, F kilograms, and pesticide, P kilograms. Every square kilometer of wheat requires F1 kilograms of fertilizer and P1 kilograms of pesticide, while every square kilometer of barley requires F2 kilograms of fertilizer and P2 kilograms of pesticide. Let S1 be the selling price of wheat per square kilometer, and S2 be the selling price of barley. If we denote the area of land planted with wheat and barley by x1 and x2 respectively, then profit can be maximized by choosing optimal values for x1 and x2. This problem can be expressed with the following linear programming problem in the standard form:

In matrix form this becomes:
 * maximize $$\begin{bmatrix} S_1 & S_2 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} $$
 * subject to $$\begin{bmatrix} 1 & 1 \\ F_1 & F_2 \\ P_1 & P_2 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} \le \begin{bmatrix} L \\ F \\ P \end{bmatrix}, \, \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} \ge \begin{bmatrix} 0 \\ 0 \end{bmatrix}. $$

Augmented form (slack form)
Linear programming problems can be converted into an augmented form in order to apply the common form of the simplex algorithm. This form introduces non-negative slack variables to replace inequalities with equalities in the constraints. The problems can then be written in the following block matrix form:
 * Maximize $$z$$:

\begin{bmatrix} 1 & -\mathbf{c}^\mathsf{T} & 0 \\ 0 & \mathbf{A} & \mathbf{I} \end{bmatrix} \begin{bmatrix} z \\ \mathbf{x} \\ \mathbf{s} \end{bmatrix} = \begin{bmatrix} 0 \\ \mathbf{b} \end{bmatrix} $$
 * $$\mathbf{x} \ge 0, \mathbf{s} \ge 0$$

where $$\mathbf{s}$$ are the newly introduced slack variables, $$\mathbf{x}$$ are the decision variables, and $$z$$ is the variable to be maximized.

Example
The example above is converted into the following augmented form:

where $$x_3, x_4, x_5$$ are (non-negative) slack variables, representing in this example the unused area, the amount of unused fertilizer, and the amount of unused pesticide.
 * colspan="2" | Maximize: $$S_1\cdot x_1+S_2\cdot x_2$$
 * (objective function)
 * subject to:
 * $$x_1 + x_2 + x_3 = L$$
 * (augmented constraint)
 * $$F_1\cdot x_1+F_2\cdot x_2 + x_4 = F$$
 * (augmented constraint)
 * $$P_1\cdot x_1 + P_2\cdot x_2 + x_5 = P$$
 * (augmented constraint)
 * $$x_1,x_2,x_3,x_4,x_5 \ge 0.$$
 * }
 * $$P_1\cdot x_1 + P_2\cdot x_2 + x_5 = P$$
 * (augmented constraint)
 * $$x_1,x_2,x_3,x_4,x_5 \ge 0.$$
 * }
 * $$x_1,x_2,x_3,x_4,x_5 \ge 0.$$
 * }
 * $$x_1,x_2,x_3,x_4,x_5 \ge 0.$$
 * }

In matrix form this becomes:
 * Maximize $$z$$:

\begin{bmatrix} 1 & -S_1 & -S_2 & 0 & 0 & 0 \\ 0 &  1    &   1    & 1 & 0 & 0 \\    0 &  F_1  &  F_2  & 0 & 1 & 0 \\ 0 & P_1    & P_2 & 0 & 0 & 1 \\ \end{bmatrix} \begin{bmatrix} z \\ x_1 \\ x_2 \\ x_3 \\ x_4 \\ x_5 \end{bmatrix} = \begin{bmatrix} 0 \\ L \\ F \\ P \end{bmatrix}, \, \begin{bmatrix} x_1 \\ x_2 \\ x_3 \\ x_4 \\ x_5 \end{bmatrix} \ge 0. $$

Duality
Every linear programming problem, referred to as a primal problem, can be converted into a dual problem, which provides an upper bound to the optimal value of the primal problem. In matrix form, we can express the primal problem as:

 * Maximize cTx subject to Ax ≤ b, x ≥ 0;
 * with the corresponding symmetric dual problem,
 * Minimize bTy  subject to ATy ≥ c, y ≥ 0.

An alternative primal formulation is:

 * Maximize cTx subject to Ax ≤ b;
 * with the corresponding asymmetric dual problem,
 * Minimize bTy subject to ATy = c, y ≥ 0.

There are two ideas fundamental to duality theory. One is the fact that (for the symmetric dual) the dual of a dual linear program is the original primal linear program. Additionally, every feasible solution for a linear program gives a bound on the optimal value of the objective function of its dual. The weak duality theorem states that the objective function value of the dual at any feasible solution is always greater than or equal to the objective function value of the primal at any feasible solution. The strong duality theorem states that if the primal has an optimal solution, x*, then the dual also has an optimal solution, y*, and cTx*=bTy*.

A linear program can also be unbounded or infeasible. Duality theory tells us that if the primal is unbounded then the dual is infeasible by the weak duality theorem. Likewise, if the dual is unbounded, then the primal must be infeasible. However, it is possible for both the dual and the primal to be infeasible. See dual linear program for details and several more examples.

Covering/packing dualities
A covering LP is a linear program of the form:
 * Minimize: bTy ,
 * subject to: ATy ≥ c, y ≥ 0 ,

such that the matrix A and the vectors b and c are non-negative.

The dual of a covering LP is a packing LP, a linear program of the form:
 * Maximize: cTx ,
 * subject to: Ax ≤ b, x ≥ 0 ,

such that the matrix A and the vectors b and c are non-negative.

Examples
Covering and packing LPs commonly arise as a linear programming relaxation of a combinatorial problem and are important in the study of approximation algorithms. For example, the LP relaxations of the set packing problem, the independent set problem, and the matching problem are packing LPs. The LP relaxations of the set cover problem, the vertex cover problem, and the dominating set problem are also covering LPs.

Finding a fractional coloring of a graph is another example of a covering LP. In this case, there is one constraint for each vertex of the graph and one variable for each independent set of the graph.

Complementary slackness
It is possible to obtain an optimal solution to the dual when only an optimal solution to the primal is known using the complementary slackness theorem. The theorem states:

Suppose that x = (x1, x2, ..., xn) is primal feasible and that y = (y1, y2, ... , ym) is dual feasible. Let (w1, w2, ..., wm) denote the corresponding primal slack variables, and let (z1, z2, ..., zn) denote the corresponding dual slack variables. Then x and y are optimal for their respective problems if and only if
 * xj zj = 0, for j = 1, 2, ..., n, and
 * wi yi = 0, for i = 1, 2, ..., m.

So if the i-th slack variable of the primal is not zero, then the i-th variable of the dual is equal to zero. Likewise, if the j-th slack variable of the dual is not zero, then the j-th variable of the primal is equal to zero.

This necessary condition for optimality conveys a fairly simple economic principle. In standard form (when maximizing), if there is slack in a constrained primal resource (i.e., there are "leftovers"), then additional quantities of that resource must have no value. Likewise, if there is slack in the dual (shadow) price non-negativity constraint requirement, i.e., the price is not zero, then there must be scarce supplies (no "leftovers").

Existence of optimal solutions
Geometrically, the linear constraints define the feasible region, which is a convex polytope. A linear function is a convex function, which implies that every local minimum is a global minimum; similarly, a linear function is a concave function, which implies that every local maximum is a global maximum.

An optimal solution need not exist, for two reasons. First, if the constraints are inconsistent, then no feasible solution exists: For instance, the constraints x ≥ 2 and x ≤ 1 cannot be satisfied jointly; in this case, we say that the LP is infeasible. Second, when the polytope is unbounded in the direction of the gradient of the objective function (where the gradient of the objective function is the vector of the coefficients of the objective function), then no optimal value is attained because it is always possible to do better than any finite value of the objective function.

Optimal vertices (and rays) of polyhedra
Otherwise, if a feasible solution exists and if the constraint set is bounded, then the optimum value is always attained on the boundary of the constraint set, by the maximum principle for convex functions (alternatively, by the minimum principle for concave functions) since linear functions are both convex and concave. However, some problems have distinct optimal solutions; for example, the problem of finding a feasible solution to a system of linear inequalities is a linear programming problem in which the objective function is the zero function (i.e., the constant function taking the value zero everywhere). For this feasibility problem with the zero-function for its objective-function, if there are two distinct solutions, then every convex combination of the solutions is a solution.

The vertices of the polytope are also called basic feasible solutions. The reason for this choice of name is as follows. Let d denote the number of variables. Then the fundamental theorem of linear inequalities implies (for feasible problems) that for every vertex x* of the LP feasible region, there exists a set of d (or fewer) inequality constraints from the LP such that, when we treat those d constraints as equalities, the unique solution is x*. Thereby we can study these vertices by means of looking at certain subsets of the set of all constraints (a discrete set), rather than the continuum of LP solutions. This principle underlies the simplex algorithm for solving linear programs.

Simplex algorithm of Dantzig
The simplex algorithm, developed by George Dantzig in 1947, solves LP problems by constructing a feasible solution at a vertex of the polytope and then walking along a path on the edges of the polytope to vertices with non-decreasing values of the objective function until an optimum is reached for sure. In many practical problems, "stalling" occurs: many pivots are made with no increase in the objective function. In rare practical problems, the usual versions of the simplex algorithm may actually "cycle". To avoid cycles, researchers developed new pivoting rules.

In practice, the simplex algorithm is quite efficient and can be guaranteed to find the global optimum if certain precautions against cycling are taken. The simplex algorithm has been proved to solve "random" problems efficiently, i.e. in a cubic number of steps, which is similar to its behavior on practical problems.

However, the simplex algorithm has poor worst-case behavior: Klee and Minty constructed a family of linear programming problems for which the simplex method takes a number of steps exponential in the problem size. In fact, for some time it was not known whether the linear programming problem was solvable in polynomial time, i.e. of complexity class P.

Criss-cross algorithm
Like the simplex algorithm of Dantzig, the criss-cross algorithm is a basis-exchange algorithm that pivots between bases. However, the criss-cross algorithm need not maintain feasibility, but can pivot rather from a feasible basis to an infeasible basis. The criss-cross algorithm does not have polynomial time-complexity for linear programming. Both algorithms visit all 2D corners of a (perturbed) cube in dimension D, the Klee–Minty cube, in the worst case.

Interior point
In contrast to the simplex algorithm, which finds an optimal solution by traversing the edges between vertices on a polyhedral set, interior-point methods move through the interior of the feasible region.

Ellipsoid algorithm, following Khachiyan
This is the first worst-case polynomial-time algorithm ever found for linear programming. To solve a problem which has n variables and can be encoded in L input bits, this algorithm runs in $$ O(n^6 L) $$ time. Leonid Khachiyan solved this long-standing complexity issue in 1979 with the introduction of the ellipsoid method. The convergence analysis has (real-number) predecessors, notably the iterative methods developed by Naum Z. Shor and the approximation algorithms by Arkadi Nemirovski and D. Yudin.

Projective algorithm of Karmarkar
Khachiyan's algorithm was of landmark importance for establishing the polynomial-time solvability of linear programs. The algorithm was not a computational break-through, as the simplex method is more efficient for all but specially constructed families of linear programs.

However, Khachiyan's algorithm inspired new lines of research in linear programming. In 1984, N. Karmarkar proposed a projective method for linear programming. Karmarkar's algorithm improved on Khachiyan's worst-case polynomial bound (giving $$O(n^{3.5}L)$$). Karmarkar claimed that his algorithm was much faster in practical LP than the simplex method, a claim that created great interest in interior-point methods. Since Karmarkar's discovery, many interior-point methods have been proposed and analyzed.

Vaidya's 87 algorithm
In 1987, Vaidya proposed an algorithm that runs in $$ O(n^3) $$ time.

Vaidya's 89 algorithm
In 1989, Vaidya developed an algorithm that runs in $$O(n^{2.5})$$ time. Formally speaking, the algorithm takes $$O( (n+d)^{1.5} n L)$$ arithmetic operations in the worst case, where $$d$$ is the number of constraints, $$ n $$ is the number of variables, and $$L$$ is the number of bits.

Input sparsity time algorithms
In 2015, Lee and Sidford showed that linear programming can be solved in $$\tilde O((nnz(A) + d^2)\sqrt{d}L)$$ time, where $$\tilde O$$ denotes the soft O notation, and $$nnz(A)$$ represents the number of non-zero elements, and it remains taking $$O(n^{2.5}L)$$ in the worst case.

Current matrix multiplication time algorithm
In 2019, Cohen, Lee and Song improved the running time to $$\tilde O( ( n^{\omega} + n^{2.5-\alpha/2} + n^{2+1/6} ) L)$$ time, $$ \omega $$ is the exponent of matrix multiplication and $$ \alpha $$ is the dual exponent of matrix multiplication. $$ \alpha $$ is (roughly) defined to be the largest number such that one can multiply an $$ n \times n $$ matrix by a $$ n \times n^\alpha $$ matrix in $$ O(n^2) $$ time. In a followup work by Lee, Song and Zhang, they reproduce the same result via a different method. These two algorithms remain $$\tilde O( n^{2+1/6} L ) $$ when $$ \omega = 2 $$ and $$ \alpha = 1 $$. The result due to Jiang, Song, Weinstein and Zhang improved $$ \tilde O ( n^{2+1/6} L) $$ to $$ \tilde O ( n^{2+1/18} L) $$.

Comparison of interior-point methods and simplex algorithms
The current opinion is that the efficiencies of good implementations of simplex-based methods and interior point methods are similar for routine applications of linear programming. However, for specific types of LP problems, it may be that one type of solver is better than another (sometimes much better), and that the structure of the solutions generated by interior point methods versus simplex-based methods are significantly different with the support set of active variables being typically smaller for the latter one.

Open problems and recent work
There are several open problems in the theory of linear programming, the solution of which would represent fundamental breakthroughs in mathematics and potentially major advances in our ability to solve large-scale linear programs.
 * Does LP admit a strongly polynomial-time algorithm?
 * Does LP admit a strongly polynomial-time algorithm to find a strictly complementary solution?
 * Does LP admit a polynomial-time algorithm in the real number (unit cost) model of computation?

This closely related set of problems has been cited by Stephen Smale as among the 18 greatest unsolved problems of the 21st century. In Smale's words, the third version of the problem "is the main unsolved problem of linear programming theory." While algorithms exist to solve linear programming in weakly polynomial time, such as the ellipsoid methods and interior-point techniques, no algorithms have yet been found that allow strongly polynomial-time performance in the number of constraints and the number of variables. The development of such algorithms would be of great theoretical interest, and perhaps allow practical gains in solving large LPs as well.

Although the Hirsch conjecture was recently disproved for higher dimensions, it still leaves the following questions open.
 * Are there pivot rules which lead to polynomial-time simplex variants?
 * Do all polytopal graphs have polynomially bounded diameter?

These questions relate to the performance analysis and development of simplex-like methods. The immense efficiency of the simplex algorithm in practice despite its exponential-time theoretical performance hints that there may be variations of simplex that run in polynomial or even strongly polynomial time. It would be of great practical and theoretical significance to know whether any such variants exist, particularly as an approach to deciding if LP can be solved in strongly polynomial time.

The simplex algorithm and its variants fall in the family of edge-following algorithms, so named because they solve linear programming problems by moving from vertex to vertex along edges of a polytope. This means that their theoretical performance is limited by the maximum number of edges between any two vertices on the LP polytope. As a result, we are interested in knowing the maximum graph-theoretical diameter of polytopal graphs. It has been proved that all polytopes have subexponential diameter. The recent disproof of the Hirsch conjecture is the first step to prove whether any polytope has superpolynomial diameter. If any such polytopes exist, then no edge-following variant can run in polynomial time. Questions about polytope diameter are of independent mathematical interest.

Simplex pivot methods preserve primal (or dual) feasibility. On the other hand, criss-cross pivot methods do not preserve (primal or dual) feasibility – they may visit primal feasible, dual feasible or primal-and-dual infeasible bases in any order. Pivot methods of this type have been studied since the 1970s. Essentially, these methods attempt to find the shortest pivot path on the arrangement polytope under the linear programming problem. In contrast to polytopal graphs, graphs of arrangement polytopes are known to have small diameter, allowing the possibility of strongly polynomial-time criss-cross pivot algorithm without resolving questions about the diameter of general polytopes.

Integer unknowns
If all of the unknown variables are required to be integers, then the problem is called an integer programming (IP) or integer linear programming (ILP) problem. In contrast to linear programming, which can be solved efficiently in the worst case, integer programming problems are in many practical situations (those with bounded variables) NP-hard. 0–1 integer programming or binary integer programming (BIP) is the special case of integer programming where variables are required to be 0 or 1 (rather than arbitrary integers). This problem is also classified as NP-hard, and in fact the decision version was one of Karp's 21 NP-complete problems.

If only some of the unknown variables are required to be integers, then the problem is called a mixed integer (linear) programming (MIP or MILP) problem. These are generally also NP-hard because they are even more general than ILP programs.

There are however some important subclasses of IP and MIP problems that are efficiently solvable, most notably problems where the constraint matrix is totally unimodular and the right-hand sides of the constraints are integers or – more general – where the system has the total dual integrality (TDI) property.

Advanced algorithms for solving integer linear programs include: Such integer-programming algorithms are discussed by Padberg and in Beasley.
 * cutting-plane method
 * Branch and bound
 * Branch and cut
 * Branch and price
 * if the problem has some extra structure, it may be possible to apply delayed column generation.

Integral linear programs
A linear program in real variables is said to be integral if it has at least one optimal solution which is integral, i.e., made of only integer values. Likewise, a polyhedron $$P = \{x \mid Ax \ge 0\}$$ is said to be integral if for all bounded feasible objective functions c, the linear program $$\{\max cx \mid x \in P\}$$ has an optimum $$x^*$$ with integer coordinates. As observed by Edmonds and Giles in 1977, one can equivalently say that the polyhedron $$P$$ is integral if for every bounded feasible integral objective function c, the optimal value of the linear program $$\{\max cx \mid x \in P\}$$ is an integer.

Integral linear programs are of central importance in the polyhedral aspect of combinatorial optimization since they provide an alternate characterization of a problem. Specifically, for any problem, the convex hull of the solutions is an integral polyhedron; if this polyhedron has a nice/compact description, then we can efficiently find the optimal feasible solution under any linear objective. Conversely, if we can prove that a linear programming relaxation is integral, then it is the desired description of the convex hull of feasible (integral) solutions.

Terminology is not consistent throughout the literature, so one should be careful to distinguish the following two concepts,
 * in an integer linear program, described in the previous section, variables are forcibly constrained to be integers, and this problem is NP-hard in general,
 * in an integral linear program, described in this section, variables are not constrained to be integers but rather one has proven somehow that the continuous problem always has an integral optimal value (assuming c is integral), and this optimal value may be found efficiently since all polynomial-size linear programs can be solved in polynomial time.

One common way of proving that a polyhedron is integral is to show that it is totally unimodular. There are other general methods including the integer decomposition property and total dual integrality. Other specific well-known integral LPs include the matching polytope, lattice polyhedra, submodular flow polyhedra, and the intersection of two generalized polymatroids/g-polymatroids – e.g. see Schrijver 2003.

Solvers and scripting (programming) languages
Permissive licenses:

Copyleft (reciprocal) licenses:

MINTO (Mixed Integer Optimizer, an integer programming solver which uses branch and bound algorithm) has publicly available source code but is not open source.

Proprietary licenses:

title: Linear programming


text:
295

Year 295 (CCXCV) was a common year starting on Tuesday (link will display the full calendar) of the Julian calendar, the 295th Year of the Common Era (CE) and Anno Domini (AD) designations, the 295th year of the 1st millennium, the 95th year and last 6 years of the 3rd century, and the 6th year of the 290s decade. At the time, it was known as the Year of the Consulship of Tuscus and Anullinus (or, less frequently, year 1048 Ab urbe condita). The denomination 295 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years.

Roman Empire

 * Emperor Diocletian defeats the Carpi.
 * Caesar Galerius completes a series of two campaigns in Upper Egypt, against the rebel cities of Coptos and Boresis, as well as the Blemmyes and Meroitic Nubians.
 * The jurist Hermogenianus, at the court of Diocletian, produces the Hermogenian Code. This new codification of Roman law complements the Gregorian Code of c. 292.
 * Diocletian, perhaps through Galerius, issues an edict against incest.

China

 * Tuoba Luguan divides the territory of the Tuoba clan into three areas. His nephews Tuoba Yilu and Tuoba Yituo become chieftains of the western and central areas of (Shanxi province). Tuoba Luguan dominates the eastern area (near Hohhot).

Religion

 * Petra rejoins the province of Palestine, and is converted to Christianity by the Syrian monk Barsauma.

Births

 * Shi Hu, Chinese emperor of Later Zhao (d. 349)

Deaths

 * Maximilian of Tebessa, Berber Christian saint and martyr

title: 295


text:
294

Year 294 (CCXCIV) was a common year starting on Monday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Constantius and (Galerius) Maximianus (or, less frequently, year 1047 Ab urbe condita). The denomination 294 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years.

Asia

 * Persian shahanshah Narseh defeats King Tiridates III of Armenia, and forces him to flee to the Roman Empire.
 * Tuoba Luguan succeeds his nephew Tuoba Fu, as chieftain of the Chinese Tuoba clan.

Births

 * Sima Bao, Chinese prince of the Jin Dynasty (d. 320)

Deaths

 * Tuoba Fu, chieftain of the Chinese Tuoba clan

title: 294


text:
296

Year 296 (CCXCVI) was a leap year starting on Wednesday (link will display the full calendar) of the Julian calendar. In the Roman Empire, it was known as the Year of the Consulship of Diocletian and Constantius (or, less frequently, year 1049 Ab urbe condita). The denomination 296 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years.

Roman Empire

 * In this or the previous year, Caesar Constantius I assembles two invasion fleets with the intent of overthrowing the usurper Allectus, who is based in Britain. The first is under the command of Asclepiodotus, Maximian's long-serving Praetorian Prefect. Asclepiodotus sails from the mouth of the Seine, and lands near the Isle of Wight, where his forces defeat Allectus in Hampshire. Allectus is killed in the fighting. Constantius leaves Boulogne with his fleet, and occupies London, where he slaughters some of Allectus' Frankish mercenaries. With this victory, the Romano-British regime first established by Carausius is overthrown, and Britain is re-incorporated into the rest of the empire.
 * Having supervised the Rhine frontier during Constantius' invasion of Britain, Maximian then marches into Spain, where he fights Frankish pirates. He then crosses into North Africa to contend with the rebellion of the Quinquegentiani.
 * The Persian king Narseh invades Roman-held Upper Mesopotamia and Arsacid western Armenia, the latter territory being under the leadership of the pro-Roman king Tiridates III. With only a small army, Caesar Galerius fights three holding actions against Narseh's army in Mesopotamia. Somewhere in the open plains between Carrhae and Callinicum, Galerius' army suffers a defeat against the Persian army, which is both more numerous and contains superior numbers of high-quality cavalry. Nevertheless, Galerius succeeds in blunting the Persian offensive.

Religion

 * April 22 – Pope Caius dies after a 13-year reign and is succeeded by Marcellinus as the 29th pope of Rome.

Births

 * Yu Bing (or Jijian), Chinese politician (d. 344)

Deaths

 * April 22 – Caius, bishop of Rome
 * Allectus, Roman treasurer and usurper-emperor
 * Guo Huai (or Yuhuang), Chinese noblewoman (b. 237)

title: 296