title: Super Columbine Massacre RPG!

text: In the next scene Harris and Klebold are standing outside their high school. The player guides them to the cafeteria to plant their timed propane bombs without being detected by security cameras or hall monitors. After the explosives are set, the two stop for a moment on a hill outside the school, discussing their alienation and hostility. After the bombs fail to explode as planned, Harris and Klebold decide to enter the school and murder as many people as they can; the final number killed is up to the player. After roaming around the school shooting innocents, Harris and Klebold commit suicide. A montage of clips showing Harris and Klebold's corpses, students comforting each other, and childhood photos of the gunmen plays.


title: Super Columbine Massacre RPG!

text: The game's second half finds Klebold alone in Hell. After combating demons and monsters from the video game "Doom", Klebold reunites with Harris, and they profess their enthusiasm for the opportunity to live out their favorite video game. The pair find themselves at the "Isle of Lost Souls", where they meet fictional characters such as Pikachu, Bart Simpson, Mega Man, Mario and personalities including J. Robert Oppenheimer, JonBenét Ramsey, Malcolm X, Ronald Reagan, and John Lennon. Next, they deliver a copy of "Ecce Homo" to Friedrich Nietzsche before fighting the "South Park" design of Satan. Upon their victory, Satan congratulates them for their deeds.


title: Super Columbine Massacre RPG!

text: The game returns to Columbine High School, where a press conference addresses the murders. Some of the dialogue appears precisely as it was spoken after the actual event, while other lines caricature the political forces at work in the aftermath of the murders. The conference references gun control advocacy, religious fundamentalism, and the media's implication of Marilyn Manson and the video games they played as culpable in the shooting.


title: Super Columbine Massacre RPG!

text: "Super Columbine Massacre" was created by Danny Ledonne of Alamosa, Colorado, then a student and independent filmmaker. As a high school student, the Columbine shootings resonated with Ledonne, who said that he himself had once been "a loner", "a misfit" and "a bullied kid" in high school like the shooters. "I was an easy target to be picked on, and that started in kindergarten", he said. "It was the kind of bullying that most kids who were bullied experienced [...] When you get pushed every day, and when you are ostracized not once, not twice, but years in and out, your perception of reality is distorted [...] These things really do warp your understanding and your perception of humanity in some almost irrevocable way", he said.


title: Super Columbine Massacre RPG!

text: In 1999, director Stanley Kubrick's death and the Columbine High School massacre occurred within months of each other; Ledonne credited the two events with changing his life. After seeing "A Clockwork Orange", Ledonne discovered that film could comment on culture; after the Columbine shootings, he realized he was headed down the same path as the shooters. "It was a bit scary, once I learned more about these boys, because it was like I was looking in the mirror and I didn't want the same fate for myself", Ledonne said. He began taking martial arts, studying film, and saw a therapist. By the time he graduated from Alamosa High School, Ledonne had a 4.0 grade point average and was voted "most likely to succeed" by his peers. He studied film at Emerson College and moved back to Colorado to form his own production company, Emberwild Productions, which mostly edits wedding videos.


title: Super Columbine Massacre RPG!

text: In November 2004, Ledonne discovered a program called RPG Maker, which allows a developer to add images, text, story and objectives to design a game; RPG Maker creates the necessary programming automatically. Ledonne had always conceptualized video games throughout his childhood but never produced one due to his lack of technical knowledge; with RPG Maker he was able to fulfill his ambition. Ledonne decided to make a game that would explore why the Columbine shootings occurred, as well as refuting pervasive myths about the shooters and the alleged role video games played in the massacre.


title: Super Columbine Massacre RPG!

text: The researching, planning, design and programming of the game took about six months and between 200 and 300 hours of work. All the footage and pictures in the game were taken from the internet. "Final Fantasy VI" influenced the sprite-based design. Many of the songs in the game are MIDI versions of 1990s grunge and alternative bands such as Radiohead, Nirvana and the Smashing Pumpkins. Ledonne paid meticulous attention to detail, including giving players access to the exact inventory the gunmen used on their rampage. He watched videos, read newspaper articles and pored over 11,000 pages of documents released by the county government regarding the massacre and the killers.


title: Super Columbine Massacre RPG!

text: Ledonne added elements to the game to criticize subjects varying from public reaction to the disaster, to stereotypical role-playing game conventions. Every victory in battle displays the message "another victory for the Trenchcoat Mafia", in reference to the gang that Harris and Klebold were mistakenly affiliated with by the media. Ledonne added the hell segment and populated it with characters from the video game "Doom", explaining that "[having the shooters] battle these monsters in an eternal recreation of their favorite videogame was a statement in and of itself." "Super Columbine Massacre" is the only video game Ledonne has created, and he has no future plans to create another.


title: Super Columbine Massacre RPG!

text: The game was made available for download on April 20, 2005, the sixth anniversary of the Columbine massacre. Ledonne sought to remain anonymous at the game's debut to avoid any possible controversy, which he would later regret as it created the impression he had something to hide. Under the alias "Columbin", Ledonne regularly engaged gamers and critics alike on a message board he established to discuss the game's depiction of the shooting and the broader implications of the shooting. Ledonne's identity was revealed by Roger Kovacs, a friend of one of the Columbine victims, Rachel Scott. Kovacs found out Ledonne's name by donating to the site via PayPal; after his name and address were posted online, Ledonne stepped forward and was greeted with requests for interviews. "That's when I decided that I had to grow a backbone and stand up for my creation", Ledonne said.


title: Super Columbine Massacre RPG!

text: The game is distributed as freeware, with donations in the amount of $1 requested to defray bandwidth costs. Initially, the game attracted little attention, and was downloaded 10,000 times in its first year. In April 2006 Patrick Dugan of web site Gamasutra wrote about the game after meeting its host at Game Developers Conference. Impressed, Dugan sent an email to Georgia Institute of Technology professor Ian Bogost, who blogged about the game. Brian Crecente of gaming news site Kotaku and the "Rocky Mountain News" subsequently interviewed Bogost, and the Associated Press and mainstream media picked up the story. The increased visibility resulted in increased coverage, controversy, and downloads; in the first half of May 2006 the game was downloaded more than 30,000 times. Ledonne announced in September 2006 that the game was no longer available for download directly through its website (instead providing download links), as the title's popularity cost too much to sustain; in a single day in September, he reported 8,000 downloads. By March 2007, the game had been downloaded more than 400,000 times.


title: Super Columbine Massacre RPG!

text: Reception of "Super Columbine Massacre" has been negative amongst the mainstream media and those personally affected by the shootings. Upon revealing Columbine's identity as Ledonne, Kovacs said "One of the girls who died [in the shootings] was a friend of mine, Rachel. We were in the same church group. Anyone playing this game can kill Rachel over and over again." The father of one victim remarked to the press that the game "disgusts me. You trivialize the actions of two murderers and the lives of the innocent." One victim of the shooting played the game and voiced reserved support, remarking that "It probably sounds a bit odd for someone like me to say, but I appreciate the fact at least to some degree that something like this was made." While he took issue with what he saw as glamorization of the shooters, he also believed it would help open a dialogue about the shooting.


title: Super Columbine Massacre RPG!

text: "Super Columbine Massacre" was largely condemned by the press. Betty Nguyen of CNN labeled the game as an example of a subculture that worships terrorists. Newspapers called the game "exploitive" and a "monstrosity". "PC World" declared the game #2 on its list of "The 10 Worst Games of All Time." Even critics who were supportive of Ledonne's intent found the game hard to play; Ben Kuchera of Ars Technica said that he left the game "shaken", but that as an easily misunderstood game "the people who are most likely to gain anything from it will never play it." Crecente felt that the message of the game was obscured by the cartoon graphics of the medium. Ledonne has refused to alter the game as it represents his thoughts on the subject at a particular point in time, but has encouraged others to rework the game themselves.


title: Super Columbine Massacre RPG!

text: The most positive reviews of "Super Columbine Massacre" came from critics who accepted Ledonne's intended message. "Wired" magazine writer Clive Thompson appreciated the game's attention to narrative detail, writing that "the upshot [of the game] is that Ledonne has done a surprisingly good job of painting the emotional landscape of [the gunmen]—whipsawing from self-pity to pompous grandiosity and blinding rage, then back again." Thompson called the game subtle, including jabs at the participants and gaming culture by using the language of games as a way to think about the killings. Writing for "The Courier Mail", Paul Syvret's advice to those who found the game controversial and in bad taste was to "lighten up". Bogost summed up his review of the game by writing "this game is not fun, it is challenging, and difficult to play—not technically difficult, but conceptually difficult. We need more of that." David Kociemba, a professor at Emerson College, agreed with Bogost and commented that "the controversy should be that there aren't more games like "Super Columbine Massacre RPG!" that are as demanding and as artistically innovative." Dugan responded to common criticisms of the game, including that the game was made in bad taste, by writing a rebuttal on his blog:


title: Super Columbine Massacre RPG!

text: I think everyone who disses the "Columbine RPG" is gutless. Most haven't played the game, or have played it with such preconceptions that they're blinded to the genuis [sic], the honesty, the beauty of its social commentary. "Super Columbine Massacre RPG" is riddled with design flaws and has mediocre graphics by 1995, the maker of the game admits this, but it regardless is a work of art. It puts you in the mindset of the killers and provides a very clear suggestion of why they did what they did; they were enacting an ideological demonstration through a terrorist act, and the game shines light on this as an indictment of the American dream and way of life painfully close to the main nerve.


title: Super Columbine Massacre RPG!

text: After the Dawson College shooting in September 2006, when gunman Kimveer Gill killed one student and injured 19 others, the "Toronto Sun" wrote that Gill had self-reported playing "Columbine Massacre" on a web site. The story was picked up by media and reported widely. Upon hearing media reports of a link to the game one of the shooting victims at Dawson College contacted Ledonne and told him that "I just suffered multiple gunshot wounds and I think you should take this game down." Ledonne expressed his reaction to the shooting and renewed media attention towards his game in an interview a week later:


title: Super Columbine Massacre RPG!

text: If one is interested in making something for the public to view—be it a painting, a book, an album, a film, or a video game, should the POSSIBLE harm that may come out of this work be grounds for its suppression from society? This is, in a sense, pre-crime. If you believe in what you're doing and you want to express yourself, the expression should be primary and any interpretations that come after must always remain of secondary importance to the creation of the work itself. On another level, the entire correlation between the Dawson College shooting and my game is unfounded. [...] What else did Kimveer like? Black clothes? Goth music? Pizza? [...] If anything, the Dawson College shooting is proof positive that games like ["Super Columbine Massacre"] "should" be made; until video games are no longer among the "usual suspects" for homicidal rampages, the public needs to more carefully consider why interactive electronic media is somehow the manufacturer of Manchurian Candidates.


title: Super Columbine Massacre RPG!

text: Developer Ryan Lambourn created a flash game called "V-Tech Rampage" in 2007, which allows players to control the actions of gunman Seung-Hui Cho in the Virginia Tech massacre. Lambourn professed empathy for Cho, and said that he was a target of bullying in high school. "No one listens to you unless you've got something sensational to do. And that's why I feel sympathy for Cho Seung-Hui [sic]. He had to go that far", Lambourn stated. On the "V-Tech Rampage" site, Lambourn posted a statement that he would take the game off of Newgrounds if donations reached $1000; at $2000 in donations he would take the game down from the main site and for another $1000 he would apologize for creating it. Ledonne posted a comment on Lambourn's website after "V-Tech Rampage" drew comparisons to "Super Columbine Massacre", calling Lambourn's statement tantamount to a "hostage note", and asking bloggers to consider "not whether a game about the Virginia Tech shooting SHOULD be made but how we might go about making a game that accomplishes more than "V-Tech Rampage" does with the subject matter." Ledonne stated that he emailed Lambourn sympathetically, but that the creator responded to his emails with profanity; he reiterated that the two games had different motivations and were not easily comparable in content.


title: Super Columbine Massacre RPG!

text: In October 2006, Sam Roberts, the Guerilla Gamemaker Competition director of the Slamdance festival, emailed Ledonne encouraging him to submit the game to the contest. Ledonne looked at the selection of the game as one of the competition's finalists in December as evidence that "all forms of art can be valid tools for societal exploration (even painful topics like school shootings)". The event's organizer, Peter Baxter, announced the removal of the game from the festival's "Guerrilla Gamemaker Competition" after its selection as a finalist. Several reasons for the change of mind were given, including threatened sponsor withdrawal, possible lawsuits, and "moral grounds"; Baxter denied that sponsor pressure caused the drop, instead affirming that "the shootings are still a very touchy subject, and rightly so. We have to be sensitive to [victims and their families'] feelings." An additional consideration reported was that unnamed parties might sue for copyright violations in the game itself. The announcement marked the first time the festival had pulled jury-selected content from the contest; the incident was dubbed "Slamgate" by the gaming press.


title: Super Columbine Massacre RPG!

text: Following the announcement, USC Interactive Media Division withdrew its sponsorship of the festival. Seven of the fourteen finalist games were removed from the contest by their developers in protest: "Braid", "flOw", "Once Upon A Time", "Toblo", "Everyday Shooter", "Book and Volume" and "Castle Crashers" ("Toblo" was later reinstated by the DigiPen Institute of Technology, who owns the rights to the game). Developer Jonathan Blow of "Braid" stated: "["Super Columbine Massacre"] lacks compassion, and I find the Artist's Statement disingenuous. But despite this, the game does have redeeming value. It does provoke important thoughts, and it does push the boundaries of what games are about. It is composed with more of an eye toward art than most games. Clearly, it belongs at the festival." Blow and the other developers sent an open letter to the festival, encouraging the reinstatement of the game as keeping with the festival's "trailblazing" efforts. Despite protests, Baxter refused to change his mind, citing consideration for the shooting's victims and their families. Ledonne told the other finalists that he planned to go to the festival anyway and distribute copies of the game. Acknowledging that the withdrawal of six finalists compromised the competition, Roberts let the attendees vote on whether any prizes would be awarded; they decided not to.


title: Super Columbine Massacre RPG!

text: Brian Flemming, director of "The God Who Wasn't There", saw Ledonne's demo of "Super Columbine Massacre" outside the festival, and convinced two fellow Slamdance film jurors to award the game a "Special Jury Prize" for Best Documentary, an unofficial award not endorsed by Slamdance itself. The jurors intended to present the special prize alongside the award for best documentary. Shortly before the ceremony, Baxter informed Flemming that he could not present the award due to "music clearance issues", and refused to allow it despite Flemming's protests. According to Ledonne, Flemming tried to hold his ground, but eventually gave in to Baxter's request.


title: Super Columbine Massacre RPG!

text: Ledonne produced a documentary film based on his experiences after the release of "Super Columbine Massacre". Titled "Playing Columbine", the documentary uses the controversy surrounding the game to investigate the large issues facing video games as a medium for artistic expression. The film premiered at AFI Fest in Los Angeles, California on November 7, 2008.


title: Super Columbine Massacre RPG!

text: As a result of the controversy of his game, Ledonne became an unwitting spokesman for the games industry, facing the medium's opponents in debates and forums. The furor resulting from Slamgate was called out by Ledonne and others in the media as a sign that video games had not yet outgrown the traditional stereotype of children's games. Keith Stuart of "The Guardian" wrote that despite being confused and tawdry, "Super Columbine Massacre" "symbolizes a growing understanding that videogames have more to say than 'shoot the enemies and pick up health.'" Authors Andreas Jahn-Sudmann and Ralf Stockmann consider controversial video games such as "Super Columbine Massacre" and the "Grand Theft Auto" "Hot coffee mod" evidence of sociopolitical tensions present between gamers and older generations. The game and others like it continue to be at the center of the video games as art debate, and Gamasutra credited "Super Columbine Massacre" and Slamgate as having two highly positive and far-reaching effects; first, forcing print game journalism to focus on the issue; and second, the "evangelization of the notion that games can be as meaningful and important as other media, even if the example is offensive to the sensibilities of most Americans [...] To win is to lose, but to play is to experience an enrichment that cannot be scored."


title: Free imperial city

text: In the Holy Roman Empire, the collective term free and imperial cities (), briefly worded free imperial city (', ), was used from the fifteenth century to denote a self-ruling city that had a certain amount of autonomy and was represented in the Imperial Diet. An imperial city held the status of Imperial immediacy, and as such, was subordinate only to the Holy Roman Emperor, as opposed to a territorial city or town (') which was subordinate to a territorial princebe it an ecclesiastical lord (prince-bishop, prince-abbot) or a secular prince (duke ('), margrave, count ('), etc.).


title: Free imperial city

text: The evolution of some German cities into self-ruling constitutional entities of the Empire was slower than that of the secular and ecclesiastical princes. In the course of the 13th and 14th centuries, some cities were promoted by the emperor to the status of Imperial Cities ('; '), essentially for fiscal reasons. Those cities, which had been founded by the German kings and emperors in the 10th through 13th centuries and had initially been administered by royal/imperial stewards ("), gradually gained independence as their city magistrates assumed the duties of administration and justice; some prominent examples are Colmar, Haguenau and Mulhouse in Alsace or Memmingen and Ravensburg in upper Swabia.


title: Free imperial city

text: The Free Cities ('; ') were those, such as Basel, Augsburg, Cologne or Strasbourg, that were initially subjected to a prince-bishop and, likewise, progressively gained independence from that lord. In a few cases, such as in Cologne, the former ecclesiastical lord continued to claim the right to exercise some residual feudal privileges over the Free City, a claim that gave rise to constant litigation almost until the end of the Empire.


title: Free imperial city

text: Over time, the difference between Imperial Cities and Free Cities became increasingly blurred, so that they became collectively known as "Free Imperial Cities", or "Free and Imperial Cities", and by the late 15th century many cities included both "Free" and "Imperial" in their name. Like the other Imperial Estates, they could wage war, make peace, and control their own trade, and they permitted little interference from outside. In the later Middle Ages, a number of Free Cities formed City Leagues ("), such as the Hanseatic League or the Alsatian , to promote and defend their interests.


title: Free imperial city

text: In the course of the Middle Ages, cities gained, and sometimesif rarelylost, their freedom through the vicissitudes of power politics. Some favored cities gained a charter by gift. Others purchased one from a prince in need of funds. Some won it by force of arms during the troubled 13th and 14th centuries and others lost their privileges during the same period by the same way. Some cities became free through the void created by the extinction of dominant families, like the Swabian . Some voluntarily placed themselves under the protection of a territorial ruler and therefore lost their independence.


title: Free imperial city

text: A few, like Protestant , which in 1607 was annexed to the Catholic Duchy of Bavaria, were stripped by the Emperor of their status as a Free Cityfor genuine or trumped-up reasons. However, this rarely happened after the Reformation, and of the sixty Free Imperial Cities that remained at the Peace of Westphalia, all but the ten Alsatian cities (which were annexed by France during the late 17th century) continued to exist until the mediatization of 1803.


title: Free imperial city

text: There were approximately four thousand towns and cities in the Empire, although around the year 1600 over nine-tenths of them had fewer than one thousand inhabitants. During the late Middle Ages, fewer than two hundred of these places ever enjoyed the status of Free Imperial Cities, and some of those did so only for a few decades. The Imperial military tax register ("") of 1521 listed eighty-five such cities, and this figure had fallen to sixty-five by the time of the Peace of Augsburg in 1555. From the Peace of Westphalia of 1648 to 1803, their number oscillated at around fifty.


title: Free imperial city

text: Unlike the Free Imperial Cities, the second category of towns and cities, now called "territorial cities" were subject to an ecclesiastical or lay lord, and while many of them enjoyed self-government to varying degrees, this was a precarious privilege which might be curtailed or abolished according to the will of the lord.


title: Free imperial city

text: Reflecting the complex constitutional set-up of the Holy Roman Empire, a third category, composed of semi-autonomous cities that belonged to neither of those two types, is distinguished by some historians. These were cities whose size and economic strength was sufficient to sustain a substantial independence from surrounding territorial lords for a considerable time, even though no formal right to independence existed. These cities were typically located in small territories where the ruler was weak. They were nevertheless the exception among the multitude of territorial towns and cities. Cities of both latter categories normally had representation in territorial diets, but not in the Imperial Diet.


title: Free imperial city

text: Free imperial cities were not officially admitted as individual Imperial Estates to the Imperial Diet until 1489, and even then their votes were usually considered only advisory ("") compared to the Benches of the electors and princes. The cities divided themselves into two groups, or benches, in the Imperial Diet, the Rhenish and the Swabian Bench.


title: Free imperial city

text: These same cities were among the 85 free imperial cities listed on the "Reichsmatrikel" of 1521, the imperial civil and military tax-schedule used for more than a century to assess the contributions of all the Imperial Estates in case of a war formally declared by the Imperial Diet. The military and monetary contribution of each city is indicated in parenthesis (for instance Cologne (30-322-600) means that Cologne had to provide 30 horsemen, 322 footmen and 600 gulden). These numbers are equivalent to one "simplum". If need be, the Diet could vote a second and a third "simplum", in which case each member's contribution was doubled or tripled. At the time, the Free imperial cities were considered wealthy and the monetary contribution of Nuremberg, Ulm and Cologne for instance were as high as that of the Electors (Mainz, Trier, Cologne, Palatinate, Saxony, Brandenburg) and the Dukes of Württemberg and of Lorraine.


title: Free imperial city

text: The following list contains the 50 Free imperial cities that took part in the Imperial Diet of 1792. They are listed according to their voting order on the Rhenish and Swabian benches.


title: Free imperial city

text: By the time of the Peace of Westphalia, the cities constituted a formal third "college" and their full vote ("") was confirmed, although they failed to secure parity of representation with the two other colleges. To avoid the possibility that they would have the casting vote in case of a tie between the Electors and the Princes, it was decided that these should decide first and consult the cities afterward.


title: Free imperial city

text: Despite this somewhat unequal status of the cities in the functioning of the Imperial Diet, their full admittance to that federal institution was crucial in clarifying their hitherto uncertain status and in legitimizing their permanent existence as full-fledged Imperial Estates. Constitutionally, if in no other way, the diminutive Free Imperial City of Isny was the equal of the Margraviate of Brandenburg.


title: Free imperial city

text: Having probably learned from experience that there was not much to gain from active, and costly, participation in the Imperial Diet's proceedings due to the lack of empathy of the princes, the cities made little use of their representation in that body. By about 1700, almost all the cities with the exception of Nuremberg, Ulm and Regensburg (where by then the Perpetual Imperial Diet was located), were represented by various Regensburg lawyers and officials who often represented several cities simultaneously. Instead, many cities found it more profitable to maintain agents at the Aulic Council in Vienna, where the risk of an adverse judgment posed a greater risk to city treasuries and independence.


title: Free imperial city

text: The territory of most Free Imperial Cities was generally quite small but there were exceptions. The largest territories formed in what is now Switzerland with cities like Bern, Zürich and Luzern, but also cities like Ulm, Nuremberg and Hamburg in what is now Germany possessed substantial hinterlands or fiefs that comprised dozens of villages and thousands of subject peasants who did not enjoy the same rights as the urban population. At the opposite end, the authority of Cologne, Aachen, Worms, Goslar, Wetzlar, Augsburg and Regensburg barely extended beyond the city walls.


title: Free imperial city

text: The constitution of Free and Imperial Cities was republican in form, but in all but the smallest cities, the city government was oligarchic in nature with a governing town council composed of an elite, hereditary patrician class, the so-called town council families ("). They were the most economically significant burgher families who had asserted themselves politically over time.


title: Free imperial city

text: Below them, with a say in the government of the city (there were exceptions, such as Nuremberg, where the patriciate ruled alone), were the citizens or burghers, the smaller, privileged section of the city's permanent population whose number varied according to the rule of citizenship of each city. To the common town dwellerwhether he lived in a prestigious Free Imperial City like Frankfurt, Augsburg or Nuremberg, or in a small market town such as there were hundreds throughout Germanyattaining burgher status (') could be his greatest aim in life. The burgher status was usually an inherited privilege renewed pro-forma in each generation of the family concerned but it could also be purchased. At times, the sale of burgher status could be a significant item of town income as fiscal records show. The ' was local and not transferable to another city.


title: Free imperial city

text: The burghers were usually the lowest social group to have political power and privilege within the Holy Roman Empire. Below them was the disenfranchised urban population, maybe half of the total in many cities, the so-called "residents" (") or "guests": smaller artisans, craftsmen, street venders, day laborers, servants and the poor, but also those whose residence in the city was temporary, such as wintering noblemen, foreign merchants, princely officials, and so on.


title: Free imperial city

text: Urban conflicts in Free Imperial Cities, which sometimes amounted to class warfare, were not uncommon in the Early Modern Age, particularly in the 17th century (Lübeck, 1598–1669; Schwäbisch Hall, 1601–1604; Frankfurt, 1612–1614; Wezlar, 1612–1615; Erfurt, 1648–1664; Cologne, 1680–1685; Hamburg 1678–1693, 1702–1708). Sometimes, as in the case of Hamburg in 1708, the situation was considered sufficiently serious to warrant the dispatch of an Imperial commissioner with troops to restore order and negotiate a compromise and a new city constitution between the warring parties.


title: Free imperial city

text: The number of Imperial Cities shrank over time until the Peace of Westphalia. There were more in areas that were very fragmented politically, such as Swabia and Franconia in the southwest, than in the North and the East where the larger and more powerful territories, such as Brandenburg and Saxony, were located, which were more prone to absorb smaller, weaker states.


title: Free imperial city

text: In the 16th and 17th century, a number of Imperial Cities were separated from the Empire due to external territorial change. Henry II of France seized the Imperial Cities connected to the Three Bishoprics of Metz, Verdun and Toul. Similarly, Louis XIV seized many cities based on claims produced by his Chambers of Reunion. That way, Strasbourg and the ten cities of the were annexed. Also, when the Old Swiss Confederacy gained its formal independence from the Empire in 1648 (it had been de facto independent since 1499), the independence of the Imperial Cities of Basel, Bern, Lucerne, St. Gallen, Schaffhausen, Solothurn, and Zürich was formally recognized.


title: Free imperial city

text: With the rise of Revolutionary France in Europe, this trend accelerated enormously. After 1795, the areas west of the Rhine were annexed to France by the revolutionary armies, suppressing the independence of Imperial Cities as diverse as Cologne, Aachen, Speyer and Worms. Then, the Napoleonic Wars led to the reorganization of the Empire in 1803 (see German Mediatisation), where all of the free cities but sixHamburg, Bremen, Lübeck, Frankfurt, Augsburg, and Nuremberglost their independence and were absorbed into neighboring territories. Finally, under pressure from Napoleon, the Holy Roman Empire was dissolved in 1806. By 1811, all of the Imperial Cities had lost their independenceAugsburg and Nuremberg had been annexed by Bavaria, Frankfurt had become the center of the Grand Duchy of Frankfurt, a Napoleonic puppet state, and the three Hanseatic cities had been directly annexed by France as part of its effort to enforce the Continental Blockade against Britain. Hamburg and Lübeck with surrounding territories formed the département of , and Bremen the .


title: Free imperial city

text: When the German Confederation was established by the Congress of Vienna in 1815, Hamburg, Lübeck, Bremen, and Frankfurt were once again made Free Cities, this time enjoying total sovereignty as all the members of the loose Confederation. Frankfurt was annexed by Prussia in consequence of the part it took in the Austro-Prussian War of 1866. The three other Free Cities became constituent states of the new German Empire in 1871 and consequently were no longer fully sovereign as they lost control over defence, foreign affairs and a few other fields. They retained that status in the Weimar Republic and into Nazi Germany, although under Hitler it became purely notional. Due to Hitler's distaste for Lübeck and its liberal tradition, the need was devised to compensate Prussia for territorial losses under the Greater Hamburg Act, and Lübeck was annexed to Prussia in 1937. In the Federal Republic of Germany which was established after the war, Bremen and Hamburg, but not Lübeck, became constituent states, a status which they retain to the present day. Berlin, which had never been a Free City in its history, also received the status of a state after the war due to its special position in divided post-war Germany.


title: Free imperial city

text: Regensburg was, apart from hosting the Imperial Diet, a most peculiar city: an officially Lutheran city that nevertheless was the seat of the Catholic prince-bishopric of Regensburg, its prince-bishop and cathedral chapter. The Imperial City also housed three Imperial abbeys: St. Emmeram, and . They were five immediate entities fully independent of each other existing in the same small city.


title: Linate Airport disaster

text: The Linate Airport disaster occurred in Italy at Linate Airport in Milan on the morning of Monday, 8 October 2001. Scandinavian Airlines System Flight 686, a McDonnell Douglas MD-87 airliner carrying 110 people bound for Copenhagen, Denmark, collided on take-off with a Cessna Citation CJ2 business jet carrying four people bound for Paris, France. All 114 people on board both aircraft were killed, as well as four people on the ground.


title: Linate Airport disaster

text: The subsequent investigation determined that the collision was caused by a number of nonfunctioning and nonconforming safety systems, standards, and procedures at the airport. It remains the deadliest accident in Italian aviation history.


title: Linate Airport disaster

text: Two aircraft were involved in the collision. The larger of the two aircraft was a McDonnell-Douglas MD-87. The cockpit crew consisted of Captain Joakim Gustafsson and First Officer Anders Hyllander, both aged 36. The Captain was hired by SAS in 1990 and had more than 5,800 hours of flight time. He had logged approximately 230 hours in the MD-87. The first officer was hired by the airline in 1997. At the time of the accident he had more than 4,300 total flying hours. He was more experienced in the aircraft type than his captain, having logged 2,000 hours of flight time in the MD-87.


title: Linate Airport disaster

text: The second aircraft was a Cessna Citation 525-A. There were two German pilots aboard. The captain, 36-year-old Horst Königsmann, had approximately 5,000 total flight hours logged, of which roughly 2,400 were accumulated in the Citation. The first officer, 64-year-old Martin Schneider, had approximately 12,000 flight hours' experience, of which 2,000 hours were in the Citation.


title: Linate Airport disaster

text: The passengers were Luca Fossati, chairman of Star – Stabilimento Alimentare S.p.A. and a Cessna sales representative. The flight was a test flight as Star was considering buying a Citation.


title: Linate Airport disaster

text: The Cessna Citation was instructed to taxi from the western apron along the northern taxiway (taxiway R5), and then via the northern apron to the main taxiway which runs parallel to Runway 36R, a route that would have kept it clear of 36R. Instead, the pilot taxied along the southern taxi route (taxiway R6), crossing Runway 36R toward the main taxiway which lay beyond it (see diagram).


title: Linate Airport disaster

text: At 08:09:28, the MD-87 was given clearance by a different controller to take off from Runway 36R. Fifty-three seconds later, the MD-87 aircraft, travelling at about , collided with the Cessna. One of the four people in the Cessna was killed on impact; the remaining three initially survived the impact, but died later from their injuries. The MD-87 lost its right engine; the pilot, Joakim Gustafsson, attempted to take off, reaching an altitude of approximately . The remaining engine lost some thrust due to debris ingestion, and the plane lost the right landing gear, came down. Gustafsson applied thrust reverser and brakes, and tried to guide the plane through its control surfaces. This was insufficient to halt the jet's momentum, and it crashed into a luggage hangar located near the runway's end, at a speed of approximately . In the impact, all the MD-87's crew and passengers were killed. The crash and subsequent fire killed four Italian ground personnel in the hangar and injured four more.


title: Linate Airport disaster

text: Of the occupants of the MD-87, 54 (46%), mainly in the back of the aircraft, suffered severe burns; their bodies were identified using forensic dentistry or DNA records. Those in the front of the aircraft suffered severe blunt trauma. All of the occupants of the MD-87 were killed by impact, not fire.


title: Linate Airport disaster

text: The accident occurred less than a month after the September 11 attacks and the day after the U.S. invasion of Afghanistan began, but the Italian government was quick to rule out a terrorist attack as the cause. This was subsequently confirmed by the investigations that followed.


title: Linate Airport disaster

text: The accident was investigated by the National Agency for the Safety of Flight (ANSV). The ANSV's final report was published on 20 January 2004 and concluded that the "immediate cause" of the accident was the incursion of the Cessna aircraft onto the active runway. The ANSV stopped short of placing the blame entirely on the Cessna pilots, who had become lost in the fog. Their report identified deficiencies in the airport layout and procedures.


title: Linate Airport disaster

text: Linate Airport was operating without a functioning ground radar system at the time, despite having had a new system approved on 30 March 1995. The previous system had been decommissioned on 29 November 1999, but the replacement had not been fully installed. The new system came online a few months later. Guidance signs along the taxiways were obscured, or badly worn, and were found not to meet regulations. After the pilots mistakenly turned onto the R6 taxiway that led to the runway, there were no signs by which they could recognize where they were. When they stopped at a taxiway stop-marking, and correctly reported its identifier, S4, the ground controller disregarded this identification because it was not on his maps and was unknown to him. Motion sensing runway incursion alarms, although present, had been deactivated to prevent false alarms from vehicles or animals. The ground controller's verbal directions used terminology to designate aprons, taxiways, and runways, which did not match their on-the-ground signage and labels. Lastly, neither pilot of the Cessna was certified for landings with visibility less than , but had landed at the airport anyway an hour before the disaster with a visibility reported by air traffic control of .


title: Linate Airport disaster

text: On 16 April 2004, a Milan court found four persons guilty for the disaster. Airport director Vincenzo Fusco and air-traffic controller Paolo Zacchetti were both sentenced to eight years in prison. Francesco Federico, former head of the airport, and Sandro Gualano, former head of the air traffic control agency, received sentences of six and a half years. The pardon law issued by the Italian Parliament on 29 July 2006 reduced all convictions by three years. On 7 July 2006, Fusco and Federico were acquitted by the Milan Appeals Court. The controller Zacchetti's sentence was reduced to three years. In addition three more people were sentenced for multiple manslaughter and negligent disaster: former ENAV director general Fabio Marzocca to four years and four months, and; former SEA airports agency officials Antonio Cavanna and Lorenzo Grecchi each to three years and three months. On 20 February 2008 the Supreme Court of Cassation (Italy) upheld the acquittal of Fusco and Federico and confirmed five convictions. (Initially, in late 2002, eleven officials and functionaries had been charged with manslaughter.)


title: Linate Airport disaster

text: The initial eight-year sentence for Zacchetti prompted outrage among air traffic controllers. His sentence has been questioned in aviation safety law commentary.


title: Linate Airport disaster

text: Victims of the crash included nationals of nine different countries. Most of the victims were Italian and Scandinavian.


title: Linate Airport disaster

text: Four memorial services were held in honour of the SAS MD-87 victims. On 12 October, three separate ceremonies were held, with one in Denmark, one in Norway, and one in Sweden. On 13 October, a fourth ceremony was held in Italy.


title: Linate Airport disaster

text: In March 2002, a forest containing 118 beeches called "Bosco dei Faggi" was inaugurated as a memorial to the victims in the Forlanini Park near the airport. A sculpture by the Swedish artist Christer Bording donated by SAS, called "Infinity Pain", was placed in the centre of the forest.


title: Linate Airport disaster

text: The disaster devastated the Swedish go-kart community as some of the country's most promising young drivers were on the flight after attending an event in Lonato. After the disaster, the Swedish national motorsports club started a memorial fund together with some of the relatives. The fund awards annual stipends to promising Swedish youth in go-kart.


title: Linate Airport disaster

text: In 2012 the accident was featured on the 11th season of the Discovery Channel Canada / National Geographic TV series "Mayday", in an episode entitled "The Invisible Plane". The episode featured interviews with accident investigators, and a dramatization of the crash and investigation.


title: Katanagatari

text: "Katanagatari" is the story of Yasuri Shichika, a swordsman who fights without a sword, and Togame, an ambitious young strategist who seeks to collect 12 legendary swords for the shogunate. Shichika is the son of an exiled war hero and the seventh head of the Kyotouryuu school of fighting who lives on the isolated Fushou Island with his elder sister, Nanami. Togame seeks him out because his bare-handed fighting style means that he will not be corrupted by the power of the swords. Togame, who has been betrayed before, convinces Shichika to accompany her on a mission to locate the Deviant Blades. They embark on a journey together across Edo-era Japan to collect the Deviant Blades, all wielded by formidable opponents.


title: Katanagatari

text: "Katanagatari" was released one volume a month throughout 2007. A spin-off novel, "Maniwagatari", was released a year later. During their panel at Anime Boston on March 30, 2018, English light novel publisher Vertical announced that they had licensed the series. They released it as four 3-in-1 omnibus volumes from November 2018 to August 2020.


title: Katanagatari

text: The anime is composed of a dozen 50-minute episodes and follows the two main characters while they are searching for the katanas, except for one episode that is centered on Nanami Yasuri. In each episode, Shichika and Togame collect a katana or a new one will be introduced. The length of the episodes is unusual since most anime have 24-minute episodes and run weekly instead of monthly. A new episode would be released every month, beginning on January 26, 2010, and finishing on December 11, 2010.


title: Katanagatari

text: For the first half of the series (episodes 1–7), the opening theme is "Meiya Kadenrō" (冥夜花伝廊) by Minami Kuribayashi while the second half of the series (episode 8–12) is "Katana to Saya" (刀と鞘) by ALI PROJECT. However, the ending theme changes for each episode. For the noitamina rerun, the new opening theme song was "Hakushukassai Utaawase" by supercell, and Piko performed the new ending theme song "Kotonoha".


title: Katanagatari

text: A Drama CD in twelve chapters, titled "Episode 0: Kyotō Yasuri" and written by Nisio Isin, was released with the DVD/BDs of the series. It is set during the rebellion twenty years before the events of the series. Each chapter has a character from the series narrating the episode.


title: La Reine Margot (1994 film)

text: La Reine Margot is a 1994 historical romantic drama film directed by Patrice Chéreau, from a screenplay he co-wrote with Danièle Thompson, based on the 1845 historical novel of the same name by Alexandre Dumas. The film stars Isabelle Adjani, Daniel Auteuil, Jean-Hugues Anglade, Vincent Perez and Virna Lisi. An abridged version of the film was released as Queen Margot in North America, and in the United Kingdom under its original French title.


title: La Reine Margot (1994 film)

text: It won the Jury Prize and Best Actress Award at the Cannes Film Festival, as well as five César Awards. A restored version was shown as part of the Cannes Classics section of the 2013 Cannes Film Festival.


title: La Reine Margot (1994 film)

text: During the late 16th century, Catholics and Protestant Huguenots are fighting over political control of France, which is ruled by the neurotic, hypochondriac King Charles IX, and his mother, Catherine de' Medici, a scheming power player. Catherine decides to make an overture of goodwill by offering up her daughter Margot in marriage to Henri de Bourbon, a prominent Huguenot and King of Navarre, although she also schemes to bring about the notorious St. Bartholomew's Day Massacre of 1572, when thousands of Protestants are slaughtered. The marriage goes forward but Margot, who does not love Henri, begins a passionate affair with the soldier La Môle, also a Protestant from a well-to-do family. Murders by poisoning follow, as court intrigues multiply and Queen Catherine's villainous plotting to place her son the Duke of Anjou on the throne threatens the lives of La Môle, Margot and Henri of Navarre. A book with pages painted with arsenic is intended for Henri but instead causes the slow, agonizing death of King Charles. Henri escapes to Navarre and sends La Môle to fetch Margot, but Guise apprehends him. La Môle is beheaded in the Bastille before Margot can save him, and King Charles finally dies. Margot escapes carrying La Môle's embalmed head as Anjou is proclaimed King of France as Henry III.


title: La Reine Margot (1994 film)

text: The film was an international co-production between by several companies based in France, Germany, and Italy, with the additional participation of StudioCanal and the American company Miramax and the support of Eurimages. Among the locations were the Mafra Palace in Portugal, the Saint-Quentin Basilica, Saint-Quentin, Aisne, and the Château de Maulnes, Cruzy-le-Châtel in France. The organ piece played during the wedding of Margaret of Valois and Henri de Bourbon was recorded by Pierre Pincemaille on the organ of the Basilica of Saint-Denis.


title: La Reine Margot (1994 film)

text: The "La Reine Margot" soundtrack was composed by Sarajevo-born composer Goran Bregović. Like most of Bregović's work, the soundtrack's melodies are heavily influenced by the Balkan folk music tradition. Additionally, Bregović refurbished some of his previous work while as the frontman of Yugoslav rock band Bijelo dugme.


title: La Reine Margot (1994 film)

text: The film opened on 13 May 1994 at the 1994 Cannes Film Festival and also opened nationally in France the same day. The version shown at Cannes and for the French theatrical run had a runtime of 162 minutes.


title: La Reine Margot (1994 film)

text: For the film’s North American release, the film's American distributor Miramax chose to market the film as a traditional costume drama, with an emphasis on the romance between Margot and La Môle. Fifteen minutes were cut from Chéreau’s version and a deleted scene of Margot and La Môle wrapped in a red cloak was reinserted. This version was shown in cinemas outside France and later on video. Miramax also changed the image on the poster; the American one features the red cloak scene of the pair of lovers, in contrast to the French poster which shows a shocked Margot in a white dress bespattered with blood. The film grossed over $1.29 million in the U.S. in 1994.


title: La Reine Margot (1994 film)

text: The original full-length version was available for a limited period in the United Kingdom on VHS in a collectors' edition box set in 1995, but all further releases until the blu-ray rerelease in 2014 used the shorter 145-minute cut. The Region 2 European DVD cover also uses the original poster.


title: La Reine Margot (1994 film)

text: The film grossed 12.7 million French Francs ($2.2 million) in its first five days in France. The following week it was the number one film in France after expanding from 248 to 428 screens. The film had a total of 2,002,915 admissions in France, for a gross of $12.26 million. In Italy, the film grossed over $2 million. In the United States and Canada, the film grossed $2,017,346 in a limited theatrical release. It had admissions of 260,000 in Germany with a gross of $1.33 million and 530,800 admissions in Argentina. It was the highest-grossing non-English language film in the UK during 1995 with a gross of £635,711 ($980,000). In Australia it grossed $890,000. Worldwide, it has grossed over $20 million.


title: La Reine Margot (1994 film)

text: For the film's 20th anniversary, Pathé restored Patrice Chéreau’s original 162-minute cut to 4k definition, and this version was given a limited theatrical release by the Cohen Media Group in 2014. This version received more critical praise than the 1994 Miramax cut, which critics said was confusing and did not give enough time for American audiences to digest various characters and plot lines.


title: La Reine Margot (1994 film)

text: Peter Sobzcynski, writing for RogerEbert.com, said the film is a "go-for-broke, blood-and-thunder saga that is as powerful and provocative today as it was when it was first released—even more so now that it has been returned to its full length", and the fact that it is one of the most expensive French films ever made shows onscreen. Scott Tobias of "The Dissolve" praised Isabelle Adjani for portraying Margot "as a figure of prismatic emotional and moral complexity, at times aggressive and seemingly reckless in pursuing her romantic and sexual interests, and at others cunning and shrewd in playing the middle of two sides locked in conflict." He noted her "uninhibited performance figures into Chéreau’s approach to history, which couldn’t be further from the decorous reserve and pageantry of other such costume epics." Sobzcynski also commended the film for putting its female characters at the forefront of the plot. J. Hoberman of "The New York Times" wrote Virna Lisi "gives a harrowing performance as the poisonous Queen Mother." Robert Abele of the "Los Angeles Times" wrote, "Chéreau’s and screenwriter Danièle Thompson’s lively adaptation of Alexandre Dumas’ novel remains a model of heaving, combustible history, in which period lavishness and performance energy aren’t mutually exclusive. Splendidly acted and tautly executed."


title: La Reine Margot (1994 film)

text: The restoration was released on Blu-ray on August 26, 2014, with a new commentary track by the New York Film Festival's director emeritus Richard Peña.


title: Polynomial ring

text: In mathematics, especially in the field of algebra, a polynomial ring or polynomial algebra is a ring (which is also a commutative algebra) formed from the set of polynomials in one or more indeterminates (traditionally also called variables) with coefficients in another ring, often a field.


title: Polynomial ring

text: Often, the term "polynomial ring" refers implicitly to the special case of a polynomial ring in one indeterminate over a field. The importance of such polynomial rings relies on the high number of properties that they have in common with the ring of the integers.


title: Polynomial ring

text: Polynomial rings occur and are often fundamental in many parts of mathematics such as number theory, commutative algebra, and algebraic geometry. In ring theory, many classes of rings, such as unique factorization domains, regular rings, group rings, rings of formal power series, Ore polynomials, graded rings, have been introduced for generalizing some properties of polynomial rings.


title: Polynomial ring

text: A closely related notion is that of the ring of polynomial functions on a vector space, and, more generally, ring of regular functions on an algebraic variety.


title: Polynomial ring

text: The polynomial ring, , in over a field (or, more generally, a commutative ring) can be defined in several equivalent ways. One of them is to define as the set of expressions, called polynomials in , of the form


title: Polynomial ring

text: where , the coefficients of , are elements of , if , and are symbols, which are considered as "powers" of , and follow the usual rules of exponentiation: , , and formula_2 for any nonnegative integers and . The symbol is called an indeterminate or variable. (The term of "variable" comes from the terminology of polynomial functions. However, here, has not any value (other than itself), and cannot vary, being a "constant" in the polynomial ring.)


title: Polynomial ring

text: One can think of the ring as arising from by adding one new element that is external to , commutes with all elements of , and has no other specific properties. This can be used for an equivalent definition of polynomial rings.


title: Polynomial ring

text: The polynomial ring in over is equipped with an addition, a multiplication and a scalar multiplication that make it a commutative algebra. These operations are defined according to the ordinary rules for manipulating algebraic expressions. Specifically, if


title: Polynomial ring

text: In these formulas, the polynomials and are extended by adding "dummy terms" with zero coefficients, so that all and that appear in the formulas are defined. Specifically, if , then for .


title: Polynomial ring

text: The scalar multiplication is the special case of the multiplication where is reduced to its "constant term" (the term that is independent of ); that is


title: Polynomial ring

text: It is straightforward to verify that these three operations satisfy the axioms of a commutative algebra over . Therefore, polynomial rings are also called "polynomial algebras".


title: Polynomial ring

text: Another equivalent definition is often preferred, although less intuitive, because it is easier to make it completely rigorous, which consists in defining a polynomial as an infinite sequence of elements of , having the property that only a finite number of the elements are nonzero, or equivalently, a sequence for which there is some so that for . In this case, and are considered as alternate notations for


title: Polynomial ring

text: the sequences and , respectively. A straightforward use of the operation rules shows that the expression


title: Polynomial ring

text: In the special case of the zero polynomial, all of whose coefficients are zero, the leading coefficient is undefined, and the degree has been variously left undefined, defined to be , or defined to be a .


title: Polynomial ring

text: It follows also that, if is an integral domain, a polynomial is a unit (that is, it has a multiplicative inverse) if and only if it is constant and is a unit in .


title: Polynomial ring

text: Given two polynomials, and , one says that "divides" , is a "divisor" of , or is a multiple of , if there is a polynomial such that .


title: Polynomial ring

text: A polynomial is irreducible if it is not the product of two non-constant polynomials, or equivalently, if its divisors are either constant polynomials or have the same degree.


title: Polynomial ring

text: Let be a field or, more generally, a commutative ring, and a ring containing . For any polynomial in and any element in , the substitution of with in defines an element of , which is denoted . This element is obtained by carrying on in after the substitution the operations indicated by the expression of the polynomial. This computation is called the evaluation of at . For example, if we have


title: Polynomial ring

text: The "polynomial function" defined by a polynomial is the function from into that is defined by formula_22 If is an infinite field, two different polynomials define different polynomial functions, but this property is false for finite fields. For example, if is a field with elements, then the polynomials and both define the zero function.


title: Polynomial ring

text: For every in , the evaluation at , that is, the map formula_23 defines an algebra homomorphism from to , which is the unique homomorphism from to that fixes , and maps to . In other words, has the following universal property:


title: Polynomial ring

text: The image of the map formula_23, that is, the subset of obtained by substituting for in elements of , is denoted . For example, formula_25, where formula_26.


title: Polynomial ring

text: As for all universal properties, this defines the pair up to a unique isomorphism, and can therefore be taken as a definition of .


title: Polynomial ring

text: If is a field, the polynomial ring has many properties that are similar to those of the ring of integers formula_27 Most of these similarities result from the similarity between the long division of integers and the long division of polynomials.


title: Polynomial ring

text: Most of the properties of that are listed in this section do not remain true if is not a field, or if one considers polynomials in several indeterminates.


title: Polynomial ring

text: Like for integers, the Euclidean division of polynomials has a property of uniqueness. That is, given two polynomials and in , there is a unique pair of polynomials such that , and either or . This makes a Euclidean domain. However, most other Euclidean domains (except integers) do not have any property of uniqueness for the division nor an easy algorithm (such as long division) for computing the Euclidean division.


title: Polynomial ring

text: The Euclidean division is the basis of the Euclidean algorithm for polynomials that computes a polynomial greatest common divisor of two polynomials. Here, "greatest" means "having a maximal degree" or, equivalently, being maximal for the preorder defined by the degree. Given a greatest common divisor of two polynomials, the other greatest common divisors are obtained by multiplication by a nonzero constant (that is, all greatest common divisors of and are associated). In particular, two polynomials that are not both zero have a unique greatest common divisor that is monic (leading coefficient equal to ).


title: Polynomial ring

text: The extended Euclidean algorithm allows computing (and proving) Bézout's identity. In the case of , it may be stated as follows. Given two polynomials and of respective degrees and , if their monic greatest common divisor has the degree , then there is a unique pair of polynomials such that


title: Polynomial ring

text: (For making this true in the limiting case where or , one has to define as negative the degree of the zero polynomial. Moreover, the equality formula_30 can occur only if and are associated.) The uniqueness property is rather specific to . In the case of the integers the same property is true, if degrees are replaced by absolute values, but, for having uniqueness, one must require .


title: Polynomial ring

text: Euclid's lemma applies to . That is, if divides , and is coprime with , then divides . Here, "coprime" means that the monic greatest common divisor is . "Proof:" By hypothesis and Bézout's identity, there are , , and such that and . So


title: Polynomial ring

text: The unique factorization property results from Euclid's lemma. In the case of integers, this is the fundamental theorem of arithmetic. In the case of , it may be stated as: "every non-constant polynomial can be expressed in a unique way as the product of a constant, and one or several irreducible monic polynomials; this decomposition is unique up to the order of the factors." In other terms is a unique factorization domain. If is the field of complex numbers, the fundamental theorem of algebra asserts that a univariate polynomial is irreducible if and only if its degree is one. In this case the unique factorization property can be restated as: "every non-constant univariate polynomial over the complex numbers can be expressed in a unique way as the product of a constant, and one or several polynomials of the form" ; "this decomposition is unique up to the order of the factors." For each factor, is a root of the polynomial, and the number of occurrences of a factor is the multiplicity of the corresponding root.


title: Polynomial ring

text: In the case of polynomials with real or complex coefficients, this is the standard derivative. The above formula defines the derivative of a polynomial even if the coefficients belong to a ring on which no notion of limit is defined. The derivative makes the polynomial ring a differential algebra.


title: Polynomial ring

text: The existence of the derivative is one of the main properties of a polynomial ring that is not shared with integers, and makes some computations easier on a polynomial ring than on integers.


title: Polynomial ring

text: Except for factorization, all previous properties of are effective, since their proofs, as sketched above, are associated with algorithms for testing the property and computing the polynomials whose existence are asserted. Moreover these algorithms are efficient, as their computational complexity is a quadratic function of the input size.


title: Polynomial ring

text: The situation is completely different for factorization: the proof of the unique factorization does not give any hint for a method for factorizing. Already for the integers, there is no known algorithm running on a classical computer for factorizing them in polynomial time. This is the basis of the RSA cryptosystem, widely used for secure Internet communications.


title: Polynomial ring

text: In the case of , the factors, and the methods for computing them, depend strongly on . Over the complex numbers, the irreducible factors (those that cannot be factorized further) are all of degree one, while, over the real numbers, there are irreducible polynomials of degree 2, and, over the rational numbers, there are irreducible polynomials of any degree. For example, the polynomial formula_34 is irreducible over the rational numbers, is factored as formula_35 over the real numbers and, and as formula_36 over the complex numbers.


title: Polynomial ring

text: The existence of a factorization algorithm depends also on the ground field. In the case of the real or complex numbers, Abel–Ruffini theorem shows that the roots of some polynomials, and thus the irreducible factors, cannot be computed exactly. Therefore, a factorization algorithm can compute only approximations of the factors. Various algorithms have been designed for computing such approximations, see Root finding of polynomials.


title: Polynomial ring

text: There is an example of a field such that there exist exact algorithms for the arithmetic operations of , but there cannot exist any algorithm for deciding whether a polynomial of the form formula_37 is irreducible or is a product of polynomials of lower degree.


title: Polynomial ring

text: On the other hand, over the rational numbers and over finite fields, the situation is better than for integer factorization, as there are factorization algorithms that have a polynomial complexity. They are implemented in most general purpose computer algebra systems.


title: Polynomial ring

text: If is an element of an associative -algebra , the polynomial evaluation at is the unique algebra homomorphism from into that maps to and does not affect the elements of itself (it is the identity map on ). It consists of "substituting" with in every polynomial. That is,


title: Polynomial ring

text: The image of this "evaluation homomorphism" is the subalgebra generated by , which is necessarily commutative.


title: Polynomial ring

text: If is injective, the subalgebra generated by is isomorphic to . In this case, this subalgebra is often denoted by . The notation ambiguity is generally harmless, because of the isomorphism.


title: Polynomial ring

text: If the evaluation homomorphism is not injective, this means that its kernel is a nonzero ideal, consisting of all polynomials that become zero when is substituted with . This ideal consists of all multiples of some monic polynomial, that is called the minimal polynomial of . The term "minimal" is motivated by the fact that its degree is minimal among the degrees of the elements of the ideal.


title: Polynomial ring

text: In field theory and number theory, an element of an extension field of is algebraic over if it is a root of some polynomial with coefficients in . The minimal polynomial over of is thus the monic polynomial of minimal degree that has as a root. Because is a field, this minimal polynomial is necessarily irreducible over . For example, the minimal polynomial (over the reals as well as over the rationals) of the complex number is formula_39. The cyclotomic polynomials are the minimal polynomials of the roots of unity.


title: Polynomial ring

text: In linear algebra, the square matrices over form an associative -algebra of finite dimension (as a vector space). Therefore the evaluation homomorphism cannot be injective, and every matrix has a minimal polynomial (not necessarily irreducible). By Cayley–Hamilton theorem, the evaluation homomorphism maps to zero the characteristic polynomial of a matrix. It follows that the minimal polynomial divides the characteristic polynomial, and therefore that the degree of the minimal polynomial is at most .


title: Polynomial ring

text: In the case of , the quotient ring by an ideal can be built, as in the general case, as a set of equivalence classes. However, as each equivalence class contains exactly one polynomial of minimal degree, another construction is often more convenient.


title: Polynomial ring

text: Given a polynomial of degree , the "quotient ring" of by the ideal generated by can be identified with the vector space of the polynomials of degrees less than , with the "multiplication modulo " as a multiplication, the "multiplication modulo" consisting of the remainder under the division by of the (usual) product of polynomials. This quotient ring is variously denoted as formula_40 formula_41 formula_42 or simply formula_43


title: Polynomial ring

text: The ring formula_44 is a field if and only if is an irreducible polynomial. In fact, if is irreducible, every nonzero polynomial of lower degree is coprime with , and Bézout's identity allows computing and such that ; so, is the multiplicative inverse of modulo . Conversely, if is reducible, then there exist polynomials of degrees lower than such that  ; so are nonzero zero divisors modulo , and cannot be invertible.


title: Polynomial ring

text: For example, the standard definition of the field of the complex numbers can be summarized by saying that it is the quotient ring


title: Polynomial ring

text: and that the image of in formula_46 is denoted by . In fact, by the above description, this quotient consists of all polynomials of degree one in , which have the form , with and in formula_47 The remainder of the Euclidean division that is needed for multiplying two elements of the quotient ring is obtained by replacing by in their product as polynomials (this is exactly the usual definition of the product of complex numbers).


title: Polynomial ring

text: Let be an algebraic element in a -algebra . By "algebraic", one means that has a minimal polynomial . The first ring isomorphism theorem asserts that the substitution homomorphism induces an isomorphism of formula_44 onto the image of the substitution homomorphism. In particular, if is a simple extension of generated by , this allows identifying and formula_49 This identification is widely used in algebraic number theory.


title: Polynomial ring

text: "K"["X"], when "K" is a field. This means that every finitely generated module over "K"["X"] may be decomposed into a direct sum of a free module and finitely many modules of the form formula_50, where "P" is an irreducible polynomial over "K" and "k" a positive integer.


title: Polynomial ring

text: is a formal product of these indeterminates, possibly raised to a nonnegative power. As usual, exponents equal to one and factors with a zero exponent can be omitted. In particular, formula_53


title: Polynomial ring

text: The tuple of exponents is called the "multidegree" or "exponent vector" of the monomial. For a less cumbersome notation, the abbreviation


title: Polynomial ring

text: A "polynomial" in these indeterminates, with coefficients in a field, or more generally a ring, is a finite linear combination of monomials


title: Polynomial ring

text: with coefficients in . The "degree" of a nonzero polynomial is the maximum of the degrees of its monomials with nonzero coefficients.


title: Polynomial ring

text: The set of polynomials in formula_51 denoted formula_58 is thus a vector space (or a free module, if is a ring) that has the monomials as a basis.


title: Polynomial ring

text: formula_59 is naturally equipped (see below) with a multiplication that makes a ring, and an associative algebra over , called "the polynomial ring in indeterminates" over (the definite article "the" reflects that it is uniquely defined up to the name and the order of the indeterminates. If the ring is commutative, formula_59 is also a commutative ring.


title: Polynomial ring

text: "Addition" and "scalar multiplication" of polynomials are those of a vector space or free module equipped by a specific basis (here the basis of the monomials). Explicitly, let


title: Polynomial ring

text: where formula_65 if formula_66 and formula_67 if formula_68 Moreover, if one has formula_69 for some formula_70 the corresponding zero term is removed from the result.


title: Polynomial ring

text: where formula_72 is the set of the sums of one exponent vector in and one other in (usual sum of vectors). In particular, the product of two monomials is a monomial whose exponent vector is the sum of the exponent vectors of the factors.


title: Polynomial ring

text: A polynomial expression is an expression built with scalars (elements of ), indeterminates, and the operators of addition, multiplication, and exponentiation to nonnegative integer powers.


title: Polynomial ring

text: As all these operations are defined in formula_59 a polynomial expression represents a polynomial, that is an element of formula_74 The definition of a polynomial as a linear combination of monomials is a particular polynomial expression, which is often called the "canonical form", "normal form", or "expanded form" of the polynomial.


title: Polynomial ring

text: Given a polynomial expression, one can compute the "expanded" form of the represented polynomial by "expanding" with the distributive law all the products that have a sum among their factors, and then using commutativity (except for the product of two scalars), and associativity for transforming the terms of the resulting sum into products of a scalar and a monomial; then one gets the canonical form by regrouping the like terms.


title: Polynomial ring

text: The distinction between a polynomial expression and the polynomial that it represents is relatively recent, and mainly motivated by the rise of computer algebra, where, for example, the test whether two polynomial expressions represent the same polynomial may be a nontrivial computation.


title: Polynomial ring

text: If is a commutative ring, the polynomial ring has the following universal property: for every commutative -algebra , and every -tuple of elements of , there is a unique algebra homomorphism from to that maps each formula_75 to the corresponding formula_76 This homomorphism is the "evaluation homomorphism" that consists in substituting formula_75 for formula_78 in every polynomial.


title: Polynomial ring

text: As it is the case for every universal property, this characterizes the pair formula_79 up to a unique isomorphism.


title: Polynomial ring

text: This may also be interpreted in terms of adjoint functors. More precisely, let and be respectively the categories of sets and commutative -algebras (here, and in the following, the morphisms are trivially defined). There is a forgetful functor formula_80 that maps algebras to their underlying sets. On the other hand, the map formula_81 defines a functor formula_82 in the other direction. (If is infinite, is the set of all polynomials in a finite number of elements of .)


title: Polynomial ring

text: The universal property of the polynomial ring means that and are adjoint functors. That is, there is a bijection


title: Polynomial ring

text: This may be expressed also by saying that polynomial rings are free commutative algebras, since they are free objects in the category of commutative algebras. Similarly, a polynomial ring with integer coefficients is the free commutative ring over its set of variables, since commutative rings and commutative algebras over the integers are the same thing.


title: Polynomial ring

text: A polynomial in formula_84 can be considered as a univariate polynomial in the indeterminate formula_85 over the ring formula_86 by regrouping the terms that contain the same power of formula_87 that is, by using the identity


title: Polynomial ring

text: that maps each indeterminate to itself. (This isomorphism is often written as an equality, which is justified by the fact that polynomial rings are defined up to a "unique" isomorphism.)


title: Polynomial ring

text: In other words, a multivariate polynomial ring can be considered as a univariate polynomial over a smaller polynomial ring. This is commonly used for proving properties of multivariate polynomial rings, by induction on the number of indeterminates.


title: Polynomial ring

text: In this section, is a commutative ring, is a field, denotes a single indeterminate, and, as usual, formula_90 is the ring of integers. Here is the list of the main ring properties that remain true when passing from to .


title: Polynomial ring

text: Polynomial rings in several variables over a field are fundamental in invariant theory and algebraic geometry. Some of their properties, such as those described above can be reduced to the case of a single indeterminate, but this is not always the case. In particular, because of the geometric applications, many interesting properties must be invariant under affine or projective transformations of the indeterminates. This often implies that one cannot select one of the indeterminates for a recurrence on the indeterminates.


title: Polynomial ring

text: Bézout's theorem, Hilbert's Nullstellensatz and Jacobian conjecture are among the most famous properties that are specific to multivariate polynomials over a field.


title: Polynomial ring

text: The Nullstellensatz (German for "zero-locus theorem") is a theorem, first proved by David Hilbert, which extends to the multivariate case some aspects of the fundamental theorem of algebra. It is foundational for algebraic geometry, as establishing a strong link between the algebraic properties of formula_84 and the geometric properties of algebraic varieties, that are (roughly speaking) set of points defined by implicit polynomial equations.


title: Polynomial ring

text: The Nullstellensatz, has three main versions, each being a corollary of any other. Two of these versions are given below. For the third version, the reader is referred to the main article on the Nullstellensatz.


title: Polynomial ring

text: The first version generalizes the fact that a nonzero univariate polynomial has a complex zero if and only if it is not a constant. The statement is: "a set of polynomials in formula_84 has a common zero in an algebraically closed field containing , if and only if" "does not belong to the ideal generated by , that is, if" "is not a linear combination of elements of with polynomial coefficients".


title: Polynomial ring

text: The second version generalizes the fact that the irreducible univariate polynomials over the complex numbers are associate to a polynomial of the form formula_110 The statement is: "If is algebraically closed, then the maximal ideals of formula_84 have the form formula_112


title: Polynomial ring

text: Bézout's theorem may be viewed as a multivariate generalization of the version of the fundamental theorem of algebra that asserts that a univariate polynomial of degree has complex roots, if they are counted with their multiplicities.


title: Polynomial ring

text: In the case of bivariate polynomials, it states that two polynomials of degrees and in two variables, which have no common factors of positive degree, have exactly common zeros in an algebraically closed field containing the coefficients, if the zeros are counted with their multiplicity and include the zeros at infinity.


title: Polynomial ring

text: For stating the general case, and not considering "zero at infinity" as special zeros, it is convenient to work with homogeneous polynomials, and consider zeros in a projective space. In this context, a "projective zero" of a homogeneous polynomial formula_113 is, up to a scaling, a -tuple formula_114 of elements of that is different form , and such that formula_115. Here, "up to a scaling" means that formula_114 and formula_117 are considered as the same zero for any nonzero formula_118 In other words, a zero is a set of homogeneous coordinates of a point in a projective space of dimension .


title: Polynomial ring

text: Then, Bézout's theorem states: Given homogeneous polynomials of degrees formula_119 in indeterminates, which have only a finite number of common projective zeros in an algebraically closed extension of , the sum of the multiplicities of these zeros is the product formula_120


title: Polynomial ring

text: Polynomial rings can be generalized in a great many ways, including polynomial rings with generalized exponents, power series rings, noncommutative polynomial rings, skew polynomial rings, and polynomial rigs.


title: Polynomial ring

text: One slight generalization of polynomial rings is to allow for infinitely many indeterminates. Each monomial still involves only a finite number of indeterminates (so that its degree remains finite), and each polynomial is a still a (finite) linear combination of monomials. Thus, any individual polynomial involves only finitely many indeterminates, and any finite computation involving polynomials remains inside some subring of polynomials in finitely many indeterminates. This generalization has the same property of usual polynomial rings, of being the free commutative algebra, the only difference is that it is a free object over an infinite set.


title: Polynomial ring

text: One can also consider a strictly larger ring, by defining as a generalized polynomial an infinite (or finite) formal sum of monomials with a bounded degree. This ring is larger than the usual polynomial ring, as it includes infinite sums of variables. However, it is smaller than the ring of power series in infinitely many variables. Such a ring is used for constructing the ring of symmetric functions over an infinite set.


title: Polynomial ring

text: A simple generalization only changes the set from which the exponents on the variable are drawn. The formulas for addition and multiplication make sense as long as one can add exponents: . A set for which addition makes sense (is closed and associative) is called a monoid. The set of functions from a monoid "N" to a ring "R" which are nonzero at only finitely many places can be given the structure of a ring known as "R"["N"], the monoid ring of "N" with coefficients in "R". The addition is defined component-wise, so that if , then for every "n" in "N". The multiplication is defined as the Cauchy product, so that if , then for each "n" in "N", "c" is the sum of all "a""b" where "i", "j" range over all pairs of elements of "N" which sum to "n".


title: Polynomial ring

text: Some authors such as go so far as to take this monoid definition as the starting point, and regular single variable polynomials are the special case where "N" is the monoid of non-negative integers. Polynomials in several variables simply take "N" to be the direct product of several copies of the monoid of non-negative integers.


title: Polynomial ring

text: Several interesting examples of rings and groups are formed by taking "N" to be the additive monoid of non-negative rational numbers, . See also Puiseux series.


title: Polynomial ring

text: Power series generalize the choice of exponent in a different direction by allowing infinitely many nonzero terms. This requires various hypotheses on the monoid "N" used for the exponents, to ensure that the sums in the Cauchy product are finite sums. Alternatively, a topology can be placed on the ring, and then one restricts to convergent infinite sums. For the standard choice of "N", the non-negative integers, there is no trouble, and the ring of formal power series is defined as the set of functions from "N" to a ring "R" with addition component-wise, and multiplication given by the Cauchy product. The ring of power series can also be seen as the ring completion of the polynomial ring with respect to the ideal generated by .


title: Polynomial ring

text: For polynomial rings of more than one variable, the products "X"⋅"Y" and "Y"⋅"X" are simply defined to be equal. A more general notion of polynomial ring is obtained when the distinction between these two formal products is maintained. Formally, the polynomial ring in "n" noncommuting variables with coefficients in the ring "R" is the monoid ring "R"["N"], where the monoid "N" is the free monoid on "n" letters, also known as the set of all strings over an alphabet of "n" symbols, with multiplication given by concatenation. Neither the coefficients nor the variables need commute amongst themselves, but the coefficients and variables commute with each other.


title: Polynomial ring

text: Just as the polynomial ring in "n" variables with coefficients in the commutative ring "R" is the free commutative "R"-algebra of rank "n", the noncommutative polynomial ring in "n" variables with coefficients in the commutative ring "R" is the free associative, unital "R"-algebra on "n" generators, which is noncommutative when "n" > 1.


title: Polynomial ring

text: A differential polynomial ring is a ring of differential operators formed from a ring "R" and a derivation "δ" of "R" into "R". This derivation operates on "R", and will be denoted "X", when viewed as an operator. The elements of "R" also operate on "R" by multiplication. The composition of operators is denoted as the usual multiplication. It follows that the relation may be rewritten


title: Polynomial ring

text: This relation may be extended to define a skew multiplication between two polynomials in "X" with coefficients in "R", which make them a noncommutative ring.


title: Polynomial ring

text: The standard example, called a Weyl algebra, takes "R" to be a (usual) polynomial ring "k"["Y" ], and "δ" to be the standard polynomial derivative formula_125. Taking "a" = "Y" in the above relation, one gets the canonical commutation relation, "X"⋅"Y" − "Y"⋅"X" = 1. Extending this relation by associativity and distributivity allows explicitly constructing the Weyl algebra. .


title: Polynomial ring

text: The skew-polynomial ring is defined similarly for a ring "R" and a ring endomorphism "f" of "R", by extending the multiplication from the relation "X"⋅"r" = "f"("r")⋅"X" to produce an associative multiplication that distributes over the standard addition. More generally, given a homomorphism "F" from the monoid N of the positive integers into the endomorphism ring of "R", the formula "X"⋅"r" = "F"("n")("r")⋅"X" allows constructing a skew-polynomial ring. Skew polynomial rings are closely related to crossed product algebras.


title: Polynomial ring

text: The definition of a polynomial ring can be generalised by relaxing the requirement that the algebraic structure "R" be a field or a ring to the requirement that "R" only be a semifield or rig; the resulting polynomial structure/extension "R"["X"] is a polynomial rig. For example, the set of all multivariate polynomials with natural number coefficients is a polynomial rig.


title: Germán Pezzella

text: Germán Alejo Pezzella (; born 27 June 1991) is an Argentine professional footballer who plays as a centre-back for La Liga club Real Betis and the Argentina national team, with whom he won the 2022 FIFA World Cup.


title: Germán Pezzella

text: Pezzella joined Club Atlético River Plate's youth setup in 2005, aged 14, after representing Club Olimpo.


title: Germán Pezzella

text: After impressing with the former's reserves he was called up to the pre-season in Canada, appearing in friendlies against Toronto FC, Montreal Impact and Everton.


title: Germán Pezzella

text: After being an unused substitute in a 0–0 away draw against Club Atlético Huracán on 18 October 2009, Pezzella made his senior debut on 7 December 2011, starting in a 1–0 home win against Defensores de Belgrano for the season's Copa Argentina. His league debut came on 2 March of the following year, where he played the full 90 minutes in a 0–0 home draw against Quilmes Atlético Club.


title: Germán Pezzella

text: Pezzella scored his first professional goal on 2 September 2012, netting the last in a 1–1 draw at Club Atlético Colón. He also scored the equalizer in a 1–1 Superclásico home draw against Boca Juniors, just three minutes after coming off the bench.


title: Germán Pezzella

text: On 10 December 2014, Pezzella scored the last in a 2014 Copa Sudamericana final 2–0 win against Atlético Nacional, as his side won its first international title after a 17-year absence.


title: Germán Pezzella

text: On 10 July 2015, Pezzella signed a five-year contract with Real Betis, newly promoted to La Liga. He made his debut for the club on 23 August, starting in a 1–1 home draw against Villarreal CF.


title: Germán Pezzella

text: After a loan spell with Serie A club Fiorentina during the 2017–18 season, Pezzella signed a five-year contract with the club that runs through the end of the 2021–22 season for an €11m transfer fee. Ahead of the 2018–19 season, he was named the club's new captain.


title: Germán Pezzella

text: Pezzella played represented Argentina in 2009 Toulon Tournament. He also appeared with the side in 2011 South American U-20 Championship and 2011 FIFA U-20 World Cup, always as a starter.


title: Germán Pezzella

text: On 1 September 2011, Pezzella was called up to the year's Pan American Games, appearing in five matches and scoring two goals during the competition.


title: Germán Pezzella

text: In October 2017, he was called up to Argentina national team's squad for the first time for the 2018 World Cup qualifiers against Peru on 5 October and Ecuador on 10 October 2017. In May 2018 he was named in the Argentina national team's preliminary 35-man for the 2018 FIFA World Cup in Russia but did not make the final 23. On 27 March 2019, he captained Argentina in a 1–0 friendly away win against Morocco. He was included in Argentina's 26-man squad for the 2022 FIFA World Cup and came on as a substitute in extra-time of the final as his nation won a third world title by defeating France on penalties.


title: Charlie and the Chocolate Factory (musical)

text: Charlie and the Chocolate Factory is a musical based on the 1964 children's novel of the same name by Roald Dahl, with book by David Greig, music by Marc Shaiman and lyrics by Shaiman and Scott Wittman.


text: Directed by Sam Mendes, the musical premiered in the West End at the Theatre Royal Drury Lane in June 2013 and ran for 3 years and 7 months before closing on 7 January 2017. In 2013 the production broke the record for weekly ticket sales in London. While receiving mixed reviews from critics, the show won two Laurence Olivier Awards in 2014 for Best Costume Design and Best Lighting Design. The show was reworked for a Broadway production opening in April 2017 at the Lunt-Fontanne Theatre and ran almost nine months before closing in January 2018. A U.S. Tour opened 21 September 2018 at Shea's Performing Arts Center in Buffalo, New York and an Australian Tour at Capitol Theatre on 11 January 2019. A second U.S. Tour launched on 1 January 2020 in Miami, Florida. The Broadway version of the musical has been acquired for licensing rights in North America, Europe, and Australia by Music Theatre International.


text: The musical is based on the 1964 children's novel by Roald Dahl. Producers held a first reading of the first act from the show in New York City in May 2010, with the intention of opening in London the following year.


text: Officially confirmed on 18 June 2012, producers announced that the show would play the London Palladium beginning in May 2013, with tickets going on sale in October 2012, before the venue was later changed to the Theatre Royal Drury Lane.


text: The book was written by playwright David Greig with original score composed by Marc Shaiman and lyrics by Scott Wittman and Shaiman. The production was directed by Sam Mendes, with choreography by Peter Darling, accompanied with the assistance of Brandon Duncan, set design by Mark Thompson and lighting design by Paul Pyant.


text: The show presents a more contemporary version of the original story. During previews, many changes were made, most significantly the addition of the Great Glass Elevator.


text: "Charlie and the Chocolate Factory" was scheduled to begin previews on 17 May 2013, at the Theatre Royal, Drury Lane, London, before holding its official opening night on 25 June 2013. The show was originally scheduled to open at the London Palladium. Previews of the show were delayed by five days until 22 May, due to "unforeseen problems in the delivery of a piece of stage engineering by a contractor". Shortly after opening night the show's producers extended booking period through May 2014, with a further extension to November 2014, after ticket sales of approximately 300,000 through October 2013. In February 2015, the production booking further extended through 3 December 2016. The show currently holds the record for the highest weekly gross in the West End, with an income of £1,080,260 during the week commencing 30 December 2013. The first major cast change took place in May 2014, when Alex Jennings replaced Hodge as Wonka. In May 2015 a second cast change took place, with Jonathan Slinger as Wonka.


text: On 23 February 2016, producers once again extended booking through January 2017. The production closed on 7 January 2017.


text: A reworked version of the show opened on Broadway in Spring 2017 with changes including new direction by Jack O'Brien, new choreography by Josh Bergasse and a new set design by original designer Mark Thompson. Due to other commitments, Mendes stayed as producer only, but did participate in the selection of O'Brien replacement as director. O'Brien stated the score would pay homage to the Leslie Bricusse/Anthony Newley songs written for the 1971 film and would also feature the songs written by Shaiman and Wittman. In August 2016, O'Brien confirmed that "The Candy Man" and "Pure Imagination" would be included in the musical.


text: On 9 May 2016, producers announced that the show would open at the Lunt-Fontanne Theatre starring Christian Borle as Willy Wonka, Jake Ryan Flynn, Ryan Foust, and Ryan Sell as Charlie Bucket, John Rubinstein as Grandpa Joe, Emily Padgett as Mrs. Bucket, Jackie Hoffman as Mrs. Teavee, Kathy Fitzgerald as Mrs. Gloop, Alan H. Green as Mr. Beauregarde, Trista Dollison as Violet Beauregarde, Ben Crawford as Mr. Salt, Mike Wartella as Mike Teavee, Emma Pfaeffle as Veruca Salt, and F. Michael Haynie as Augustus Gloop. Previews began on 28 March 2017 with the opening night on 23 April 2017. Reviews of the production were mixed to negative, with some critics citing poor staging and restructuring of the story as primary issues.


text: For this production, the characters of Augustus Gloop, Violet Beauregarde, Veruca Salt and Mike Teavee are played by adult actors, unlike the child actors in the London production, while the character of Charlie is still filled by a child actor.


text: On 15 November 2017, producers announced that production would close on 14 January 2018, after 27 previews and 305 performances.


text: The 1st National Tour of "Charlie and the Chocolate Factory" premiered on 21 September 2018 in Buffalo, New York at Shea's Performing Arts Center. It was a replica of the Broadway production, with an updated set, primarily using several LED screens around the stage. The show starred Noah Weisberg as Willy Wonka, James Young as Grandpa Joe and Amanda Rose as Mrs. Bucket, with the role of Charlie being alternated between Henry Boshart, Collin Jeffery and Rueby Wood. Reviews for the 1st National Tour were mixed. The production closed on 13 October 2019 in Tampa, Florida.


text: The 2nd National Tour started in Miami, Florida in January 2020 featuring Non-Equity actors. Willy Wonka was played by Cody Garcia, Grandpa Joe was played by Steve McCoy, Mrs. Bucket was played by Caitlin Lester-Sams, and the role of Charlie Bucket alternated between both Brody Bett and Ryan Umbarila. The 2nd National Tour had another update on set design, using one LED projection screen instead of several. This tour took a pause in March 2020 (while in Grand Rapids, Michigan), due to the COVID-19 pandemic. The 2nd National Tour resumed on 12 October 2021 in Syracuse, New York. As Charlie Bucket, the three boys alternating the role were Kai Edgar, Coleman Simmons, and William Goldsman. The tour closed on 19 June 2022 in Salt Lake City, Utah, at the Eccles Theatre.


text: Previews of the Australian premiere of the musical was held at Sydney's Capitol Theatre on 5 January 2019 and opened on the 11th. The musical is a replica production of the US tour. On 13 October the primary cast was announced and includes U.S. actor Paul Slade Smith (who played Grandpa George in the original cast on Broadway) as Willy Wonka alongside Australian actors Tony Sheldon as Grandpa Joe and Lucy Maunder as Mrs Bucket. In Sydney, the role of Charlie was shared between Tommy Blair, Ryan Yates, Xion Jarvis and Oliver Alkhair. After ending its Sydney run on Sunday 28 July, the show transferred to Melbourne in August 2019 at Her Majesty's Theatre. The show was initially scheduled to head to Brisbane in March 2020 at the Lyric Theatre, QPAC, but was postponed due to the COVID-19 pandemic. The show reopened in Brisbane on 2 September 2021. Stephen Anderson, who previously played Mr. Salt in the production took over the role of Willy Wonka. The tour made its final stop Perth in November 2021.


text: The musical will have its UK regional premiere at the Leeds Playhouse from 18 November 2022 until 28 January 2023 in a new production directed by James Brining and designed by Simon Higlett. Following the run in Leeds, the production will tour the UK and Ireland from February 2023. The casting was announced on 26 September 2022 including Gareth Snook as Willy Wonka. Reviews for the UK and Ireland Tour so far have been positive to mixed.


text: The first non-English production of Charlie and the Chocolate Factory opened on 8 November 2019 at La Fabbrica del Vapore in Milan, Italy. The production starred Christian Ginepro as Willy Wonka, with the role of Charlie shared between Gregorio Jeesee Cattaneo, Alessandro Notari, and Alberto Salve. The show closed on 23 February 2020, due to the Coronavirus pandemic.


text: A Norwegian production of the show opened on 9 November 2019 at Det Norske Teatret. Fridtjof Stensæth Josefsen portrayed Willy Wonka, while Ole Opsal Stavrum and Peter Andreas Hjellnes Moseng shared the role of Charlie.


text: A Brazilian production was announced in November 2019, produced by Atelier de Cultura. Cleto Baccic stars as Willy Wonka. The five kids are played by child actors, as in the original London production. The show was initially set to open in March 2020, at the Teatro Alfa in São Paulo. However, due to the Coronavirus pandemic, the season was postponed. The show eventually opened on 17 September 2021 at the Teatro Renault. The production closed on 19 December 2021.


text: In November 2019, Alexandre Piot announced that a French production of Charlie and the Chocolate Factory would open in Paris on 23 September 2020 at the Théâtre du Gymnase Marie Bell, with Arnaud Denissel in the role of Willy Wonka. Like the London production, the five kids are all played by child actors. Due to the COVID-19 pandemic, the show was postponed. The show opened on 31 October 2021. The show moved to the Théâtre Marigny on 18 February 2022 and closed on 9 April 2022.