query: When did Final Fantasy Type-0 come out?

title: Final Fantasy Type-0

text: Final Fantasy Type-0[Jp. 1] is an action role-playing game developed and published by Square Enix for the PlayStation Portable (PSP). Released in Japan on October 27, 2011, Type-0 is part of the Fabula Nova Crystallis subseries, a set of games sharing a common mythos which includes Final Fantasy XIII and Final Fantasy XV. The gameplay, similar to Crisis Core: Final Fantasy VII, has the player taking control of characters in real-time combat during missions across Orience. The player also engages in large-scale strategy-based battles on the world map, and has access to a multiplayer option during story missions and side quests.

title: Final Fantasy Agito

text: The game was developed around director Hajime Tabata's original concept for "Final Fantasy Type-0" as a mobile game which would give players easy access to a universe within the "Fabula Nova Crystallis" series and would be influenced by player choice. The title stems from "Type-0"s earlier title "Final Fantasy Agito XIII". Many of "Type-0"s staff returned, with Takeharu Ishimoto composing new music for the title, and former level designer Masayasu Nishida and texture artist Sayoko Hoshino returning respectively as producer and art director.

title: Fabula Nova Crystallis Final Fantasy

text: "Agito XIII" and "Versus XIII" both began production in 2006. By 2008, "Agito XIII" had been moved onto the PlayStation Portable, then later renamed "Final Fantasy Type-0". The stated reason for the change of title was that "Final Fantasy XIII" and "Type-0" shared little besides the core mythos. The title change also resulted in the "XIII" numeral being dropped from the series title as it "would have been an issue". Late in its development, "Final Fantasy XIII" also changed from being an exclusive when an Xbox 360 version was announced, significantly delaying its release. A port for Microsoft Windows was considered, but not followed up due to platform-specific concerns and the company's view of the video game market. Later, "Final Fantasy XIII" and its sequels would receive PC ports through Steam. As early as 2007, Square Enix considered re-branding "Versus XIII" as a numbered entry in the main series due to the rapidly growing scale of the project. The game was eventually re-branded in 2011. As part of its later marketing, "Final Fantasy XV" was deliberately distanced from the "Fabula Nova Crystallis" brand to remove the consequent limitation on their target audience, although lore and design elements were retained. The game was also moved fully onto eighth generation consoles and developed using the company's new Luminous Studio engine. The PS3 version was abandoned due to concerns about the console's continued viability. "Type-0"s western release was delayed due to the flagging PSP market in western territories. A high-definition port to the same platforms as "Final Fantasy XV" was co-developed by Square Enix and HexaDrive, and was eventually announced for a western release.

title: Final Fantasy Type-0

text: Note: The plot of Type-0 is the same in its original version and the high-definition remaster Final Fantasy Type-0 HD, so the terms and quotes used in the text are from the localization of the high-definition remaster rather than unofficial translations.

title: Final Fantasy Type-0 HD

text: "Final Fantasy Type-0 HD" is an action role-playing video game that utilizes a real-time battle system similar to "". The player controls Class Zero, an elite fighting force of fourteen students from Rubrum's Akademeia. Outside mission environments and Akademeia (Class Zero's home base), Class Zero navigates Orience through a scaled-down world map. The world can be navigated on foot, using chocobos (recurring galliform birds in the "Final Fantasy" series) or via an airship. "Type-0 HD" is split into missions with free periods in between. During these free periods between missions, players can explore Akademeia, breed chocobos for personal use, and complete side quests for characters in Akademeia and liberated towns.

title: World of Final Fantasy

text: "World of Final Fantasy" was produced and overseen by Square Enix, with development support provided by Tose. The initial concept for "World of Final Fantasy" was created between series producer Shinji Hashimoto, and Square Enix staff member Hiroki Chiba. Chiba's previous work on the series had been as a scenario writer and event planner for several titles including "" and "Final Fantasy Type-0", titles that had been noted for the dark tone and stories. Hashimoto and Chiba noticed that the series age demographic had shifted to adolescents and adults, with few young people coming to the series. "World of Final Fantasy" was intended to "lower the threshold" for players so more people could enjoy the series. "World of Final Fantasy" was Chiba's directorial debut. The original concepts that form part of "World of Final Fantasy" were created for a simulation video game. When that project ran into difficulties, it was scrapped and its aesthetic elements reused in the smartphone title "Pictlogica Final Fantasy".

title: Mobius Final Fantasy

text: Collaboration events with "Final Fantasy Record Keeper", "Final Fantasy X", "Final Fantasy Type-0", "Final Fantasy VII Remake", "Terra Battle", "Final Fantasy XII", "Final Fantasy XIII", "Hoshi No Dragon Quest", "Final Fantasy XV", "Final Fantasy VII" and "Final Fantasy XIV" have also occurred in the game.

title: Development of Final Fantasy XV

text: After the game's name and platform change in 2012, there were multiple staff reshuffles, though Shimomura, Hashimoto, Hasewaga and Nozue retained their original positions. Nomura became co-director alongside Hajime Tabata, the director of "Final Fantasy Type-0", then was moved to other projects and replaced as full director by Tabata. Saori Itamuro became the new scriptwriter, using Nojima's original scenario as a base for the new work. Kitase left as co-producer, while Yusuke Naora, Isamu Kamikokuryo, and many artists involved in the development of "Type-0" were involved. Non-Japanese staff included character designer Roberto Ferrari, game designer Prasert Prasertvithyakarn, and party interaction designer Wan Hazmer. The staff as formed in 2012, not counting later additions, was made up of the combined "Final Fantasy XV" and "Type-0" development teams. By 2014, between 200 and 300 people were working on the game.

title: Final Fantasy Type-0

text: While working on Final Fantasy XV, Tabata decided to make a high-definition remaster of Type-0 for eighth-generation consoles. Developed by Square Enix and HexaDrive, Final Fantasy Type-0 HD was originally announced at E3 2014, and released worldwide in March 2015.[127][128] After Type-0's release, Tabata stated in an interview that he wished to explore the distant history of Orience after the events of the game.[72] Trademarks for Type-1, Type-2 and Type-3 were registered shortly after the Type-0 trademark, but it was suggested that they were simply a protective measure.[129] During interviews given in 2014, Tabata commented that he wished to work on Type-1 after completing XV, and later explained the conceptual Type series as a means of publishing Final Fantasy games too experimental for the main series. He hoped to continue with the Type series if Type-0 HD was commercially successful.[130][131]

title: Final Fantasy Agito

text: The idea for "Final Fantasy Agito" originated with the early origins of "Type-0". Originally, "Type-0" was a game for mobiles titled "Final Fantasy Agito XIII", but eventually changed platforms and title. "Type-0"s director Hajime Tabata still liked the "Agito" title and the original concepts for the game, which included an episodic storyline that hinged on player choice and day-night cycles linked to real-world time. With this in mind, Tabata decided to revisit it and began development of "Agito": eventually, they settled on smartphones as the release platform of choice, partly because the platforms' progress since "Type-0" started development. One of Tabata's wishes for the title was that players unfamiliar with "Type-0" would download and play it. Development on the game began in September 2012. During development, Tabata considered "Type-0" to have become the prototype for "Agito", although it did not share much with its predecessor. The game's story grew out of what he originally conceived for "Agito XIII" before it evolved into "Type-0". In contrast to "Type-0"s dark and serious storyline, the team decided to give "Agito" a lighter atmosphere, although serious dramatic scenes were still present. Along with returning staff, mobile developer Tayutau K. K. helped with development. The previous game's level designer, Masayasu Nishida, returned to direct, and original character texture artist Sayako Hoshino became art director. To create the characters' portrait animations for the smartphone environment, the team used Silicon Studio's Motion Portrait middleware. The game was developed using the Unity engine. The game's designer was Kensuke Shimoda, an industry veteran who had experience with Unity, and was in charge of designing the game's battle system. His involvement with the game ended after its release.

title: Compilation of Final Fantasy VII

text: The process of thought behind the "Compilation" would later inspire the creation of "Fabula Nova Crystallis Final Fantasy", a subseries of games linked by a common mythos, and would use lessons learned from the "Compilation" production process. On an individual level, "Before Crisis"s popularity would inspire the creation of another mobile title within the "Fabula Nova Crystallis" subseries: originally titled "Final Fantasy Agito XIII", it would later change platforms and be renamed "Final Fantasy Type-0". The battle sequences in "Advent Children" also served as inspiration for Motomu Toriyama when creating the battle system for "Final Fantasy XIII". Former staff members have blamed the "Compilation", in conjunction with other extensions of titles like "Final Fantasy X", for undermining the series' market presence and fan trust in the West.

title: Final Fantasy Type-0

text: Final Fantasy Type-0 was originally titled Final Fantasy Agito XIII, envisioned as a game for mobile devices. It was conceived in 2005 as part of Fabula Nova Crystallis Final Fantasy, a subseries of Final Fantasy games linked by a common mythos. Agito XIII was the final original Fabula Nova Crystallis game to be created. The decision to make it a mobile game was based on the popularity of Before Crisis: Final Fantasy VII. Hajime Tabata, who contributed to the Fabula Nova Crystallis mythos, was searching for a new project after finishing Before Crisis and became the game's director.[45][46] Before Crisis producer Kosei Ito acted as producer before his move to Capcom prior to 2009.[47][48] Beginning development in 2006, it was first announced at that year's Electronic Entertainment Expo (E3). It was said to offer on-the-go access to the Fabula Nova Crystallis universe, using gameplay functions exclusive to mobile phones of the time.[47][49][50] The concept was to deliver a game for mobile platforms equivalent to a console game from the main Final Fantasy series, and to make it available in its entirety upon release rather than in episodic format.[51]

title: Final Fantasy Type-0

text: In 2008, it was decided to make Type-0 a PSP exclusive, cancelling the mobile version of the game as the developers did not want to wait for mobile technology to reach a level which could handle their full vision for the game. Full development began that year by the same team who developed Crisis Core, but was again slowed as most of them were completing work on The 3rd Birthday.[4][57][58][59][60] Because of these conflicting projects, Type-0 came close to being cancelled outright.[61] Between 2009 and 2011, the title was changed to distance it from Final Fantasy XIII, since after the platform change the two games had little in common other than their shared mythos. One of the titles considered and rejected was Final Fantasy Live, referring to the game's multiplayer element. The new title, Final Fantasy Type-0, was intended to indicate the game's separation from the main series. It was also the beginning of an alternative numbering system parallel to the main series.[62][63][64] The game made its first official public appearance under the new title at the Square Enix 1st Production Department Premier in Tokyo, along with a new trailer that was released to the public on January 27, 2011.[65]

title: Recurring elements in the Final Fantasy series

text: Other artists have also contributed to the series. Hideo Minaba contributed character designs to "Final Fantasy IX", worked as an art director for "Final Fantasy XII", and would later design characters for "Final Fantasy XIII-2". Italian-born artist Roberto Ferrari worked as a secondary character designer for "Final Fantasy Type-0", "Final Fantasy XV" and "Final Fantasy VII Remake". Yusaku Nakaaki worked with Naora and Nomura to create characters for "Final Fantasy Type-0", and along with Ferrari created secondary characters for "Final Fantasy XV". Akira Oguro created the character artwork for the mobile titles "" and "Final Fantasy Dimensions". Toshitaka Matsuda's first major work was on "Final Fantasy XII: Revenant Wings", and he would later serve as a costume and character designer for "Lightning Returns: Final Fantasy XIII". Toshiyuki Itahana first worked on character designs for "Final Fantasy IX", then later served as a main artist for the "Crystal Chronicles" spin-off series, "Lightning Returns: Final Fantasy XIII", and the mobile game "Mobius Final Fantasy". A key designer for much of the series' life was Kazuko Shibuya, who did sprite designs from "Final Fantasy" to "Final Fantasy VI". She also did work on "Final Fantasy Dimensions". A notable outside collaborator was Hiromu Takahara, lead designer for Japanese fashion house Roen, who created the clothing for the main cast of "Final Fantasy XV".

title: Final Fantasy Type-0

text: The game was originally announced as a title for mobile phones and the PSP called Final Fantasy Agito XIII.[Jp. 2] It was directed by Hajime Tabata, who took up the project after completing Before Crisis: Final Fantasy VII. Initially designed to provide players with easy access to the Fabula Nova Crystallis universe, the mobile version was eventually cancelled and the game's title was changed to distance it from the subseries' flagship title Final Fantasy XIII. Releasing to strong sales, it received praise for its story and gameplay, but was criticized for its camera control and artificial intelligence. Further games related to Type-0 have also been developed, including a high definition remaster that released internationally in March 2015.

title: Final Fantasy XV

text: Initially announced in 2006 alongside "XIII" and "Type-0", the game was publicly rebranded at the 2013 Electronic Entertainment Expo, with regular updates on the title beginning the following year. A demo titled "Final Fantasy XV: Episode Duscae" was released in March 2015 as a limited addition to "Final Fantasy Type-0 HD". The game's localization was handled by Dan Inoue, who used different accents for characters to denote their origins on different parts of Eos. In addition to English, Japanese and European languages, the game was localized for Latin America with Latin American Spanish and Brazilian Portuguese text: this was the first time a "Final Fantasy" title was localized into these languages.

title: Final Fantasy Type-0

text: Type-0 affected several other works in multiple ways. During its development, several staff members and voice actors who had worked on Final Fantasy X reunited. Their meeting triggered the development of Final Fantasy X/X-2 HD Remaster.[120] In the September 2013 issue of Famitsu Weekly, Square Enix revealed Final Fantasy Agito, an online companion game to Type-0 for iOS and Android mobile devices.[121] The game was released in May 2014, and a localization was announced alongside that of Type-0.[122][123] Its servers were closed down in November 2015, with its localization being cancelled as a result.[124][125] A new online game set in the Type-0 universe, Final Fantasy Awakening, released in Asian and English-speaking territories between 2016 and 2018.[126]

title: Characters of the Final Fantasy Type-0 universe

text: "Final Fantasy Type-0", an action role-playing game developed and published by Square Enix in 2011, revolves around a war between four nations in the world of Orience. An episodic companion game, "Final Fantasy Agito", was released in 2014. "Type-0" was re-released internationally in 2015 as a high-definition remaster for PlayStation 4 and Xbox One. The main protagonists are Class Zero, a group of students at the magical academy in Rubrum. The story is told through two new members of Class Zero: Machina Kunagiri and Rem Tokimiya. The main character of "Agito" is a player-created cadet at the Rubrum magical academy. The world and characters were designed by Yusuke Naora, Yusaku Nakaaki and Tetsuya Nomura. Their stories were created by Hajime Tabata, Hiroki Chiba and Sarah Obake.

title: Final Fantasy Type-0 HD

text: A commercial Blu-ray release for "Type-0 HD"s soundtrack, "Final Fantasy Type-0 HD Original Soundtrack", was released on March 25, 2015. It includes the entire soundtrack, the newly composed tracks, tracks from "Final Fantasy Agito" and ten bonus MP3 tracks selected by Ishimoto from his previous work as a "Best of Collection". The Blu-ray album reached #189 in the Oricon charts, and remained in the charts for one week. The album, and music in general, have received positive comments from music critics and reviewers of the game.

title: Final Fantasy Type-0

text: In the first week on sale, Final Fantasy Type-0 sold 472,253 units, topping Japanese sales charts and selling through 79.08% of its initial shipments.[116][117] As of January 16, 2012, the game had sold 746,203 copies in Japan.[118] It was the best-selling game of 2011 for Japanese media retail shop Tsutaya, beating Monster Hunter Portable 3rd (PlayStation Portable) and Final Fantasy XIII-2 (PlayStation 3). It was also the store's best-selling PSP title of the year, followed by Monster Hunter Portable 3rd and Dissidia 012 Final Fantasy.[119]

title: Fabula Nova Crystallis Final Fantasy

text: A recurring race in the games are god-like beings created by Pulse and Lindzei to act as their servants in the mortal world. In the original mythos and the "XIII" games, the demigods are called fal'Cie . They take the form of crystal-powered mechanical beings in the "XIII" games. In the universe of "Type-0", they are both semi-sentient crystals and humanoid beings living among the people. The fal'Cie have the ability to imbue chosen humans with magical powers and assign them a task to complete either willingly or unwillingly. "Final Fantasy XIII" and "Type-0" refer to these people as l'Cie and the task given to them as a Focus. In the worlds of "XIII" and "Type-0", there are two possible outcomes for l'Cie: once their Focus is fulfilled, they can go into 'crystal stasis', transforming into a crystal statue, and gain eternal life, but if they fail they become mindless crystalline monsters. In "Type-0", l'Cie are chosen by the crystal of their country, and given great power to fulfill their assigned Focus, but lose their memories if emotionally unstable. While not referred to as such using the original terminology, humans imbued with magic and burdened with a task exist in "Final Fantasy XV", one of them being the main protagonist Noctis.

title: Final Fantasy Type-0

text: Multiple pieces of merchandise were created for the game. An Ultimania, part of a series of dedicated guidebooks, was released in the same month as the original game. It contained story and character breakdowns, concept art, and interviews with developers.[101] A different book, Final Fantasy Type-0 World Preview,[Jp. 5] was also released in October. It featured character biographies, details on the world of Orience, and interviews with the voice actors for Class Zero.[102] The following year, a dedicated art book was released containing artwork of the game's characters and monsters, and an interview with Tabata.[103] Characters from the game, including Ace, Machina and other members of Class Zero, appeared in the fourth series of releases for the Final Fantasy Trading Card Game.[104] In November 2011, a manga adaptation of Type-0, illustrated by Takatoshi Shiozawa, began serialization in Young Gangan magazine.[105] The manga has been collected into a tankōbon volume and was released on April 21, 2012.[106] Another manga titled Final Fantasy Type-0 Side Story: Reaper of the Icy Blade,[Jp. 6] also illustrated by Shiozawa, began publication in Young Gangan in April 2012.[107] It ended in January 2014, with a bonus chapter being published in February of that year,[108][109] and was later released in five compiled volumes. Yen Press began distribution of the manga in the west in July 2015.[110] Square Enix released two novel adaptations, in April and June 2012, depicting an alternate version of Type-0's story: Final Fantasy Type-0: Change the World -The Answer-[Jp. 7] and Final Fantasy Type-0: Change the World Volume 2 -The Penultimate Truth-.[Jp. 8] The novels were written by Sōki Tsukishima.[111][112]

title: Final Fantasy Artniks

text: Characters, monsters and items from all the main "Final Fantasy" games appear, as well as "Final Fantasy Tactics", "Final Fantasy Crystal Chronicles", "Dissidia Final Fantasy", "Final Fantasy Type-0", and others. Well known events from previous Final Fantasy titles are occasionally encountered. The game receives updates periodically in the form of "Most Wanted" villains for players to share information about to find and defeat to earn rewards. The first update featured Kefka Palazzo from "Final Fantasy VI" and the second being Sephiroth from "Final Fantasy VII".

title: Dissidia Final Fantasy NT

text: The arcade version featured fourteen characters at launch, including thirteen main heroes from the previous "Dissidia" titles and a new hero from "Final Fantasy XIV". However, new characters have continued to be added to the roster as post-launch updates, including characters from spin-off titles such as "Final Fantasy Tactics" and "Final Fantasy Type-0". "NT" includes every character available in the arcade version at the time of its release, for a total of twenty-eight. The developers are targeting a total roster of 50 characters, including all characters from the previous "Dissidia" titles. Future updates will come to the arcade version first before releasing on PlayStation 4 as DLC after a short window of exclusivity.

text: The original scenario and concept of "Final Fantasy Type-0", originally a mobile title named "Final Fantasy Agito XIII", was conceived by Hajime Tabata. He wished for a group-driven story as he felt that a single playable character would not be able to properly convey the scope and themes of the story. Because Tabata wanted to show a history of survival told from the point of view of young people caught in a war, it was decided to set the story during a war between four nations. Much of the original story, which mainly revolved about defying the gods, was drawn from popular anime and manga and did not survive. After the platform change to PlayStation Portable, Tabata adopted a story-telling style similar to a documentary film: a direct inspiration for this was "Centuries of Picture", a documentary series broadcast on NHK. Alongside that, multiple war films were used as inspiration. "Type-0"s script was written by Hiroki Chiba and Sarah Okabe. During the rough draft stage, elements such as extra plot points involving Khalia Chival, a boss fight with Arecia, and a main plot thread involving Joker and Tiz were planned. Most of these elements were cut from the final product, meaning elements such as Joker and Tiz's role needed to be included in written texts found in-game so they were not left hanging. The deaths of Class Zero were planned from an early stage, and to emphasize the state of the world, a large number of the supporting cast were killed off near the end. Tabata wanted to create a story depicting different fates for "Type-0"s characters, and this decision was supported by both staff members and fans of the original. He also implemented the ability for players to decide the course of the story, which was to have been included in the "Type-0" when it was still known as "Agito XIII". "Final Fantasy Agito" was given a more upbeat atmosphere when compared to "Type-0", although dark and more dramatic moments were still present. The story grew out of what Tabata originally envisioned for "Type-0".

title: Final Fantasy XIII

text: At the beginning of the development, the game was intended to be released on the PlayStation 2. In May 2005, however, after the positive reception of the tech demo of "Final Fantasy VII", the team decided to move the game to the PlayStation 3 and developed it with the new Crystal Tools engine, a seventh generation multiplatform game engine created by Square Enix for its next generation games. Square Enix believed that developing a new engine would speed up development time later in the project, though it would initially cause a delay in the game's development. However, the delay was longer than originally anticipated as the engine had to accommodate the requirements of several other games in addition to "XIII". Another factor in the platform move was the delayed release of "Final Fantasy XII", which came out a very short time before the release of the PlayStation 3. A PC port was considered during development, but was decided against due to how Square Enix saw the video game market situation at the time as well as additional complexities that Square Enix did not have experience with related to the PC platform, such as security issues. "Final Fantasy XIII" was first shown at the 2006 E3 convention. The trailer shown was an artistic concept that did not represent the final concept for the game, since at the time there was no playable form of the game. Announced alongside the game was "Final Fantasy Versus XIII", later retitled as "Final Fantasy XV", and the PlayStation Portable game "Final Fantasy Type-0", originally titled "Final Fantasy Agito XIII", the three of which form the "Fabula Nova Crystallis Final Fantasy" series. Square Enix explained that although all three games are thematically linked, they are not directly related in terms of story.

text: is a supporting character from "Final Fantasy Agito". A member of Class Second, she is the representative for the cadets in the Vermillion Peristylium. Her true identity, as revealed with the coming of Tempus Finis, is , a servant of Gala who oversees the Lulusath Army. Her defeat signals the coming of Tempus Finis, as the first cycle is deemed a failure. She later appears at the end of the second cycle, pondering with Arecia whether to continue with the experiment. She is voiced by Haruka Tomatsu in Japanese. Miyu as Myuria appears in concept art for "Type-0", but she was cut from the game.Characters from the game, including Ace, Mog, Machina and other members of Class Zero, appeared in the fourth series of releases for the "Final Fantasy Trading Card Game". On November 2011, a manga adaptation of "Type-0" began serialization. It is illustrated by Takatoshi Shiozawa and published in "Young Gangan" magazine. The manga has been collected into a tankōbon volume and was released on April 21, 2012. An English translation was released with the Collector's Edition of "Type-0 HD" in March 2015, exclusive to Square Enix's website. Another manga titled . The manga is also illustrated by Shiozawa, supervised by Tetsuya Nomura and published in "Young Gangan" magazine from April 2012. The manga ended in January 2014, with a bonus chapter being published in February. It was later released in five compiled volumes. Yen Press will begin distribution of the manga in the west in July 2015. A novel adaptation titled has been released by Square Enix on April 21, 2012. A second novel adaptation titled was released by Square Enix on June 28, 2012. The novels depict an alternate version of "Type-0"s story.

text: Other notable artists include Akihiko Yoshida, Isamu Kamikokuryo and Yusuke Naora. Yoshida's first major games were "Final Fantasy Tactics" and "Vagrant Story", which he worked on together with Hiroshi Minagawa. He also did design work for "Final Fantasy Tactics Advance", creating the Bangaa race that would later appear in "Final Fantasy XII". For "Final Fantasy XII", he designed the main characters. As inspiration for their physical appearances, Yoshida used a variety of influences from multiple cultures. He returned to work on "Final Fantasy XIV", where he needed to adjust from working on a static project to designing for the more fluid environment of an MMORPG. He would also contribute designs to "A Realm Reborn", and its first expansion "Heavensward". Isamu Kamikokuryo first did work on "Final Fantasy VIII" and "Final Fantasy X", then became art director for "Final Fantasy XII". He would return to this role for "", and the "Final Fantasy XIII" games: he had a major role in the design of Lightning's new appearance in "Final Fantasy XIII-2". He was also involved in the world design of "Final Fantasy XV". Yusuke Naora has had a presence within the series since "Final Fantasy VII", for which he designed the kanji logo for the antagonistic Shinra Corporation. His involvement in the series has primarily been as an art director for titles such as "Final Fantasy X" and "Final Fantasy XV", in addition to creating character designs for "Final Fantasy XIII-2" and "Final Fantasy Type-0".

text: The battle system for "Final Fantasy XIII" was designed to retain the strategic elements of earlier titles while emulating the cinematic action of "Final Fantasy VII: Advent Children". While retaining the ATB system, elements such as magic points were removed, and a strategic role-change system dubbed the Paradigm System was implemented, with the roles being based on "Final Fantasy" jobs. "Final Fantasy XIII-2" continued using the Paradigm system with added gameplay functions based on criticism of the first game, while "Lightning Returns: Final Fantasy XIII" changed to a more action-based, single-character version that incorporated design elements cut from "Final Fantasy XIII". "Final Fantasy XV" used an action-based system that was described as a "realistic" version of those used in the "Kingdom Hearts" series and spin-off title "Final Fantasy Type-0". Unlike all previous mainline "Final Fantasy" titles, the players could only control one character out of the four-strong party. While the team experimented with multiple character control, it was decided that it presented too many development difficulties.

title: Fabula Nova Crystallis Final Fantasy

text: The series, originally announced in 2006 as "Fabula Nova Crystallis Final Fantasy XIII", currently consists of seven games across multiple platforms. "Final Fantasy XIII", designed as the series' flagship title, was released in 2009. The creative forces behind the series include many developers from previous "Final Fantasy" titles, including Shinji Hashimoto and Motomu Toriyama. The mythos was conceived and written by Kazushige Nojima. The first games announced for the series were "Final Fantasy XIII", "Final Fantasy XV" (as "Versus XIII"), and "Final Fantasy Type-0" (as "Agito XIII"). All three games went through delays. After "Final Fantasy XIII" and "Type-0"s releases, their respective teams used ideas and concepts from development to create additional games. For later games, other studios have been brought in to help with aspects of development. "Final Fantasy XV" was distanced from the series brand for marketing purposes despite retaining thematic connections.


query: Which piece is Mykola Dmytrovych Leontovych most famous for?

title: Mykola Leontovych

text: Mykola Leontovych's Shchedryk is his most well-known piece. In its English version as a Christmas carol, it is known as the holiday favourite Carol of the Bells.[1][2][4][16] It is famous for its four-note ostinato motif and has been arranged over 150 times since 2004.[1] The original Ukrainian text of Shchedryk used hemiola, a shifting of accents within each measure between 6/8 and 3/4, which is lost in the English versions. The most popular English adaptation was composed in 1936 by Peter J Wilhousky who was influenced by the culture of his Eastern European parents and the traditional Christian story of carols ringing out at the birth of Jesus, although other English adaptations of the song were also made in 1947 by M. L. Holman, 1957, and 1972.[20]

title: Ukrainian folklore

text: Folk songs have provided inspiration for many Ukrainian composers, such as Mykola Lysenko, Mykola Leontovych, and Kyrylo Stetsenko. The famous Russian composers Peter Tchaikovsky, Nikolai Rimsky-Korsakov, and Serge Rachmaninoff also collected and used Ukrainian folk melodies in their works. Today many folk songs are still used, and are even used by contemporary artists.

title: Mykola Leontovych

text: After reviewing Leontovych's Second Compilation of Songs from Podolia, Lysenko wrote: "Leontovych has an original, illustrious gift. In his arrangements I found separate passages, movement of voices, which later developed in a geniously weaved musical network."[12][n 4]

title: Mykola Leontovych

text: During the October Revolution and the establishment of the Ukrainian People's Republic in 1918, Leontovych relocated without his family to Ukraine's capital Kyiv, where he was active as both a conductor and composer. Several of his pieces gained popularity among professional and amateurs groups alike, who added them to their repertoire. In the beginning of 1919, the rest of his family also relocated to Kyiv. During this period, Leontovych also began teaching choir conducting alongside Hryhoriy Veryovka at the Kyiv Conservatory, and also taught at the Mykola Lysenko Institute of Music and Drama.[8] Leontovych was one of the organisers of the first Ukrainian State Orchestra. He participated in the founding of the Ukrainian Republic Capella of which he was the commissioner.[4]

title: Mykola Leontovych

text: Financial hardships prompted Leontovych to accept an offer to move to the city of Vinnytsia to instruct at the Church-Educators' College. Again, he organised a choir and, later, a concert band, with which he performed both secular and spiritual music. In 1903, he published his Second Compilation of Songs from Podolia which he dedicated to Mykola Lysenko.[4]

title: Carol of the Old Ones

text: "Carol of the Old Ones" is a song originally published in the 1988 HPLHS Solstice Carol Songbook, released by the H. P. Lovecraft Historical Society. With lyrics written by Andrew Leman, it is sung and performed to the tune of "Carol of the Bells" by Mykola Dmytrovych Leontovych (itself sung to the tune of Shchedryk), with soprano lead vocals and four-part harmony at various points in the song. The song is performed by The Dagon Tabernacle Choir; the performers' names are Rebecca Marcotte, Digby Dolmen, J.D. Titan, and Walter Forsythe. It can be found on the album "A Very Scary Solstice".

title: Mykola Leontovych

text: Ukrainian writer and politician of the Ukrainian Soviet Socialist Republic, Pavlo Tychyna, was an admirer of Leontovych and wrote about the composer's death in prose. Poets Maksym Rylskyi and Mykola Bazhan also dedicated poetry to him.[13]

title: Mykola Leontovych

text: Mykola Leontovych specialised in a cappella choral music.[16] He is remembered today mostly through the musical works he left behind, which include over 150 choral compositions. These range from artistic arrangements of folk songs, religious works (including his liturgy), cantatas, and choral compositions set to the words of various Ukrainian poets.[1] His two most famous works are the choral miniatures Schedryk and Dudaryk.[16]

title: Mykola Leontovych

text: Leontovych was born and raised in the Podolia province of the Russian Empire (now in Ukraine). He was educated as a priest in the Kamianets-Podilskyi Theological Seminary and later furthered his musical education at the Saint Petersburg Court Capella and private lessons with Boleslav Yavorsky. With the independence of the Ukrainian state in the 1917 revolution, Leontovych moved to Kyiv where he worked at the Kyiv Conservatory and the Mykola Lysenko Institute of Music and Drama. He is recognised for composing Shchedryk in 1904 (which premiered in 1916), known to the English-speaking world as Carol of the Bells or Ring, Christmas Bells. He is known as a martyr in the Eastern Orthodox Ukrainian Church, where he is also remembered for his liturgy, the first liturgy composed in the vernacular, specifically in the modern Ukrainian language. He was assassinated by a Soviet agent in 1921.

title: Mykola Leontovych

text: After several conflicts with the school's administration, Leontovych got a new job as a teacher of church music and calligraphy at the Theological College in Tyvriv.[4] Besides working with the college choir, Leontovych organised an amateur orchestra that often performed at college events. As he did earlier with choirs, Leontovych included arrangements of folk songs among the usual religious works sung in theological schools. These included arrangements by Mykola Lysenko, his own choral arrangements of folk songs, and entirely original works. One such work was based on a poem by Taras Shevchenko titled Зоре моя вечірняя (Oh My Evening Star).[4]

title: Mykola Leontovych

text: Mykola Dmytrovych Leontovych (Ukrainian: Микола Дмитрович Леонтович; sometimes spelt Leontovich; December 13[O.S. December 1]1877–23 January 1921) was a Ukrainian composer, choral conductor, and teacher of international renown. His music was inspired by Mykola Lysenko and the Ukrainian National Music School. Leontovych specialised in a cappella choral music, ranging from original compositions, to church music, to elaborate arrangements of folk music.

title: Mykola Leontovych

text: Mykola Leontovych grew up in a highly religious environment. He was a member of the Orthodox Church, descended from a line of village priests. He was also a graduate of the Podollia Theological Seminary in Kamianets-Podilskyi, which, for the most part, trained Orthodox Christian clergy.[3]

title: Mykola Leontovych

text: On 1 February 1921, nine days after Leontovych's death, a large number of artists, professors, and students of the Mykola Lysenko Institute of Music and Drama in Kiev gathered to commemorate him, as is expected according to Christian tradition. They established the Committee for the Memory of Mykola Leontovych, which later became the All-Ukrainian Mykola Leontovych Music Society, and promoted Ukrainian music until 1928.[8]

title: Mykola Leontovych

text: When the seminary's choir director died, the school administration requested that Leontovych take over this position. As the conductor of the choir, Leontovych added secular music to the repertoire of traditional church music. This included Ukrainian folk songs arranged by Mykola Lysenko, Profyriy Demutskiy, and himself.[4] Leontovych graduated from the Kamianets-Podilskiy Theological Seminary in 1899 and broke the family tradition by becoming a music teacher instead of a priest.[3][4]

title: Mykola Leontovych

text: Mykola Leontovych was born on December 13[O.S. 1 December]1877 in the Monastyrok community, near the village of Selevyntsi, in the Podolia province of Ukraine (then a part of the Russian Empire).[1] His father, grandfather, and great grandfather were village priests.[2] His father, Dmytro Feofanovych Leontovych, was skilled at singing and playing cello, double bass, harmonium, violin, and guitar, in addition to directing a school choir. Leontovych received his first musical lessons from him. His mother, Mariya Yosypivna Leontovych, was also a singer.[3][4]

title: Mykola Leontovych

text: This period in his career was among the most productive, as he created numerous choral arrangements. These included his famous Shchedryk, as well as Піють півні (The Roosters are Singing), Мала мати одну дочку (A Mother had One Daughter), Дударик (Little Dudka Player), Ой зійшла зоря (Oh, the Star has Risen), amongst others. In 1914, Stetsenko convinced Leontovych to have his music performed by the student choir of the Kyiv University under the leadership of Alexander Koshetz. On 26 December 1916, the performance of his arrangement of Shchedryk brought Leontovych great success from the public in Kyiv and raised the interest of intellectuals.[8]

title: Music of Ukraine

text: The first category is closely tied with the Ukrainian national school of music spearheaded by Mykola Lysenko. It includes such composers as Kyrylo Stetsenko, Mykola Leontovych, Levko Revutsky, and Sydir Vorobkevych. Most of their music contains Ukrainian folk figures and are composed to Ukrainian texts.

title: Mykola Leontovych

text: One of the largest influences in Mykola Leontovych's music is that of Mykola Lysenko,[16] who is considered "the father of Ukrainian classical music".[18][19] Leontovych admired Lysenko's music ever since he was a student at the Kamianets-Podilskyi Theological Seminary, when he had the seminary's choir perform the composer's music. Since then, he would perform Lysenko's music in concerts wherever he worked.[4]

title: Liturgy of St. John Chrysostom (Leontovych)

text: The Liturgy of St. John Chrysostom (, tr. "Liturhiya Ivana Zlatoustoho") is the musical setting of the Divine Liturgy of St. John Chrysostom by Mykola Leontovych. Consistent with Orthodox tradition, in which service is sung exclusively a cappella, the piece is set for unaccompanied choir and soloist. It was first performed in the Mykolaiv Cathedral at the Kiev Pechersk Lavra on May 22, 1919, with Leontovych himself conducting.

title: Mykola Leontovych

text: During his studies there, Leontovych continued to advance his skills on the violin and learnt to play a variety of other instruments.[2] He also participated in the seminary's choir, and when an orchestra was formed during his third year of study, Leontovych joined, playing the violin until his graduation. Leontovych studied music theory and started writing choral arrangements as a student at the seminary.[4]

title: Mykola Leontovych

text: For most of his career, Leontovych kept his music to himself, only performing it during his own concerts. This was because of the composer's highly self-critical and shy personality.[13] Leontovych's first critic was his friend and fellow priest and composer Kyrylo Stetsenko, who described him to be "a great expert of both choral singing and theoretical studies".[2] He also convinced Leontovych to publish his music and have it performed by the Kiev University.[4]

title: Mykola Leontovych

text: Leontovych's move to Tulchyn marked the beginning of a period of compositional maturity and major artistic achievements in the life of the composer.[4] In Tulchyn, Leontovych taught vocal and instrumental music at the Tulchyn Eparchy Women's College to the daughters of village priests.[8] There, he met composer Kyrylo Stetsenko who was a student of Mykola Lysenko and also specialised in choral music. Stetsenko lived in a nearby village at the time where he was working as a priest, and their acquaintance developed into a lasting friendship that influenced Leontovych's music.[4] Stetsenko was the first critic of Leontovych's music, saying, "Leontovych is a famous music expert from Podolia. He recorded many folk songs... These songs are harmonised for mixed choir. These harmonisations have revealed the author to be a great expert of both choral singing and theoretical studies".[2] Leontovych also transitioned to more renowned music during his choir performances, such as Russian composers Mikhail Glinka, Alexey Verstovsky, and Peter Tchaikovsky in addition to Ukrainian composers Mykola Lysenko, Kyrylo Stetsenko, and Petro Nishchynskyi.[8]

title: Mykola Leontovych

text: During the night of 22–23 January 1921, Mykola Leontovych was murdered by Chekist (Soviet state security) agent Afanasy Grishchenko. Leontovych was staying at the home of his parents, whom he was visiting for the Orthodox Feast of the Nativity (25 December of the Julian calendar, which, on the Gregorian calendar, adopted by the USSR only in 1918, falls in January). The undercover Chekist had also asked to stay the night at the house and shared a room with Mykola. At dawn he shot the composer (who died of blood loss a few hours later) after robbing his family.[4][8][10][11]

title: Mykola Leontovych

text: Mykola Leontovych was highly critical of himself. According to his first biographer Oles' Chapkivskyi, a contemporary of the composer, Leontovych would sometimes work on one choral setting without letting anyone else see it for up to four years.[3] After the publication of his Second Compilation of Songs from Podolia, he changed his mind and was not fully satisfied with it, and as a result he bought all 300 copies and had them destroyed.[8]

title: Music of Ukraine

text: Mykola Lysenko, Mykola Leontovych, Kyrylo Stetsenko, Yakiv Stepovy

title: Mykola Leontovych

text: In the summer of 1879, Mykola Leontovych was moved to a new parish located in the village of Shershni in suburbs of Bar, Ukraine in Bar's district, where he would spend his childhood.[4] Then, in 1887, Leontovych was admitted to Nemyriv gymnasium. Due to financial problems a year later, however, his father transferred him to the Sharhorod Spiritual Beginners School, whose pupils received full financial support.[5] At the school, Leontovych mastered singing, and was able to freely read difficult passages from religious choral texts.[4]

title: Leontovych Bandurist Capella

text: In 1946 Hryhory Nazarenko together with the Honcharenko brothers left the Ukrainian Bandurist Chorus and started working on establishing a new bandurist capella. This new capella was formed in the British zone in Germany in the city of Goslar and was called the Leontovych Bandurist Capella after the Ukrainian composer Mykola Leontovych.

title: Mykola Leontovych

text: The successful debut of "Shchedryk" earnt Leontovych popularity among specialists and fans of choral music in Kiev.[4] Leontovych's mentor-turned-coworker at the Kiev Conservatory, Boleslav Yavorsky, also positively evaluated his newly written works.[4] During another concert, Leontovych's Lehenda, set to a poem by Mykola Voronyi, gained great popularity.[30]

title: Mykola Leontovych

text: In 1892, Leontovych began his studies at the theological seminary in Kamianets-Podilskyi, which both his father and grandfather had attended. His younger brother Oleksandr was enrolled as well, graduating two years after Mykola.[4]

text: Unlike his compositions based on poetry and folk themes, which were constantly performed throughout the twentieth century, Leontovych's sacred music, and that of his predecessors, was banned in the Soviet Union. For this reason, the sacred music of Mykola Leontovych, including his liturgy, are not well known.


query: Who is considered the founder of algebra?

title: Algebra

text: In the context where algebra is identified with the theory of equations, the Greek mathematician Diophantus has traditionally been known as the "father of algebra" and in context where it is identified with rules for manipulating and solving equations, Persian mathematician al-Khwarizmi is regarded as "the father of algebra".[14][15][16][17] A debate now exists whether who (in general sense) is more entitled to be known as "the father of algebra". Those who support Diophantus point to the fact that the algebra found in Al-Jabr is slightly more elementary than the algebra found in Arithmetica and that Arithmetica is syncopated while Al-Jabr is fully rhetorical.[18] Those who support Al-Khwarizmi point to the fact that he introduced the methods of "reduction" and "balancing" (the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation) which the term al-jabr originally referred to,[19] and that he gave an exhaustive explanation of solving quadratic equations,[20] supported by geometric proofs, while treating algebra as an independent discipline in its own right.[21] His algebra was also no longer concerned "with a series of problems to be resolved, but an exposition which starts with primitive terms in which the combinations must give all possible prototypes for equations, which henceforward explicitly constitute the true object of study". He also studied an equation for its own sake and "in a generic manner, insofar as it does not simply emerge in the course of solving a problem, but is specifically called on to define an infinite class of problems".[22]

title: Exterior algebra

text: Exterior algebras of vector bundles are frequently considered in geometry and topology. There are no essential differences between the algebraic properties of the exterior algebra of finite-dimensional vector bundles and those of the exterior algebra of finitely generated projective modules, by the Serre–Swan theorem. More general exterior algebras can be defined for sheaves of modules.

title: Super-Poincaré algebra

text: The super-Poincaré algebra was first proposed in the context of the Haag–Łopuszański–Sohnius theorem, as a means of avoiding the conclusions of the Coleman–Mandula theorem. That is, the Coleman–Mandula theorem is a no-go theorem that states that the Poincaré algebra cannot be extended with additional symmetries that might describe the internal symmetries of the observed physical particle spectrum. However, the Coleman–Mandula theorem assumed that the algebra extension would be by means of a commutator; this assumption, and thus the theorem, can be avoided by considering the anti-commutator, that is, by employing anti-commuting Grassmann numbers. The proposal was to consider a supersymmetry algebra, defined as the semidirect product of a central extension of the super-Poincaré algebra by a compact Lie algebra of internal symmetries.

title: Abstract algebra

text: These processes were occurring throughout all of mathematics, but became especially pronounced in algebra. Formal definition through primitive operations and axioms were proposed for many basic algebraic structures, such as groups, rings, and fields. Hence such things as group theory and ring theory took their places in pure mathematics. The algebraic investigations of general fields by Ernst Steinitz and of commutative and then general rings by David Hilbert, Emil Artin and Emmy Noether, building up on the work of Ernst Kummer, Leopold Kronecker and Richard Dedekind, who had considered ideals in commutative rings, and of Georg Frobenius and Issai Schur, concerning representation theory of groups, came to define abstract algebra. These developments of the last quarter of the 19th century and the first quarter of 20th century were systematically exposed in Bartel van der Waerden's "Moderne algebra", the two-volume monograph published in 1930–1931 that forever changed for the mathematical world the meaning of the word "algebra" from "the theory of equations" to the "theory of algebraic structures".

title: Surface (mathematics)

text: Most authors consider as an algebraic surface only algebraic varieties of dimension two, but some also consider as surfaces algebraic sets all of whose irreducible components have the dimension two.

title: List of people considered a founder in a Humanities field

text: Those known as the father, mother, or considered a founder in a Humanities field are those who have made important contributions to that field. In some fields several people are considered the founders, while in others the title of being the "father" is debatable. Some of the people who have humanity are given in REFERENCES.

title: Commutative algebra

text: The main figure responsible for the birth of commutative algebra as a mature subject was Wolfgang Krull, who introduced the fundamental notions of localization and completion of a ring, as well as that of regular local rings. He established the concept of the Krull dimension of a ring, first for Noetherian rings before moving on to expand his theory to cover general valuation rings and Krull rings. To this day, Krull's principal ideal theorem is widely considered the single most important foundational theorem in commutative algebra. These results paved the way for the introduction of commutative algebra into algebraic geometry, an idea which would revolutionize the latter subject.

title: Quantum enveloping algebra

text:
Michio Jimbo considered the algebras with three generators related by the three commutators
When formula_6, these reduce to the commutators that define the special linear Lie algebra formula_4. In contrast, for nonzero formula_8, the algebra defined by these relations is not a Lie algebra but instead an associative algebra that can be regarded as a deformation of the universal enveloping algebra of formula_4.

title: Interior algebra

text: Any monadic Boolean algebra can be considered to be an interior algebra where the interior operator is the universal quantifier and the closure operator is the existential quantifier. The monadic Boolean algebras are then precisely the variety of interior algebras satisfying the identity "x" = "x". In other words, they are precisely the interior algebras in which every open element is closed or equivalently, in which every closed element is open. Moreover, such interior algebras are precisely the semisimple interior algebras. They are also the interior algebras corresponding to the modal logic S5, and so have also been called S5 algebras.

title: Kac–Moody algebra

text: A real (possibly infinite-dimensional) Lie algebra is also considered a Kac–Moody algebra if its complexification is a Kac–Moody algebra.

title: Non-associative algebra

text: An algebra "A" over a field "K" is in particular a "K"-vector space and so one can consider the associative algebra End("A") of "K"-linear vector space endomorphism of "A". We can associate to the algebra structure on "A" two subalgebras of End("A"), the derivation algebra and the (associative) enveloping algebra.

title: Israel Halperin Prize

text: The Israel Halperin Prize is awarded every five years by the Canadian Annual Symposium on Operator Theory and Operator Algebras to a member of the Canadian mathematical community who has recently obtained a doctorate and has made contributions to operator theory or operator algebras. It honors Israel Halperin, the founder of a group of researchers in operator algebras and operator theory at the University of Toronto who strongly influenced the field across Canada. First awarded in 1980.

title: Ladislav Rieger

text: Ladislav Svante Rieger (1916–1963) was a Czech mathematician who worked in the areas of algebra, mathematical logic, and axiomatic set theory. He is considered to be the founder of mathematical logic in the Czech Republic and Slovakia, having begun his work around 1957.

title: Von Neumann algebra

text: The Hilbert space tensor product of two Hilbert spaces is the completion of their algebraic tensor product. One can define a tensor product of von Neumann algebras (a completion of the algebraic tensor product of the algebras considered as rings), which is again a von Neumann algebra, and act on the tensor product of the corresponding Hilbert spaces. The tensor product of two finite algebras is finite, and the tensor product of an infinite algebra and a non-zero algebra is infinite. The type of the tensor product of two von Neumann algebras (I, II, or III) is the maximum of their types. The commutation theorem for tensor products states that

title: History of algebra

text: Algebra can essentially be considered as doing computations similar to those of arithmetic but with non-numerical mathematical objects. However, until the 19th century, algebra consisted essentially of the theory of equations. For example, the fundamental theorem of algebra belongs to the theory of equations and is not, nowadays, considered as belonging to algebra (in fact, every proof must use the completeness of the real numbers, which is not an algebraic property).

title: Pre-Lie algebra

text: Pre-Lie algebras have been considered under some other names, among which one can cite left-symmetric algebras, right-symmetric algebras or Vinberg algebras.

title: Quasi-Lie algebra

text: In characteristic other than 2, these are equivalent (in the presence of bilinearity), so this distinction doesn't arise when considering real or complex Lie algebras. It can however become important, when considering "Lie algebras" over the integers.

title: Łukasiewicz–Moisil algebra

text: Antonio Monteiro showed that for every monadic Boolean algebra one can construct a trivalent Łukasiewicz algebra (by taking certain equivalence classes) and that any trivalent Łukasiewicz algebra is isomorphic to a Łukasiewicz algebra thus derived from a monadic Boolean algebra. Cignoli summarizes the importance of this result as: "Since it was shown by Halmos that monadic Boolean algebras are the algebraic counterpart of classical first order monadic calculus, Monteiro considered that the representation of three-valued Łukasiewicz algebras into monadic Boolean algebras gives a proof of the consistency of Łukasiewicz three-valued logic relative to classical logic."

title: C*-algebra

text: C-algebras (pronounced "C-star") are subjects of research in functional analysis, a branch of mathematics. A C*-algebra is a complex algebra "A" of continuous linear operators on a complex Hilbert space with two additional properties:C*-algebras were first considered primarily for their use in quantum mechanics to model algebras of physical observables. This line of research began with Werner Heisenberg's matrix mechanics and in a more mathematically developed form with Pascual Jordan around 1933. Subsequently, John von Neumann attempted to establish a general framework for these algebras which culminated in a series of papers on rings of operators. These papers considered a special class of C*-algebras which are now known as von Neumann algebras.

title: Projectionless C*-algebra

text: In mathematics, a projectionless C*-algebra is a C*-algebra with no nontrivial projections. For a unital C*-algebra, the projections 0 and 1 are trivial. While for a non-unital C*-algebra, only 0 is considered trivial. The problem of whether simple infinite-dimensional C*-algebras with this property exist was posed in 1958 by Irving Kaplansky, and the first example of one was published in 1981 by Bruce Blackadar. For commutative C*-algebras, being projectionless is equivalent to its spectrum being connected. Due to this, being projectionless can be considered as a noncommutative analogue of a connected space.

title: Algebraic curve

text: More generally, one may consider algebraic curves that are not contained in the plane, but in a space of higher dimension. A curve that is not contained in some plane is called a skew curve. The simplest example of a skew algebraic curve is the twisted cubic. One may also consider algebraic curves contained in the projective space and even algebraic curves that are defined independently to any embedding in an affine or projective space. This leads to the most general definition of an algebraic curve:

title: Lie algebra extension

text:
A loop group is taken as a group of smooth maps from the unit circle into a Lie group with the group structure defined by the group structure on . The Lie algebra of a loop group is then a vector space of mappings from into the Lie algebra of . Any subalgebra of such a Lie algebra is referred to as a loop algebra. Attention here is focused on polynomial loop algebras of the form
To see this, consider elements near the identity in for in the loop group, expressed in a basis for
where the are real and small and the implicit sum is over the dimension of .
Now write
to obtain
Thus the functions
constitute the Lie algebra.
A little thought confirms that these are loops in as goes from to . The operations are the ones defined pointwise by the operations in . This algebra is isomorphic with the algebra
where is the algebra of Laurent polynomials,
The Lie bracket is
In this latter view the elements can be considered as polynomials with (constant!) coefficients in . In terms of a basis and structure constants,

title: Algebraic structure

text: Identities are equations formulated using only the operations the structure allows, and variables that are tacitly universally quantified over the relevant universe. Identities contain no connectives, existentially quantified variables, or relations of any kind other than the allowed operations. The study of varieties is an important part of universal algebra. An algebraic structure in a variety may be understood as the quotient algebra of term algebra (also called "absolutely free algebra") divided by the equivalence relations generated by a set of identities. So, a collection of functions with given signatures generate a free algebra, the term algebra "T". Given a set of equational identities (the axioms), one may consider their symmetric, transitive closure "E". The quotient algebra "T"/"E" is then the algebraic structure or variety. Thus, for example, groups have a signature containing two operators: the multiplication operator "m", taking two arguments, and the inverse operator "i", taking one argument, and the identity element "e", a constant, which may be considered an operator that takes zero arguments. Given a (countable) set of variables "x", "y", "z", etc. the term algebra is the collection of all possible terms involving "m", "i", "e" and the variables; so for example, "m(i(x), m(x,m(y,e)))" would be an element of the term algebra. One of the axioms defining a group is the identity "m(x, i(x)) = e"; another is "m(x,e) = x". The axioms can be represented as trees. These equations induce equivalence classes on the free algebra; the quotient algebra then has the algebraic structure of a group.

title: Dmitry Grave

text: Grave became professor at Kharkov in 1897 and, from 1902, he was appointed professor at the University of Kiev, where he remained for the rest of his life. Grave is considered as the founder of the Kiev school of algebra which was to become the centre for algebra in the USSR.

title: Thābit ibn Qurra

text: Thābit ibn Qurrah made important discoveries in algebra, geometry, and astronomy. In astronomy, Thābit is considered one of the first reformers of the Ptolemaic system, and in mechanics he was a founder of statics.

title: Algebra

text: Abstract algebra was developed in the 19th century, deriving from the interest in solving equations, initially focusing on what is now called Galois theory, and on constructibility issues.[28] George Peacock was the founder of axiomatic thinking in arithmetic and algebra. Augustus De Morgan discovered relation algebra in his Syllabus of a Proposed System of Logic. Josiah Willard Gibbs developed an algebra of vectors in three-dimensional space, and Arthur Cayley developed an algebra of matrices (this is a noncommutative algebra).[29]

title: C*-algebra

text: The algebra M("n", C) of "n" × "n" matrices over C becomes a C*-algebra if we consider matrices as operators on the Euclidean space, C, and use the operator norm ||·|| on matrices. The involution is given by the conjugate transpose. More generally, one can consider finite direct sums of matrix algebras. In fact, all C*-algebras that are finite dimensional as vector spaces are of this form, up to isomorphism. The self-adjoint requirement means finite-dimensional C*-algebras are semisimple, from which fact one can deduce the following theorem of Artin–Wedderburn type:

title: Semisimple Lie algebra

text: In mathematics, a Lie algebra is semisimple if it is a direct sum of simple Lie algebras, i.e., non-abelian Lie algebras formula_1 whose only ideals are {0} and formula_1 itself. It is important to emphasize that a one-dimensional Lie algebra (which is necessarily abelian) is by definition not considered a simple Lie algebra, even though such an algebra certainly has no nontrivial ideals. Thus, one-dimensional algebras are not allowed as summands in a semisimple Lie algebra.

title: Biquaternion

text: The algebra of biquaternions can be considered as a tensor product (taken over the reals) where is the field of complex numbers and is the division algebra of (real) quaternions. In other words, the biquaternions are just the complexification of the quaternions. Viewed as a complex algebra, the biquaternions are isomorphic to the algebra of complex matrices . They are also isomorphic to several Clifford algebras including , the Pauli algebra , and the even part of the spacetime algebra.

title: Banach–Stone theorem

text: More significantly, the Banach–Stone theorem suggests the philosophy that one can replace a "space" (a geometric notion) by an "algebra", with no loss. Reversing this, it suggests that one can consider algebraic objects, even if they do not come from a geometric object, as a kind of "algebra of scalars". In this vein, any "commutative" C*-algebra is the algebra of scalars on a Hausdorff space. Thus one may consider "non"commutative C*-algebras (and their Spec) as non-commutative spaces. This is the basis of the field of noncommutative geometry.

title: Italian school of algebraic geometry

text: According to Guerraggio & Nastasi (page 9, 2005) Luigi Cremona is "considered the founder of the Italian school of algebraic geometry". Later they explain that in Turin the collaboration of Enrico D'Ovidio and Corrado Segre "would bring, either by their own efforts or those of their students, Italian algebraic geometry to full maturity". A one-time student of Segre, H.F. Baker wrote (1926, page 269), [Corrado Segre] "may probably be said to be the father of that wonderful Italian school which has achieved so much in the birational theory of algebraical loci." On this topic, Brigaglia & Ciliberto (2004) say "Segre had headed and maintained the school of geometry that Luigi Cremona had established in 1860." Reference to the Mathematics Genealogy Project shows that, in terms of "Italian doctorates", the real productivity of the school began with Guido Castelnuovo and Federigo Enriques. In the USA Oscar Zariski inspired many Ph.D.s.


query: Who coined the term asteroid?

title: Asteroid

text: The first asteroid to be discovered, Ceres, was originally considered to be a new planet.[note 1] This was followed by the discovery of other similar bodies, which, with the equipment of the time, appeared to be points of light, like stars, showing little or no planetary disc, though readily distinguishable from stars due to their apparent motions. This prompted the astronomer Sir William Herschel to propose the term "asteroid",[note 2] coined in Greek as ἀστεροειδής, or asteroeidēs, meaning 'star-like, star-shaped', and derived from the Ancient Greek ἀστήρ astēr 'star, planet'. In the early second half of the nineteenth century, the terms "asteroid" and "planet" (not always qualified as "minor") were still used interchangeably. [note 3]

title: Opposition surge

text: The existence of the opposition surge was described in 1956 by Tom Gehrels during his study of the reflected light from an asteroid. Gehrels' later studies showed that the same effect could be shown in the moon's brightness. He coined the term "opposition effect" for the phenomenon, but the more intuitive "opposition surge" is now more widely used.

title: Clifford Cunningham

text: After years of research, Dr. Cunningham finally discovered who coined the word 'asteroid'. Although 'asteroid' has been attributed to the famous astronomer William Herschel, Cunningham found evidence that it was proposed by Greek expert Charles Burney, Jr., the son of a friend of Herschel. In 2014 he discovered a previously unrecognised allusion to the aurora borealis in Milton's "Paradise Lost".

title: Asteroid

text: The minor planets beyond Jupiter's orbit are sometimes also called "asteroids", especially in popular presentations.[note 5] However, it is becoming increasingly common for the term "asteroid" to be restricted to minor planets of the inner Solar System.[47] Therefore, this article will restrict itself for the most part to the classical asteroids: objects of the asteroid belt, Jupiter trojans, and near-Earth objects.

title: Ceres (dwarf planet)

text:
Ceres is the largest object in the asteroid belt.
It is sometimes assumed that Ceres has been "re"classified as a dwarf planet, and that it is therefore no longer considered an asteroid. For example, a news update at Space.com spoke of "Pallas, the largest asteroid, and Ceres, the dwarf planet formerly classified as an asteroid", whereas an IAU question-and-answer posting states, "Ceres is (or now we can say it was) the largest asteroid", though it then speaks of "other asteroids" crossing Ceres' path and otherwise implies that Ceres is still considered an asteroid. The Minor Planet Center notes that such bodies may have dual designations. The 2006 IAU decision that classified Ceres as a dwarf planet never addressed whether it is or is not an asteroid. Indeed, the IAU has never defined the word 'asteroid' at all, having preferred the term 'minor planet' until 2006, and preferring the terms 'small Solar System body' and 'dwarf planet' after 2006. Lang (2011) comments "the [IAU has] added a new designation to Ceres, classifying it as a dwarf planet. ... By [its] definition, Eris, Haumea, Makemake and Pluto, as well as the largest asteroid, 1 Ceres, are all dwarf planets", and describes it elsewhere as "the dwarf planet–asteroid 1 Ceres". NASA continues to refer to Ceres as an asteroid, as do various academic textbooks.

title: Asteroid family

text: An asteroid family is a population of asteroids that share similar proper orbital elements, such as semimajor axis, eccentricity, and orbital inclination. The members of the families are thought to be fragments of past asteroid collisions. An asteroid family is a more specific term than asteroid group whose members, while sharing some broad orbital characteristics, may be otherwise unrelated to each other.

title: Asteroid

text: When found, asteroids were seen as a class of objects distinct from comets, and there was no unified term for the two until "small Solar System body" was coined in 2006. The main difference between an asteroid and a comet is that a comet shows a coma due to sublimation of near surface ices by solar radiation. A few objects have ended up being dual-listed because they were first classified as minor planets but later showed evidence of cometary activity. Conversely, some (perhaps all) comets are eventually depleted of their surface volatile ices and become asteroid-like. A further distinction is that comets typically have more eccentric orbits than most asteroids; most "asteroids" with notably eccentric orbits are probably dormant or extinct comets.[45]

title: Flatlander (Niven)

text: The in-universe term "flatlander" refers to any human born on Earth, in contrast to those who live on other planets or space habitats. The derogatory term was coined by Belters, whose space habitats are either enclosed, or located on large asteroids with visibly curving horizons. Whereas from any point on the surface of Earth the horizon looks "flat".

title: Symplast

text: The symplastic transport was first realized by Eduard Tangl in 1879, who also discovered the plasmodesmata, a term coined by Eduard Strasburger, 1901. In 1880, Hanstein coined the term symplast. The contrasting terms apoplast and symplast were used together in 1930 by Münch.

title: Asteroid laser ablation

text: A stand-on system consists of a small laser array which is sent to the target asteroid. The system would be limited to small or medium size asteroids and would require detection relatively far in advance. For a short notice threat a stand-on system would be ineffective, due to the time required to build and send the system to the target. Additionally, a new system would be required for each target. In the short term a stand-on system could be affordable and feasible; however, in the long term a larger system able to deflect asteroids of all sizes is more practical.

title: Definition of planet

text: The definition of "planet", since the word was coined by the ancient Greeks, has included within its scope a wide range of celestial bodies. Greek astronomers employed the term "asteres planetai" (ἀστέρες πλανῆται), "wandering stars", for star-like objects which apparently moved over the sky. Over the millennia, the term has included a variety of different objects, from the Sun and the Moon to satellites and asteroids.

title: Asteroids (video game)

text: "Asteroids" was immediately successful upon release. It displaced "Space Invaders" by popularity in the United States and became Atari's best selling arcade game of all time, with over 70,000 units sold. Atari earned an estimated $150 million in sales from the game, and arcade operators earned a further $500 million from coin drops. Atari had been in the process of manufacturing another vector game, "Lunar Lander", but demand for "Asteroids" was so high "that several hundred "Asteroids" games were shipped in "Lunar Lander" cabinets". "Asteroids" was so popular that some video arcade operators had to install large boxes to hold the number of coins spent by players.

title: Asteroid

text: Asteroids are minor planets, especially of the inner Solar System. Larger asteroids have also been called planetoids. These terms have historically been applied to any astronomical object orbiting the Sun that did not resemble a planet-like disc and was not observed to have characteristics of an active comet such as a tail. As minor planets in the outer Solar System were discovered they were typically found to have volatile-rich surfaces similar to comets. As a result, they were often distinguished from objects found in the main asteroid belt.[1] In this article, the term "asteroid" refers to the minor planets of the inner Solar System including those co-orbital with Jupiter.

title: Extinct comet

text: When discovered, asteroids were seen as a class of objects distinct from comets, and there was no unified term for the two until "small Solar System body" was coined by the IAU in 2006. The main difference between an asteroid and a comet is that a comet shows a coma due to sublimation of near-surface ices by solar radiation. A few objects have ended up being dual-listed because they were first classified as minor planets but later showed evidence of cometary activity. Conversely, some (perhaps all) comets are eventually depleted of their surface volatile ices and develop the appearance of asteroids. A further distinction is that comets typically have more eccentric orbits than most asteroids; most "asteroids" with notably eccentric orbits are probably dormant or extinct comets. Also, they are theorized to be common objects amongst the celestial bodies orbiting close to the Sun.

title: Spaceguard

text:
Arthur C. Clarke coined the term in his novel "Rendezvous with Rama" (1972) where "Project Spaceguard" was the name of an early warning system created following a fictional catastrophic asteroid impact. This name was later adopted by a number of real life efforts to discover and study near-Earth objects. The name was used for the Survey "with the permission and encouragement of Clarke."
A 1992 US Congressional study produced a "Spaceguard Survey Report" which led to a mandate that NASA locate 90% of near-Earth asteroids larger than 1 km within 10 years. This is often referred to as the "Spaceguard Goal." A number of efforts which receive money through NASA are all considered to be working on the "Spaceguard Project."

title: List of objects at Lagrangian points

text: Asteroids in the and Sun–Mars Lagrangian points are sometimes called "Mars trojans," with a lower-case t, as "Trojan asteroid" was originally defined as a term for Lagrangian asteroids of Jupiter. They may also be called "Mars Lagrangian asteroids."

title: Hypercane

text: A hypercane is a hypothetical class of extreme tropical cyclone that could form if ocean temperatures reached , which is warmer than the warmest ocean temperature ever recorded. Such an increase could be caused by a large asteroid or comet impact, a large supervolcanic eruption, or extensive global warming. There is some speculation that a series of hypercanes resulting from an impact by a large asteroid or comet contributed to the demise of the non-avian dinosaurs. The hypothesis was created by Kerry Emanuel of MIT, who also coined the term.

title: Chinese numismatic charm

text: Sometimes, the nickname for the Yansheng coin also includes the so-called ""flower coin"" or ""patterned coin"" (). They are alternatively referred to as "play coins" (wanqian, 玩钱) in China. Historically the term "Yansheng coin" was more popular but in modern China and Taiwan the term "flower coin" has become the more common name.

title: Asteroid belt

text: The asteroid belt is the circumstellar disc in the Solar System located roughly between the orbits of the planets Mars and Jupiter. It is occupied by numerous irregularly shaped bodies called asteroids or minor planets. The asteroid belt is also termed the main asteroid belt or main belt to distinguish it from other asteroid populations in the Solar System such as near-Earth asteroids and trojan asteroids. About half the mass of the belt is contained in the four largest asteroids: Ceres, Vesta, Pallas, and Hygiea. The total mass of the asteroid belt is approximately 4% that of the Moon, or 22% that of Pluto, and roughly twice that of Pluto's moon Charon (whose diameter is 1200 km).

title: Ceres (dwarf planet)

text: As other objects were discovered in the neighborhood of Ceres, it was realized that Ceres represented the first of a new class of objects. In 1802, with the discovery of 2 Pallas, William Herschel coined the term "asteroid" ("star-like") for these bodies, writing that "they resemble small stars so much as hardly to be distinguished from them, even by very good telescopes". As the first such body to be discovered, Ceres was given the designation 1 Ceres under the modern system of minor-planet designations. By the 1860s, the existence of a fundamental difference between asteroids such as Ceres and the major planets was widely accepted, though a precise definition of "planet" was never formulated.

title: Boiling liquid expanding vapor explosion

text: The term "BLEVE" was coined by three researchers at Factory Mutual, in the analysis of an accident there in 1957 involving a chemical reactor vessel. Anthony Santos was one of the Factory Mutual chemical engineers who coined the term.

title: List of objects at Lagrangian points

text:
Asteroids in the and Sun–Jupiter Lagrangian points are known as "Jupiter Trojan asteroids" or simply "Trojan asteroids".Minor planets in the and Sun–Neptune Lagrangian points are called Neptune trojans, with a lower-case "t", as "Trojan asteroid" was originally defined as a term for Lagrangian asteroids of Jupiter.
Source: Minor Planet Center

title: Asteroid belt

text: The expression "asteroid belt" came into use in the very early 1850s, although it is hard to pinpoint who coined the term. The first English use seems to be in the 1850 translation (by E. C. Otté) of Alexander von Humboldt's "Cosmos": "[...] and the regular appearance, about the 13th of November and the 11th of August, of shooting stars, which probably form part of a belt of asteroids intersecting the Earth's orbit and moving with planetary velocity". Another early appearance occurred in Robert James Mann's "A Guide to the Knowledge of the Heavens": "The orbits of the asteroids are placed in a wide belt of space, extending between the extremes of [...]". The American astronomer Benjamin Peirce seems to have adopted that terminology and to have been one of its promoters.

title: Slang terms for money

text: In the United Kingdom the term "shrapnel" may be used for an inconvenient pocketful of loose change because of the association with a shrapnel shell and "wad" or "wedge" for a bundle of banknotes, with "tightwad" a derogatory term for someone who is reluctant to spend money. Similar to " shrapnel" the use of "washers" in Scotland denotes a quantity of low value coinage. Quantities of UK 1p and 2p coins may be referred to as "Copper", 5p, 10p, 20p, and 50p coins as "Silver" and £1 and £2 coins as "Bronze" due to their colour and apparent base metal type. "Brass" is northern English slang for any amount of money.

title: Lookism

text: However, the term "lookism" was first coined in the 1970s within the fat acceptance movement. It was used in "The Washington Post" Magazine in 1978, which asserted that the term was coined by fat people who created the word to refer to "discrimination based on looks." The word appears in several major English language dictionaries. There is some overlap between the terms teratophobia, cacophobia and lookism.

title: Asteroid

text: In 2006, the term "small Solar System body" was also introduced to cover both most minor planets and comets.[note 4][42] Other languages prefer "planetoid" (Greek for "planet-like"), and this term is occasionally used in English especially for larger minor planets such as the dwarf planets as well as an alternative for asteroids since they are not star-like.[43] The word "planetesimal" has a similar meaning, but refers specifically to the small building blocks of the planets that existed when the Solar System was forming. The term "planetule" was coined by the geologist William Daniel Conybeare to describe minor planets,[44] but is not in common use. The three largest objects in the asteroid belt, Ceres, Pallas, and Vesta, grew to the stage of protoplanets. Ceres is a dwarf planet, the only one in the inner Solar System.

title: Gravitational keyhole

text: A gravitational keyhole is a tiny region of space where a planet's gravity would alter the orbit of a passing asteroid such that the asteroid would collide with that planet on a given future orbital pass. The word "keyhole" contrasts the large uncertainty of trajectory calculations (between the time of the observations of the asteroid and the first encounter with the planet) with the relatively narrow bundle(s) of critical trajectories. The term was coined by P. W. Chodas in 1999. It gained some public interest when it became clear, in January 2005, that the Asteroid 99942 Apophis would miss the Earth in 2029 but may go through one or another keyhole leading to impacts in 2036 or 2037. Further research has since been done, however, which revealed the probability of Apophis passing through the keyhole was extremely insignificant.

title: Eduard Suess

text: His son, Franz Eduard Suess (1867–1942), was superintendent and geologist at the "Imperial Geological Institute" in Vienna, who studied moldavites and coined the term tektite. The asteroid 12002 Suess, discovered by Czech astronomers Petr Pravec and Lenka Kotková in 1996, was named in his honor.

title: Knowledge process outsourcing

text: Out of all those who say they coined the term, Ashish Gupta, COO of Evalueserve has the best claim. Published authors have credited him for coining the term in their works.

title: Cantopop

text: It was at this time that the term "Cantopop" was first coined. The "Billboard" correspondent Hans Ebert, who had earlier coined the term "Cantorock" in 1974, noted a change in its style to something similar to British-American soft rock, therefore started to use the term Cantopop instead in 1978.