hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Reciprocal polynomial
In algebra, given a polynomial

with coefficients from an arbitrary field, its reciprocal polynomial or reflected polynomial, denoted by p∗ or pR, is the polynomial

That is, the coefficients of p∗ are the coefficients of p in reverse order. Reciprocal polynomials arise naturally in linear algebra as the characteristic polynomial of the inverse of a matrix.

In the special case where the field is the complex numbers, when

the conjugate reciprocal polynomial, denoted p†, is defined by,

where  denotes the complex conjugate of , and is also called the reciprocal polynomial when no confusion can arise.

A polynomial p is called self-reciprocal or palindromic if p(x) = p∗(x).
The coefficients of a self-reciprocal polynomial satisfy ai = an−i for all i.

Cyclotomic polynomial
In mathematics, the -th cyclotomic polynomial, for any positive integer , is the unique irreducible polynomial with integer coefficients that is a divisor of  and is not a divisor of  for any . Its roots are all -th primitive roots of unity
, where  runs over the positive integers up to  and coprime to  (where  is the imaginary unit). In other words, the -th cyclotomic polynomial is equal to

It may also be defined as the monic polynomial with integer coefficients that is the minimal polynomial over the field of the rational numbers of any primitive nth-root of unity ( is an example of such a root).

An important relation linking cyclotomic polynomials and primitive roots of unity is

showing that  is a root of  if and only if it is a -th primitive root of unity for some  that divides .
Buck Lake, Alberta
Buck Lake is a hamlet in central Alberta, Canada within the County of Wetaskiwin No. 10. It is located on Highway 13, approximately 109 kilometres (68 mi) southwest of Edmonton. It is located on the shore of Buck Lake.

Buck Lake (Alberta)
Buck Lake is a lake in the County of Wetaskiwin in Alberta. Through its outlet into Buck Lake Creek on its north shore, the lake is part of the North Saskatchewan River system.

The hamlet of Buck Lake is situated on the southwest shore of the lake. The Calhoun Bay Provincial Recreation Area, with campsites and water supply, is located on the central eastern shore. While the shoreline of Buck Lake is home to several developments, including Greystones and Oakes Bay on the northeast arm, most of the shoreline remains undeveloped. Buck Lake is set amidst gently rolling hills in the County of Wetaskiwin, 105 km southwest of the city of Edmonton and 70 km north of the town of Rocky  Mountain House. The northernmost end of the lake borders the Buck Mountain Provincial Grazing Reserve, in which the nearby Buck Mountain is situated.
2009 Vancouver gang war
In early 2009, a series of gang-related shootings occurred due to what police describe as a gang war in Vancouver, British Columbia, Canada. Alleged participants include the Independent Soldiers, the Sanghera Crime Family, the Buttar Crime Family, the United Nations Gang, the Red Scorpions, and the Vancouver chapters of the Hells Angels.

Bacon Brothers (gangsters)
The Bacon Brothers, Jonathan, Jarrod, and Jamie Bacon, are a trio of gangsters from Abbotsford, British Columbia, who are suspected of multiple firearms and drug trafficking charges and implicated in a rash of homicides that took place in the Fraser Valley and Greater Vancouver area. Jonathan, the oldest brother, was murdered in Kelowna on August 14, 2011.
Zuntalin
Zuntalin is a village in Ye Township in the Mon State of south-east Burma. It is located north-west of Ye city.

Nearby towns and villages include Andin (4.0 nm), Saiye (4.0 nm), Awainggale (1.4 nm), Hmeinsein (1.0 nm), Sonmatha (2.2 nm), Hnyihnu (4.2 nm), Kyonpaw (4.1 nm) and Zayat (3.6 nm)

Hmeinsein
Hmeinsein is a village in Ye Township in the Mon State of south-east Burma. It is located north-west of Ye city.

Nearby towns and villages include Awainggale (2.2 nm), Zuntalin (1.0 nm), Taungbon (3.1 nm).
Sakale (2.8 nm) and Sonmatha (1.4 nm).
Grant High School (Los Angeles)
Ulysses S. Grant High School is a public high school located in the Valley Glen neighborhood of Los Angeles, California, United States, in the east central San Fernando Valley. It is located adjacent to Los Angeles Valley College.

It is part of District North 2 of the Los Angeles Unified School District. The school serves several areas, including Valley Glen, much of Sherman Oaks, and sections of both Van Nuys and North Hollywood.

Los Angeles Valley College
Los Angeles Valley College (LAVC, Valley College, or Valley) is a public community college in Los Angeles, California. It is part of the Los Angeles Community College District.

The college is adjacent to Grant High School in the neighborhood of Valley Glen. Often called "Valley College" or simply "Valley" by those who frequent the campus, it opened its doors to the public on September 12, 1949, at which time the campus was located on the site of Van Nuys High School. The college moved to its current location in 1951, a 105-acre (42 ha) site bounded by Fulton Avenue on the west, Ethel Avenue/Coldwater Canyon Boulevard on the east, Burbank Boulevard on the south, and Oxnard Street on the north.

Los Angeles Valley College is one of nine colleges in the Los Angeles Community College District (LACCD) and is accredited by the Accrediting Commission for Community and Junior Colleges.

The sports teams are the Monarchs and the school colors are green and yellow.
Wittenberghorn
The Wittenberghorn is a mountain of the Bernese Alps, located on the border between the Swiss cantons of Vaud and Bern. It lies approximately halfway between L'Etivaz (Vaud) and Feutersoey (Bern), south of the Col de Jable.

Col de Jable
The Col de Jable (1,884 m) is a mountain pass in the western Swiss Alps, connecting L'Etivaz in the canton of Vaud to Gstaad in the canton of Bern. The pass is located between the Gummfluh and the Wittenberghorn. It is traversed by a trail.
Methanococcus
Methanococcus is a genus of coccoid methanogens of the family Methanococcaceae. They are all mesophiles, except the thermophilic M. thermolithotrophicus and the hyperthermophilic M. jannaschii. The latter was discovered at the base of a "white smoker" chimney at 21°N on the East Pacific Rise and it was the first archaeal genome to be completely sequenced, revealing many novel and eukaryote-like elements.

Methanocaldococcus jannaschii
Methanocaldococcus jannaschii (formerly Methanococcus jannaschii) is a thermophilic methanogenic archaean in the class Methanococci that lives at temperatures from 48° to 94 °C and at pressures of more than 200 atmospheres. It was the first archaeon, and third organism, to have its complete genome sequenced. The sequencing identified many genes unique to the archaea. Many of the synthesis pathways for methanogenic cofactors were worked out biochemically in this organism, as were several other archaeal-specific metabolic pathways.
Ma On Shan Road
Ma On Shan Road (Chinese: 馬鞍山路) is a major road in the new town of Ma On Shan in the New Territories of Hong Kong. The road extends northward from Tate's Cairn Highway near Tai Shui Hang along the eastern bank of the Shing Mun River. It ends in the north when it joins Sai Sha Road near Wu Kai Sha. Its branch road, the Ma On Shan Bypass, redirects traffic between Sha Tin and Sai Kung North away from the town centre near the Heng On Estate. It is the primary thoroughfare to Ma On Shan. A short section of the road north of Tate's Cairn Highway is an expressway.

Public housing estates in Ma On Shan
The following is a list of Public housing estates in Ma On Shan, Hong Kong, including Home Ownership Scheme (HOS), Private Sector Participation Scheme (PSPS), Sandwich Class Housing Scheme (SCHS), Flat-for-Sale Scheme (FFSS), and Tenants Purchase Scheme (TPS) estates.
Statue of Richard Grosvenor, Second Marquess of Westminster
The Statue of Richard Grosvenor, Second Marquess of Westminster is in Grosvenor Park, Chester, Cheshire. England.  It was designed by Thomas Thornycroft and was erected to commemorate the generosity of the Marquess.  The statue was unveiled in 1869, and was paid for by public subscription.  It is recorded in the National Heritage List for England as a designated Grade II listed building.

Grosvenor Park, Chester
Grosvenor Park is a public park in the city of Chester, Cheshire, England (grid reference SJ412663). It consists of 20 acres (8.1 ha) of land overlooking the River Dee. It is regarded as one of the finest and most complete examples of Victorian parks in the North West of England, if not nationally. On 22 August 2013 the designation of the park was raised from Grade II in the National Register of Historic Parks and Gardens to Grade II*.
Francis Marsh
Francis Marsh (23 October 1626 – 16 November 1693) was Archbishop of Dublin from 1682 to 1693.

He was admitted to Emmanuel College, Cambridge in April 1642 as the son of Henry Marsh esq. of Edgeworth, Gloucestershire.
He had previously been Dean of Connor (1660–1661), Dean of Armagh (1661–1667), Bishop of Limerick, Ardfert and Aghadoe and Kilmore and Ardagh. He married Mary, the daughter of Bishop Jeremy Taylor. Their son Jeremiah Marsh was the Dean of Kilmore.
From his father-in-law, Jeremy Taylor, he inherited a silver watch, said to have been a gift from Charles I. This watch remained in the family of his great-grandson, Francis Marsh, barrister-at-law.

Dean of Connor
The Dean of Connor is based at Christ Church Cathedral, Lisburn in the Diocese of Connor (Church of Ireland) within the Church of Ireland. The chapter is however known as the Chapter of St Saviours, Connor after the previous (prior to 1662) cathedral church in Connor.

The current incumbent is the Very Reverend Sam Wright.
Gmina Szepietowo
Gmina Szepietowo is an urban-rural gmina (administrative district) in Wysokie Mazowieckie County, Podlaskie Voivodeship, in north-eastern Poland. Its seat is the town of Szepietowo, which lies approximately 6 kilometres (4 mi) south of Wysokie Mazowieckie and 51 km (32 mi) south-west of the regional capital Białystok.

The gmina covers an area of 151.9 square kilometres (58.6 sq mi), and as of 2006 its total population is 7,485. (Before 1 January 2010, when Szepietowo became a town, the district was classed as a rural gmina.)

Szepietowo
Szepietowo [ʂɛpjɛˈtɔvɔ] is a town in Wysokie Mazowieckie County, Podlaskie Voivodeship, in north-eastern Poland. It is the seat of the gmina (administrative district) called Gmina Szepietowo.

Szepietowo has a population of 2,412. It gained town status on 1 January 2010.
Gaoligong Mountains
The Gaoligong Mountains (Chinese: 高黎贡山; pinyin: Gāolígòng Shān) are a mountainous sub-range of the southern Hengduan Mountain Range, located in the western Yunnan highlands and straddling the border of southwestern China and northern Myanmar (Burma). It is described as a "global biodiversity hotspot" and one of the "biologically richest places on Earth.

World Network of Biosphere Reserves in Asia and the Pacific
Biosphere reserves are areas comprising terrestrial, marine and coastal ecosystems. Under UNESCO's Man and Biosphere Reserve Programme, there are 142 biosphere reserves recognized as part of the World Network of Biosphere Reserves in Asia and the Pacific as of April 2016. These are distributed across 24 countries in the region.
Shut Up, Little Man!
Shut Up, Little Man! is the title of audio vérité recordings of two argumentative and violent alcoholics, Peter J. Haskett and Raymond Huffman in San Francisco. Bananafish magazine arranged for a commercial release of the tapes in 1992.

The recordings were made by "Eddie Lee Sausage" and "Mitchell D.", who lived in a bright pink apartment building at 237 Steiner Street (dubbed the "Pepto Bismol Palace") in San Francisco's Lower Haight district. Eddie Lee and Mitchell moved into the apartment in 1987, and discovered that their neighbors, Haskett and Huffman, argued nearly constantly, with Peter often shouting "shut up, little man!" at Ray.  Eddie and Mitchell began tape recording the arguments, and distributing copies among their friends. Eddie Lee and Mitchell sometimes goaded Ray and Peter with prank telephone calls.

In 1992, Huffman died of a heart attack brought on by colon cancer, pancreatitis, and alcoholism. Haskett died in 1996 of liver problems due to alcoholism.

Bananafish Magazine
Bananafish was a magazine begun in 1987 in San Francisco, California, published under the name Seymour Glass, focusing on various aspects of underground culture, particularly musical genres such as noise music. The magazine ceased publication in 2004.
Selbu Municipality
Selbu is a municipality in Trøndelag county, Norway. The administrative centre of the municipality is the village of Mebonden. Other villages in Selbu include Flora, Fossan, Hyttbakken, Innbygda, Selbustrand, Trøa, Tømra, and Vikvarvet.

The 1,235-square-kilometre (477 sq mi) municipality is the 86th largest by area out of the 357 municipalities in Norway. Selbu Municipality is the 200th most populous municipality in Norway with a population of 4,216. The municipality's population density is 3.4 inhabitants per square kilometre (8.8/sq mi) and its population has increased by 4.6% over the previous 10-year period.

Selbustrand
Selbustrand is a village in Selbu Municipality in Trøndelag county, Norway. It is located about 5 kilometres (3.1 mi) across the lake Selbusjøen from the municipal center of Mebonden. The village of Fossan lies about 3 kilometres (1.9 mi) to the northeast of Selbustrand. The Selbustrand Church is located in this village.
Field system
The study of field systems (collections of fields) in landscape history is concerned with the size, shape and orientation of a number of fields. These are often adjacent, but may be separated by a later feature.

Landscape history
Landscape history is the study of the way in which humanity has changed the physical appearance of the environment – both present and past. It is sometimes referred to as landscape archaeology. It was first recognised as a separate area of study during the 20th century and uses evidence and approaches from other disciplines including archaeology, architecture, ecology, aerial photography, rephotography, local history and historical geography.
Division No. 8, Saskatchewan
Division No. 8 is one of eighteen census divisions in the province of Saskatchewan, Canada, as defined by Statistics Canada. It is located in the west-southwestern part of the province, bordering Alberta. The most populous community in this division is Swift Current.

Rural Municipality of Monet No. 257
The Rural Municipality of Monet No. 257 (2016 population: 445) is a rural municipality (RM) in the Canadian province of Saskatchewan within Census Division No. 8 and SARM Division No. 3. It is located in the southwest portion of the province.
2025 Davis Cup Qualifiers second round
The 2025 Davis Cup qualifiers second round will be held from 12 to 14 September 2025. The seven winners of this round will qualify for the 2025 Davis Cup Finals (also known as the Final 8) while the seven losers will play at the 2026 Davis Cup qualifiers first round.

2025 Davis Cup Finals
Two-time defending champions Italy defeated Spain in the final, 2–0 to win the 2025 Davis Cup. It was Italy's fourth Davis Cup title. Italy was the first country to win the event three consecutive times since the United States in 1972.

The Finals (also called the Final 8) were the highest level of Davis Cup competition in 2025 and were played from 18 to 23 November 2025. They featured the host nation (Italy) and the seven winners from the Qualifiers second round. The ties were contested in a best-of-three rubbers format and played on one day. There were two singles matches followed, if necessary, by a doubles match.
The Constant Nymph (1933 film)
The Constant Nymph is a 1933 British drama film directed by Basil Dean and starring Victoria Hopper, Brian Aherne and Leonora Corbett. It is an adaptation of the 1924 novel The Constant Nymph by Margaret Kennedy and the 1926 stage play adaptation written by Kennedy and Dean. Dean tried to persuade Ivor Novello to reprise his appearance from the 1928 silent version The Constant Nymph but was turned down and cast Aherne in the part instead. The film is set in Tyrol, western Austria. Previously filmed in 1928, the sentimental Margaret Kennedy novel The Constant Nymph was sumptuously remade by Gaumont-British Picture Corporation in 1933.

The Constant Nymph (novel)
The Constant Nymph is a 1924 novel by Margaret Kennedy. It tells how a teenage girl, Tessa Sanger, falls in love with a family friend, who eventually marries her cousin. It explores the protagonists' complex family histories, focusing on class, education and creativity.
Rex Barnett
Rex Barnett (born October 22, 1938) is an American politician who represented District 4 in the Missouri House of Representatives from 1995 to 2003.

A Republican, he represented Missouri's 4th congressional district, comprising Atchison, Nodaway and Worth Counties in the Missouri House of Representatives for four terms. During this time, he sat on committees for criminal law, public safety and law enforcement, and appropriations for corrections and public safety.

Daisy Coleman
Catherine Daisy Coleman (March 30, 1997 – August 4, 2020) was an American sexual assault victim advocate who was the subject of the 2016 documentary film Audrie & Daisy, for which she received a Cinema Eye Honor. Coleman co-founded the non-profit organization SafeBAE, which was aimed at preventing sexual assault in schools. She died by suicide at the age of 23.
South African Class 4 4-8-2
The South African Railways Class 4 4-8-2 of 1911 was a steam locomotive from the pre-Union era in the Cape of Good Hope.

In 1911, the Cape Government Railways placed two steam locomotives with a 4-8-2 Mountain type wheel arrangement in service. They were renumbered and designated Class 4 when they were assimilated into the South African Railways a year later.

4-8-2
Under the Whyte notation for the classification of steam locomotives, 4-8-2 represents the wheel arrangement of four leading wheels, eight powered and coupled driving wheels and two trailing wheels. This type of steam locomotive is commonly known as the Mountain type, though the New York Central Railroad used the name Mohawk for their 4-8-2s.
Thomas Pollock (ice hockey)
Thomas Allen Pollock (August 1, 1925 – August 17, 1994) was a Canadian ice hockey player. He was a member of the Edmonton Mercurys that won a gold medal at the 1952 Winter Olympics. Pollock died of a stroke in 1994; he was the first member of the 1952 Olympic team to die.

Edmonton Mercurys
The Edmonton Mercurys were a Canadian intermediate-level senior ice hockey team based in Edmonton, Alberta, during the 1940s and 1950s. The team represented the Canada men's national ice hockey team twice, winning the 1950 World Ice Hockey Championships in London and the 1952 Winter Olympics Gold Medal in Oslo.
Seymour Medal
The Dr. Harold and Dorothy Seymour Medal, often simply referred to as the Seymour Medal, is an annual literary award given by the Society for American Baseball Research (SABR) to the best baseball historical or biographical book. The award was named in honor of baseball historians Harold Seymour and Dorothy Seymour Mills, co-authors of the Baseball trilogy, a highly acclaimed baseball history series.

First award in 1996, it was initially given to the winner at the annual SABR Conference but is now award at the banquet of the annual NINE Spring Training conference in Tempe, Arizona. The winner is given a bronze medal 3 1/2 inches in circumference. The obverse side shows the profiles of the Seymours, along with their names and background sketch of a baseball diamond. On the reverse side is SABR's name and logo, with crossed bats and a glove holding a baseball etched onto the background, an open book.

Society for American Baseball Research
The Society for American Baseball Research (SABR) is a membership organization dedicated to fostering the research and dissemination of the history and statistical record of baseball. The organization was founded in Cooperstown, New York, on August 10, 1971, at a meeting of 16 "statistorians" coordinated by sportswriter Bob Davids. The organization now reports a membership of over 7,500 and is based in Phoenix, Arizona.
Birkenes
Birkenes is a municipality in Agder county, Norway. It is located in the traditional district of Sørlandet. The administrative centre of the municipality is the village of Birkeland, where about half the municipal population lives. Other villages in Birkenes include Ås, Engesland, Flakk, Håbbesland, Herefoss, Mollestad, Oggevatn, Rugsland, Senumstad, Søre Herefoss, Svaland, Tveide, and Væting.

The 637-square-kilometre (246 sq mi) municipality is the 183rd largest by area out of the 356 municipalities in Norway. Birkenes is the 175th most populous municipality in Norway with a population of 5,390. The municipality's population density is 9 inhabitants per square kilometre (23/sq mi) and its population has increased by 9.2% over the previous 10-year period.

Rugsland
Rugsland is a village in Birkenes municipality in Agder county, Norway. The village is located on the western shore of the river Tovdalselva, about 5 kilometres (3.1 mi) south of the village of Mollestad. The village of Svaland lies about 5 kilometres (3.1 mi) to the northwest.
Czech Gothic architecture
Czech Gothic architecture refers to the architectural period primarily of the Late Middle Ages in the area of the present-day Czech Republic (former Crown of Bohemia, primarily consisting of the Kingdom of Bohemia and Margraviate of Moravia).

The Gothic style first appeared in the Czech lands in the first half of the 13th century and was common there until the early 16th century. The phases of the development of the Gothic architecture in the Czech lands are often named after the Bohemian ruling dynasty of the corresponding time:

Early Gothic – Přemyslid Gothic (13th and early 14th century)

High Gothic – Luxembourg Gothic (14th and early 15th century)

Late Gothic – Jagiellonian Gothic (approximately 1471–1526)

The most significant Gothic architects who worked in the Czech lands (especially in Bohemia) were Peter Parler and Benedikt Ried.

St. Procopius Basilica in Třebíč
St. Procopius Basilica (Czech: Bazilika svatého Prokopa) is a Romanesque-Gothic Christian church in Třebíč, Czech Republic. It was built on the site of the original Virgin Mary's Chapel of the Benedictine monastery in 1240–1260. It became a national cultural monument in 2002 as a part of the "monastery with St. Procopius church". The basilica together with the Jewish Quarter in Třebíč were inscribed as a UNESCO World Heritage Site in 2003, because of their exceptional testimony to the exchange of culture and values in the regions.

The basilica was originally dedicated to the Assumption of the Virgin Mary. Saint Procopius became the Patron saint of the basilica on the quincentenary his canonization in 1704. Jan Karel, Count of Valdštejn established a castle chapel of St. Procopius from the presbytery of the basilica.

As of 2013, the renovated Třebíč castle is a museum adjacent to the Basilica.
ArenaBowl XVII
ArenaBowl XVII was played on June 22, 2003 at the St. Pete Times Forum (formerly the Ice Palace) in Tampa, Florida before a sellout crowd of 20,496.  The Tampa Bay Storm earned their AFL record fifth ArenaBowl title, by defeating the Arizona Rattlers, 43–29.  The win was just months after the NFL's Tampa Bay Buccaneers won Super Bowl XXXVII, making Tampa Bay the first metropolitan area to simultaneously hold both NFL and AFL championships.

Lawrence Samuels
Lawrence "Law Dogg" Samuels (born May 1, 1970) is an American football coach and former player. He played college football at Livingston University, and was an Arena Football League (AFL) wide receiver/linebacker from 1994 to 2010. He was head coach of the Tampa Bay Storm of the AFL from 2014 to 2016.