OpenLLM-France/wikimedia huggingface dataset:
# National Winter Games of China

The National Winter Games of China is a nationwide Chinese winter sports competition typically held every 4 to 5 years in conjunction with the National Games of China. The 2016 games featured 1,388 participants from 52 delegations, including Hong Kong and Macau. The 2020 winter games, which were to take place in February in Inner Mongolia, have been postponed to 2024 due to the global COVID-19 pandemic.

## Editions

* 1959 - 1st National Winter Games, Jilin, Harbin
* 1965 - 2nd National Winter Games, -- (suspended)
* 1976 - 3rd National Winter Games, Harbin, Shangzhi
* 1979 - 4th National Winter Games, Shangzhi, Ürümqi, Beijing
* 1983 - 5th National Winter Games, Harbin, Yabuli
* 1987 - 6th National Winter Games, Changchun, Changbaishan
* 1991 - 7th National Winter Games, Harbin
* 1995 - 8th National Winter Games, Jilin
* 1999 - 9th National Winter Games, Changchun
* 2003 - 10th National Winter Games, Harbin, Yabuli
* 2008 - 11th National Winter Games, Jan 17 - Jan 27, 2008 in Qiqihar
* 2012 - 12th National Winter Games, Jan 1 - Jan 13 2012 in Changchun
* 2016 - 13th Chinese National Winter Games, Jan 20 - Jan 30, 2016 in Ürümqi, Xinjiang
* 2024 - 14th Chinese National Winter Games, originally scheduled to be held from Feb 16 - Feb 26, 2020 in Hailar and Yakeshi, Inner Mongolia Autonomous Region—postponed to 2024
# National reserves of New Zealand

A national reserve in New Zealand is an area that has been designated as having national importance under section 13 of the Reserves Act 1977. They are administered by the Department of Conservation.

## Legislation

Section 13 of the Reserves Act 1977 ("Governor-General may declare reserve to be national reserve") deals with national reserves. It is outlined that the governor-general can, through Order in Council (i.e. a process by which a government's decision is given effect) and made on recommendation by the minister (i.e. the Minister of Conservation, as that minister is responsible for the Department of Conservation), declare national reserves.

## Existing national reserves

There are three national historic reserves:
* Hāpūpū / J M Barker Historic Reserve, Chatham Islands – containing Moriori tree carvings
* Puhi Kai Iti / Cook Landing Site National Historic Reserve, Kaiti, Gisborne – where Captain James Cook first landed in New Zealand in 1769
* Te Kuri a Paoa/Young Nick’s Head National Historic Reserve – made a national reserve by the Ngai Tāmanuhiri Claims Settlement Act 2012, per section 13 of the Reserves Act 1977
National nature reserves include:
* Antipodes Islands National Nature Reserve
* Auckland Islands National Nature Reserve
* Bounty Islands National Nature Reserve
* Campbell Islands National Nature Reserve
* Snares Islands National Nature Reserve
Other national reserves include:
* Lewis Pass National Scenic Reserve – gazetted in 1981
The historic reserves are small reserves with historic value. The Lewis Pass reserve is much larger (13,737 hectares), with conservation values, including parts with scenic and ecological values. The Subantarctic Islands are collectively a UNESCO World Heritage Site.

## Other areas

The area known as the Waitangi National Reserve, where the Treaty of Waitangi was signed, is not a national reserve, despite its name. The area has never been a national reserve (or any other kind of reserve) under the Reserves Act. It has always been administered by the Waitangi National Trust Board under the Waitangi National Trust Board Act 1932.
Takapūneke is the site of an 1830 massacre adjacent to present-day Akaroa. The historical significance has not always been known and in 1960, Akaroa County built a sewage treatment plant in the area that was the core of the kāinga. In 2018, Christchurch City Council asked the Minister of Conservation to declare Takapūneke Reserve a national reserve.
# German submarine U-987

German submarine U-987 was a Type VIIC U-boat of Nazi Germany's Kriegsmarine during World War II.
She was ordered on 25 May 1941, and was laid down on 2 October 1942 at Blohm & Voss, Hamburg, as yard number 187. She was launched on 2 June 1943 and commissioned under the command of Oberleutnant zur See Hilmar-Karl Schreyer on 8 July 1943.

## Design

German Type VIIC submarines were preceded by the shorter Type VIIB submarines. U-987 had a displacement of 769 tonnes (757 long tons) when at the surface and 871 tonnes (857 long tons) while submerged. She had a total length of 67.10 m (220 ft 2 in), a pressure hull length of 50.50 m (165 ft 8 in), a beam of 6.20 m (20 ft 4 in), a height of 9.60 m (31 ft 6 in), and a draught of 4.74 m (15 ft 7 in). The submarine was powered by two Germaniawerft F46 four-stroke, six-cylinder supercharged diesel engines producing a total of 2,800 to 3,200 metric horsepower (2,060 to 2,350 kW; 2,760 to 3,160 shp) for use while surfaced, two Garbe, Lahmeyer & Co. RP 137/c double-acting electric motors producing a total of 750 metric horsepower (550 kW; 740 shp) for use while submerged. She had two shafts and two 1.23 m (4 ft) propellers. The boat was capable of operating at depths of up to 230 metres (750 ft).
The submarine had a maximum surface speed of 17.7 knots (32.8 km/h; 20.4 mph) and a maximum submerged speed of 7.6 knots (14.1 km/h; 8.7 mph). When submerged, the boat could operate for 80 nautical miles (150 km; 92 mi) at 4 knots (7.4 km/h; 4.6 mph); when surfaced, she could travel 8,500 nautical miles (15,700 km; 9,800 mi) at 10 knots (19 km/h; 12 mph). U-987 was fitted with five 53.3 cm (21 in) torpedo tubes (four fitted at the bow and one at the stern), fourteen torpedoes or 26 TMA mines, one 8.8 cm (3.46 in) SK C/35 naval gun, 220 rounds, and one twin 2 cm (0.79 in) C/30 anti-aircraft gun. The boat had a complement of between 44 — 52 men.

## Service history

On 15 June 1944, 19 days out of Stavanger on her first, and only war patrol, U-987 was sunk by torpedoes west of Narvik, in the Norwegian Sea. U-987 was attacked by the British submarine HMS Satyr. All Fifty-three of her crew were lost.
The wreck is located at 68°01′N 05°08′E﻿ / ﻿68.017°N 5.133°E﻿ / 68.017; 5.133.

### Wolfpacks

U-987 took part in one wolfpack, namely:
* Trutz (2 – 15 June 1944)
# German submarine U-986

German submarine U-986 was a Type VIIC U-boat of Nazi Germany's Kriegsmarine during World War II.
She was ordered on 25 May 1941, and was laid down on 18 September 1942 at Blohm & Voss, Hamburg, as yard number 186. She was launched on 20 May 1943 and commissioned under the command of Oberleutnant zur See Karl-Ernst Kaiser on 1 July 1943.

## Design

German Type VIIC submarines were preceded by the shorter Type VIIB submarines. U-986 had a displacement of 769 tonnes (757 long tons) when at the surface and 871 tonnes (857 long tons) while submerged. She had a total length of 67.10 m (220 ft 2 in), a pressure hull length of 50.50 m (165 ft 8 in), a beam of 6.20 m (20 ft 4 in), a height of 9.60 m (31 ft 6 in), and a draught of 4.74 m (15 ft 7 in). The submarine was powered by two Germaniawerft F46 four-stroke, six-cylinder supercharged diesel engines producing a total of 2,800 to 3,200 metric horsepower (2,060 to 2,350 kW; 2,760 to 3,160 shp) for use while surfaced, two Garbe, Lahmeyer & Co. RP 137/c double-acting electric motors producing a total of 750 metric horsepower (550 kW; 740 shp) for use while submerged. She had two shafts and two 1.23 m (4 ft) propellers. The boat was capable of operating at depths of up to 230 metres (750 ft).
The submarine had a maximum surface speed of 17.7 knots (32.8 km/h; 20.4 mph) and a maximum submerged speed of 7.6 knots (14.1 km/h; 8.7 mph). When submerged, the boat could operate for 80 nautical miles (150 km; 92 mi) at 4 knots (7.4 km/h; 4.6 mph); when surfaced, she could travel 8,500 nautical miles (15,700 km; 9,800 mi) at 10 knots (19 km/h; 12 mph). U-986 was fitted with five 53.3 cm (21 in) torpedo tubes (four fitted at the bow and one at the stern), fourteen torpedoes or 26 TMA mines, one 8.8 cm (3.46 in) SK C/35 naval gun, 220 rounds, and one twin 2 cm (0.79 in) C/30 anti-aircraft gun. The boat had a complement of between 44 — 52 men.

## Service history

On 8 February 1944, U-986 left Kiel on her first war patrol, sailing through the Iceland passage en route to the North Atlantic. U-986 reported on 10 April 1944 for the last time, stating that she would be commencing her return in two days, at that time U-986 was ordered to Lorient but when she failed to arrive in port she was posted missing on 20 April 1944, all hands, 50 crewmen, lost.
Last known location 51°30′N 20°00′W﻿ / ﻿51.500°N 20.000°W﻿ / 51.500; -20.000.

### Wolfpacks

U-986 took part in one wolfpack, namely:
* Preussen (2 – 22 March 1944)
# Gianni Zanasi

Gianni Zanasi is an Italian film director, screenwriter and actor.

## Early life and education

Gianni Zanasi was born in Vignola in 1965. After studying philosophy at the University of Bologna, he enrolled in a school of theatrical writing and a course in film directed by Nanni Moretti. He attended the Experimental Center of Cinematography in Rome, where in 1992 he graduated from directing.
In 1992 made his first short film Le belle prove, which won a prize at the Torino Film Festival. Two years later the same cast was reassembled for his first feature film, Nella mischia (1995), which was the first feature selected for Director's Fortnight of the Cannes Film Festival.
Zanasi also directed the television miniseries Fathers and Sons and the documentary Life is short but the day is long.
He returned to feature films in 2007, with the comedy Don't Think About It, starring Valerio Mastandrea, Anita Caprioli, Giuseppe Battiston, Caterina Murino, and others. Critically acclaimed, the film gave rise in 2009 to a television series of the same name, broadcast by Fox Italy, directed by Zanasi and Pellegrini, with the same cast as the original title.
In 2018 he directed Troppa grazia.

## Filmography

Director :
| Title | Year | Notes |
| Nella mischia | 1995 | As director |
| Fuori di me | 1999 | Direction and screenplay |
| Don't Think About It | 2007 | Direction and screenplay |
| The Complexity of Happiness | 2015 | Direction and screenplay |
| Lucia's Grace | 2018 | Direction and screenplay |
Writer :
| Title | Notes | Year |
| Le belle prove | Short film | 1993 |
| Nella mischia | | 1995 |
| A domani | Director and screenplay | 1999 |
| Beside Myself | As an actor also | 1999 |
| The life's short but the day is long | Documentary. Original Title - La vita è breve ma la giornata è lunghissima | 2004 |
| Don't Think About It | Original Title - Non pensarci | 2007 |
| Non pensarci, la serie | TV series | 2009 |

### Others

* Cinque pezzi facili (2009)
* La grande abbuffata (2009)
* Il candidato (2009)
* Il padrino (2009)
* Pretty Woman (2009)
# Gianni Zanon

Gianni Zanon (born 3 March 1960 in Treviso) is a former Italian rugby union player and a current coach. He played as a flanker.
Zanon started his career at Tarvisium, where he played until 1979/80. He moved then to Benetton Treviso, where he stayed from 1980/81 to 1992/93. He won three Italian Championship titles, in 1982/83, 1988/89 and 1991/92.
He had 45 caps for Italy, from 1981 to 1991, scoring 9 tries, 36 points on aggregate. He was called for the 1987 Rugby World Cup, playing in a single game, and for the 1991 Rugby World Cup, where he was the captain, playing in two games. He never scored in either occasions.
After finishing his player career, he became a coach. He was one of the two head coaches of Benetton Rugby Treviso, with Oscar Collodo, from 1993/94 to 1996/97, winning the National Championship in 1996/97. He was the coach of Udine Rugby, from 1997/98 to 1998/99. He returned to Benetton Rugby in 2005/06, being in charge of the second team and of the U-16 and U-20 categories, until 2009/10. In 2010, he was nominated technical coordinator of the youth categories.
# Maciré Sylla

Maciré Sylla is a Guinean singer-songwriter and dancer. She was born in Conakry but raised in Tayiré, a village to the north of Conakry.
Sylla sings mainly in Soussou and her style is inspired by Mandingo, Afropop, and Funk music.
She has released five albums to date.
She sold 200,000 copies of her first LP "Mariama" in Guinea, which made her the "best Guinean female singer of year 1998."
Her song "Perenperen" from the album "Massa" was included in the 2008 compilation album "African Party" from New Orleans label Putumayo World Music.

## Discography

* Mariama (1996, Djembé Faré/Misslin)
* Maya Irafama (2001, Djembé Faré/Trace)
* Sarefi (2004, Ethnomad/Arion)
* Massa (2005, Djembé Faré/Nocturne)
* Talitha (2010, Djembé Faré/Disques Office)
# Geylang West Single Member Constituency

Geylang West Single Member Constituency was an electoral constituency in Singapore. It used to exist from 1959 to 1988 where it was absorbed into Jalan Besar GRC.

## Member of Parliament

| Election | Member of Parliament | Party |
| Legislative Assembly of Singapore ||||
| 1959 | Yong Nyuk Lin | PAP |
| 1963 | Yong Nyuk Lin | PAP |
| Parliament of Singapore ||||
| 1968 | Yong Nyuk Lin | PAP |
| 1972 | Yong Nyuk Lin | PAP |
| 1976 | Yong Nyuk Lin | PAP |
| 1979 | Teh Cheang Wan | PAP |
| 1980 | Teh Cheang Wan | PAP |
| 1984 | Teh Cheang Wan | PAP |

## Elections

Note : Elections Department Singapore do not include rejected votes for calculation of candidate's vote share. Hence, the total of all candidates' vote share will be 100%.

### Elections in the 1950s

General Election 1959: Geylang West :
| Party | Party | Candidate | Votes | % |
| | PAP | Yong Nyuk Lin | 8,923 | 67.60 |
| | SPA | Kwek Sam Hock | 4,276 | 32.40 |
| Majority | Majority | Majority | 4,647 | 35.20 |
| Registered electors | Registered electors | Registered electors | 15,528 | |
| Turnout | Turnout | Turnout | 13,550 | 87.26 |
| | PAP win (new seat) | PAP win (new seat) | PAP win (new seat) | PAP win (new seat) |

### Elections in the 1960s

General Election 1963: Geylang West :
| Party | Party | Candidate | Votes | % | ±% |
| | PAP | Yong Nyuk Lin | 6,288 | 43.63 | 23.97 |
| | BS | Un Hon Kun | 5,670 | 39.34 | N/A |
| | UPP | Kum Teng Hock | 1,541 | 10.69 | N/A |
| | SA | Mohamed bin Haji Yacob | 914 | 6.34 | 26.06 |
| Majority | Majority | Majority | 618 | 4.29 | 30.91 |
| Registered electors | Registered electors | Registered electors | 15,386 | | 0.91 |
| Turnout | Turnout | Turnout | 14,575 | 94.73 | |
| | PAP hold | PAP hold | Swing | 23.97 | |
General Election 1968: Geylang West :
| Party | Party | Candidate | Votes | % | ±% |
| | PAP | Yong Nyuk Lin | Unopposed | Unopposed | Unopposed |
| Registered electors | Registered electors | Registered electors | 14,609 | | 5.05 |
| | PAP hold | PAP hold | PAP hold | PAP hold |

### Elections in the 1970s

General Election 1972: Geylang West :
| Party | Party | Candidate | Votes | % | ±% |
| | PAP | Yong Nyuk Lin | 7,320 | 69.28 | N/A |
| | WP | Quek Doh Lam | 3,246 | 30.72 | N/A |
| Majority | Majority | Majority | 4,074 | 38.56 | N/A |
| Registered electors | Registered electors | Registered electors | 11,653 | | 20.23 |
| | PAP hold | PAP hold | PAP hold | PAP hold | PAP hold |
General Election 1976: Geylang West :
| Party | Party | Candidate | Votes | % | ±% |
| | PAP | Yong Nyuk Lin | 11,912 | 71.18 | 1.90 |
| | UF | Lim Tiong Hock | 4,822 | 28.82 | N/A |
| Majority | Majority | Majority | 7,090 | 42.36 | 3.80 |
| Registered electors | Registered electors | Registered electors | 18,101 | | 55.33 |
| | PAP hold | PAP hold | PAP hold | PAP hold | PAP hold |
By-election 1979: Geylang West :
| Party | Party | Candidate | Votes | % | ±% |
| | PAP | Teh Cheang Wan | Unopposed | Unopposed | Unopposed |
| Registered electors | Registered electors | Registered electors | 20,874 | | 15.32 |
| | PAP hold | PAP hold | PAP hold | PAP hold | PAP hold |
# Geymond Vital

Geymond Vital (24 January 1897 – 6 December 1987) was a French film, stage and television actor.

## Filmography

| Year | Title | Role | Notes |
| 1924 | La galerie des monstres | | |
| 1926 | Destinée | Carlo Strabini | |
| 1927 | L'île enchantée | Ferrari | |
| 1928 | The Italian Straw Hat | Le lieutenant Tavernier | |
| 1928 | Misdeal | Marcellin Maldone | |
| 1929 | The Lighthouse Keepers | Yvon Bréhan | |
| 1930 | Le masque d'Hollywood | Jimmy Doyle | |
| 1930 | Lopez, le bandit | Pancho Lopez | |
| 1931 | Le père célibataire | | |
| 1931 | L'aviateur | | |
| 1931 | Révolte dans la prison | Dopey | |
| 1931 | Spanish Nights | Le marquis de Lupa | |
| 1932 | Le Fils de l'autre | Paul Niles / Victor Whitcomb | |
| 1933 | The Agony of the Eagles | Le messager de Nantes | |
| 1934 | Rapt | Firmin | |
| 1936 | Royal Waltz | René | |
| 1936 | The Gardens of Murcia | Pencho | |
| 1937 | Double Crime in the Maginot Line | Lieutenant Le Guenn | |
| 1938 | L'Étrange Monsieur Victor | Petit rôle | Uncredited |
| 1938 | La Piste du sud | Braun | |
| 1938 | Education of a Prince | Le général Braoulitch | |
| 1939 | The Five Cents of Lavarede | Le policier | |
| 1944 | First on the Rope | Maxime Vouillaz | |
| 1946 | Le bateau à soupe | Pedro | |
| 1947 | A Cop | Daniel | |
| 1949 | Doctor Laennec | Dr. Pierre Bayle | |
| 1949 | Cage of Girls | Pierre Mansois, oncle de Micheline | |
| 1950 | Le Crime des justes | Monsieur Combaroux | |
| 1955 | Blackmail | L'avocat de la partie civile | |
| 1956 | Law of the Streets | | |
| 1958 | Maigret Sets a Trap | Un journaliste | Uncredited |
| 1958 | Prisons de femmes | | |
| 1959 | Too Late to Love | Maître Augier - l'avocat général | |
| 1960 | The Baron of the Locks | La Ramée | Uncredited |
| 1961 | The Count of Monte Cristo | Himself | |
| 1964 | Diary of a Chambermaid | Le brigadier sur le quai de la gare | |
| 1964 | Angélique, Marquise des Anges | Le père Kirscher | Uncredited |
| 1967 | Le Crime de David Levinstein | Le grand-père | |
# MV Krasnodar

A number of motor vessels have been named Krasnodar, after the city in Russia, including
* MV Krasnodar (1925), a Soviet cargo ship in service 1946–75. IMO Number 5196438
* MV Krasnodar (2003), a Liberian tanker built in 2003. IMO Number 9270517
* Russian submarine Krasnodar (K-148), a Russian Oscar-class submarine
# Macrovipera lebetinus cernovi

Macrovipera lebetinus cernovi, known as the Chernov blunt-nosed viper, is a viper subspecies endemic to Asia. Like all other vipers, it is venomous.

## Etymology

The subspecific name, cernovi, is in honor of Soviet herpetologist Sergius Aleksandrovich Chernov (1903–1964).

## Description

This subspecies normally has semidivided supraoculars.

## Geographic range

It is found in northeastern Iran, southern Turkmenistan, and parts of northern Afghanistan and Pakistan.
# Ghana Baptist University College

The Ghana Baptist University College is a Baptist Christian university college located at Kumasi in Ghana. The university has been granted accreditation by the National Accreditation Board. It is affiliated with the Ghana Baptist Convention.

## History

The school was founded in 2006 by the Ghana Baptist Convention in Kumasi.
In 2022, it received 100 acres of land in Ejura for the construction of a branch campus.

## Campus

The university has two campuses.
* City Campus - Amakom
* Abuakwa campus - Abuakwa

## Affiliations

Ghana Baptist University College is affiliated to the University of Cape Coast, the Ghana Baptist Convention and the Association of Ghana Private Universities.
# Mack Canyon Archeological Site

The Mack Canyon Archeological Site (Smithsonian trinomial: 35SH23) is a prehistoric archeological site in Sherman County, Oregon, United States. Consisting of an extensive series of pit houses in a sheltered canyon, the site was occupied seasonally in winter by Columbia River tribes for about 7,000 years from after 5000 BCE to the early 19th century CE.
The site was added to the National Register of Historic Places in 1975.
# Gerrhopilus oligolepis

Gerrhopilus oligolepis, also known as the few-scaled worm snake or Wall's worm snake, is a harmless blind snake species found in northern India and Nepal. No subspecies are currently recognized.

## Geographic range

Found in the eastern Himalayas in India in the area of Sikkim and Darjeeling and in Nepal. The type locality given is "Nagri Valley below Darjeeling [India] at an altitude of about 5000 feet."
# Nadhour

Nadhour is a town and commune in the Zaghouan Governorate, Tunisia. As of 2004 it had a population of 5,207.
# Netgear WGR614L

The WGR614L (also known as the WGR614v8) is an 802.11b/g wireless network router created by Netgear. It was officially launched on June 30, 2008. The WGR614L runs an open source linux firmware and supports the installation of third party packages such as DD-WRT, Tomato, and OpenWrt.

## Hardware

* Broadcom BCM5354 240 MHz SoC
* 4 MB Flash memory
* 16 MB RAM
* 16 kB instruction cache
* 16 kB data cache
* 1000 byte pre-fetch cache
* 4 MB CPU cache
* 2 dBi gain antennas (1 internal and 1 external dipole)
* 802.11 b/g wireless support
* Certified for use with Windows Vista

## Features

* Supports installation of OpenWrt, Tomato firmware, and DD-WRT
* Supports Wi-Fi Protected Setup (WPS)
* Automatically detects ISP type, exposed host (DMZ), MAC address authentication, URL content filtering, logs and email alerts of Internet activity
* Static & dynamic routing with TCP/IP, VPN pass-through (IPsec, L2TP), NAT, PPTP, PPPoE, DHCP (client & server)

## Applications

The WGR614L is designed to be used in home or business environments. It is often used in connection with third-party firmware and solutions, such as SputnikNet and Titan Hotspots. The router can also be used as a wireless client bridge (utilizing OpenWrt firmware) and as a wireless repeater bridge (using DD-WRT firmware).
# Ovid Township, Michigan

Ovid Township is the name of some places in the U.S. state of Michigan:
* Ovid Township, Branch County, Michigan
* Ovid Township, Clinton County, Michigan
# Starr House

Starr House may refer to:
* Starr Manor, Glenwood Springs, Colorado, listed on the National Register of Historic Places (NRHP) in Garfield County, Colorado
* C. J. Starr Barn and Carriage House, Stamford, Connecticut, NRHP-listed
* Starr House (Wilmington, Delaware), NRHP-listed
* Starr-Truscott House, Birmingham, Ohio, listed on the NRHP in Erie County, Ohio
* Horace C. Starr House and Carriage Barns, Elyria, Ohio, listed on the NRHP in Lorain County, Ohio
* Edwin and Anna Starr House, Monroe, Oregon, listed on the National Register of Historic Places in Benton County, Oregon
* Starr House (Marshall, Texas), listed on the National Register of Historic Places in Harrison County, Texas
* Starr Ranch, Hanksville, Utah, listed on the NRHP in Garfield County, Utah
# Newton polytope

In mathematics, the Newton polytope is an integral polytope associated with a multivariate polynomial. It can be used to analyze the polynomial's behavior when specific variables are considered negligible relative to the others. Specifically, given a vector $\mathbf {x} =(x_{1},\ldots ,x_{n})$ of variables and a finite family $(\mathbf {a} _{k})_{k}$ of pairwise distinct vectors from $\mathbb {N} ^{n}$ each encoding the exponents within a monomial, consider the multivariate polynomial
    $f(\mathbf {x} )=\sum _{k}c_{k}\mathbf {x} ^{\mathbf {a} _{k}}$
where we use the shorthand notation $(x_{1},\ldots ,x_{n})^{(y_{1},\ldots ,y_{n})}$ for the monomial $x_{1}^{y_{1}}x_{2}^{y_{2}}\cdots x_{n}^{y_{n}}$. Then the Newton polytope associated to $f$ is the convex hull of the vectors $\mathbf {a} _{k}$; that is
    $\operatorname {Newt} (f)=\left\{\sum _{k}\alpha _{k}\mathbf {a} _{k}:\sum _{k}\alpha _{k}=1\;\&\;\forall j\,\,\alpha _{j}\geq 0\right\}\!.$
In order to make this well-defined, we assume that all coefficients $c_{k}$ are non-zero. The Newton polytope satisfies the following homomorphism-type property:
    $\operatorname {Newt} (fg)=\operatorname {Newt} (f)+\operatorname {Newt} (g)$
where the addition is in the sense of Minkowski.
Newton polytopes are the central object of study in tropical geometry and characterize the Gröbner bases for an ideal.