CoCoA

Not to be confused with Cocoa (API).
CoCoA
Original author(s)Abbott, J. and Bigatti, A. M. and Robbiano, L.[1]
Initial release1988; 37 years ago (1988)[2]
Stable release
5.4.0 / 11 April 2022; 2 years ago (2022-04-11)[3]
Preview release
5.4.1j / 21 February 2023; 22 months ago (2023-02-21)[3]
Written inC++
Operating systemWindows, Linux/Unix, macOS,
TypeComputer algebra system
LicenseGNU GPL
Websitecocoa.dima.unige.it
CoCoALib
Original author(s)Abbott, J. and Bigatti, A. M.[1]
Initial release9 March 2007; 17 years ago (2007-03-09)[4]
Stable release
0.99800 / 28 April 2022; 2 years ago (2022-04-28)[5]
Preview release
0.99718 / 14 February 2022; 2 years ago (2022-02-14)[5]
Written inC++
TypeLibrary
LicenseGNU GPL
Websitecocoa.dima.unige.it Edit this on Wikidata

CoCoA (Computations in Commutative Algebra)[6] is a free computer algebra system developed by the University of Genova, Italy, used to compute with numbers and polynomials. The CoCoA Library (CoCoALib[7]) is available under GNU General Public License. CoCoA has been ported to many operating systems including Macintosh on PPC and x86, Linux on x86, Unix x86-64 & PPC, Solaris on SPARC and Windows on x86. CoCoA is mainly used by researchers (see citations at[8] and[9]), but can be useful even for "simple" computations.

CoCoA's features include:

It is able to perform simple and sophisticated operations on multivariate polynomials and on various data related to them (ideals, modules, matrices, rational functions). For example, it can readily compute Gröbner basis, syzygies and minimal free resolutions, intersection, division, the radical of an ideal, the ideal of zero-dimensional schemes, Poincaré series and Hilbert functions, factorization of polynomials, and toric ideals. The capabilities of CoCoA and the flexibility of its use are further enhanced by the dedicated high-level programming language.

Its mathematical core, CoCoALib, has been designed as an open source C++ library, focussing on ease of use and flexibility.

CoCoALib is based on GNU Multi-Precision Library.

CoCoALib is used by ApCoCoA[10] and NmzIntegrate[11]

See also

Wikimedia Commons has media related to Computations in Commutative Algebra.

References

  1. ^ a b "Citing CoCoA". cocoa.dima.unige.it. Retrieved 2022-07-06.
  2. ^ "CoCoA History". cocoa.dima.unige.it. Archived from the original on 1998-01-09. Retrieved 2023-03-09.{{cite web}}: CS1 maint: bot: original URL status unknown (link)
  3. ^ a b "CoCoA 5 Release Notes". cocoa.dima.unige.it. Retrieved 2022-07-06.
  4. ^ "CoCoALib Beta Archive". cocoa.dima.unige.it. Archived from the original on 2007-04-26. Retrieved 2023-03-09.
  5. ^ a b "CoCoALib". cocoa.dima.unige.it. Retrieved 2022-07-06.
  6. ^ "CoCoA website".
  7. ^ "CoCoALib home page".
  8. ^ "CoCoA - Mathematical software - swMATH".
  9. ^ "CoCoA in GoogleScholar".
  10. ^ "ApCoCoA website".
  11. ^ "Normaliz website". Archived from the original on 2015-12-08. Retrieved 2014-05-22.

Read other articles:

Cyrtophora unicolor

Cyrtophora unicolor Klasifikasi ilmiah Kerajaan: Animalia Filum: Arthropoda Kelas: Arachnida Ordo: Araneae Famili: Araneidae Spesies: Cyrtophora unicolor Nama binomial Cyrtophora unicolorDoleschall, 1857 Cyrtophora unicolor adalah spesies laba-laba yang tergolong famili Araneidae. Spesies ini juga merupakan bagian dari ordo Araneae. Nama ilmiah dari spesies ini pertama kali diterbitkan pada tahun 1857 oleh Doleschall. Laba-laba ini biasanya banyak ditemui di Sri Lanka hingga Japang, Filipina...

 

LOT Polish Airlines

Pour les articles homonymes, voir Lot. LOT Polish Airlines Polskie Linie Lotnicze LOT Codes IATAOACIIndicatif d'appel LO LOT LOT Repères historiques Date de création 29 décembre 1928 Généralités Basée à Aéroport Frédéric Chopin de Varsovie Autres bases Aéroport Jean-Paul II de Cracovie Programme de fidélité Miles & More Alliance Star Alliance Taille de la flotte 78 Nombre de destinations 131 Siège social Pologne, Varsovie Société mère LOT Polish Airlines Filiales EuroLO...

 

الدوري الإيطالي 1964–65

يفتقر محتوى هذه المقالة إلى الاستشهاد بمصادر. فضلاً، ساهم في تطوير هذه المقالة من خلال إضافة مصادر موثوق بها. أي معلومات غير موثقة يمكن التشكيك بها وإزالتها. (أبريل 2019) الدوري الإيطالي الدرجة الأولى تفاصيل الموسم 1964–1965 النسخة 63  البلد إيطاليا  التاريخ بداية:13 سبتمبر 196...

crux gemmata

Detil mosaik, Basilika Sant' Apollinare in Classe, Ravenna (549). Crux gemmata (Latin untuk: salib perhiasan) adalah sebuah bentuk salib khas dari seni rupa Gereja Perdana dan Abad Pertengahan Awal, di mana salib, atau setidaknya sisi depannya, biasanya dipasangi dengan perhiasan. Pada salib yang sebenarnya, alih-alih gambar yang dilukis, sisi belakangnya sering kali memiliki gambar engravir dari Penyaliban Yesus atau subyek lainnya. Referensi Friesen, Ilse E., The Female Crucifix: Images of ...

 

Présidence du Bengale

Présidence du BengaleBengal Presidency 1699–1947 Carte de la présidence du Bengale en 1858.Informations générales Statut Territoire britannique Capitale Calcutta Langue(s) Anglais, bengali, hindoustani Histoire et événements 1612 Autorisation de l'empire moghol d'occuper le territoire 1757 Bataille de Plassey 1764 Bataille de Buxar 1826 Traité de Yandabo 1947 Partition des Indes Entités précédentes : Empire moghol Entités suivantes : Bengale oriental modifier - modifie...

 

العلاقات الصومالية اليمنية

العلاقات الصومالية اليمنية الصومال اليمن   الصومال   اليمن تعديل مصدري - تعديل   العلاقات الصومالية اليمنية هي العلاقات الثنائية التي تجمع بين الصومال واليمن.[1][2][3][4][5] مقارنة بين البلدين هذه مقارنة عامة ومرجعية للدولتين: وجه المقارنة الص�...

العلاقات العمانية الموزمبيقية

العلاقات العمانية الموزمبيقية سلطنة عمان موزمبيق   سلطنة عمان   موزمبيق تعديل مصدري - تعديل   العلاقات العمانية الموزمبيقية هي العلاقات الثنائية التي تجمع بين سلطنة عمان وموزمبيق.[1][2][3][4][5] مقارنة بين البلدين هذه مقارنة عامة ومرجعية للدول...

 

Partizanskaya (Metro Moskwa)

PartizanskayaПартизанскаяStasiun Metro MoskwaLokasiDistrik IzmaylovoOkrug Administratif TimurMoskwaRusiaKoordinat55°47′19″N 37°45′02″E / 55.7886°N 37.7506°E / 55.7886; 37.7506Koordinat: 55°47′19″N 37°45′02″E / 55.7886°N 37.7506°E / 55.7886; 37.7506PemilikMoskovsky MetropolitenJalur!B9989013877113  3  Jalur Arbatsko-Pokrovskaya Jumlah peron2 peron pulauJumlah jalur3KonstruksiKedalaman9 meter...

 

Edong Yangtze River Bridge

Bridge in Hubei, ChinaEdong Bridge鄂东长江大桥Coordinates30°15′39″N 115°04′28″E / 30.260707°N 115.074438°E / 30.260707; 115.074438Carries G45 Daqing–Guangzhou Expressway G50 Shanghai–Chongqing ExpresswayCrossesYangtze RiverLocaleHuangshigang, Hubei, ChinaCharacteristicsDesignCable-stayedMaterialConcreteTotal lengthspan length 1,486 m (4,875 ft)Width33 m (108 ft)Height242.5 m (796 ft)Longest span926 m (3,038 ...

Binna Burra, Queensland

This article is about the locality. For the tourist lodge within the locality, see Binna Burra Lodge. Map all coordinates using OpenStreetMap Download coordinates as: KML GPX (all coordinates) GPX (primary coordinates) GPX (secondary coordinates) Suburb of Scenic Rim Region, Queensland, AustraliaBinna BurraQueenslandBinna Burra rainforest at sunset, 2014Binna BurraCoordinates28°12′11″S 153°10′56″E / 28.2030°S 153.1822°E / -28.2030; 153.1822 (Binna B...

 

SPAD S.XIII

French WW1 fighter aircraft S.XIII SPAD S.XIII in the colors and markings of Capt. Eddie Rickenbacker, U.S. 94th Aero Squadron. This aircraft is on display at the National Museum of the U.S. Air Force near Dayton, Ohio. Role biplane fighterType of aircraft National origin France Manufacturer SPAD Designer Louis Béchéreau First flight 4 April 1917[1] Primary users Aéronautique MilitaireRoyal Flying Corps (Royal Air Force from April 1918) United States Army Air Service Number bu...

 

Новотитаровское сельское поселение

Сельское поселение России (МО 2-го уровня)Новотитаровское сельское поселение Флаг[d] Герб 45°14′09″ с. ш. 38°58′16″ в. д.HGЯO Страна  Россия Субъект РФ Краснодарский край Район Динской Включает 4 населённых пункта Адм. центр Новотитаровская Глава сельского пос�...

2016年美國總統選舉

2016年美國總統選舉 ← 2012 2016年11月8日 2020 → 538個選舉人團席位獲勝需270票民意調查投票率55.7%[1][2] ▲ 0.8 %   获提名人 唐納·川普 希拉莉·克林頓 政党 共和黨 民主党 家鄉州 紐約州 紐約州 竞选搭档 迈克·彭斯 蒂姆·凱恩 选举人票 304[3][4][註 1] 227[5] 胜出州/省 30 + 緬-2 20 + DC 民選得票 62,984,828[6] 65,853,514[6]...

 

Pandémie de Covid-19 en Europe

Wikipédia ne donne pas de conseils médicaux ou sanitaires. Cet article est susceptible de contenir des informations obsolètes ou inexactes. Seul un professionnel de la santé est apte à vous fournir un avis médical, et seules les autorités sanitaires de votre pays sont compétentes pour donner des consignes de santé publique relatives à la pandémie de Covid-19. Pandémie de Covid-19 en EuropeDécès confirmés mois par mois dus à la Covid-19 en Europe de janvier 2020 à mars 2022[S...

 

Christopher Tugendhat, Baron Tugendhat

British politician, life peer (born 1937) The Right HonourableThe Lord TugendhatLord Tugendhat's parliamentary portrait, 2020Chancellor of the University of BathIn office1998–2013Vice-ChancellorDavid VandeLindeGlynis BreakwellPreceded bySir Denys HendersonSucceeded byPrince Edward, Duke of EdinburghFirst Vice-President of the European CommissionIn office6 January 1981 – 5 January 1985PresidentGaston ThornPreceded byFrançois-Xavier OrtoliSucceeded byFrans AndriessenEuropean Commi...

Morsasco

Artikel ini tidak memiliki referensi atau sumber tepercaya sehingga isinya tidak bisa dipastikan. Tolong bantu perbaiki artikel ini dengan menambahkan referensi yang layak. Tulisan tanpa sumber dapat dipertanyakan dan dihapus sewaktu-waktu.Cari sumber: Morsasco – berita · surat kabar · buku · cendekiawan · JSTOR Morsasco komune di Italia Morsasco (it) Tempat Negara berdaulatItaliaDaerah di ItaliaPiemonteProvinsi di ItaliaProvinsi Alessandria NegaraItal...

 

Avezzano

Comune in Abruzzo, ItalyAvezzano Avezzàne (Neapolitan)ComuneCittà di AvezzanoView of Avezzano from Mount Salviano Coat of armsLocation of Avezzano AvezzanoLocation of Avezzano in ItalyShow map of ItalyAvezzanoAvezzano (Abruzzo)Show map of AbruzzoCoordinates: 42°02′28″N 13°26′23″E / 42.04111°N 13.43972°E / 42.04111; 13.43972CountryItalyRegionAbruzzoProvinceL'Aquila (AQ)FrazioniAntrosano, Castelnuovo, Cese dei Marsi, Paterno, San Pelino, San Giuseppe d...

 

List of casinos in the United States

Casinos on Paradise Road in Winchester, Nevada in 2013 This is a list of casinos in the United States. Lists by locale See also: Category:Lists of casinos in the United States City List of Atlantic City casinos that never opened List of Las Vegas casinos that never opened State List of casinos in Alabama List of casinos in Arizona List of casinos in Arkansas List of casinos in California List of casinos in Colorado List of casinos in Delaware List of casinos in Florida List of casinos in Ida...

Blondes for Export

1950 film by Eugen York Blondes for ExportDirected byEugen YorkWritten byNorbert Jacques (novel)Produced byFranz TappersWilli WiesnerStarringLotte KochCatja GörnaRené DeltgenCinematographyOskar SchnirchEdited byWalter FredersdorfMusic byWolfgang ZellerProductioncompanyStandard-FilmverleihDistributed byLloyd FilmRelease date 10 April 1950 (1950-04-10) Running time81 minutesCountryWest GermanyLanguageGerman Blondes for Export (German: Export in Blond) is a 1950 West German crim...

 

Hairy-footed flying squirrel

Species of rodent Hairy-footed flying squirrel Conservation status Data Deficient  (IUCN 3.1)[1] Scientific classification Domain: Eukaryota Kingdom: Animalia Phylum: Chordata Class: Mammalia Order: Rodentia Family: Sciuridae Genus: Belomys Species: B. pearsonii Binomial name Belomys pearsonii(J. E. Gray, 1842) Synonyms Sciuropterus pearsonii Gray, 1842 Trogopterus pearsonii (Gray, 1842) The hairy-footed flying squirrel (Belomys pearsonii) is a flying squirrel found in the m...