„Normaliz" – Versionsunterschied
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{{Infobox (削除) Software (削除ここまで)
{{Infobox (追記) software (追記ここまで)
| (削除) Hersteller (削除ここまで) (削除) = (削除ここまで) (削除) University (削除ここまで) (削除) of (削除ここまで) (削除) Osnabrück (削除ここまで)
| (追記) name (追記ここまで) (追記) = Normaliz (追記ここまで)
| title = Normaliz
| AktuelleVersion = <!-- Versionen bitte absatzweise eintragen -->
| logo =
3.4.0 ([[Linux]], [[macOS]] und [[Microsoft Windows|Windows]])<br /><small>{{Datum|17|10|2017}}</small>
| logo caption =
| Betriebssystem = [[Unix]], [[Linux]], [[FreeBSD]], [[macOS]], [[Microsoft Windows|Windows]]
| (削除) Kategorie (削除ここまで) = (削除) [[Computeralgebrasystem]] (削除ここまで)
| (追記) logo_size (追記ここまで) =
| (削除) Lizenz (削除ここまで) (削除) = (削除ここまで) (削除) [[GNU (削除ここまで) (削除) General (削除ここまで) (削除) Public (削除ここまで) (削除) License|GPL]] (削除ここまで) (削除) ([[Freie (削除ここまで) (削除) Software]]) (削除ここまで)
| (追記) logo_alt (追記ここまで) (追記) = (追記ここまで)
| (削除) Deutsch (削除ここまで) = (削除) nein (削除ここまで)
| (追記) screenshot (追記ここまで) = (追記) HilbertBasis.gif (追記ここまで)
| caption =
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| (削除) Website (削除ここまで) = (削除) [ (削除ここまで)http://(削除) www. (削除ここまで)normaliz.uni-osnabrueck.de(削除) normaliz.uni-osnabrueck.de] (削除ここまで)
| screenshot_size =
| screenshot_alt =
| collapsible =
| author = Winfried Bruns, Robert Koch, Bogdan Ichim, Christof Soeger
| developer =
| released = <!-- {{Start date and age|YYYY|MM|DD|df=yes/no}} -->
| discontinued =
| latest release version =
| latest release date = <!-- {{Start date and age|YYYY|MM|DD|df=yes/no}} -->
| latest preview version =
| latest preview date = <!-- {{Start date and age|YYYY|MM|DD|df=yes/no}} -->
| frequently updated = <!-- DO NOT include this parameter unless you know what it does -->
| status =
| programming language = [[C++]], [[C]] and [[Python (programming language)|Python]]
| operating system =
| platform =
| size =
| language =
| language count = <!-- DO NOT include this parameter unless you know what it does -->
| language footnote =
| genre = [[Computer algebra system]]
| license = [[GNU General Public License]], version 3
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| (追記) website (追記ここまで) = (追記) {{URL| (追記ここまで)http://normaliz.uni-osnabrueck.de(追記) /}} (追記ここまで)
}}
}}
'''Normaliz''' (削除) ist (削除ここまで) (削除) ein (削除ここまで) (削除) freies (削除ここまで) (削除) Computeralgebra-System, (削除ここまで) (削除) das (削除ここまで) (削除) von (削除ここまで) Winfried Bruns, Robert Koch (1998-2002), Bogdam Ichim (2007/08) (削除) und (削除ここまで) Christof Soeger (2009-2016)(削除) entwickelt wurde (削除ここまで). (削除) Es (削除ここまで) (削除) ist (削除ここまで) (削除) unter (削除ここまで) (削除) der (削除ここまで) GNU General Public License (削除) Version (削除ここまで) 2(削除) veröffentlicht (削除ここまで).
'''Normaliz''' (追記) is (追記ここまで) (追記) a (追記ここまで) (追記) [[Free (追記ここまで) (追記) software|free]] [[computer algebra system]] (追記ここまで) (追記) developed (追記ここまで) (追記) by (追記ここまで) Winfried Bruns, Robert Koch (1998-2002), Bogdam Ichim (2007/08) (追記) and (追記ここまで) Christof Soeger (2009-2016). (追記) It (追記ここまで) (追記) is (追記ここまで) (追記) published (追記ここまで) (追記) under (追記ここまで) (追記) the [[ (追記ここまで)GNU General Public License(追記) ]] (追記ここまで) (追記) version (追記ここまで) 2.(追記) (追記ここまで)
Normaliz computes lattice points in rational [[polyhedra]], or, in other terms, solves [[Diophantine_equation#System_of_linear_Diophantine_equations|linear diophantine systems of inequalities]], equations and congruences. Special tasks are the computation of lattice points in bounded rational polytopes and [[Hilbert basis (linear programming)|Hilbert bases]] of rational cones. Normaliz also computes enumerative data, such as multiplicities (volumes) and [[Hilbert series]]. The kernel of Normaliz is a templated C++ class library. For multivariate polynomial arithmetic it uses [[CoCoA|CoCoALib]].
Normaliz berechnet Gitterpunkte in rationalen Polyedern oder löst lineare diophantische Systeme von Ungleichungen, Gleichungen und Kongruenzen. Spezielle Aufgaben sind die Berechnung von Gitterpunkten in beschränkten rationalen Polytopen und Hilbert-Basen von rationalen Kegeln. Normaliz berechnet auch enumerative Daten wie Multiplizitäten (Volumina) und Hilbert-Reihen. Der Kern von Normaliz ist eine Templated-C ++ - Klassenbibliothek. Für multivariate Polynomialarithmetik wird CoCoALib verwendet.
Normaliz (削除) hat (削除ここまで) (削除) Schnittstellen (削除ここまで) (削除) zu (削除ここまで) (削除) mehreren (削除ここまで) (削除) allgemeinen (削除ここまで) (削除) Computeralgebra-Systemen (削除ここまで): CoCoA, GAP, Macaulay2 (削除) und (削除ここまで) Singular. (削除) Es (削除ここまで) (削除) kann (削除ここまで) (削除) interaktiv (削除ここまで) (削除) über (削除ここまで) (削除) seine (削除ここまで) (削除) Python-Schnittstelle (削除ここまで) (削除) PyNormaliz (削除ここまで) (削除) verwendet (削除ここまで) (削除) werden (削除ここまで). (削除) Seine (削除ここまで) (削除) Verwendung (削除ここまで) in SageMath (削除) ist (削除ここまで) in (削除) Vorbereitung (削除ここまで).
Normaliz (追記) has (追記ここまで) (追記) interfaces (追記ここまで) (追記) to (追記ここまで) (追記) several (追記ここまで) (追記) general (追記ここまで) (追記) computer algebra systems (追記ここまで): (追記) [[ (追記ここまで)CoCoA(追記) ]] (追記ここまで), (追記) [[ (追記ここまで)GAP(追記) (computer algebra system)|GAP]] (追記ここまで), (追記) [[ (追記ここまで)Macaulay2(追記) ]] (追記ここまで) (追記) and (追記ここまで) (追記) [[ (追記ここまで)Singular(追記) (software)|Singular]] (追記ここまで). (追記) It (追記ここまで) (追記) can (追記ここまで) (追記) be (追記ここまで) (追記) used (追記ここまで) (追記) interactively (追記ここまで) (追記) via (追記ここまで) (追記) its (追記ここまで) (追記) Python (追記ここまで) (追記) interface PyNormaliz (追記ここまで). (追記) Its (追記ここまで) (追記) use (追記ここまで) in SageMath (追記) is (追記ここまで) in (追記) preparation (追記ここまで).
[[Jesús A. De_Loera]] cites Normaliz among his favorite programs for computing [[Hilbert basis (linear programming)|Hilbert basis]]<ref>[https://www.math.ucdavis.edu/~deloera/TEACHING/MATH246/NOTES/chapter2.tex Mathe Notes]</ref>.
Jesús A. De_Loera zitiert Normaliz zu seinen Lieblingsprogrammen für die Berechnung der Hilbert-Basis [1].
==See also==
==See also==
Version vom 17. Oktober 2017, 14:19 Uhr
Normaliz is a free computer algebra system developed by Winfried Bruns, Robert Koch (1998-2002), Bogdam Ichim (2007/08) and Christof Soeger (2009-2016). It is published under the GNU General Public License version 2.
Normaliz computes lattice points in rational polyhedra, or, in other terms, solves linear diophantine systems of inequalities, equations and congruences. Special tasks are the computation of lattice points in bounded rational polytopes and Hilbert bases of rational cones. Normaliz also computes enumerative data, such as multiplicities (volumes) and Hilbert series. The kernel of Normaliz is a templated C++ class library. For multivariate polynomial arithmetic it uses CoCoALib.
Normaliz has interfaces to several general computer algebra systems: CoCoA, GAP, Macaulay2 and Singular. It can be used interactively via its Python interface PyNormaliz. Its use in SageMath is in preparation.
Jesús A. De_Loera cites Normaliz among his favorite programs for computing Hilbert basis [1] .
See also
Portal: Free software – Übersicht zu Wikipedia-Inhalten zum Thema Free software
