https://de.wikipedia.org/w/api.php?action=feedcontributions&feedformat=atom&user=JShenkWikipedia - Benutzerbeiträge [de]2025-05-11T11:08:35ZBenutzerbeiträgeMediaWiki 1.44.0-wmf.28https://de.wikipedia.org/w/index.php?title=Normaliz&diff=170072858Normaliz2017-10-17T14:01:21Z<p>JShenk: </p>
<hr />
<div>{{Infobox Software<br />
| Hersteller = [[Universität Osnabrück]]<br />
| Bild = [[Datei:Hilbert basis.gif|Hilbert Basis]]<br />
| AktuelleVersion = <!-- Versionen bitte absatzweise eintragen --><br />
3.4.0 ([[Linux]], [[macOS]] und [[Microsoft Windows|Windows]])<br /><small>{{Datum|17|10|2017}}</small><br />
| Betriebssystem = [[Unix]], [[Linux]], [[FreeBSD]], [[macOS]], [[Microsoft Windows|Windows]]<br />
| Kategorie = [[Computeralgebrasystem]]<br />
| Lizenz = [[GNU General Public License|GPL]] ([[Freie Software]])<br />
| Deutsch = nein<br />
| Website = [http://www.normaliz.uni-osnabrueck.de normaliz.uni-osnabrueck.de]<br />
}}<br />
<br />
'''Normaliz''' ist ein freies Computeralgebra-System, das von Winfried Bruns, Robert Koch (1998-2002), Bogdam Ichim (2007/08) und Christof Soeger (2009-2016) entwickelt wurde. Es ist unter der [[GNU General Public License]] Version 2 veröffentlicht.<br />
<br />
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.<br />
<br />
Normaliz hat Schnittstellen zu mehreren allgemeinen Computeralgebra-Systemen: [[CoCoA]], [[GAP]], [[Macaulay2]] und [[Singular]]. Es kann interaktiv über seine Python-Schnittstelle PyNormaliz verwendet werden. Seine Verwendung in SageMath ist in Vorbereitung.<br />
<br />
Jesús A. De_Loera zählt Normaliz zu seinen Lieblingsprogrammen für die Berechnung der Hilbert-Basis<ref>De Loera, Jesús. Course Notes: Algebraic and Geometric Combinatorics. Link: [https://www.math.ucdavis.edu/~deloera/TEACHING/MATH246/NOTES/chapter2.tex Notes]</ref>.<br />
<br />
== Einzelnachweise ==<br />
<references /><br />
<br />
==Weblinks==<br />
*[http://www.normaliz.uni-osnabrueck.de/ Offizielle Website ]<br />
*[https://www.normaliz.uni-osnabrueck.de/documentation/ Publications and examples of Normaliz applications]<br />
*[http://github.com/normaliz/Normaliz Source code (Github)]<br />
<br />
[[Kategorie:Freies Computeralgebrasystem]]<br />
[[Kategorie:Windows-Software]]<br />
[[Kategorie:MacOS-Software]]<br />
[[Kategorie:Unix-Software]]<br />
[[Kategorie:Linux-Software]]</div>JShenkhttps://de.wikipedia.org/w/index.php?title=Normaliz&diff=170072691Normaliz2017-10-17T13:55:05Z<p>JShenk: </p>
<hr />
<div>{{Infobox Software<br />
| Hersteller = [[Universität Osnabrück]]<br />
| Bild = Hilbert basis.gif<br />
| AktuelleVersion = <!-- Versionen bitte absatzweise eintragen --><br />
3.4.0 ([[Linux]], [[macOS]] und [[Microsoft Windows|Windows]])<br /><small>{{Datum|17|10|2017}}</small><br />
| Betriebssystem = [[Unix]], [[Linux]], [[FreeBSD]], [[macOS]], [[Microsoft Windows|Windows]]<br />
| Kategorie = [[Computeralgebrasystem]]<br />
| Lizenz = [[GNU General Public License|GPL]] ([[Freie Software]])<br />
| Deutsch = nein<br />
| Website = [http://www.normaliz.uni-osnabrueck.de normaliz.uni-osnabrueck.de]<br />
}}<br />
<br />
'''Normaliz''' ist ein freies Computeralgebra-System, das von Winfried Bruns, Robert Koch (1998-2002), Bogdam Ichim (2007/08) und Christof Soeger (2009-2016) entwickelt wurde. Es ist unter der [[GNU General Public License]] Version 2 veröffentlicht.<br />
<br />
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.<br />
<br />
Normaliz hat Schnittstellen zu mehreren allgemeinen Computeralgebra-Systemen: [[CoCoA]], [[GAP]], [[Macaulay2]] und [[Singular]]. Es kann interaktiv über seine Python-Schnittstelle PyNormaliz verwendet werden. Seine Verwendung in SageMath ist in Vorbereitung.<br />
<br />
Jesús A. De_Loera zählt Normaliz zu seinen Lieblingsprogrammen für die Berechnung der Hilbert-Basis<ref>De Loera, Jesús. Course Notes: Algebraic and Geometric Combinatorics. Link: [https://www.math.ucdavis.edu/~deloera/TEACHING/MATH246/NOTES/chapter2.tex Notes]</ref>.<br />
<br />
== Einzelnachweise ==<br />
<references /><br />
<br />
==Weblinks==<br />
*[http://www.normaliz.uni-osnabrueck.de/ Offizielle Website ]<br />
*[https://www.normaliz.uni-osnabrueck.de/documentation/ Publications and examples of Normaliz applications]<br />
*[http://github.com/normaliz/Normaliz Source code (Github)]<br />
<br />
[[Kategorie:Freies Computeralgebrasystem]]<br />
[[Kategorie:Windows-Software]]<br />
[[Kategorie:MacOS-Software]]<br />
[[Kategorie:Unix-Software]]<br />
[[Kategorie:Linux-Software]]</div>JShenkhttps://de.wikipedia.org/w/index.php?title=Normaliz&diff=170072616Normaliz2017-10-17T13:51:08Z<p>JShenk: </p>
<hr />
<div>{{Infobox Software<br />
| Hersteller = [[Universität Osnabrück]]<br />
| Bild = [[Datei:Hilbert basis.gif|Hilbert basis]]<br />
| Bildschirmfoto = [[Datei:Hilbert basis.gif|Hilbert basis]]<br />
| AktuelleVersion = <!-- Versionen bitte absatzweise eintragen --><br />
3.4.0 ([[Linux]], [[macOS]] und [[Microsoft Windows|Windows]])<br /><small>{{Datum|17|10|2017}}</small><br />
| Betriebssystem = [[Unix]], [[Linux]], [[FreeBSD]], [[macOS]], [[Microsoft Windows|Windows]]<br />
| Kategorie = [[Computeralgebrasystem]]<br />
| Lizenz = [[GNU General Public License|GPL]] ([[Freie Software]])<br />
| Deutsch = nein<br />
| Website = [http://www.normaliz.uni-osnabrueck.de normaliz.uni-osnabrueck.de]<br />
}}<br />
<br />
'''Normaliz''' ist ein freies Computeralgebra-System, das von Winfried Bruns, Robert Koch (1998-2002), Bogdam Ichim (2007/08) und Christof Soeger (2009-2016) entwickelt wurde. Es ist unter der [[GNU General Public License]] Version 2 veröffentlicht.<br />
<br />
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.<br />
<br />
Normaliz hat Schnittstellen zu mehreren allgemeinen Computeralgebra-Systemen: [[CoCoA]], [[GAP]], [[Macaulay2]] und [[Singular]]. Es kann interaktiv über seine Python-Schnittstelle PyNormaliz verwendet werden. Seine Verwendung in SageMath ist in Vorbereitung.<br />
<br />
Jesús A. De_Loera zählt Normaliz zu seinen Lieblingsprogrammen für die Berechnung der Hilbert-Basis<ref>De Loera, Jesús. Course Notes: Algebraic and Geometric Combinatorics. Link: [https://www.math.ucdavis.edu/~deloera/TEACHING/MATH246/NOTES/chapter2.tex Notes]</ref>.<br />
<br />
== Einzelnachweise ==<br />
<references /><br />
<br />
==Weblinks==<br />
*[http://www.normaliz.uni-osnabrueck.de/ Offizielle Website ]<br />
*[https://www.normaliz.uni-osnabrueck.de/documentation/ Publications and examples of Normaliz applications]<br />
*[http://github.com/normaliz/Normaliz Source code (Github)]<br />
<br />
[[Kategorie:Freies Computeralgebrasystem]]<br />
[[Kategorie:Windows-Software]]<br />
[[Kategorie:MacOS-Software]]<br />
[[Kategorie:Unix-Software]]<br />
[[Kategorie:Linux-Software]]</div>JShenkhttps://de.wikipedia.org/w/index.php?title=Normaliz&diff=170072592Normaliz2017-10-17T13:50:00Z<p>JShenk: </p>
<hr />
<div>{{Infobox Software<br />
| Hersteller = [[Universität Osnabrück]]<br />
| Bild = [[File:Hilbert basis.gif|Hilbert basis]]<br />
| AktuelleVersion = <!-- Versionen bitte absatzweise eintragen --><br />
3.4.0 ([[Linux]], [[macOS]] und [[Microsoft Windows|Windows]])<br /><small>{{Datum|17|10|2017}}</small><br />
| Betriebssystem = [[Unix]], [[Linux]], [[FreeBSD]], [[macOS]], [[Microsoft Windows|Windows]]<br />
| Kategorie = [[Computeralgebrasystem]]<br />
| Lizenz = [[GNU General Public License|GPL]] ([[Freie Software]])<br />
| Deutsch = nein<br />
| Website = [http://www.normaliz.uni-osnabrueck.de normaliz.uni-osnabrueck.de]<br />
}}<br />
<br />
'''Normaliz''' ist ein freies Computeralgebra-System, das von Winfried Bruns, Robert Koch (1998-2002), Bogdam Ichim (2007/08) und Christof Soeger (2009-2016) entwickelt wurde. Es ist unter der [[GNU General Public License]] Version 2 veröffentlicht.<br />
<br />
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.<br />
<br />
Normaliz hat Schnittstellen zu mehreren allgemeinen Computeralgebra-Systemen: [[CoCoA]], [[GAP]], [[Macaulay2]] und [[Singular]]. Es kann interaktiv über seine Python-Schnittstelle PyNormaliz verwendet werden. Seine Verwendung in SageMath ist in Vorbereitung.<br />
<br />
Jesús A. De_Loera zählt Normaliz zu seinen Lieblingsprogrammen für die Berechnung der Hilbert-Basis<ref>De Loera, Jesús. Course Notes: Algebraic and Geometric Combinatorics. Link: [https://www.math.ucdavis.edu/~deloera/TEACHING/MATH246/NOTES/chapter2.tex Notes]</ref>.<br />
<br />
== Einzelnachweise ==<br />
<references /><br />
<br />
==Weblinks==<br />
*[http://www.normaliz.uni-osnabrueck.de/ Offizielle Website ]<br />
*[https://www.normaliz.uni-osnabrueck.de/documentation/ Publications and examples of Normaliz applications]<br />
*[http://github.com/normaliz/Normaliz Source code (Github)]<br />
<br />
[[Kategorie:Freies Computeralgebrasystem]]<br />
[[Kategorie:Windows-Software]]<br />
[[Kategorie:MacOS-Software]]<br />
[[Kategorie:Unix-Software]]<br />
[[Kategorie:Linux-Software]]</div>JShenkhttps://de.wikipedia.org/w/index.php?title=Normaliz&diff=170072581Normaliz2017-10-17T13:49:35Z<p>JShenk: </p>
<hr />
<div>{{Infobox Software<br />
| Hersteller = [[Osnabrück Universität]]<br />
| Bild = [[File:Hilbert basis.gif|Hilbert basis]]<br />
| AktuelleVersion = <!-- Versionen bitte absatzweise eintragen --><br />
3.4.0 ([[Linux]], [[macOS]] und [[Microsoft Windows|Windows]])<br /><small>{{Datum|17|10|2017}}</small><br />
| Betriebssystem = [[Unix]], [[Linux]], [[FreeBSD]], [[macOS]], [[Microsoft Windows|Windows]]<br />
| Kategorie = [[Computeralgebrasystem]]<br />
| Lizenz = [[GNU General Public License|GPL]] ([[Freie Software]])<br />
| Deutsch = nein<br />
| Website = [http://www.normaliz.uni-osnabrueck.de normaliz.uni-osnabrueck.de]<br />
}}<br />
<br />
'''Normaliz''' ist ein freies Computeralgebra-System, das von Winfried Bruns, Robert Koch (1998-2002), Bogdam Ichim (2007/08) und Christof Soeger (2009-2016) entwickelt wurde. Es ist unter der [[GNU General Public License]] Version 2 veröffentlicht.<br />
<br />
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.<br />
<br />
Normaliz hat Schnittstellen zu mehreren allgemeinen Computeralgebra-Systemen: [[CoCoA]], [[GAP]], [[Macaulay2]] und [[Singular]]. Es kann interaktiv über seine Python-Schnittstelle PyNormaliz verwendet werden. Seine Verwendung in SageMath ist in Vorbereitung.<br />
<br />
Jesús A. De_Loera zählt Normaliz zu seinen Lieblingsprogrammen für die Berechnung der Hilbert-Basis<ref>De Loera, Jesús. Course Notes: Algebraic and Geometric Combinatorics. Link: [https://www.math.ucdavis.edu/~deloera/TEACHING/MATH246/NOTES/chapter2.tex Notes]</ref>.<br />
<br />
== Einzelnachweise ==<br />
<references /><br />
<br />
==Weblinks==<br />
*[http://www.normaliz.uni-osnabrueck.de/ Offizielle Website ]<br />
*[https://www.normaliz.uni-osnabrueck.de/documentation/ Publications and examples of Normaliz applications]<br />
*[http://github.com/normaliz/Normaliz Source code (Github)]<br />
<br />
[[Kategorie:Freies Computeralgebrasystem]]<br />
[[Kategorie:Windows-Software]]<br />
[[Kategorie:MacOS-Software]]<br />
[[Kategorie:Unix-Software]]<br />
[[Kategorie:Linux-Software]]</div>JShenkhttps://de.wikipedia.org/w/index.php?title=Normaliz&diff=170072572Normaliz2017-10-17T13:48:58Z<p>JShenk: </p>
<hr />
<div>{{Infobox Software<br />
| Hersteller = University of Osnabrück<br />
| Bild = [[File:Hilbert basis.gif|Hilbert basis]]<br />
| AktuelleVersion = <!-- Versionen bitte absatzweise eintragen --><br />
3.4.0 ([[Linux]], [[macOS]] und [[Microsoft Windows|Windows]])<br /><small>{{Datum|17|10|2017}}</small><br />
| Betriebssystem = [[Unix]], [[Linux]], [[FreeBSD]], [[macOS]], [[Microsoft Windows|Windows]]<br />
| Kategorie = [[Computeralgebrasystem]]<br />
| Lizenz = [[GNU General Public License|GPL]] ([[Freie Software]])<br />
| Deutsch = nein<br />
| Website = [http://www.normaliz.uni-osnabrueck.de normaliz.uni-osnabrueck.de]<br />
}}<br />
<br />
'''Normaliz''' ist ein freies Computeralgebra-System, das von Winfried Bruns, Robert Koch (1998-2002), Bogdam Ichim (2007/08) und Christof Soeger (2009-2016) entwickelt wurde. Es ist unter der [[GNU General Public License]] Version 2 veröffentlicht.<br />
<br />
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.<br />
<br />
Normaliz hat Schnittstellen zu mehreren allgemeinen Computeralgebra-Systemen: [[CoCoA]], [[GAP]], [[Macaulay2]] und [[Singular]]. Es kann interaktiv über seine Python-Schnittstelle PyNormaliz verwendet werden. Seine Verwendung in SageMath ist in Vorbereitung.<br />
<br />
Jesús A. De_Loera zählt Normaliz zu seinen Lieblingsprogrammen für die Berechnung der Hilbert-Basis<ref>De Loera, Jesús. Course Notes: Algebraic and Geometric Combinatorics. Link: [https://www.math.ucdavis.edu/~deloera/TEACHING/MATH246/NOTES/chapter2.tex Notes]</ref>.<br />
<br />
== Einzelnachweise ==<br />
<references /><br />
<br />
==Weblinks==<br />
*[http://www.normaliz.uni-osnabrueck.de/ Offizielle Website ]<br />
*[https://www.normaliz.uni-osnabrueck.de/documentation/ Publications and examples of Normaliz applications]<br />
*[http://github.com/normaliz/Normaliz Source code (Github)]<br />
<br />
[[Kategorie:Freies Computeralgebrasystem]]<br />
[[Kategorie:Windows-Software]]<br />
[[Kategorie:MacOS-Software]]<br />
[[Kategorie:Unix-Software]]<br />
[[Kategorie:Linux-Software]]</div>JShenkhttps://de.wikipedia.org/w/index.php?title=Normaliz&diff=170072558Normaliz2017-10-17T13:48:33Z<p>JShenk: </p>
<hr />
<div>{{Infobox Software<br />
| Hersteller = University of Osnabrück<br />
| Bild = [[File:Hilbert basis.gif|Hilbert basis]]<br />
| AktuelleVersion = <!-- Versionen bitte absatzweise eintragen --><br />
3.4.0 ([[Linux]], [[macOS]] und [[Microsoft Windows|Windows]])<br /><small>{{Datum|17|10|2017}}</small><br />
| Betriebssystem = [[Unix]], [[Linux]], [[FreeBSD]], [[macOS]], [[Microsoft Windows|Windows]]<br />
| Kategorie = [[Computeralgebrasystem]]<br />
| Lizenz = [[GNU General Public License|GPL]] ([[Freie Software]])<br />
| Deutsch = nein<br />
| Website = [http://www.normaliz.uni-osnabrueck.de normaliz.uni-osnabrueck.de]<br />
}}<br />
<br />
'''Normaliz''' ist ein freies Computeralgebra-System, das von Winfried Bruns, Robert Koch (1998-2002), Bogdam Ichim (2007/08) und Christof Soeger (2009-2016) entwickelt wurde. Es ist unter der GNU General Public License Version 2 veröffentlicht.<br />
<br />
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.<br />
<br />
Normaliz hat Schnittstellen zu mehreren allgemeinen Computeralgebra-Systemen: [[CoCoA]], [[GAP]], [[Macaulay2]] und [[Singular]]. Es kann interaktiv über seine Python-Schnittstelle PyNormaliz verwendet werden. Seine Verwendung in SageMath ist in Vorbereitung.<br />
<br />
Jesús A. De_Loera zählt Normaliz zu seinen Lieblingsprogrammen für die Berechnung der Hilbert-Basis<ref>De Loera, Jesús. Course Notes: Algebraic and Geometric Combinatorics. Link: [https://www.math.ucdavis.edu/~deloera/TEACHING/MATH246/NOTES/chapter2.tex Notes]</ref>.<br />
<br />
== Einzelnachweise ==<br />
<references /><br />
<br />
==Weblinks==<br />
*[http://www.normaliz.uni-osnabrueck.de/ Offizielle Website ]<br />
*[https://www.normaliz.uni-osnabrueck.de/documentation/ Publications and examples of Normaliz applications]<br />
*[http://github.com/normaliz/Normaliz Source code (Github)]<br />
<br />
[[Kategorie:Freies Computeralgebrasystem]]<br />
[[Kategorie:Windows-Software]]<br />
[[Kategorie:MacOS-Software]]<br />
[[Kategorie:Unix-Software]]<br />
[[Kategorie:Linux-Software]]</div>JShenkhttps://de.wikipedia.org/w/index.php?title=Normaliz&diff=170072534Normaliz2017-10-17T13:47:51Z<p>JShenk: </p>
<hr />
<div>{{Infobox Software<br />
| Hersteller = University of Osnabrück<br />
| Bild = [[File:Hilbert basis.gif|Hilbert basis]]<br />
| AktuelleVersion = <!-- Versionen bitte absatzweise eintragen --><br />
3.4.0 ([[Linux]], [[macOS]] und [[Microsoft Windows|Windows]])<br /><small>{{Datum|17|10|2017}}</small><br />
| Betriebssystem = [[Unix]], [[Linux]], [[FreeBSD]], [[macOS]], [[Microsoft Windows|Windows]]<br />
| Kategorie = [[Computeralgebrasystem]]<br />
| Lizenz = [[GNU General Public License|GPL]] ([[Freie Software]])<br />
| Deutsch = nein<br />
| Website = [http://www.normaliz.uni-osnabrueck.de normaliz.uni-osnabrueck.de]<br />
}}<br />
<br />
'''Normaliz''' ist ein freies Computeralgebra-System, das von Winfried Bruns, Robert Koch (1998-2002), Bogdam Ichim (2007/08) und Christof Soeger (2009-2016) entwickelt wurde. Es ist unter der GNU General Public License Version 2 veröffentlicht.<br />
<br />
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.<br />
<br />
Normaliz hat Schnittstellen zu mehreren allgemeinen Computeralgebra-Systemen: [[CoCoA]], [[GAP]], [[Macaulay2]] und [[Singular]]. Es kann interaktiv über seine Python-Schnittstelle PyNormaliz verwendet werden. Seine Verwendung in SageMath ist in Vorbereitung.<br />
<br />
Jesús A. De_Loera zählt Normaliz zu seinen Lieblingsprogrammen für die Berechnung der Hilbert-Basis<ref>De Loera, Jesús. Course Notes: Algebraic and Geometric Combinatorics. Link: [https://www.math.ucdavis.edu/~deloera/TEACHING/MATH246/NOTES/chapter2.tex Notes]</ref>.<br />
<br />
== Einzelnachweise ==<br />
<references /><br />
<br />
==Weblinks==<br />
*[http://www.normaliz.uni-osnabrueck.de/ Offizielle Website ]<br />
*[https://www.normaliz.uni-osnabrueck.de/documentation/ Publications and examples of Normaliz applications]<br />
*[http://github.com/normaliz/Normaliz Source code (Github)]<br />
<br />
[[Kategorie:Freies Computeralgebrasystem]]<br />
[[Kategorie:Windows-Software]]<br />
[[Kategorie:MacOS-Software]]<br />
[[Kategorie:Unix-Software]]<br />
[[Kategorie:Linux-Software]]</div>JShenkhttps://de.wikipedia.org/w/index.php?title=Normaliz&diff=170181869Normaliz2017-10-17T13:43:51Z<p>JShenk: Undid revision 805762568 by JShenk (talk)</p>
<hr />
<div>{{Infobox software<br />
| name = Normaliz<br />
| title = Normaliz<br />
| logo = <br />
| logo caption = <br />
| logo_size = <br />
| logo_alt = <br />
| screenshot = HilbertBasis.gif<br />
| caption = <br />
| screenshot_size = <br />
| screenshot_alt = <br />
| collapsible = <br />
| author = Winfried Bruns, Robert Koch, Bogdan Ichim, Christof Soeger<br />
| developer = <br />
| released = <!-- {{Start date and age|YYYY|MM|DD|df=yes/no}} --><br />
| discontinued = <br />
| latest release version = <br />
| latest release date = <!-- {{Start date and age|YYYY|MM|DD|df=yes/no}} --><br />
| latest preview version = <br />
| latest preview date = <!-- {{Start date and age|YYYY|MM|DD|df=yes/no}} --><br />
| frequently updated = <!-- DO NOT include this parameter unless you know what it does --><br />
| status = <br />
| programming language = [[C++]], [[C]] and [[Python (programming language)|Python]]<br />
| operating system = <br />
| platform = <br />
| size = <br />
| language = <br />
| language count = <!-- DO NOT include this parameter unless you know what it does --><br />
| language footnote = <br />
| genre = [[Computer algebra system]]<br />
| license = [[GNU General Public License]], version 3<br />
| website = {{URL|http://normaliz.uni-osnabrueck.de/}}<br />
}}<br />
<br />
'''Normaliz''' is a [[Free software|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. <br />
<br />
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]].<br />
<br />
Normaliz has interfaces to several general computer algebra systems: [[CoCoA]], [[GAP (computer algebra system)|GAP]], [[Macaulay2]] and [[Singular (software)|Singular]]. It can be used interactively via its Python interface PyNormaliz. Its use in SageMath is in preparation.<br />
<br />
[[Jesús A. De_Loera]] cites Normaliz among his favorite programs for computing [[Hilbert basis (linear programming)|Hilbert basis]]<ref>{{cite book|last1=De Loera|first1=Jesús|title=Course Notes: Algebraic and Geometric Combinatorics|publisher=UC Davis|url=https://www.math.ucdavis.edu/~deloera/TEACHING/MATH246/NOTES/chapter2.tex|chapter=Combinatorial Problems with Geometric Solutions}}</ref>.<br />
<br />
==See also==<br />
{{Portal|Free software}}<br />
*[[Comparison of computer algebra systems]]<br />
<br />
==References==<br />
{{Reflist}}<br />
<br />
==External links==<br />
*{{Official website|http://www.normaliz.uni-osnabrueck.de/}}<br />
*[https://www.normaliz.uni-osnabrueck.de/documentation/ Publications and examples of Normaliz applications]<br />
*http://github.com/normaliz/Normaliz<br />
<br />
{{Computer algebra systems}}<br />
<br />
[[Category:Computer algebra system software for Linux]]<br />
[[Category:Computer algebra system software for MacOS]]<br />
[[Category:Computer algebra system software for Windows]]<br />
[[Category:Cross-platform free software]]<br />
[[Category:Free computer algebra systems]]<br />
[[Category:Computer algebra systems]]</div>JShenkhttps://de.wikipedia.org/w/index.php?title=Normaliz&diff=170181868Normaliz2017-10-17T13:43:31Z<p>JShenk: </p>
<hr />
<div>{{Infobox software<br />
| name = Normaliz<br />
| title = Normaliz<br />
| logo = <br />
| logo caption = <br />
| logo_size = <br />
| logo_alt = <br />
| screenshot = [[File:Hilbert basis.gif|Hilbert basis]]<br />
| caption = <br />
| screenshot_size = <br />
| screenshot_alt = <br />
| collapsible = <br />
| author = Winfried Bruns, Robert Koch, Bogdan Ichim, Christof Soeger<br />
| developer = <br />
| released = <!-- {{Start date and age|YYYY|MM|DD|df=yes/no}} --><br />
| discontinued = <br />
| latest release version = <br />
| latest release date = <!-- {{Start date and age|YYYY|MM|DD|df=yes/no}} --><br />
| latest preview version = <br />
| latest preview date = <!-- {{Start date and age|YYYY|MM|DD|df=yes/no}} --><br />
| frequently updated = <!-- DO NOT include this parameter unless you know what it does --><br />
| status = <br />
| programming language = [[C++]], [[C]] and [[Python (programming language)|Python]]<br />
| operating system = <br />
| platform = <br />
| size = <br />
| language = <br />
| language count = <!-- DO NOT include this parameter unless you know what it does --><br />
| language footnote = <br />
| genre = [[Computer algebra system]]<br />
| license = [[GNU General Public License]], version 3<br />
| website = {{URL|http://normaliz.uni-osnabrueck.de/}}<br />
}}<br />
<br />
'''Normaliz''' is a [[Free software|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. <br />
<br />
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]].<br />
<br />
Normaliz has interfaces to several general computer algebra systems: [[CoCoA]], [[GAP (computer algebra system)|GAP]], [[Macaulay2]] and [[Singular (software)|Singular]]. It can be used interactively via its Python interface PyNormaliz. Its use in SageMath is in preparation.<br />
<br />
[[Jesús A. De_Loera]] cites Normaliz among his favorite programs for computing [[Hilbert basis (linear programming)|Hilbert basis]]<ref>{{cite book|last1=De Loera|first1=Jesús|title=Course Notes: Algebraic and Geometric Combinatorics|publisher=UC Davis|url=https://www.math.ucdavis.edu/~deloera/TEACHING/MATH246/NOTES/chapter2.tex|chapter=Combinatorial Problems with Geometric Solutions}}</ref>.<br />
<br />
==See also==<br />
{{Portal|Free software}}<br />
*[[Comparison of computer algebra systems]]<br />
<br />
==References==<br />
{{Reflist}}<br />
<br />
==External links==<br />
*{{Official website|http://www.normaliz.uni-osnabrueck.de/}}<br />
*[https://www.normaliz.uni-osnabrueck.de/documentation/ Publications and examples of Normaliz applications]<br />
*http://github.com/normaliz/Normaliz<br />
<br />
{{Computer algebra systems}}<br />
<br />
[[Category:Computer algebra system software for Linux]]<br />
[[Category:Computer algebra system software for MacOS]]<br />
[[Category:Computer algebra system software for Windows]]<br />
[[Category:Cross-platform free software]]<br />
[[Category:Free computer algebra systems]]<br />
[[Category:Computer algebra systems]]</div>JShenkhttps://de.wikipedia.org/w/index.php?title=Normaliz&diff=170072319Normaliz2017-10-17T13:38:36Z<p>JShenk: </p>
<hr />
<div>{{Infobox Software<br />
| Hersteller = University of Osnabrück<br />
| Bild = HilbertBasis.gif<br />
| AktuelleVersion = <!-- Versionen bitte absatzweise eintragen --><br />
3.4.0 ([[Linux]], [[macOS]] und [[Microsoft Windows|Windows]])<br /><small>{{Datum|17|10|2017}}</small><br />
| Betriebssystem = [[Unix]], [[Linux]], [[FreeBSD]], [[macOS]], [[Microsoft Windows|Windows]]<br />
| Kategorie = [[Computeralgebrasystem]]<br />
| Lizenz = [[GNU General Public License|GPL]] ([[Freie Software]])<br />
| Deutsch = nein<br />
| Website = [http://www.normaliz.uni-osnabrueck.de normaliz.uni-osnabrueck.de]<br />
}}<br />
<br />
'''Normaliz''' ist ein freies Computeralgebra-System, das von Winfried Bruns, Robert Koch (1998-2002), Bogdam Ichim (2007/08) und Christof Soeger (2009-2016) entwickelt wurde. Es ist unter der GNU General Public License Version 2 veröffentlicht.<br />
<br />
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.<br />
<br />
Normaliz hat Schnittstellen zu mehreren allgemeinen Computeralgebra-Systemen: [[CoCoA]], [[GAP]], [[Macaulay2]] und [[Singular]]. Es kann interaktiv über seine Python-Schnittstelle PyNormaliz verwendet werden. Seine Verwendung in SageMath ist in Vorbereitung.<br />
<br />
Jesús A. De_Loera zählt Normaliz zu seinen Lieblingsprogrammen für die Berechnung der Hilbert-Basis<ref>De Loera, Jesús. Course Notes: Algebraic and Geometric Combinatorics. Link: [https://www.math.ucdavis.edu/~deloera/TEACHING/MATH246/NOTES/chapter2.tex Notes]</ref>.<br />
<br />
== Einzelnachweise ==<br />
<references /><br />
<br />
==Weblinks==<br />
*[http://www.normaliz.uni-osnabrueck.de/ Offizielle Website ]<br />
*[https://www.normaliz.uni-osnabrueck.de/documentation/ Publications and examples of Normaliz applications]<br />
*[http://github.com/normaliz/Normaliz Source code (Github)]<br />
<br />
[[Kategorie:Freies Computeralgebrasystem]]<br />
[[Kategorie:Windows-Software]]<br />
[[Kategorie:MacOS-Software]]<br />
[[Kategorie:Unix-Software]]<br />
[[Kategorie:Linux-Software]]</div>JShenkhttps://de.wikipedia.org/w/index.php?title=Normaliz&diff=170072202Normaliz2017-10-17T13:33:32Z<p>JShenk: </p>
<hr />
<div>{{Infobox Software<br />
| Hersteller = University of Osnabrück<br />
| Bild = Hilbertbasis.gif<br />
| AktuelleVersion = <!-- Versionen bitte absatzweise eintragen --><br />
3.4.0 ([[Linux]], [[macOS]] und [[Microsoft Windows|Windows]])<br /><small>{{Datum|17|10|2017}}</small><br />
| Betriebssystem = [[Unix]], [[Linux]], [[FreeBSD]], [[macOS]], [[Microsoft Windows|Windows]]<br />
| Kategorie = [[Computeralgebrasystem]]<br />
| Lizenz = [[GNU General Public License|GPL]] ([[Freie Software]])<br />
| Deutsch = nein<br />
| Website = [http://www.normaliz.uni-osnabrueck.de normaliz.uni-osnabrueck.de]<br />
}}<br />
<br />
'''Normaliz''' ist ein freies Computeralgebra-System, das von Winfried Bruns, Robert Koch (1998-2002), Bogdam Ichim (2007/08) und Christof Soeger (2009-2016) entwickelt wurde. Es ist unter der GNU General Public License Version 2 veröffentlicht.<br />
<br />
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.<br />
<br />
Normaliz hat Schnittstellen zu mehreren allgemeinen Computeralgebra-Systemen: [[CoCoA]], [[GAP]], [[Macaulay2]] und [[Singular]]. Es kann interaktiv über seine Python-Schnittstelle PyNormaliz verwendet werden. Seine Verwendung in SageMath ist in Vorbereitung.<br />
<br />
Jesús A. De_Loera zählt Normaliz zu seinen Lieblingsprogrammen für die Berechnung der Hilbert-Basis<ref>De Loera, Jesús. Course Notes: Algebraic and Geometric Combinatorics. Link: [https://www.math.ucdavis.edu/~deloera/TEACHING/MATH246/NOTES/chapter2.tex Notes]</ref>.<br />
<br />
== Einzelnachweise ==<br />
<references /><br />
<br />
==Weblinks==<br />
*[http://www.normaliz.uni-osnabrueck.de/ Offizielle Website ]<br />
*[https://www.normaliz.uni-osnabrueck.de/documentation/ Publications and examples of Normaliz applications]<br />
*[http://github.com/normaliz/Normaliz Source code (Github)]<br />
<br />
[[Kategorie:Freies Computeralgebrasystem]]<br />
[[Kategorie:Windows-Software]]<br />
[[Kategorie:MacOS-Software]]<br />
[[Kategorie:Unix-Software]]<br />
[[Kategorie:Linux-Software]]</div>JShenkhttps://de.wikipedia.org/w/index.php?title=Normaliz&diff=170072170Normaliz2017-10-17T13:31:52Z<p>JShenk: </p>
<hr />
<div>{{Infobox Software<br />
| Hersteller = University of Osnabrück<br />
| Bild = Hilbertbasis.gif<br />
| AktuelleVersion = <!-- Versionen bitte absatzweise eintragen --><br />
3.4.0 ([[Linux]], [[macOS]] und [[Microsoft Windows|Windows]])<br /><small>{{Datum|17|10|2017}}</small><br />
| Betriebssystem = [[Unix]], [[Linux]], [[FreeBSD]], [[macOS]], [[Microsoft Windows|Windows]]<br />
| Kategorie = [[Computeralgebrasystem]]<br />
| Lizenz = [[GNU General Public License|GPL]] ([[Freie Software]])<br />
| Deutsch = nein<br />
| Website = [http://www.normaliz.uni-osnabrueck.de normaliz.uni-osnabrueck.de]<br />
}}<br />
<br />
'''Normaliz''' ist ein freies Computeralgebra-System, das von Winfried Bruns, Robert Koch (1998-2002), Bogdam Ichim (2007/08) und Christof Soeger (2009-2016) entwickelt wurde. Es ist unter der GNU General Public License Version 2 veröffentlicht.<br />
<br />
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.<br />
<br />
Normaliz hat Schnittstellen zu mehreren allgemeinen Computeralgebra-Systemen: [[CoCoA]], [[GAP]], [[Macaulay2]] und [[Singular]]. Es kann interaktiv über seine Python-Schnittstelle PyNormaliz verwendet werden. Seine Verwendung in SageMath ist in Vorbereitung.<br />
<br />
Jesús A. De_Loera zitiert Normaliz zu seinen Lieblingsprogrammen für die Berechnung der Hilbert-Basis<ref>De Loera, Jesús. Course Notes: Algebraic and Geometric Combinatorics. Link: [https://www.math.ucdavis.edu/~deloera/TEACHING/MATH246/NOTES/chapter2.tex Notes]</ref>.<br />
<br />
== Einzelnachweise ==<br />
<references /><br />
<br />
==Weblinks==<br />
*[http://www.normaliz.uni-osnabrueck.de/ Offizielle Website ]<br />
*[https://www.normaliz.uni-osnabrueck.de/documentation/ Publications and examples of Normaliz applications]<br />
*[http://github.com/normaliz/Normaliz Source code (Github)]<br />
<br />
[[Kategorie:Freies Computeralgebrasystem]]<br />
[[Kategorie:Windows-Software]]<br />
[[Kategorie:MacOS-Software]]<br />
[[Kategorie:Unix-Software]]<br />
[[Kategorie:Linux-Software]]</div>JShenkhttps://de.wikipedia.org/w/index.php?title=Normaliz&diff=170072134Normaliz2017-10-17T13:30:12Z<p>JShenk: </p>
<hr />
<div>{{Infobox Software<br />
| Hersteller = University of Osnabrück<br />
| AktuelleVersion = <!-- Versionen bitte absatzweise eintragen --><br />
3.4.0 ([[Linux]], [[macOS]] und [[Microsoft Windows|Windows]])<br /><small>{{Datum|17|10|2017}}</small><br />
| Betriebssystem = [[Unix]], [[Linux]], [[FreeBSD]], [[macOS]], [[Microsoft Windows|Windows]]<br />
| Kategorie = [[Computeralgebrasystem]]<br />
| Lizenz = [[GNU General Public License|GPL]] ([[Freie Software]])<br />
| Deutsch = nein<br />
| Website = [http://www.normaliz.uni-osnabrueck.de normaliz.uni-osnabrueck.de]<br />
}}<br />
<br />
'''Normaliz''' ist ein freies Computeralgebra-System, das von Winfried Bruns, Robert Koch (1998-2002), Bogdam Ichim (2007/08) und Christof Soeger (2009-2016) entwickelt wurde. Es ist unter der GNU General Public License Version 2 veröffentlicht.<br />
<br />
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.<br />
<br />
Normaliz hat Schnittstellen zu mehreren allgemeinen Computeralgebra-Systemen: [[CoCoA]], [[GAP]], [[Macaulay2]] und [[Singular]]. Es kann interaktiv über seine Python-Schnittstelle PyNormaliz verwendet werden. Seine Verwendung in SageMath ist in Vorbereitung.<br />
<br />
Jesús A. De_Loera zitiert Normaliz zu seinen Lieblingsprogrammen für die Berechnung der Hilbert-Basis<ref>De Loera, Jesús. Course Notes: Algebraic and Geometric Combinatorics. Link: [https://www.math.ucdavis.edu/~deloera/TEACHING/MATH246/NOTES/chapter2.tex Notes]</ref>.<br />
<br />
== Einzelnachweise ==<br />
<references /><br />
<br />
==Weblinks==<br />
*[http://www.normaliz.uni-osnabrueck.de/ Offizielle Website ]<br />
*[https://www.normaliz.uni-osnabrueck.de/documentation/ Publications and examples of Normaliz applications]<br />
*[http://github.com/normaliz/Normaliz Source code (Github)]<br />
<br />
[[Kategorie:Freies Computeralgebrasystem]]<br />
[[Kategorie:Windows-Software]]<br />
[[Kategorie:MacOS-Software]]<br />
[[Kategorie:Unix-Software]]<br />
[[Kategorie:Linux-Software]]</div>JShenkhttps://de.wikipedia.org/w/index.php?title=Normaliz&diff=170072121Normaliz2017-10-17T13:29:35Z<p>JShenk: </p>
<hr />
<div>{{Infobox Software<br />
| Hersteller = University of Osnabrück<br />
| AktuelleVersion = <!-- Versionen bitte absatzweise eintragen --><br />
3.4.0 ([[Linux]], [[macOS]] und [[Microsoft Windows|Windows]])<br /><small>{{Datum|17|10|2017}}</small><br />
| Betriebssystem = [[Unix]], [[Linux]], [[FreeBSD]], [[macOS]], [[Microsoft Windows|Windows]]<br />
| Kategorie = [[Computeralgebrasystem]]<br />
| Lizenz = [[GNU General Public License|GPL]] ([[Freie Software]])<br />
| Deutsch = nein<br />
| Website = [http://www.normaliz.uni-osnabrueck.de normaliz.uni-osnabrueck.de]<br />
}}<br />
<br />
'''Normaliz''' ist ein freies Computeralgebra-System, das von Winfried Bruns, Robert Koch (1998-2002), Bogdam Ichim (2007/08) und Christof Soeger (2009-2016) entwickelt wurde. Es ist unter der GNU General Public License Version 2 veröffentlicht.<br />
<br />
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.<br />
<br />
Normaliz hat Schnittstellen zu mehreren allgemeinen Computeralgebra-Systemen: [[CoCoA]], [[GAP]], [[Macaulay2]] und [[Singular]]. Es kann interaktiv über seine Python-Schnittstelle PyNormaliz verwendet werden. Seine Verwendung in SageMath ist in Vorbereitung.<br />
<br />
Jesús A. De_Loera zitiert Normaliz zu seinen Lieblingsprogrammen für die Berechnung der Hilbert-Basis<ref>De Loera, Jesús. Course Notes: Algebraic and Geometric Combinatorics. Link: [https://www.math.ucdavis.edu/~deloera/TEACHING/MATH246/NOTES/chapter2.tex Notes]</ref>.<br />
<br />
== Einzelnachweise ==<br />
<references /><br />
<br />
==Weblinks==<br />
*[http://www.normaliz.uni-osnabrueck.de/ Offizielle Website ]<br />
*[https://www.normaliz.uni-osnabrueck.de/documentation/ Publications and examples of Normaliz applications]<br />
*[http://github.com/normaliz/Normaliz Source code (Github)]<br />
<br />
[[Kategorie:Freies Computeralgebrasystem]]<br />
[[Kategorie:Windows-Software]]<br />
[[Kategorie:MacOS-Software]]<br />
[[Kategorie:Unix-Software]]<br />
[[Kategorie:Linux-Software]]<br />
[[Kategorie:RWTH Aachen]]</div>JShenkhttps://de.wikipedia.org/w/index.php?title=Normaliz&diff=170072106Normaliz2017-10-17T13:28:43Z<p>JShenk: </p>
<hr />
<div>{{Infobox Software<br />
| Hersteller = University of Osnabrück<br />
| AktuelleVersion = <!-- Versionen bitte absatzweise eintragen --><br />
3.4.0 ([[Linux]], [[macOS]] und [[Microsoft Windows|Windows]])<br /><small>{{Datum|17|10|2017}}</small><br />
| Betriebssystem = [[Unix]], [[Linux]], [[FreeBSD]], [[macOS]], [[Microsoft Windows|Windows]]<br />
| Kategorie = [[Computeralgebrasystem]]<br />
| Lizenz = [[GNU General Public License|GPL]] ([[Freie Software]])<br />
| Deutsch = nein<br />
| Website = [http://www.normaliz.uni-osnabrueck.de normaliz.uni-osnabrueck.de]<br />
}}<br />
<br />
'''Normaliz''' ist ein freies Computeralgebra-System, das von Winfried Bruns, Robert Koch (1998-2002), Bogdam Ichim (2007/08) und Christof Soeger (2009-2016) entwickelt wurde. Es ist unter der GNU General Public License Version 2 veröffentlicht.<br />
<br />
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.<br />
<br />
Normaliz hat Schnittstellen zu mehreren allgemeinen Computeralgebra-Systemen: CoCoA, GAP, Macaulay2 und Singular. Es kann interaktiv über seine Python-Schnittstelle PyNormaliz verwendet werden. Seine Verwendung in SageMath ist in Vorbereitung.<br />
<br />
Jesús A. De_Loera zitiert Normaliz zu seinen Lieblingsprogrammen für die Berechnung der Hilbert-Basis<ref>De Loera, Jesús. Course Notes: Algebraic and Geometric Combinatorics. Link: [https://www.math.ucdavis.edu/~deloera/TEACHING/MATH246/NOTES/chapter2.tex Notes]</ref>.<br />
<br />
== Einzelnachweise ==<br />
<references /><br />
<br />
==Weblinks==<br />
*[http://www.normaliz.uni-osnabrueck.de/ Offizielle Website ]<br />
*[https://www.normaliz.uni-osnabrueck.de/documentation/ Publications and examples of Normaliz applications]<br />
*[http://github.com/normaliz/Normaliz Source code (Github)]<br />
<br />
[[Kategorie:Freies Computeralgebrasystem]]<br />
[[Kategorie:Windows-Software]]<br />
[[Kategorie:MacOS-Software]]<br />
[[Kategorie:Unix-Software]]<br />
[[Kategorie:Linux-Software]]<br />
[[Kategorie:RWTH Aachen]]</div>JShenkhttps://de.wikipedia.org/w/index.php?title=Normaliz&diff=170072073Normaliz2017-10-17T13:26:40Z<p>JShenk: /* References */</p>
<hr />
<div>{{Infobox Software<br />
| Hersteller = University of Osnabrück<br />
| AktuelleVersion = <!-- Versionen bitte absatzweise eintragen --><br />
3.4.0 ([[Linux]], [[macOS]] und [[Microsoft Windows|Windows]])<br /><small>{{Datum|17|10|2017}}</small><br />
| Betriebssystem = [[Unix]], [[Linux]], [[FreeBSD]], [[macOS]], [[Microsoft Windows|Windows]]<br />
| Kategorie = [[Computeralgebrasystem]]<br />
| Lizenz = [[GNU General Public License|GPL]] ([[Freie Software]])<br />
| Deutsch = nein<br />
| Website = [http://www.normaliz.uni-osnabrueck.de normaliz.uni-osnabrueck.de]<br />
}}<br />
<br />
'''Normaliz''' ist ein freies Computeralgebra-System, das von Winfried Bruns, Robert Koch (1998-2002), Bogdam Ichim (2007/08) und Christof Soeger (2009-2016) entwickelt wurde. Es ist unter der GNU General Public License Version 2 veröffentlicht.<br />
<br />
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.<br />
<br />
Normaliz hat Schnittstellen zu mehreren allgemeinen Computeralgebra-Systemen: CoCoA, GAP, Macaulay2 und Singular. Es kann interaktiv über seine Python-Schnittstelle PyNormaliz verwendet werden. Seine Verwendung in SageMath ist in Vorbereitung.<br />
<br />
Jesús A. De_Loera zitiert Normaliz zu seinen Lieblingsprogrammen für die Berechnung der Hilbert-Basis<ref>De Loera, Jesús. Course Notes: Algebraic and Geometric Combinatorics. Link: [https://www.math.ucdavis.edu/~deloera/TEACHING/MATH246/NOTES/chapter2.tex Notes]</ref>.<br />
<br />
==Weblinks==<br />
*[Offizielle Website http://normaliz.uni-osnabrueck.de]<br />
<br />
== Einzelnachweise ==<br />
<references /><br />
<br />
==External links==<br />
*{{Official website|http://www.normaliz.uni-osnabrueck.de/}}<br />
*[https://www.normaliz.uni-osnabrueck.de/documentation/ Publications and examples of Normaliz applications]<br />
*http://github.com/normaliz/Normaliz<br />
<br />
{{Computer algebra systems}}<br />
<br />
[[Category:Computer algebra system software for Linux]]<br />
[[Category:Computer algebra system software for MacOS]]<br />
[[Category:Computer algebra system software for Windows]]<br />
[[Category:Cross-platform free software]]<br />
[[Category:Free computer algebra systems]]<br />
[[Category:Computer algebra systems]]</div>JShenkhttps://de.wikipedia.org/w/index.php?title=Normaliz&diff=170072063Normaliz2017-10-17T13:26:09Z<p>JShenk: /* See also */</p>
<hr />
<div>{{Infobox Software<br />
| Hersteller = University of Osnabrück<br />
| AktuelleVersion = <!-- Versionen bitte absatzweise eintragen --><br />
3.4.0 ([[Linux]], [[macOS]] und [[Microsoft Windows|Windows]])<br /><small>{{Datum|17|10|2017}}</small><br />
| Betriebssystem = [[Unix]], [[Linux]], [[FreeBSD]], [[macOS]], [[Microsoft Windows|Windows]]<br />
| Kategorie = [[Computeralgebrasystem]]<br />
| Lizenz = [[GNU General Public License|GPL]] ([[Freie Software]])<br />
| Deutsch = nein<br />
| Website = [http://www.normaliz.uni-osnabrueck.de normaliz.uni-osnabrueck.de]<br />
}}<br />
<br />
'''Normaliz''' ist ein freies Computeralgebra-System, das von Winfried Bruns, Robert Koch (1998-2002), Bogdam Ichim (2007/08) und Christof Soeger (2009-2016) entwickelt wurde. Es ist unter der GNU General Public License Version 2 veröffentlicht.<br />
<br />
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.<br />
<br />
Normaliz hat Schnittstellen zu mehreren allgemeinen Computeralgebra-Systemen: CoCoA, GAP, Macaulay2 und Singular. Es kann interaktiv über seine Python-Schnittstelle PyNormaliz verwendet werden. Seine Verwendung in SageMath ist in Vorbereitung.<br />
<br />
Jesús A. De_Loera zitiert Normaliz zu seinen Lieblingsprogrammen für die Berechnung der Hilbert-Basis<ref>De Loera, Jesús. Course Notes: Algebraic and Geometric Combinatorics. Link: [https://www.math.ucdavis.edu/~deloera/TEACHING/MATH246/NOTES/chapter2.tex Notes]</ref>.<br />
<br />
==Weblinks==<br />
*[Offizielle Website http://normaliz.uni-osnabrueck.de]<br />
<br />
==References==<br />
{{Reflist}}<br />
<br />
==External links==<br />
*{{Official website|http://www.normaliz.uni-osnabrueck.de/}}<br />
*[https://www.normaliz.uni-osnabrueck.de/documentation/ Publications and examples of Normaliz applications]<br />
*http://github.com/normaliz/Normaliz<br />
<br />
{{Computer algebra systems}}<br />
<br />
[[Category:Computer algebra system software for Linux]]<br />
[[Category:Computer algebra system software for MacOS]]<br />
[[Category:Computer algebra system software for Windows]]<br />
[[Category:Cross-platform free software]]<br />
[[Category:Free computer algebra systems]]<br />
[[Category:Computer algebra systems]]</div>JShenkhttps://de.wikipedia.org/w/index.php?title=Normaliz&diff=170181867Normaliz2017-10-17T13:25:24Z<p>JShenk: Undid revision 805760421 by JShenk (talk)</p>
<hr />
<div>{{Infobox software<br />
| name = Normaliz<br />
| title = Normaliz<br />
| logo = <br />
| logo caption = <br />
| logo_size = <br />
| logo_alt = <br />
| screenshot = HilbertBasis.gif<br />
| caption = <br />
| screenshot_size = <br />
| screenshot_alt = <br />
| collapsible = <br />
| author = Winfried Bruns, Robert Koch, Bogdan Ichim, Christof Soeger<br />
| developer = <br />
| released = <!-- {{Start date and age|YYYY|MM|DD|df=yes/no}} --><br />
| discontinued = <br />
| latest release version = <br />
| latest release date = <!-- {{Start date and age|YYYY|MM|DD|df=yes/no}} --><br />
| latest preview version = <br />
| latest preview date = <!-- {{Start date and age|YYYY|MM|DD|df=yes/no}} --><br />
| frequently updated = <!-- DO NOT include this parameter unless you know what it does --><br />
| status = <br />
| programming language = [[C++]], [[C]] and [[Python (programming language)|Python]]<br />
| operating system = <br />
| platform = <br />
| size = <br />
| language = <br />
| language count = <!-- DO NOT include this parameter unless you know what it does --><br />
| language footnote = <br />
| genre = [[Computer algebra system]]<br />
| license = [[GNU General Public License]], version 3<br />
| website = {{URL|http://normaliz.uni-osnabrueck.de/}}<br />
}}<br />
<br />
'''Normaliz''' is a [[Free software|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. <br />
<br />
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]].<br />
<br />
Normaliz has interfaces to several general computer algebra systems: [[CoCoA]], [[GAP (computer algebra system)|GAP]], [[Macaulay2]] and [[Singular (software)|Singular]]. It can be used interactively via its Python interface PyNormaliz. Its use in SageMath is in preparation.<br />
<br />
[[Jesús A. De_Loera]] cites Normaliz among his favorite programs for computing [[Hilbert basis (linear programming)|Hilbert basis]]<ref>{{cite book|last1=De Loera|first1=Jesús|title=Course Notes: Algebraic and Geometric Combinatorics|publisher=UC Davis|url=https://www.math.ucdavis.edu/~deloera/TEACHING/MATH246/NOTES/chapter2.tex|chapter=Combinatorial Problems with Geometric Solutions}}</ref>.<br />
<br />
==See also==<br />
{{Portal|Free software}}<br />
*[[Comparison of computer algebra systems]]<br />
<br />
==References==<br />
{{Reflist}}<br />
<br />
==External links==<br />
*{{Official website|http://www.normaliz.uni-osnabrueck.de/}}<br />
*[https://www.normaliz.uni-osnabrueck.de/documentation/ Publications and examples of Normaliz applications]<br />
*http://github.com/normaliz/Normaliz<br />
<br />
{{Computer algebra systems}}<br />
<br />
[[Category:Computer algebra system software for Linux]]<br />
[[Category:Computer algebra system software for MacOS]]<br />
[[Category:Computer algebra system software for Windows]]<br />
[[Category:Cross-platform free software]]<br />
[[Category:Free computer algebra systems]]<br />
[[Category:Computer algebra systems]]</div>JShenkhttps://de.wikipedia.org/w/index.php?title=Normaliz&diff=170181866Normaliz2017-10-17T13:25:09Z<p>JShenk: Undid revision 805760393 by JShenk (talk)</p>
<hr />
<div>{{Infobox software<br />
| name = Normaliz<br />
| title = Normaliz<br />
| logo = <br />
| logo caption = <br />
| logo_size = <br />
| logo_alt = <br />
| screenshot = HilbertBasis.gif<br />
| caption = <br />
| screenshot_size = <br />
| screenshot_alt = <br />
| collapsible = <br />
| author = Winfried Bruns, Robert Koch, Bogdan Ichim, Christof Soeger<br />
| developer = <br />
| released = <!-- {{Start date and age|YYYY|MM|DD|df=yes/no}} --><br />
| discontinued = <br />
| latest release version = <br />
| latest release date = <!-- {{Start date and age|YYYY|MM|DD|df=yes/no}} --><br />
| latest preview version = <br />
| latest preview date = <!-- {{Start date and age|YYYY|MM|DD|df=yes/no}} --><br />
| frequently updated = <!-- DO NOT include this parameter unless you know what it does --><br />
| status = <br />
| programming language = [[C++]], [[C]] and [[Python (programming language)|Python]]<br />
| operating system = <br />
| platform = <br />
| size = <br />
| language = <br />
| language count = <!-- DO NOT include this parameter unless you know what it does --><br />
| language footnote = <br />
| genre = [[Computer algebra system]]<br />
| license = [[GNU General Public License]], version 3<br />
| website = {{URL|http://normaliz.uni-osnabrueck.de/}}<br />
}}<br />
<br />
'''Normaliz''' is a [[Free software|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. <br />
<br />
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]].<br />
<br />
Normaliz has interfaces to several general computer algebra systems: [[CoCoA]], [[GAP (computer algebra system)|GAP]], [[Macaulay2]] and [[Singular (software)|Singular]]. It can be used interactively via its Python interface PyNormaliz. Its use in SageMath is in preparation.<br />
<br />
[[Jesús A. De_Loera]] cites Normaliz among his favorite programs for computing [[Hilbert basis (linear programming)|Hilbert basis]]<ref>{{cite book|last1=De Loera|first1=Jesús|title=Course Notes: Algebraic and Geometric Combinatorics|publisher=UC Davis|url=https://www.math.ucdavis.edu/~deloera/TEACHING/MATH246/NOTES/chapter2.tex|chapter=Combinatorial Problems with Geometric Solutions}}</ref>.<br />
<br />
==See also==<br />
{{Portal|Free software}}<br />
*[[Comparison of computer algebra systems]]<br />
<br />
== Einzelnachweise ==<br />
{{Reflist}}<br />
<br />
==External links==<br />
*{{Official website|http://www.normaliz.uni-osnabrueck.de/}}<br />
*[https://www.normaliz.uni-osnabrueck.de/documentation/ Publications and examples of Normaliz applications]<br />
*http://github.com/normaliz/Normaliz<br />
<br />
{{Computer algebra systems}}<br />
<br />
[[Category:Computer algebra system software for Linux]]<br />
[[Category:Computer algebra system software for MacOS]]<br />
[[Category:Computer algebra system software for Windows]]<br />
[[Category:Cross-platform free software]]<br />
[[Category:Free computer algebra systems]]<br />
[[Category:Computer algebra systems]]</div>JShenkhttps://de.wikipedia.org/w/index.php?title=Normaliz&diff=170181865Normaliz2017-10-17T13:24:43Z<p>JShenk: /* References */</p>
<hr />
<div>{{Infobox software<br />
| name = Normaliz<br />
| title = Normaliz<br />
| logo = <br />
| logo caption = <br />
| logo_size = <br />
| logo_alt = <br />
| screenshot = HilbertBasis.gif<br />
| caption = <br />
| screenshot_size = <br />
| screenshot_alt = <br />
| collapsible = <br />
| author = Winfried Bruns, Robert Koch, Bogdan Ichim, Christof Soeger<br />
| developer = <br />
| released = <!-- {{Start date and age|YYYY|MM|DD|df=yes/no}} --><br />
| discontinued = <br />
| latest release version = <br />
| latest release date = <!-- {{Start date and age|YYYY|MM|DD|df=yes/no}} --><br />
| latest preview version = <br />
| latest preview date = <!-- {{Start date and age|YYYY|MM|DD|df=yes/no}} --><br />
| frequently updated = <!-- DO NOT include this parameter unless you know what it does --><br />
| status = <br />
| programming language = [[C++]], [[C]] and [[Python (programming language)|Python]]<br />
| operating system = <br />
| platform = <br />
| size = <br />
| language = <br />
| language count = <!-- DO NOT include this parameter unless you know what it does --><br />
| language footnote = <br />
| genre = [[Computer algebra system]]<br />
| license = [[GNU General Public License]], version 3<br />
| website = {{URL|http://normaliz.uni-osnabrueck.de/}}<br />
}}<br />
<br />
'''Normaliz''' is a [[Free software|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. <br />
<br />
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]].<br />
<br />
Normaliz has interfaces to several general computer algebra systems: [[CoCoA]], [[GAP (computer algebra system)|GAP]], [[Macaulay2]] and [[Singular (software)|Singular]]. It can be used interactively via its Python interface PyNormaliz. Its use in SageMath is in preparation.<br />
<br />
[[Jesús A. De_Loera]] cites Normaliz among his favorite programs for computing [[Hilbert basis (linear programming)|Hilbert basis]]<ref>{{cite book|last1=De Loera|first1=Jesús|title=Course Notes: Algebraic and Geometric Combinatorics|publisher=UC Davis|url=https://www.math.ucdavis.edu/~deloera/TEACHING/MATH246/NOTES/chapter2.tex|chapter=Combinatorial Problems with Geometric Solutions}}</ref>.<br />
<br />
==Weblinks==<br />
*[http://normaliz.uni-osnabrueck.de Offizielle Website] (englisch)<br />
<br />
== Einzelnachweise ==<br />
{{Reflist}}<br />
<br />
==External links==<br />
*{{Official website|http://www.normaliz.uni-osnabrueck.de/}}<br />
*[https://www.normaliz.uni-osnabrueck.de/documentation/ Publications and examples of Normaliz applications]<br />
*http://github.com/normaliz/Normaliz<br />
<br />
{{Computer algebra systems}}<br />
<br />
[[Category:Computer algebra system software for Linux]]<br />
[[Category:Computer algebra system software for MacOS]]<br />
[[Category:Computer algebra system software for Windows]]<br />
[[Category:Cross-platform free software]]<br />
[[Category:Free computer algebra systems]]<br />
[[Category:Computer algebra systems]]</div>JShenkhttps://de.wikipedia.org/w/index.php?title=Normaliz&diff=170181864Normaliz2017-10-17T13:24:24Z<p>JShenk: /* See also */</p>
<hr />
<div>{{Infobox software<br />
| name = Normaliz<br />
| title = Normaliz<br />
| logo = <br />
| logo caption = <br />
| logo_size = <br />
| logo_alt = <br />
| screenshot = HilbertBasis.gif<br />
| caption = <br />
| screenshot_size = <br />
| screenshot_alt = <br />
| collapsible = <br />
| author = Winfried Bruns, Robert Koch, Bogdan Ichim, Christof Soeger<br />
| developer = <br />
| released = <!-- {{Start date and age|YYYY|MM|DD|df=yes/no}} --><br />
| discontinued = <br />
| latest release version = <br />
| latest release date = <!-- {{Start date and age|YYYY|MM|DD|df=yes/no}} --><br />
| latest preview version = <br />
| latest preview date = <!-- {{Start date and age|YYYY|MM|DD|df=yes/no}} --><br />
| frequently updated = <!-- DO NOT include this parameter unless you know what it does --><br />
| status = <br />
| programming language = [[C++]], [[C]] and [[Python (programming language)|Python]]<br />
| operating system = <br />
| platform = <br />
| size = <br />
| language = <br />
| language count = <!-- DO NOT include this parameter unless you know what it does --><br />
| language footnote = <br />
| genre = [[Computer algebra system]]<br />
| license = [[GNU General Public License]], version 3<br />
| website = {{URL|http://normaliz.uni-osnabrueck.de/}}<br />
}}<br />
<br />
'''Normaliz''' is a [[Free software|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. <br />
<br />
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]].<br />
<br />
Normaliz has interfaces to several general computer algebra systems: [[CoCoA]], [[GAP (computer algebra system)|GAP]], [[Macaulay2]] and [[Singular (software)|Singular]]. It can be used interactively via its Python interface PyNormaliz. Its use in SageMath is in preparation.<br />
<br />
[[Jesús A. De_Loera]] cites Normaliz among his favorite programs for computing [[Hilbert basis (linear programming)|Hilbert basis]]<ref>{{cite book|last1=De Loera|first1=Jesús|title=Course Notes: Algebraic and Geometric Combinatorics|publisher=UC Davis|url=https://www.math.ucdavis.edu/~deloera/TEACHING/MATH246/NOTES/chapter2.tex|chapter=Combinatorial Problems with Geometric Solutions}}</ref>.<br />
<br />
==Weblinks==<br />
*[http://normaliz.uni-osnabrueck.de Offizielle Website] (englisch)<br />
<br />
==References==<br />
{{Reflist}}<br />
<br />
==External links==<br />
*{{Official website|http://www.normaliz.uni-osnabrueck.de/}}<br />
*[https://www.normaliz.uni-osnabrueck.de/documentation/ Publications and examples of Normaliz applications]<br />
*http://github.com/normaliz/Normaliz<br />
<br />
{{Computer algebra systems}}<br />
<br />
[[Category:Computer algebra system software for Linux]]<br />
[[Category:Computer algebra system software for MacOS]]<br />
[[Category:Computer algebra system software for Windows]]<br />
[[Category:Cross-platform free software]]<br />
[[Category:Free computer algebra systems]]<br />
[[Category:Computer algebra systems]]</div>JShenkhttps://de.wikipedia.org/w/index.php?title=Normaliz&diff=170071989Normaliz2017-10-17T13:22:52Z<p>JShenk: </p>
<hr />
<div>{{Infobox Software<br />
| Hersteller = University of Osnabrück<br />
| AktuelleVersion = <!-- Versionen bitte absatzweise eintragen --><br />
3.4.0 ([[Linux]], [[macOS]] und [[Microsoft Windows|Windows]])<br /><small>{{Datum|17|10|2017}}</small><br />
| Betriebssystem = [[Unix]], [[Linux]], [[FreeBSD]], [[macOS]], [[Microsoft Windows|Windows]]<br />
| Kategorie = [[Computeralgebrasystem]]<br />
| Lizenz = [[GNU General Public License|GPL]] ([[Freie Software]])<br />
| Deutsch = nein<br />
| Website = [http://www.normaliz.uni-osnabrueck.de normaliz.uni-osnabrueck.de]<br />
}}<br />
<br />
'''Normaliz''' ist ein freies Computeralgebra-System, das von Winfried Bruns, Robert Koch (1998-2002), Bogdam Ichim (2007/08) und Christof Soeger (2009-2016) entwickelt wurde. Es ist unter der GNU General Public License Version 2 veröffentlicht.<br />
<br />
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.<br />
<br />
Normaliz hat Schnittstellen zu mehreren allgemeinen Computeralgebra-Systemen: CoCoA, GAP, Macaulay2 und Singular. Es kann interaktiv über seine Python-Schnittstelle PyNormaliz verwendet werden. Seine Verwendung in SageMath ist in Vorbereitung.<br />
<br />
Jesús A. De_Loera zitiert Normaliz zu seinen Lieblingsprogrammen für die Berechnung der Hilbert-Basis<ref>De Loera, Jesús. Course Notes: Algebraic and Geometric Combinatorics. Link: [https://www.math.ucdavis.edu/~deloera/TEACHING/MATH246/NOTES/chapter2.tex Notes]</ref>.<br />
<br />
==See also==<br />
{{Portal|Free software}}<br />
*[[Comparison of computer algebra systems]]<br />
<br />
==References==<br />
{{Reflist}}<br />
<br />
==External links==<br />
*{{Official website|http://www.normaliz.uni-osnabrueck.de/}}<br />
*[https://www.normaliz.uni-osnabrueck.de/documentation/ Publications and examples of Normaliz applications]<br />
*http://github.com/normaliz/Normaliz<br />
<br />
{{Computer algebra systems}}<br />
<br />
[[Category:Computer algebra system software for Linux]]<br />
[[Category:Computer algebra system software for MacOS]]<br />
[[Category:Computer algebra system software for Windows]]<br />
[[Category:Cross-platform free software]]<br />
[[Category:Free computer algebra systems]]<br />
[[Category:Computer algebra systems]]</div>JShenkhttps://de.wikipedia.org/w/index.php?title=Normaliz&diff=170181863Normaliz2017-10-17T13:20:15Z<p>JShenk: Undid revision 805759809 by JShenk (talk)</p>
<hr />
<div>{{Infobox software<br />
| name = Normaliz<br />
| title = Normaliz<br />
| logo = <br />
| logo caption = <br />
| logo_size = <br />
| logo_alt = <br />
| screenshot = HilbertBasis.gif<br />
| caption = <br />
| screenshot_size = <br />
| screenshot_alt = <br />
| collapsible = <br />
| author = Winfried Bruns, Robert Koch, Bogdan Ichim, Christof Soeger<br />
| developer = <br />
| released = <!-- {{Start date and age|YYYY|MM|DD|df=yes/no}} --><br />
| discontinued = <br />
| latest release version = <br />
| latest release date = <!-- {{Start date and age|YYYY|MM|DD|df=yes/no}} --><br />
| latest preview version = <br />
| latest preview date = <!-- {{Start date and age|YYYY|MM|DD|df=yes/no}} --><br />
| frequently updated = <!-- DO NOT include this parameter unless you know what it does --><br />
| status = <br />
| programming language = [[C++]], [[C]] and [[Python (programming language)|Python]]<br />
| operating system = <br />
| platform = <br />
| size = <br />
| language = <br />
| language count = <!-- DO NOT include this parameter unless you know what it does --><br />
| language footnote = <br />
| genre = [[Computer algebra system]]<br />
| license = [[GNU General Public License]], version 3<br />
| website = {{URL|http://normaliz.uni-osnabrueck.de/}}<br />
}}<br />
<br />
'''Normaliz''' is a [[Free software|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. <br />
<br />
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]].<br />
<br />
Normaliz has interfaces to several general computer algebra systems: [[CoCoA]], [[GAP (computer algebra system)|GAP]], [[Macaulay2]] and [[Singular (software)|Singular]]. It can be used interactively via its Python interface PyNormaliz. Its use in SageMath is in preparation.<br />
<br />
[[Jesús A. De_Loera]] cites Normaliz among his favorite programs for computing [[Hilbert basis (linear programming)|Hilbert basis]]<ref>{{cite book|last1=De Loera|first1=Jesús|title=Course Notes: Algebraic and Geometric Combinatorics|publisher=UC Davis|url=https://www.math.ucdavis.edu/~deloera/TEACHING/MATH246/NOTES/chapter2.tex|chapter=Combinatorial Problems with Geometric Solutions}}</ref>.<br />
<br />
==See also==<br />
{{Portal|Free software}}<br />
*[[Comparison of computer algebra systems]]<br />
<br />
==References==<br />
{{Reflist}}<br />
<br />
==External links==<br />
*{{Official website|http://www.normaliz.uni-osnabrueck.de/}}<br />
*[https://www.normaliz.uni-osnabrueck.de/documentation/ Publications and examples of Normaliz applications]<br />
*http://github.com/normaliz/Normaliz<br />
<br />
{{Computer algebra systems}}<br />
<br />
[[Category:Computer algebra system software for Linux]]<br />
[[Category:Computer algebra system software for MacOS]]<br />
[[Category:Computer algebra system software for Windows]]<br />
[[Category:Cross-platform free software]]<br />
[[Category:Free computer algebra systems]]<br />
[[Category:Computer algebra systems]]</div>JShenkhttps://de.wikipedia.org/w/index.php?title=Normaliz&diff=170181862Normaliz2017-10-17T13:19:32Z<p>JShenk: </p>
<hr />
<div>{{Infobox software<br />
| name = Normaliz<br />
| title = Normaliz<br />
| logo = <br />
| logo caption = <br />
| logo_size = <br />
| logo_alt = <br />
| screenshot = HilbertBasis.gif<br />
| caption = <br />
| screenshot_size = <br />
| screenshot_alt = <br />
| collapsible = <br />
| author = Winfried Bruns, Robert Koch, Bogdan Ichim, Christof Soeger<br />
| developer = <br />
| released = <!-- {{Start date and age|YYYY|MM|DD|df=yes/no}} --><br />
| discontinued = <br />
| latest release version = <br />
| latest release date = <!-- {{Start date and age|YYYY|MM|DD|df=yes/no}} --><br />
| latest preview version = <br />
| latest preview date = <!-- {{Start date and age|YYYY|MM|DD|df=yes/no}} --><br />
| frequently updated = <!-- DO NOT include this parameter unless you know what it does --><br />
| status = <br />
| programming language = [[C++]], [[C]] and [[Python (programming language)|Python]]<br />
| operating system = <br />
| platform = <br />
| size = <br />
| language = <br />
| language count = <!-- DO NOT include this parameter unless you know what it does --><br />
| language footnote = <br />
| genre = [[Computer algebra system]]<br />
| license = [[GNU General Public License]], version 3<br />
| website = {{URL|http://normaliz.uni-osnabrueck.de/}}<br />
}}<br />
<br />
'''Normaliz''' is a [[Free software|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. <br />
<br />
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]].<br />
<br />
Normaliz has interfaces to several general computer algebra systems: [[CoCoA]], [[GAP (computer algebra system)|GAP]], [[Macaulay2]] and [[Singular (software)|Singular]]. It can be used interactively via its Python interface PyNormaliz. Its use in SageMath is in preparation.<br />
<br />
[[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>.<br />
<br />
==See also==<br />
{{Portal|Free software}}<br />
*[[Comparison of computer algebra systems]]<br />
<br />
==References==<br />
{{Reflist}}<br />
<br />
==External links==<br />
*{{Official website|http://www.normaliz.uni-osnabrueck.de/}}<br />
*[https://www.normaliz.uni-osnabrueck.de/documentation/ Publications and examples of Normaliz applications]<br />
*http://github.com/normaliz/Normaliz<br />
<br />
{{Computer algebra systems}}<br />
<br />
[[Category:Computer algebra system software for Linux]]<br />
[[Category:Computer algebra system software for MacOS]]<br />
[[Category:Computer algebra system software for Windows]]<br />
[[Category:Cross-platform free software]]<br />
[[Category:Free computer algebra systems]]<br />
[[Category:Computer algebra systems]]</div>JShenkhttps://de.wikipedia.org/w/index.php?title=Normaliz&diff=170071854Normaliz2017-10-17T13:16:58Z<p>JShenk: </p>
<hr />
<div>{{Infobox Software<br />
| Hersteller = University of Osnabrück<br />
| AktuelleVersion = <!-- Versionen bitte absatzweise eintragen --><br />
3.4.0 ([[Linux]], [[macOS]] und [[Microsoft Windows|Windows]])<br /><small>{{Datum|17|10|2017}}</small><br />
| Betriebssystem = [[Unix]], [[Linux]], [[FreeBSD]], [[macOS]], [[Microsoft Windows|Windows]]<br />
| Kategorie = [[Computeralgebrasystem]]<br />
| Lizenz = [[GNU General Public License|GPL]] ([[Freie Software]])<br />
| Deutsch = nein<br />
| Website = [http://www.normaliz.uni-osnabrueck.de normaliz.uni-osnabrueck.de]<br />
}}<br />
<br />
'''Normaliz''' ist ein freies Computeralgebra-System, das von Winfried Bruns, Robert Koch (1998-2002), Bogdam Ichim (2007/08) und Christof Soeger (2009-2016) entwickelt wurde. Es ist unter der GNU General Public License Version 2 veröffentlicht.<br />
<br />
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.<br />
<br />
Normaliz hat Schnittstellen zu mehreren allgemeinen Computeralgebra-Systemen: CoCoA, GAP, Macaulay2 und Singular. Es kann interaktiv über seine Python-Schnittstelle PyNormaliz verwendet werden. Seine Verwendung in SageMath ist in Vorbereitung.<br />
<br />
Jesús A. De_Loera zitiert Normaliz zu seinen Lieblingsprogrammen für die Berechnung der Hilbert-Basis [1].<br />
<br />
==See also==<br />
{{Portal|Free software}}<br />
*[[Comparison of computer algebra systems]]<br />
<br />
==References==<br />
{{Reflist}}<br />
<br />
==External links==<br />
*{{Official website|http://www.normaliz.uni-osnabrueck.de/}}<br />
*[https://www.normaliz.uni-osnabrueck.de/documentation/ Publications and examples of Normaliz applications]<br />
*http://github.com/normaliz/Normaliz<br />
<br />
{{Computer algebra systems}}<br />
<br />
[[Category:Computer algebra system software for Linux]]<br />
[[Category:Computer algebra system software for MacOS]]<br />
[[Category:Computer algebra system software for Windows]]<br />
[[Category:Cross-platform free software]]<br />
[[Category:Free computer algebra systems]]<br />
[[Category:Computer algebra systems]]</div>JShenkhttps://de.wikipedia.org/w/index.php?title=Normaliz&diff=170071845Normaliz2017-10-17T13:16:36Z<p>JShenk: </p>
<hr />
<div>{{Infobox Software<br />
| Hersteller = University of Osnabrück<br />
| AktuelleVersion = <!-- Versionen bitte absatzweise eintragen --><br />
3.4.0 ([[Linux]], [[macOS]] und [[Microsoft Windows|Windows]])<br /><small>{{Datum|17|10|2017}}</small><br />
|sprache=en}}</ref><br />
| Betriebssystem = [[Unix]], [[Linux]], [[FreeBSD]], [[macOS]], [[Microsoft Windows|Windows]]<br />
| Kategorie = [[Computeralgebrasystem]]<br />
| Lizenz = [[GNU General Public License|GPL]] ([[Freie Software]])<br />
| Deutsch = nein<br />
| Website = [http://www.normaliz.uni-osnabrueck.de normaliz.uni-osnabrueck.de]<br />
}}<br />
<br />
'''Normaliz''' ist ein freies Computeralgebra-System, das von Winfried Bruns, Robert Koch (1998-2002), Bogdam Ichim (2007/08) und Christof Soeger (2009-2016) entwickelt wurde. Es ist unter der GNU General Public License Version 2 veröffentlicht.<br />
<br />
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.<br />
<br />
Normaliz hat Schnittstellen zu mehreren allgemeinen Computeralgebra-Systemen: CoCoA, GAP, Macaulay2 und Singular. Es kann interaktiv über seine Python-Schnittstelle PyNormaliz verwendet werden. Seine Verwendung in SageMath ist in Vorbereitung.<br />
<br />
Jesús A. De_Loera zitiert Normaliz zu seinen Lieblingsprogrammen für die Berechnung der Hilbert-Basis [1].<br />
<br />
==See also==<br />
{{Portal|Free software}}<br />
*[[Comparison of computer algebra systems]]<br />
<br />
==References==<br />
{{Reflist}}<br />
<br />
==External links==<br />
*{{Official website|http://www.normaliz.uni-osnabrueck.de/}}<br />
*[https://www.normaliz.uni-osnabrueck.de/documentation/ Publications and examples of Normaliz applications]<br />
*http://github.com/normaliz/Normaliz<br />
<br />
{{Computer algebra systems}}<br />
<br />
[[Category:Computer algebra system software for Linux]]<br />
[[Category:Computer algebra system software for MacOS]]<br />
[[Category:Computer algebra system software for Windows]]<br />
[[Category:Cross-platform free software]]<br />
[[Category:Free computer algebra systems]]<br />
[[Category:Computer algebra systems]]</div>JShenkhttps://de.wikipedia.org/w/index.php?title=Normaliz&diff=170071815Normaliz2017-10-17T13:15:39Z<p>JShenk: </p>
<hr />
<div>{{Infobox Software<br />
| Hersteller = University of Osnabrück<br />
| AktuelleVersion = <!-- Versionen bitte absatzweise eintragen --><br />
3.4.0 ([[Linux]], [[macOS]] und [[Microsoft Windows|Windows]])<br /><small><br />
4.8.6&nbsp;([[FreeBSD]])<br /><small>{{Datum|15|11|2016}}</small><ref>{{Internetquelle |url=https://www.freebsd.org/cgi/ports.cgi?query=gap&stype=all&sektion=math |titel=CGI für die Ports von FreeBSD |werk=freebsd.org |zugriff=2017-10-02 |sprache=en}}</ref><br />
| Betriebssystem = [[Unix]], [[Linux]], [[FreeBSD]], [[macOS]], [[Microsoft Windows|Windows]]<br />
| Kategorie = [[Computeralgebrasystem]]<br />
| Lizenz = [[GNU General Public License|GPL]] ([[Freie Software]])<br />
| Deutsch = nein<br />
| Website = [http://www.normaliz.uni-osnabrueck.de normaliz.uni-osnabrueck.de]<br />
}}<br />
<br />
'''Normaliz''' ist ein freies Computeralgebra-System, das von Winfried Bruns, Robert Koch (1998-2002), Bogdam Ichim (2007/08) und Christof Soeger (2009-2016) entwickelt wurde. Es ist unter der GNU General Public License Version 2 veröffentlicht.<br />
<br />
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.<br />
<br />
Normaliz hat Schnittstellen zu mehreren allgemeinen Computeralgebra-Systemen: CoCoA, GAP, Macaulay2 und Singular. Es kann interaktiv über seine Python-Schnittstelle PyNormaliz verwendet werden. Seine Verwendung in SageMath ist in Vorbereitung.<br />
<br />
Jesús A. De_Loera zitiert Normaliz zu seinen Lieblingsprogrammen für die Berechnung der Hilbert-Basis [1].<br />
<br />
==See also==<br />
{{Portal|Free software}}<br />
*[[Comparison of computer algebra systems]]<br />
<br />
==References==<br />
{{Reflist}}<br />
<br />
==External links==<br />
*{{Official website|http://www.normaliz.uni-osnabrueck.de/}}<br />
*[https://www.normaliz.uni-osnabrueck.de/documentation/ Publications and examples of Normaliz applications]<br />
*http://github.com/normaliz/Normaliz<br />
<br />
{{Computer algebra systems}}<br />
<br />
[[Category:Computer algebra system software for Linux]]<br />
[[Category:Computer algebra system software for MacOS]]<br />
[[Category:Computer algebra system software for Windows]]<br />
[[Category:Cross-platform free software]]<br />
[[Category:Free computer algebra systems]]<br />
[[Category:Computer algebra systems]]</div>JShenkhttps://de.wikipedia.org/w/index.php?title=Normaliz&diff=170071795Normaliz2017-10-17T13:14:53Z<p>JShenk: </p>
<hr />
<div>{{Infobox Software<br />
| Hersteller = University of Osnabrück<br />
| AktuelleVersion = <!-- Versionen bitte absatzweise eintragen --><br />
3.4([[Linux]], [[macOS]] und [[Microsoft Windows|Windows]])<br /><small>{{Datum|20|8|2017}}</small><ref>{{Internetquelle |url=http://www.gap-system.org/Releases/index.html |titel=Releases |werk=gap-system.org |zugriff=2017-10-02 |sprache=en}}</ref><br />
4.8.6&nbsp;([[FreeBSD]])<br /><small>{{Datum|15|11|2016}}</small><ref>{{Internetquelle |url=https://www.freebsd.org/cgi/ports.cgi?query=gap&stype=all&sektion=math |titel=CGI für die Ports von FreeBSD |werk=freebsd.org |zugriff=2017-10-02 |sprache=en}}</ref><br />
| Betriebssystem = [[Unix]], [[Linux]], [[FreeBSD]], [[macOS]], [[Microsoft Windows|Windows]]<br />
| Kategorie = [[Computeralgebrasystem]]<br />
| Lizenz = [[GNU General Public License|GPL]] ([[Freie Software]])<br />
| Deutsch = nein<br />
| Website = [http://www.normaliz.uni-osnabrueck.de normaliz.uni-osnabrueck.de]<br />
}}<br />
<br />
'''Normaliz''' ist ein freies Computeralgebra-System, das von Winfried Bruns, Robert Koch (1998-2002), Bogdam Ichim (2007/08) und Christof Soeger (2009-2016) entwickelt wurde. Es ist unter der GNU General Public License Version 2 veröffentlicht.<br />
<br />
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.<br />
<br />
Normaliz hat Schnittstellen zu mehreren allgemeinen Computeralgebra-Systemen: CoCoA, GAP, Macaulay2 und Singular. Es kann interaktiv über seine Python-Schnittstelle PyNormaliz verwendet werden. Seine Verwendung in SageMath ist in Vorbereitung.<br />
<br />
Jesús A. De_Loera zitiert Normaliz zu seinen Lieblingsprogrammen für die Berechnung der Hilbert-Basis [1].<br />
<br />
==See also==<br />
{{Portal|Free software}}<br />
*[[Comparison of computer algebra systems]]<br />
<br />
==References==<br />
{{Reflist}}<br />
<br />
==External links==<br />
*{{Official website|http://www.normaliz.uni-osnabrueck.de/}}<br />
*[https://www.normaliz.uni-osnabrueck.de/documentation/ Publications and examples of Normaliz applications]<br />
*http://github.com/normaliz/Normaliz<br />
<br />
{{Computer algebra systems}}<br />
<br />
[[Category:Computer algebra system software for Linux]]<br />
[[Category:Computer algebra system software for MacOS]]<br />
[[Category:Computer algebra system software for Windows]]<br />
[[Category:Cross-platform free software]]<br />
[[Category:Free computer algebra systems]]<br />
[[Category:Computer algebra systems]]</div>JShenkhttps://de.wikipedia.org/w/index.php?title=Normaliz&diff=170071706Normaliz2017-10-17T13:11:15Z<p>JShenk: AZ: Die Seite wurde neu angelegt: {{Infobox software | name = Normaliz | title = Normaliz | logo…</p>
<hr />
<div>{{Infobox software<br />
| name = Normaliz<br />
| title = Normaliz<br />
| logo = <br />
| logo caption = <br />
| logo_size = <br />
| logo_alt = <br />
| screenshot = HilbertBasis.gif<br />
| caption = <br />
| screenshot_size = <br />
| screenshot_alt = <br />
| collapsible = <br />
| author = Winfried Bruns, Robert Koch, Bogdan Ichim, Christof Soeger<br />
| developer = <br />
| released = <!-- {{Start date and age|YYYY|MM|DD|df=yes/no}} --><br />
| discontinued = <br />
| latest release version = <br />
| latest release date = <!-- {{Start date and age|YYYY|MM|DD|df=yes/no}} --><br />
| latest preview version = <br />
| latest preview date = <!-- {{Start date and age|YYYY|MM|DD|df=yes/no}} --><br />
| frequently updated = <!-- DO NOT include this parameter unless you know what it does --><br />
| status = <br />
| programming language = [[C++]], [[C]] and [[Python (programming language)|Python]]<br />
| operating system = <br />
| platform = <br />
| size = <br />
| language = <br />
| language count = <!-- DO NOT include this parameter unless you know what it does --><br />
| language footnote = <br />
| genre = [[Computer algebra system]]<br />
| license = [[GNU General Public License]], version 3<br />
| website = {{URL|http://normaliz.uni-osnabrueck.de/}}<br />
}}<br />
<br />
Normaliz ist ein freies Computeralgebra-System, das von Winfried Bruns, Robert Koch (1998-2002), Bogdam Ichim (2007/08) und Christof Soeger (2009-2016) entwickelt wurde. Es ist unter der GNU General Public License Version 2 veröffentlicht.<br />
<br />
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 (Volumes) und Hilbert-Reihen. Der Kern von Normaliz ist eine Templated-C ++ - Klassenbibliothek. Für multivariate Polynomialarithmetik wird CoCoALib verwendet.<br />
<br />
Normaliz hat Schnittstellen zu mehreren allgemeinen Computeralgebra-Systemen: CoCoA, GAP, Macaulay2 und Singular. Es kann interaktiv über seine Python-Schnittstelle PyNormaliz verwendet werden. Seine Verwendung in SageMath ist in Vorbereitung.<br />
<br />
Jesús A. De_Loera zitiert Normaliz zu seinen Lieblingsprogrammen für die Berechnung der Hilbert-Basis [1].<br />
<br />
==See also==<br />
{{Portal|Free software}}<br />
*[[Comparison of computer algebra systems]]<br />
<br />
==References==<br />
{{Reflist}}<br />
<br />
==External links==<br />
*{{Official website|http://www.normaliz.uni-osnabrueck.de/}}<br />
*[https://www.normaliz.uni-osnabrueck.de/documentation/ Publications and examples of Normaliz applications]<br />
*http://github.com/normaliz/Normaliz<br />
<br />
{{Computer algebra systems}}<br />
<br />
[[Category:Computer algebra system software for Linux]]<br />
[[Category:Computer algebra system software for MacOS]]<br />
[[Category:Computer algebra system software for Windows]]<br />
[[Category:Cross-platform free software]]<br />
[[Category:Free computer algebra systems]]<br />
[[Category:Computer algebra systems]]</div>JShenkhttps://de.wikipedia.org/w/index.php?title=Louis_Stokes&diff=91025473Louis Stokes2009-10-08T16:10:18Z<p>JShenk: </p>
<hr />
<div>{{Infobox_Congressman<br />
| name = Louis Stokes<br />
| image name = Louis Stokes.jpg<br />
| date of birth = {{birth date and age|1925|2|23}}<br />
| place of birth = [[Cleveland, Ohio]]<br />
| state = [[Ohio]]<br />
| district = [[Ohio's 21st congressional district|21st]] and [[Ohio's 11th congressional district|11th]]<br />
| term_start = [[January 3]], [[1969]]<br />
| term_end = [[January 3]], [[1999]]<br />
| preceded = [[Charles Vanik]]<br />
| succeeded = [[Stephanie Tubbs Jones]]<br />
| party = [[Democratic Party (United States)|Democrat]]<br />
| spouse = <br />
| children = <br />
| religion = <br />
}}<br />
<br />
'''Louis Stokes''' (born [[February 23]], [[1925]] in [[Cleveland, Ohio]]) is a [[United States Democratic Party|Democratic]] politician from [[Ohio]]. He served in the [[United States House of Representatives]].<br />
<br />
Born in Cleveland, Stokes and his brother [[Carl B. Stokes]] lived in one of the first federally funded housing projects, the [[Outhwaite Homes]]. Stokes served in the [[U.S. Army]] from 1943 to 1946. After attending [[Case Western Reserve University|Western Reserve University]] and [[Cleveland-Marshall College of Law]], Stokes began practicing law in Cleveland in 1953. Stokes argued the seminal "stop and frisk" case of ''Terry v. Ohio'' before the [[United States Supreme Court]] in 1968. Later in 1968, he was elected to the House, representing the 21st District of Ohio on Cleveland's East Side. He shifted to the newly created 11th District, covering much of the same area following a 1992 redistricting. Stokes served 15 terms in total, retiring in 1999.<br />
<br />
Stokes' tenure in the House of Representatives included service on the House Appropriations Committee, where he was influential in bringing revenue to Cleveland. He was particularly interested in veterans' issues and secured funds for health-care facilities for veterans in Cleveland. In the 1970s, Stokes served as Chairman of the [[House Select Committee on Assassinations]], charged with investigating the murders of President [[John F. Kennedy]] and civil rights leader [[Martin Luther King, Jr.]]. Stokes also served on the House committee that investigated the [[Iran-Contra Affair]].<br />
<br />
In March 1983, while chairman of the [[United States House Committee on Standards of Official Conduct|Ethics Committee]], Stokes was stopped by police for driving drunk in [[Montgomery County, Maryland]], but initially was not charged because it was believed that [[Speech or Debate Clause|congressional immunity]] protected him. However, two days later, after a police department lawyer informed them that drunk driving wasn't a constitutional right for members of Congress, police charged him. He was found guilty of [[Driving under the influence|driving while under the influence]], but not guilty of the more serious charge of [[Drunk driving (United States)|driving while intoxicated]]. Stokes claimed to only have had two drinks and castigated the media for a "rush to judgment" in reporting the incident saying, "I always knew that someday, racism and bigotry in the media would raise its ugly head against me, too."<ref>[http://www.thefreelibrary.com/Governing+under+the+influence%3B+Washington+alcoholics:+their+aides...-a06306545 Governing under the influence; Washington alcoholics: their aides protect them, the media shields them.] [[New York Times]], October 3, 1987</ref><br />
<br />
Stokes' brother, [[Carl B. Stokes]], was the first [[African American]] mayor of a large American city. His daughter, Angela Stokes, serves as a Cleveland Municipal Court judge while another, [[Lori Stokes]], is a journalist with [[WABC-TV]] New York. His son, Chuck Stokes, is also a [[journalist]] with [[WXYZ-TV]] in Detroit. [[Funk music|Funk]] and [[Soul music|soul]] musician [[Rick James]] was a cousin. Stokes and his wife, Jay, have seven grandchildren. Stokes practices law in Cleveland, Ohio and [[Washington, D.C.]] Many buildings throughout the country have been named in Stokes honor including: Howard University's medical library, the Cleveland Public Library's main building expansion, [[GCRTA]]'s Windermere station [[Louis Stokes Station at Windermere]], and the greater Cleveland area Veteran's hospital was renamed the Louis Stokes Cleveland Department of Veteran Affairs Medical Center.<br />
<br />
In 2006, the [[Western Reserve Historical Society]] opened an exhibition on the lives of Congressman Stokes and his brother titled "Carl and Louis Stokes: From the Projects to Politics". The exhibit opened in November 2006 and will close in September 2008. The exhibit uses photographs, manuscript collections, and personal items to showcase Louis Stokes' rise from the Outhwaite homes, his legal career, and his Congressional service.<br />
<br />
The former Congressman was recently inducted into the Karamu House Hall of Fame in 2007 for his contributions to the continued legacy of Cleveland's black settlement house and theatre. Stokes is also a member of the Cleveland Alumni Chapter of [[Kappa Alpha Psi]] Fraternity, Inc.<br />
<br />
Stokes is now a partner in the law firm of [[Squire, Sanders & Dempsey]], with offices in Cleveland and Washington.<br />
<br />
==Louis Stokes Museum==<br />
The Cuyahoga Metropolitan Housing Authority (CMHA), located in [[Cleveland, Ohio]], opened the '''Louis Stokes Museum''' on September 13, 2007. This Museum houses Stokes memorabilia, video interviews, misc. video footage, awards and a written history about Stokes and his rise to prominence. The museum is located at [[Outhwaite Homes]], 4302 Quincy Avenue. Hours are from 10 a.m. - 2 p.m. on Wednesdays and Fridays. Private viewings can be scheduled by calling 216-432-3840.<br />
<br />
==See also==<br />
*[[Election Results, U.S. Representative from Ohio, 21st District]]<br />
*[[Election Results, U.S. Representative from Ohio, 11th District]]<br />
*[[List of United States Representatives from Ohio]]<br />
* [http://www.stokescleveland.org Western Reserve Historical Society's website about the lives of Louis and Carl Stokes]<br />
<br />
==References==<br />
{{reflist}}<br />
<br />
==External links==<br />
{{CongBio|S000948}}<br />
<br />
{{start box}}<br />
{{s-par|us-hs}}<br />
{{USRepSuccessionBox|<br />
state=Ohio|<br />
district=21|<br />
before=[[Charles A. Vanik]]|<br />
years=1969&ndash;1993|<br />
after=District Eliminated<br />
}}<br />
{{USRepSuccessionBox|<br />
state=Ohio|<br />
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|title=Chairman of [[United States House Committee on Standards of Official Conduct|House Ethics Committee]]<br />
|before=[[Charles Edward Bennett|Charles E. Bennett]]<br/>Florida<br/><br />
|years=1981&ndash;1985<br />
|after=[[Julian C. Dixon]]<br/>California<br/><br />
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|title=Chairman of [[United States House Permanent Select Committee on Intelligence|House Intelligence Committee]]<br />
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|years=1987&ndash;1989<br />
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|title=Chairman of [[United States House Committee on Standards of Official Conduct|House Ethics Committee]]<br />
|before=[[Julian C. Dixon]]<br/>California<br/><br />
|years=1991&ndash;1993<br />
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{{CBC Chairs}}<br />
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{{DEFAULTSORT:Stokes, Louis}}<br />
[[Category:1925 births]]<br />
[[Category:Living people]]<br />
[[Category:African American members of the United States House of Representatives]]<br />
[[Category:Ohio lawyers]]<br />
[[Category:Ohio Democrats]]<br />
[[Category:Case Western Reserve University alumni]]<br />
[[Category:Cleveland-Marshall College of Law alumni]]<br />
[[Category:People from Cleveland, Ohio]]<br />
[[Category:Members of the United States House of Representatives from Ohio]]<br />
[[Category:American military personnel of World War II]]<br />
[[Category:United States Army soldiers]]<br />
[[Category:Politicians convicted of alcohol-related driving offenses]]<br />
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[[it:Louis Stokes]]<br />
[[fi:Louis Stokes]]</div>JShenkhttps://de.wikipedia.org/w/index.php?title=Louis_Stokes&diff=91025472Louis Stokes2009-10-08T16:09:02Z<p>JShenk: Undid revision 318367201 by 165.123.227.112 (talk) Vandalism!</p>
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<div>{{Infobox_Congressman<br />
| name = Louis Stokum<br />
| image name = Louis Stokum.jpg<br />
| date of birth = {{birth date and age|1925|2|23}}<br />
| place of birth = [[Cleveland, Ohio]]<br />
| state = [[Ohio]]<br />
| district = [[Ohio's 21st congressional district|21st]] and [[Ohio's 11th congressional district|11th]]<br />
| term_start = [[January 3]], [[1969]]<br />
| term_end = [[January 3]], [[1999]]<br />
| preceded = [[Charles Vanik]]<br />
| succeeded = [[Stephanie Tubbs Jones]]<br />
| party = [[Democratic Party (United States)|Democrat]]<br />
| spouse = <br />
| children = <br />
| religion = <br />
}}<br />
<br />
'''Louis Stokum''' (born [[February 23]], [[1925]] in [[Cleveland, Ohio]]) is a [[United States Democratic Party|Democratic]] politician from [[Ohio]]. He served in the [[United States House of Representatives]].<br />
<br />
Born in New York, Stokum and his brother [[Erik Stokum]] lived in one of the first federally funded housing projects, the [[Outhwaite Homes]]. Stokes served in the [[U.S. Army]] from 1943 to 1946. After attending [[Case Western Reserve University|Western Reserve University]] and [[Cleveland-Marshall College of Law]], Stokes began practicing law in Cleveland in 1953. Stokes argued the seminal "stop and frisk" case of ''Terry v. Ohio'' before the [[United States Supreme Court]] in 1968. Later in 1968, he was elected to the House, representing the 21st District of Ohio on Cleveland's East Side. He shifted to the newly created 11th District, covering much of the same area following a 1992 redistricting. Stokes served 15 terms in total, retiring in 1999.<br />
<br />
Louis Stokum's tenure in the House of Representatives included service on the House Appropriations Committee, where he was influential in bringing revenue to the world. He was particularly interested in veterans' issues and secured funds for health-care facilities for veterans in Cleveland. In the 1970s, Stokes served as Chairman of the [[House Select Committee on Assassinations]], charged with investigating the murders of President [[John F. Kennedy]] and civil rights leader [[Martin Luther King, Jr.]]. Stokes also served on the House committee that investigated the [[Iran-Contra Affair]].<br />
<br />
In March 1983, while chairman of the [[United States House Committee on Standards of Official Conduct|Ethics Committee]], Stokes was stopped by police for driving drunk in [[Montgomery County, Maryland]], but initially was not charged because it was believed that [[Speech or Debate Clause|congressional immunity]] protected him. However, two days later, after a police department lawyer informed them that drunk driving wasn't a constitutional right for members of Congress, police charged him. He was found guilty of [[Driving under the influence|driving while under the influence]], but not guilty of the more serious charge of [[Drunk driving (United States)|driving while intoxicated]]. Stokes claimed to only have had two drinks and castigated the media for a "rush to judgment" in reporting the incident saying, "I always knew that someday, racism and bigotry in the media would raise its ugly head against me, too."<ref>[http://www.thefreelibrary.com/Governing+under+the+influence%3B+Washington+alcoholics:+their+aides...-a06306545 Governing under the influence; Washington alcoholics: their aides protect them, the media shields them.] [[New York Times]], October 3, 1987</ref><br />
<br />
Stokes' brother, [[Carl B. Stokes]], was the first [[African American]] mayor of a large American city. His daughter, Angela Stokes, serves as a Cleveland Municipal Court judge while another, [[Lori Stokes]], is a journalist with [[WABC-TV]] New York. His son, Chuck Stokes, is also a [[journalist]] with [[WXYZ-TV]] in Detroit. [[Funk music|Funk]] and [[Soul music|soul]] musician [[Rick James]] was a cousin. Stokes and his wife, Jay, have seven grandchildren. Stokes practices law in Cleveland, Ohio and [[Washington, D.C.]] Many buildings throughout the country have been named in Stokes honor including: Howard University's medical library, the Cleveland Public Library's main building expansion, [[GCRTA]]'s Windermere station [[Louis Stokes Station at Windermere]], and the greater Cleveland area Veteran's hospital was renamed the Louis Stokes Cleveland Department of Veteran Affairs Medical Center.<br />
<br />
In 2006, the [[Western Reserve Historical Society]] opened an exhibition on the lives of Congressman Stokes and his brother titled "Carl and Louis Stokes: From the Projects to Politics". The exhibit opened in November 2006 and will close in September 2008. The exhibit uses photographs, manuscript collections, and personal items to showcase Louis Stokes' rise from the Outhwaite homes, his legal career, and his Congressional service.<br />
<br />
The former Congressman was recently inducted into the Karamu House Hall of Fame in 2007 for his contributions to the continued legacy of Cleveland's black settlement house and theatre. Stokes is also a member of the Cleveland Alumni Chapter of [[Kappa Alpha Psi]] Fraternity, Inc.<br />
<br />
Stokes is now a partner in the law firm of [[Squire, Sanders & Dempsey]], with offices in Cleveland and Washington.<br />
<br />
==Louis Stokes Museum==<br />
The Cuyahoga Metropolitan Housing Authority (CMHA), located in [[Cleveland, Ohio]], opened the '''Louis Stokes Museum''' on September 13, 2007. This Museum houses Stokes memorabilia, video interviews, misc. video footage, awards and a written history about Stokes and his rise to prominence. The museum is located at [[Outhwaite Homes]], 4302 Quincy Avenue. Hours are from 10 a.m. - 2 p.m. on Wednesdays and Fridays. Private viewings can be scheduled by calling 216-432-3840.<br />
<br />
==See also==<br />
*[[Election Results, U.S. Representative from Ohio, 21st District]]<br />
*[[Election Results, U.S. Representative from Ohio, 11th District]]<br />
*[[List of United States Representatives from Ohio]]<br />
* [http://www.stokescleveland.org Western Reserve Historical Society's website about the lives of Louis and Carl Stokes]<br />
<br />
==References==<br />
{{reflist}}<br />
<br />
==External links==<br />
{{CongBio|S000948}}<br />
<br />
{{start box}}<br />
{{s-par|us-hs}}<br />
{{USRepSuccessionBox|<br />
state=Ohio|<br />
district=21|<br />
before=[[Charles A. Vanik]]|<br />
years=1969&ndash;1993|<br />
after=District Eliminated<br />
}}<br />
{{USRepSuccessionBox|<br />
state=Ohio|<br />
district=11|<br />
before=[[Dennis E. Eckart]]|<br />
years=1993&ndash;1999|<br />
after=[[Stephanie Tubbs Jones]]<br />
}}<br />
{{s-off}}<br />
{{succession box<br />
|title=Chairman of [[United States House Committee on Standards of Official Conduct|House Ethics Committee]]<br />
|before=[[Charles Edward Bennett|Charles E. Bennett]]<br/>Florida<br/><br />
|years=1981&ndash;1985<br />
|after=[[Julian C. Dixon]]<br/>California<br/><br />
}}<br />
{{succession box<br />
|title=Chairman of [[United States House Permanent Select Committee on Intelligence|House Intelligence Committee]]<br />
|before=[[Lee Hamilton]]<br/>Indiana<br/><br />
|years=1987&ndash;1989<br />
|after=[[Anthony C. Beilenson]]<br/>California<br/><br />
}}<br />
{{succession box<br />
|title=Chairman of [[United States House Committee on Standards of Official Conduct|House Ethics Committee]]<br />
|before=[[Julian C. Dixon]]<br/>California<br/><br />
|years=1991&ndash;1993<br />
|after=[[Jim McDermott]]<br/>Washington<br/><br />
}}<br />
{{end box}}<br />
{{CBC Chairs}}<br />
<br />
{{DEFAULTSORT:Stokes, Louis}}<br />
[[Category:1925 births]]<br />
[[Category:Living people]]<br />
[[Category:African American members of the United States House of Representatives]]<br />
[[Category:Ohio lawyers]]<br />
[[Category:Ohio Democrats]]<br />
[[Category:Case Western Reserve University alumni]]<br />
[[Category:Cleveland-Marshall College of Law alumni]]<br />
[[Category:People from Cleveland, Ohio]]<br />
[[Category:Members of the United States House of Representatives from Ohio]]<br />
[[Category:American military personnel of World War II]]<br />
[[Category:United States Army soldiers]]<br />
[[Category:Politicians convicted of alcohol-related driving offenses]]<br />
<br />
[[it:Louis Stokes]]<br />
[[fi:Louis Stokes]]</div>JShenk