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MatricesForHomalg

Matrices for the homalg project

Version 2015.11.06

June 2015

(this manual is still under construction)

This manual is best viewed as an HTML document. The latest version is available online at:

http://homalg.math.rwth-aachen.de/~barakat/homalg-project/MatricesForHomalg/chap0.html

An offline version should be included in the documentation subfolder of the package. This package is part of the homalg-project:

http://homalg.math.rwth-aachen.de/index.php/core-packages/matricesforhomalg

Mohamed Barakat
Email: barakat@mathematik.uni-kl.de
Homepage: http://www.mathematik.uni-kl.de/~barakat/
Address:
Department of Mathematics,
University of Kaiserslautern,
67653 Kaiserslautern,
Germany

Markus Lange-Hegermann
Email: markus.lange.hegermann@rwth-aachen.de
Homepage: http://wwwb.math.rwth-aachen.de/~markus/
Address:
Lehrstuhl B für Mathematik, RWTH Aachen, Templergraben 64, 52056 Aachen, Germany

Vinay Wagh
Email: waghoba@gmail.com
Homepage: http://www.iitg.ernet.in/vinay.wagh/
Address:
E-102, Department of Mathematics,
Indian Institute of Technology Guwahati,
Guwahati, Assam, India.
PIN: 781 039.

Copyright

© 2007-2015 by Mohamed Barakat and Markus Lange-Hegermann

This package may be distributed under the terms and conditions of the GNU Public License Version 2.

Contents

1 Introduction
2 Installation of the MatricesForHomalg Package
3 Rings
 3.3 Rings: Properties

  3.3-1 IsZero

  3.3-2 ContainsAField

  3.3-3 IsRationalsForHomalg

  3.3-4 IsFieldForHomalg

  3.3-5 IsDivisionRingForHomalg

  3.3-6 IsIntegersForHomalg

  3.3-7 IsResidueClassRingOfTheIntegers

  3.3-8 IsBezoutRing

  3.3-9 IsIntegrallyClosedDomain

  3.3-10 IsUniqueFactorizationDomain

  3.3-11 IsKaplanskyHermite

  3.3-12 IsDedekindDomain

  3.3-13 IsDiscreteValuationRing

  3.3-14 IsFreePolynomialRing

  3.3-15 IsWeylRing

  3.3-16 IsLocalizedWeylRing

  3.3-17 IsGlobalDimensionFinite

  3.3-18 IsLeftGlobalDimensionFinite

  3.3-19 IsRightGlobalDimensionFinite

  3.3-20 HasInvariantBasisProperty

  3.3-21 HasLeftInvariantBasisProperty

  3.3-22 HasRightInvariantBasisProperty

  3.3-23 IsLocal

  3.3-24 IsSemiLocalRing

  3.3-25 IsIntegralDomain

  3.3-26 IsHereditary

  3.3-27 IsLeftHereditary

  3.3-28 IsRightHereditary

  3.3-29 IsHermite

  3.3-30 IsLeftHermite

  3.3-31 IsRightHermite

  3.3-32 IsNoetherian

  3.3-33 IsLeftNoetherian

  3.3-34 IsRightNoetherian

  3.3-35 IsCohenMacaulay

  3.3-36 IsGorenstein

  3.3-37 IsKoszul

  3.3-38 IsArtinian

  3.3-39 IsLeftArtinian

  3.3-40 IsRightArtinian

  3.3-41 IsOreDomain

  3.3-42 IsLeftOreDomain

  3.3-43 IsRightOreDomain

  3.3-44 IsPrincipalIdealRing

  3.3-45 IsLeftPrincipalIdealRing

  3.3-46 IsRightPrincipalIdealRing

  3.3-47 IsRegular

  3.3-48 IsFiniteFreePresentationRing

  3.3-49 IsLeftFiniteFreePresentationRing

  3.3-50 IsRightFiniteFreePresentationRing

  3.3-51 IsSimpleRing

  3.3-52 IsSemiSimpleRing

  3.3-53 IsSuperCommutative

  3.3-54 BasisAlgorithmRespectsPrincipalIdeals

  3.3-55 AreUnitsCentral

  3.3-56 IsMinusOne

  3.3-57 IsMonic

  3.3-58 IsMonicUptoUnit

  3.3-59 IsLeftRegular

  3.3-60 IsRightRegular

  3.3-61 IsRegular
4 Ring Maps
5 Matrices
6 Ring Relations
A The Basic Matrix Operations
B The Matrix Tool Operations
C Logic Subpackages
D The subpackage ResidueClassRingForHomalg as a sample ring package
E Debugging MatricesForHomalg
F Overview of the MatricesForHomalg Package Source Code
References
Index

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