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MatricesForHomalg

A GAP4 Meta-Package for Homological Algebra

Version 2010.03.19

March 2010

(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/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://wwwb.math.rwth-aachen.de/~barakat/
Address:
Department of Mathematics,
University of Kaiserslautern,
67653 Kaiserslautern,
Germany

Copyright

© 2007-2010 by Mohamed Barakat

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 ContainsAField

  3.3-2 IsRationalsForHomalg

  3.3-3 IsFieldForHomalg

  3.3-4 IsDivisionRingForHomalg

  3.3-5 IsIntegersForHomalg

  3.3-6 IsResidueClassRingOfTheIntegers

  3.3-7 IsBezoutRing

  3.3-8 IsIntegrallyClosedDomain

  3.3-9 IsUniqueFactorizationDomain

  3.3-10 IsKaplanskyHermite

  3.3-11 IsDedekindDomain

  3.3-12 IsDiscreteValuationRing

  3.3-13 IsFreePolynomialRing

  3.3-14 IsWeylRing

  3.3-15 IsGlobalDimensionFinite

  3.3-16 IsLeftGlobalDimensionFinite

  3.3-17 IsRightGlobalDimensionFinite

  3.3-18 HasInvariantBasisProperty

  3.3-19 HasLeftInvariantBasisProperty

  3.3-20 HasRightInvariantBasisProperty

  3.3-21 IsLocalRing

  3.3-22 IsSemiLocalRing

  3.3-23 IsIntegralDomain

  3.3-24 IsHereditary

  3.3-25 IsLeftHereditary

  3.3-26 IsRightHereditary

  3.3-27 IsHermite

  3.3-28 IsLeftHermite

  3.3-29 IsRightHermite

  3.3-30 IsNoetherian

  3.3-31 IsLeftNoetherian

  3.3-32 IsRightNoetherian

  3.3-33 IsArtinian

  3.3-34 IsLeftArtinian

  3.3-35 IsRightArtinian

  3.3-36 IsOreDomain

  3.3-37 IsLeftOreDomain

  3.3-38 IsRightOreDomain

  3.3-39 IsPrincipalIdealRing

  3.3-40 IsLeftPrincipalIdealRing

  3.3-41 IsRightPrincipalIdealRing

  3.3-42 IsRegular

  3.3-43 IsFiniteFreePresentationRing

  3.3-44 IsLeftFiniteFreePresentationRing

  3.3-45 IsRightFiniteFreePresentationRing

  3.3-46 IsSimpleRing

  3.3-47 IsSemiSimpleRing

  3.3-48 BasisAlgorithmRespectsPrincipalIdeals

  3.3-49 IsMinusOne
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

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