Overview of the &GradedRingForHomalg; Package Source Code This appendix is included in the documentation to shine some light on the mathematical backgrounds of this Package. Neither is it needed to work with this package nor should the methods presented here be called directly. The functions documented here are entries of the so called ring table and not to be called directly. There are higher level methods in declared and installed in &MatricesForHomalg;, which call this functions (&see; ?MatricesForHomalg:The Basic Matrix Operations).
The generic Methods We will present some methods as an example, to show the idea: <#Include Label="BasisOfRowModule"> <#Include Label="DecideZeroRows"> <#Include Label="SyzygiesGeneratorsOfRows">
Tools The package &GradedRingForHomalg; also implements tool functions. These are referred to from &MatricesForHomalg; automatically. We list the implemented methods here are and refer to the &MatricesForHomalg; documentation (&see; ?MatricesForHomalg: The Matrix Tool Operations and ?MatricesForHomalg:RingElement) for details. All tools functions from &MatricesForHomalg; not listed here are also supported by fallback tools. IsZero IsOne Minus DivideByUnit IsUnit Sum Product ShallowCopy ZeroMatrix IdentityMatrix AreEqualMatrices Involution TransposedMatrix CertainRows CertainColumns UnionOfRows UnionOfColumns DiagMat KroneckerMat DualKroneckerMat MulMat AddMat SubMat Compose NrRows NrColumns IsZeroMatrix IsDiagonalMatrix ZeroRows ZeroColumns