The Matrix Tool Operations

The functions listed below are components of the homalgTable object stored in the ring. They are only indirectly accessible through standard methods that invoke them.

The Tool Operations without a Fallback Method

There are matrix methods for which &homalg; needs a homalgTable entry for non-internal rings, as it cannot provide a suitable fallback. Below is the list of these homalgTable entries.

<#Include Label="InitialMatrix:homalgTable_entry"> <#Include Label="InitialIdentityMatrix:homalgTable_entry">

<#Include Label="ZeroMatrix:homalgTable_entry"> <#Include Label="IdentityMatrix:homalgTable_entry">

<#Include Label="Involution:homalgTable_entry"> <#Include Label="CertainRows:homalgTable_entry"> <#Include Label="CertainColumns:homalgTable_entry"> <#Include Label="UnionOfRows:homalgTable_entry"> <#Include Label="UnionOfColumns:homalgTable_entry"> <#Include Label="DiagMat:homalgTable_entry"> <#Include Label="KroneckerMat:homalgTable_entry"> <#Include Label="MulMat:homalgTable_entry"> <#Include Label="AddMat:homalgTable_entry"> <#Include Label="SubMat:homalgTable_entry"> <#Include Label="Compose:homalgTable_entry">

<#Include Label="IsZeroMatrix:homalgTable_entry"> <#Include Label="NrRows:homalgTable_entry"> <#Include Label="NrColumns:homalgTable_entry"> <#Include Label="Determinant:homalgTable_entry">

The Tool Operations with a Fallback Method

These are the methods for which it is recommended for performance reasons to have a homalgTable entry for non-internal rings. &homalg; only provides a generic fallback method.

<#Include Label="AreEqualMatrices:homalgTable_entry"> <#Include Label="IsIdentityMatrix:homalgTable_entry"> <#Include Label="IsDiagonalMatrix:homalgTable_entry">

<#Include Label="ZeroRows:homalgTable_entry"> <#Include Label="ZeroColumns:homalgTable_entry">

<#Include Label="GetColumnIndependentUnitPositions:homalgTable_entry"> <#Include Label="GetRowIndependentUnitPositions:homalgTable_entry"> <#Include Label="GetUnitPosition:homalgTable_entry">

<#Include Label="DegreesOfEntries:homalgTable_entry">