Book a Demo!
CoCalc Logo Icon
StoreFeaturesDocsShareSupportNewsAboutPoliciesSign UpSign In
Download

GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

563641 views
1
<?xml version="1.0" encoding="UTF-8"?>
2
3
<!--
4
5
Tools.xml MatricesForHomalg package documentation Mohamed Barakat
6
7
Copyright (C) 2007-2009, Mohamed Barakat, RWTH-Aachen
8
9
-->
10
11
<Appendix Label="Tool_Operations">
12
<Heading>The Matrix Tool Operations</Heading>
13
14
The functions listed below are components of the <C>homalgTable</C>
15
object stored in the ring. They are only indirectly accessible through
16
standard methods that invoke them.
17
18
<Section Label="ToolsNoFallBack">
19
<Heading>The Tool Operations <E>without</E> a Fallback Method</Heading>
20
21
There are matrix methods for which &homalg; needs a
22
<C>homalgTable</C> entry for non-internal rings, as it cannot provide
23
a suitable fallback. Below is the list of these <C>homalgTable</C>
24
entries.
25
26
<#Include Label="InitialMatrix:homalgTable_entry">
27
<#Include Label="InitialIdentityMatrix:homalgTable_entry">
28
29
<#Include Label="ZeroMatrix:homalgTable_entry">
30
<#Include Label="IdentityMatrix:homalgTable_entry">
31
32
<#Include Label="Involution:homalgTable_entry">
33
<#Include Label="CertainRows:homalgTable_entry">
34
<#Include Label="CertainColumns:homalgTable_entry">
35
<#Include Label="UnionOfRows:homalgTable_entry">
36
<#Include Label="UnionOfColumns:homalgTable_entry">
37
<#Include Label="DiagMat:homalgTable_entry">
38
<#Include Label="KroneckerMat:homalgTable_entry">
39
<#Include Label="MulMat:homalgTable_entry">
40
<#Include Label="AddMat:homalgTable_entry">
41
<#Include Label="SubMat:homalgTable_entry">
42
<#Include Label="Compose:homalgTable_entry">
43
44
<#Include Label="IsZeroMatrix:homalgTable_entry">
45
<#Include Label="NrRows:homalgTable_entry">
46
<#Include Label="NrColumns:homalgTable_entry">
47
<#Include Label="Determinant:homalgTable_entry">
48
49
</Section>
50
51
<Section Label="ToolsFallBack">
52
<Heading>The Tool Operations with a Fallback Method</Heading>
53
54
These are the methods for which it is recommended for performance
55
reasons to have a <C>homalgTable</C> entry for non-internal
56
rings. &homalg; only provides a generic fallback method.
57
58
<#Include Label="AreEqualMatrices:homalgTable_entry">
59
<#Include Label="IsIdentityMatrix:homalgTable_entry">
60
<#Include Label="IsDiagonalMatrix:homalgTable_entry">
61
62
<#Include Label="ZeroRows:homalgTable_entry">
63
<#Include Label="ZeroColumns:homalgTable_entry">
64
65
<#Include Label="GetColumnIndependentUnitPositions:homalgTable_entry">
66
<#Include Label="GetRowIndependentUnitPositions:homalgTable_entry">
67
<#Include Label="GetUnitPosition:homalgTable_entry">
68
69
<#Include Label="PositionOfFirstNonZeroEntryPerRow:homalgTable_entry">
70
<#Include Label="PositionOfFirstNonZeroEntryPerColumn:homalgTable_entry">
71
72
</Section>
73
74
<!-- ############################################################ -->
75
76
</Appendix>
77
78
79