CoCalc -- Matrices.xml

GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
gap4r8 / pkg / MatricesForHomalg-2018.01.07 / doc / Matrices.xml
⁵⁶³⁵⁰¹ views
1
<?xml version="1.0" encoding="UTF-8"?>
2

3
<!-- 
4

5
  Matrices.xml            MatricesForHomalg package documentation            Mohamed Barakat
6

7
         Copyright (C) 2007-2009, Mohamed Barakat, RWTH-Aachen
8

9
-->
10

11
<Chapter Label="Matrices">
12
<Heading>Matrices</Heading>
13

14
<Section Label="Matrices:Category">
15
<Heading>Matrices: Category and Representations</Heading>
16

17
<#Include Label="IsHomalgMatrix">
18

19
<#Include Label="IsHomalgInternalMatrixRep">
20

21
</Section>
22

23
<Section Label="Matrices:Constructors">
24
<Heading>Matrices: Constructors</Heading>
25

26
<#Include Label="HomalgInitialMatrix">
27
<#Include Label="HomalgInitialIdentityMatrix">
28
<#Include Label="HomalgZeroMatrix">
29
<#Include Label="HomalgIdentityMatrix">
30
<#Include Label="HomalgVoidMatrix">
31
<#Include Label="HomalgMatrix">
32
<#Include Label="HomalgDiagonalMatrix">
33
<#Include Label="\*:MatrixBaseChange">
34

35
</Section>
36

37
<Section Label="Matrices:Properties">
38
<Heading>Matrices: Properties</Heading>
39

40
<#Include Label="IsZero:matrix">
41
<#Include Label="IsOne:matrix">
42
<#Include Label="IsUnitFree">
43
<#Include Label="IsPermutationMatrix">
44
<#Include Label="IsSpecialSubidentityMatrix">
45
<#Include Label="IsSubidentityMatrix">
46
<#Include Label="IsLeftRegular">
47
<#Include Label="IsRightRegular">
48
<#Include Label="IsInvertibleMatrix">
49
<#Include Label="IsLeftInvertibleMatrix">
50
<#Include Label="IsRightInvertibleMatrix">
51
<#Include Label="IsEmptyMatrix">
52
<#Include Label="IsDiagonalMatrix">
53
<#Include Label="IsScalarMatrix">
54
<#Include Label="IsUpperTriangularMatrix">
55
<#Include Label="IsLowerTriangularMatrix">
56
<#Include Label="IsStrictUpperTriangularMatrix">
57
<#Include Label="IsStrictLowerTriangularMatrix">
58
<#Include Label="IsUpperStairCaseMatrix">
59
<#Include Label="IsLowerStairCaseMatrix">
60
<#Include Label="IsTriangularMatrix">
61
<#Include Label="IsBasisOfRowsMatrix">
62
<#Include Label="IsBasisOfColumnsMatrix">
63
<#Include Label="IsReducedBasisOfRowsMatrix">
64
<#Include Label="IsReducedBasisOfColumnsMatrix">
65
<#Include Label="IsInitialMatrix">
66
<#Include Label="IsInitialIdentityMatrix">
67
<#Include Label="IsVoidMatrix">
68

69
</Section>
70

71
<Section Label="Matrices:Attributes">
72
<Heading>Matrices: Attributes</Heading>
73

74
<#Include Label="NrRows">
75
<#Include Label="NrColumns">
76
<#Include Label="DeterminantMat">
77
<#Include Label="ZeroRows">
78
<#Include Label="ZeroColumns">
79
<#Include Label="NonZeroRows">
80
<#Include Label="NonZeroColumns">
81
<#Include Label="PositionOfFirstNonZeroEntryPerRow">
82
<#Include Label="PositionOfFirstNonZeroEntryPerColumn">
83
<#Include Label="RowRankOfMatrix">
84
<#Include Label="ColumnRankOfMatrix">
85
<#Include Label="LeftInverse">
86
<#Include Label="RightInverse">
87

88
<#Include Label="CoefficientsOfUnreducedNumeratorOfHilbertPoincareSeries">
89
<#Include Label="CoefficientsOfNumeratorOfHilbertPoincareSeries">
90
<#Include Label="UnreducedNumeratorOfHilbertPoincareSeries">
91
<#Include Label="NumeratorOfHilbertPoincareSeries">
92
<#Include Label="HilbertPoincareSeries">
93
<#Include Label="HilbertPolynomial">
94
<#Include Label="AffineDimension">
95
<#Include Label="AffineDegree">
96
<#Include Label="ProjectiveDegree">
97
<#Include Label="ConstantTermOfHilbertPolynomial">
98
<#Include Label="MatrixOfSymbols">
99

100
</Section>
101

102
<Section Label="Matrices:Operations">
103
<Heading>Matrices: Operations and Functions</Heading>
104

105
<#Include Label="HomalgRing:matrix">
106

107
<#Include Label="LeftInverse:method">
108
<#Include Label="RightInverse:method">
109

110
<#Include Label="LeftInverseLazy">
111
<#Include Label="RightInverseLazy">
112

113
<#Include Label="Involution">
114
<#Include Label="CertainRows">
115
<#Include Label="CertainColumns">
116
<#Include Label="UnionOfRows">
117
<#Include Label="UnionOfColumns">
118
<#Include Label="DiagMat">
119
<#Include Label="KroneckerMat">
120
<#Include Label="MulMat">
121
<#Include Label="AddMat">
122
<#Include Label="SubMat">
123
<#Include Label="Compose:matrix">
124

125
<#Include Label="EQ:matrix">
126

127
<#Include Label="GetColumnIndependentUnitPositions">
128
<#Include Label="GetRowIndependentUnitPositions">
129
<#Include Label="GetUnitPosition">
130
<#Include Label="Eliminate">
131

132
<#Include Label="BasisOfRowModule">
133
<#Include Label="BasisOfColumnModule">
134
<#Include Label="DecideZeroRows">
135
<#Include Label="DecideZeroColumns">
136
<#Include Label="SyzygiesGeneratorsOfRows">
137
<#Include Label="SyzygiesGeneratorsOfColumns">
138

139
<#Include Label="RelativeSyzygiesGeneratorsOfRows">
140
<#Include Label="RelativeSyzygiesGeneratorsOfColumns">
141

142
<#Include Label="ReducedBasisOfRowModule">
143
<#Include Label="ReducedBasisOfColumnModule">
144
<#Include Label="ReducedSyzygiesGeneratorsOfRows">
145
<#Include Label="ReducedSyzygiesGeneratorsOfColumns">
146

147
<#Include Label="BasisOfRowsCoeff">
148
<#Include Label="BasisOfColumnsCoeff">
149
<#Include Label="DecideZeroRowsEffectively">
150
<#Include Label="DecideZeroColumnsEffectively">
151

152
<#Include Label="BasisOfRows">
153
<#Include Label="BasisOfColumns">
154
<#Include Label="DecideZero:matrix_rel">
155
<#Include Label="SyzygiesOfRows">
156
<#Include Label="SyzygiesOfColumns">
157

158
<#Include Label="ReducedSyzygiesOfRows">
159
<#Include Label="ReducedSyzygiesOfColumns">
160

161
<#Include Label="RightDivide">
162
<#Include Label="LeftDivide">
163
<#Include Label="RelativeRightDivide">
164
<#Include Label="RelativeLeftDivide">
165

166
<#Include Label="GenerateSameRowModule">
167
<#Include Label="GenerateSameColumnModule">
168

169
</Section>
170

171
<!-- ############################################################ -->
172

173
</Chapter>
174

175
Product

Resources

Company
