CoCalc Logo Icon
StoreFeaturesDocsShareSupportNewsAboutSign UpSign In

Real-time collaboration for Jupyter Notebooks, Linux Terminals, LaTeX, VS Code, R IDE, and more,
all in one place.

| Download

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

Views: 418346
Tweet
Share
Share
1
  

2
  

3
                                 RingsForHomalg

4
  

5
  

6
           Dictionaries of External Rings for the GAP Package homalg

7
  

8
  

9
                               Version 2018.01.07

10
  

11
  

12
                                 September 2015

13
  

14
  

15
                                Mohamed Barakat

16
  

17
                                 Simon Goertzen

18
  

19
                                Markus Kirschmer

20
  

21
                             Markus Lange-Hegermann

22
  

23
                                Oleksandr Motsak

24
  

25
                                 Max Neunhöffer

26
  

27
                                 Daniel Robertz

28
  

29
                                Hans Schönemann

30
  

31
                                Andreas Steenpaß

32
  

33
                                   Vinay Wagh

34
  

35
  

36
  

37
            (this manual is still under construction)

38
            This  manual  is  best  viewed  as an HTML document. The

39
            latest version is available online at:

40
            http://homalg.math.rwth-aachen.de/~barakat/homalg-project/RingsForHomalg/chap0.html

41
            An   offline   version   should   be   included  in  the

42
            documentation  subfolder of the package. This package is

43
            part of the homalg-project:

44
            http://homalg.math.rwth-aachen.de/index.php/core-packages/ringsforhomalg

45
  

46
  

47
  

48
  Mohamed Barakat

49
      Email:    mailto:[email protected]

50
      Homepage: http://www.mathematik.uni-kl.de/~barakat/

51
      Address:  Department of Mathematics,

52
                University of Kaiserslautern,

53
                67653 Kaiserslautern,

54
                Germany

55
  

56
  

57
  Simon Goertzen

58
      Email:    mailto:[email protected]

59
      Homepage: http://wwwb.math.rwth-aachen.de/~simon/

60
      Address:  Lehrstuhl B für Mathematik,

61
                RWTH Aachen,

62
                Templergraben 64,

63
                52056 Aachen,

64
                Germany

65
  

66
  

67
  Markus Kirschmer

68
      Email:    mailto:[email protected]

69
      Homepage: http://www.math.rwth-aachen.de/~Markus.Kirschmer/

70
      Address:  Lehrstuhl D für Mathematik,

71
                RWTH Aachen,

72
                Templergraben 64,

73
                52056 Aachen,

74
                Germany

75
  

76
  

77
  Markus Lange-Hegermann

78
      Email:    mailto:[email protected]

79
      Homepage: http://wwwb.math.rwth-aachen.de/~markus/

80
      Address:  Lehrstuhl B für Mathematik,

81
                RWTH Aachen,

82
                Templergraben 64,

83
                52056 Aachen,

84
                Germany

85
  

86
  

87
  Oleksandr Motsak

88
      Email:    mailto:[email protected]

89
      Homepage: http://www.mathematik.uni-kl.de/~motsak/

90
      Address:  Department of Mathematics,

91
                University of Kaiserslautern,

92
                67653 Kaiserslautern,

93
                Germany

94
  

95
  

96
  Max Neunhöffer

97
      Email:    mailto:[email protected]

98
      Homepage: http://www-groups.mcs.st-and.ac.uk/~neunhoef/

99
      Address:  St Andrews University,

100
                School of Mathematics and Statistics,

101
                Mathematical Institute,

102
                North Haugh,

103
                St Andrews, Fife KY16 9SS,

104
                Scotland, UK

105
  

106
  

107
  Daniel Robertz

108
      Email:    mailto:[email protected]

109
      Homepage: http://wwwb.math.rwth-aachen.de/~daniel

110
      Address:  Lehrstuhl B für Mathematik,

111
                RWTH Aachen,

112
                Templergraben 64,

113
                52056 Aachen,

114
                Germany

115
  

116
  

117
  Hans Schönemann

118
      Email:    mailto:[email protected]

119
      Homepage: http://www.mathematik.uni-kl.de/~hannes/

120
      Address:  Department of Mathematics,

121
                University of Kaiserslautern,

122
                67653 Kaiserslautern,

123
                Germany

124
  

125
  

126
  Andreas Steenpaß

127
      Email:    mailto:[email protected]

128
      Homepage: 

129
      Address:  Department of Mathematics,

130
                University of Kaiserslautern,

131
                67653 Kaiserslautern,

132
                Germany

133
  

134
  

135
  Vinay Wagh

136
      Email:    mailto:[email protected]

137
      Homepage: http://www.iitg.ernet.in/vinay.wagh/

138
      Address:  E-102, Department of Mathematics,

139
                Indian Institute of Technology Guwahati,

140
                Guwahati, Assam, India.

141
                PIN: 781 039.

142
  

143
  

144
  

145
  -------------------------------------------------------

146
  Copyright

147
  ©  2007-2015  by  Mohamed  Barakat,  Simon Görtzen, Markus Kirschmer, Markus

148
  Lange-Hegermann,  Oleksandr Motsak, Max Neunhöffer, Daniel Robertz, and Hans

149
  Schönemann.

150
  

151
  This  package  may  be distributed under the terms and conditions of the GNU

152
  Public License Version 2.

153
  

154
  

155
  -------------------------------------------------------

156
  

157
  

158
  Contents (RingsForHomalg)

159
  

160
  1 Introduction

161
    1.1 Ring Constructions for Supported External Computer Algebra Systems

162
      1.1-1 external GAP

163
      1.1-2 Singular

164
      1.1-3 MAGMA

165
      1.1-4 Macaulay2

166
      1.1-5 Sage

167
      1.1-6 Maple

168
  2 Installation of the RingsForHomalg Package

169
  3 The Ring Table

170
    3.1 An Example for a Ring Table - Singular

171
      3.1-1 BasisOfRowModule

172
      3.1-2 BasisOfRowModule

173
      3.1-3 BasisOfColumnModule

174
      3.1-4 BasisOfColumnModule

175
      3.1-5 DecideZeroRows

176
      3.1-6 DecideZeroRows

177
      3.1-7 DecideZeroColumns

178
      3.1-8 DecideZeroColumns

179
      3.1-9 SyzygiesGeneratorsOfRows

180
      3.1-10 SyzygiesGeneratorsOfRows

181
      3.1-11 SyzygiesGeneratorsOfColumns

182
      3.1-12 SyzygiesGeneratorsOfColumns

183
      3.1-13 BasisOfRowsCoeff

184
      3.1-14 BasisOfRowsCoeff

185
      3.1-15 BasisOfColumnsCoeff

186
      3.1-16 BasisOfColumnsCoeff

187
      3.1-17 DecideZeroRowsEffectively

188
      3.1-18 DecideZeroRowsEffectively

189
      3.1-19 DecideZeroColumnsEffectively

190
      3.1-20 DecideZeroColumnsEffectively

191
      3.1-21 RelativeSyzygiesGeneratorsOfRows

192
      3.1-22 RelativeSyzygiesGeneratorsOfRows

193
      3.1-23 RelativeSyzygiesGeneratorsOfColumns

194
      3.1-24 RelativeSyzygiesGeneratorsOfColumns

195
      3.1-25 ReducedSyzygiesGeneratorsOfRows

196
      3.1-26 ReducedSyzygiesGeneratorsOfRows

197
      3.1-27 ReducedSyzygiesGeneratorsOfColumns

198
      3.1-28 ReducedSyzygiesGeneratorsOfColumns

199
  

200
  

201
  

202


203