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
<?xml version="1.0" encoding="UTF-8"?>

2


3
<!-- 

4


5
  Basic.xml            MatricesForHomalg package documentation            Mohamed Barakat

6


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

8


9
-->

10


11
<Appendix Label="Basic_Operations">

12
<Heading>The Basic Matrix Operations</Heading>

13


14
These are the operations used to solve one-sided (in)homogeneous

15
linear systems <M>XA=B</M> resp. <M>AX=B</M>.

16


17
<!--

18
(&see; Appendix <Ref Chap="homalg-Idea"/>)

19
-->

20


21
<Section Label="Main">

22
<Heading>Main</Heading>

23


24
<List>

25
  <Item><Ref Oper="BasisOfRowModule" Label="for matrices"/></Item>

26
  <Item><Ref Oper="BasisOfColumnModule" Label="for matrices"/></Item>

27
</List>

28


29
<List>

30
  <Item><Ref Oper="DecideZeroRows" Label="for pairs of matrices"/></Item>

31
  <Item><Ref Oper="DecideZeroColumns" Label="for pairs of matrices"/></Item>

32
</List>

33


34
<List>

35
  <Item><Ref Oper="SyzygiesGeneratorsOfRows" Label="for matrices"/></Item>

36
  <Item><Ref Oper="SyzygiesGeneratorsOfColumns" Label="for matrices"/></Item>

37
</List>

38


39
</Section>

40


41
<Section Label="Effective">

42
<Heading>Effective</Heading>

43


44
<List>

45
  <Item><Ref Oper="BasisOfRowsCoeff" Label="for matrices"/></Item>

46
  <Item><Ref Oper="BasisOfColumnsCoeff" Label="for matrices"/></Item>

47
</List>

48


49
<List>

50
  <Item><Ref Oper="DecideZeroRowsEffectively" Label="for pairs of matrices"/></Item>

51
  <Item><Ref Oper="DecideZeroColumnsEffectively" Label="for pairs of matrices"/></Item>

52
</List>

53


54
</Section>

55


56
<Section Label="Relative">

57
<Heading>Relative</Heading>

58


59
<List>

60
  <Item><Ref Oper="SyzygiesGeneratorsOfRows" Label="for pairs of matrices"/></Item>

61
  <Item><Ref Oper="SyzygiesGeneratorsOfColumns" Label="for pairs of matrices"/></Item>

62
</List>

63


64
</Section>

65


66
<Section Label="Reduced">

67
<Heading>Reduced</Heading>

68


69
<List>

70
  <Item><Ref Oper="ReducedBasisOfRowModule" Label="for matrices"/></Item>

71
  <Item><Ref Oper="ReducedBasisOfColumnModule" Label="for matrices"/></Item>

72
</List>

73


74
<List>

75
  <Item><Ref Oper="ReducedSyzygiesGeneratorsOfRows" Label="for matrices"/></Item>

76
  <Item><Ref Oper="ReducedSyzygiesGeneratorsOfColumns" Label="for matrices"/></Item>

77
</List>

78


79
</Section>

80


81
<!-- ############################################################ -->

82


83
</Appendix>

84


85


86