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LessGenerators

Find smaller generating sets for modules

2022.07-01

5 July 2022

Mohamed Barakat
Email: mohamed.barakat@uni-siegen.de
Homepage: https://mohamed-barakat.github.io/
Address:
Walter-Flex-Str. 3
57068 Siegen
Germany

Anna Fabiańska
Email: fabianska@momo.math.rwth-aachen.de
Homepage: http://wwwb.math.rwth-aachen.de/~fabianska/
Address:
Lehrstuhl B fuer Mathematik, RWTH Aachen
Templergraben 64
52062 Aachen
Germany

Vinay Wagh
Email: waghoba@gmail.com
Homepage: http://www.iitg.ernet.in/vinay.wagh/
Address:
E-102, Department of Mathematics,
Indian Institute of Technology Guwahati,
Guwahati, Assam, India.
PIN: 781 039.
India

1 Quillen-Suslin

1.1 Tool procedures

  1.1-1 SuslinLemma
  1.1-2 SuslinLemma
  1.1-3 Horrocks
  1.1-4 Patch

1.2 Main procedures

1.2-1 QuillenSuslinUnipotent
1.2-2 QuillenSuslin

2 Tools

2.1 Tools for matrices

  2.1-1 EliminateIfRowObsoleteForUnimodularityAsRightInverse
  2.1-2 EliminateUnitInAColumnAsRightInverse
  2.1-3 EliminateUnimodularPairPositionPerColumnAsRightInverse

2.2 Tools for rows

  2.2-1 GetFirstMonicOfSmallestDegreeInRow
  2.2-2 CleanRowUsingMonicUptoUnit
  2.2-3 GetObsoleteColumnForUnimodularity
  2.2-4 GetObsoleteColumnForUnimodularity
  2.2-5 GetObsoleteColumnForUnimodularity
  2.2-6 EliminateIfColumnObsoleteForUnimodularity
  2.2-7 GetUnimodularPairPositionPerRow
  2.2-8 EliminateUnimodularPairPositionPerRow
  2.2-9 EliminateUnitInARow

2.3 Tools for columns

  2.3-1 GetFirstMonicOfSmallestDegreeInColumn
  2.3-2 CleanColumnUsingMonicUptoUnit
  2.3-3 GetObsoleteRowForUnimodularity
  2.3-4 GetObsoleteRowForUnimodularity
  2.3-5 GetObsoleteRowForUnimodularity
  2.3-6 EliminateIfRowObsoleteForUnimodularity
  2.3-7 GetUnimodularPairPositionPerColumn
  2.3-8 EliminateUnimodularPairPositionPerColumn
  2.3-9 EliminateUnitInAColumn

References

Index

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