GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
12[1X The [5XGauss[105X Package Manual[101X345[1XExtended Gauss Functionality for [5XGAP[105X[101X678Version 2017.12.0791011March 2013121314Simon Goertzen15161718Simon Goertzen19Email: [7Xmailto:[email protected][107X20Homepage: [7Xhttp://wwwb.math.rwth-aachen.de/goertzen/[107X21Address: [33X[0;14YLehrstuhl B für Mathematik[133X22[33X[0;14YTemplergraben 64[133X23[33X[0;14Y52062 Aachen[133X24[33X[0;14Y(Germany)[133X25262728-------------------------------------------------------29[1XAbstract[101X30[33X[0;0YThis document explains the primary uses of the [5XGauss[105X package. Included is a31documented list of the most important methods and functions needed to work32with sparse matrices and the algorithms provided by the [5XGauss[105X package.[133X333435-------------------------------------------------------36[1XCopyright[101X37[33X[0;0Y© 2007-2013 by Simon Goertzen[133X3839[33X[0;0YThis package may be distributed under the terms and conditions of the GNU40Public License Version 2.[133X414243-------------------------------------------------------44[1XAcknowledgements[101X45[33X[0;0YThe [5XGauss[105X package would not have been possible without the helpful46contributions by[133X4748[30X [33X[0;6YMax Neunhöffer, University of St Andrews, and[133X4950[30X [33X[0;6YMohamed Barakat, Lehrstuhl B für Mathematik, RWTH Aachen.[133X5152[33X[0;0YMany thanks to these two and the Lehrstuhl B für Mathematik in general. It53should be noted that the [5XGAP[105X algorithms for [10XSemiEchelonForm[110X and other54methods formed an important and informative basis for the development of the55extended Gaussian algorithms. This manual was created with the help of the56[5XGAPDoc[105X package by F. Lübeck and M. Neunhöffer [LN08].[133X575859-------------------------------------------------------606162[1XContents (Gauss)[101X63641 [33X[0;0YIntroduction[133X651.1 [33X[0;0YOverview over this manual[133X661.2 [33X[0;0YInstallation of the [5XGauss[105X Package[133X672 [33X[0;0YExtending Gauss Functionality[133X682.1 [33X[0;0YThe need for extended functionality[133X692.2 [33X[0;0YThe applications of the [5XGauss[105X package algorithms[133X703 [33X[0;0YThe Sparse Matrix Data Type[133X713.1 [33X[0;0YThe inner workings of [5XGauss[105X sparse matrices[133X723.1-1 [33X[0;0YA special case: GF(2)[133X733.2 [33X[0;0YMethods and functions for sparse matrices[133X743.2-1 SparseMatrix753.2-2 ConvertSparseMatrixToMatrix763.2-3 CopyMat773.2-4 GetEntry783.2-5 SetEntry793.2-6 AddToEntry803.2-7 SparseZeroMatrix813.2-8 SparseIdentityMatrix823.2-9 TransposedSparseMat833.2-10 CertainRows843.2-11 CertainColumns853.2-12 UnionOfRows863.2-13 UnionOfColumns873.2-14 SparseDiagMat883.2-15 Nrows893.2-16 Ncols903.2-17 IndicesOfSparseMatrix913.2-18 EntriesOfSparseMatrix923.2-19 RingOfDefinition934 [33X[0;0YGaussian Algorithms[133X944.1 [33X[0;0YA list of the available algorithms[133X954.2 [33X[0;0YMethods and Functions for [5XGauss[105Xian algorithms[133X964.2-1 EchelonMat974.2-2 EchelonMatTransformation984.2-3 ReduceMat994.2-4 ReduceMatTransformation1004.2-5 KernelMat1014.2-6 Rank102A [33X[0;0YAn Overview of the [5XGauss[105X package source code[133X103104105[32X106107108