MeatAxe swMATH ID: 4906 Software Authors: Michael Ringe Description: The MeatAxe - Computing with Modular Representations. The MeatAxe is a set of programs for working with matrices over finite fields. Its primary purpose is the calculation of modular character tables, although it can be used for other purposes, such as investigating subgroup structure, module structure etc. Indeed, there is a set of programs (see The Lattice Programs) to compute automatically the submodule lattice of a given module. Each of the programs is self-contained, reading its input from files, and writing its output to files. To make the MeatAxe usable, therefore, it is necessary to write operating system commands to run the various programs. This documentation is primarily for the programs, and further documentation is necessary for the various implementations in differing operating environments. The primitive objects are of two types: matrices and permutations. Permutation objects can be handled, but not as smoothly as you might expect. For example, it is hoped that programs such as split (zsp) and multiply (zmu) will be able to work with mixed types, but at present ZSP is restricted to matrices only, and ZMU can multiply a matrix by a permutation, but not vice versa. Homepage: http://www.math.rwth-aachen.de/~MTX/ Keywords: decomposition matrices; symmetric groups; computational group theory; modular representations; modular characters; irreducible characters; condensation Related Software: GAP; Magma; ATLAS Group Representations; CTblLib; GAP Character Table Library; AtlasRep; orb; SageMath; CHEVIE; Macaulay2; recog; STAR/MPI; matrixss; StandardFF; Algorithm 898; M4RI; PolyBoRi; Mathematica; SmallGroups Library; Cython Cited in: 69 Publications Further Publications: http://www.math.rwth-aachen.de/~MTX/doc24/index.html Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year The 2-modular decomposition matrices of the symmetric groups \(S_{15}\), \(S_{16}\), and \(S_{17}\). Zbl 0982.20008Müller, Jürgen 2000 all top 5 Cited by 70 Authors 19 Müller, Jürgen 9 Lux, Klaus Martin 8 Wilson, Robert Arnott 6 O’Brien, Eamonn A. 5 Hiss, Gerhard 5 Holt, Derek F. 4 Brooksbank, Peter A. 4 Leedham-Green, Charles R. 3 Bäärnhielm, Henrik 3 Breuer, Thomas 3 Glasby, Stephen Peter 3 Koshitani, Shigeo 3 Lübeck, Frank 3 Neunhöffer, Max 3 Wilson, James B. 2 Cannon, John J. 2 Carlson, Jon Frederick 2 Cooperman, Gene 2 Danz, Susanne 2 Eick, Bettina 2 Green, David John 2 Jansen, Christoph 2 Noeske, Felix 2 Ryba, Alexander J. E. 2 Suleiman, Ibrahim A. I. 2 Szőke, Magdolna 2 Walsh, Peter Gerard 1 Albrecht, Martin R. 1 Bard, Gregory V. 1 Bray, John N. 1 Bryant, Roger M. 1 Conder, Marston Donald Edward 1 Corr, Brian P. 1 Erdmann, Karin 1 Fawcett, Joanna B. 1 Geck, Meinolf 1 Görgen, Lukas 1 Green, Edward Lee 1 Heath, Lenwood S. 1 Henke, Anne 1 Höfling, Burkhard 1 Holmes, Petra E. 1 Hulpke, Alexander Jörg 1 Ivanyos, Gábor 1 King, Simon A. 1 Korhonen, Mikko 1 Künzer, Matthias 1 Külshammer, Burkhard 1 Magaard, Kay 1 Matthews, Graham 1 Murray, Scott H. 1 Okuyama, Tetsuro 1 Pahlings, Herbert 1 Parker, Richard A. 1 Požar, Rok 1 Praeger, Cheryl Elisabeth 1 Rees, Sarah 1 Ringe, Michael 1 Robinson, Eric E. 1 Röhr, Frank 1 Roney-Dougal, Colva M. 1 Rosenboom, Jens 1 Schaps, Mary Elizabeth 1 Slattery, Michael C. 1 Steel, Allan K. 1 Struble, Craig A. 1 Waki, Katsushi 1 Weller, Michael 1 Wiegelmann, Markus 1 Zimmermann, René all top 5 Cited in 18 Serials 24 Journal of Algebra 10 Journal of Symbolic Computation 6 Communications in Algebra 6 Experimental Mathematics 3 LMS Journal of Computation and Mathematics 2 Journal of the London Mathematical Society. Second Series 2 Journal of Pure and Applied Algebra 2 Transactions of the American Mathematical Society 1 Bulletin of the Australian Mathematical Society 1 Mathematics of Computation 1 ACM Transactions on Mathematical Software 1 International Journal of Algebra and Computation 1 Applicable Algebra in Engineering, Communication and Computing 1 Transformation Groups 1 Journal of Group Theory 1 Cambridge Studies in Advanced Mathematics 1 Lecture Notes in Mathematics 1 London Mathematical Society Lecture Note Series all top 5 Cited in 12 Fields 58 Group theory and generalizations (20-XX) 25 Computer science (68-XX) 14 Associative rings and algebras (16-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 3 Combinatorics (05-XX) 2 Numerical analysis (65-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Number theory (11-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Functions of a complex variable (30-XX) Citations by Year