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.

References in zbMATH (referenced in 45 articles , 1 standard article )

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  1. Bäärnhielm, Henrik; Holt, Derek; Leedham-Green, C.R.; O’Brien, E.A.: A practical model for computation with matrix groups. (2015)
  2. Brooksbank, Peter A.; Wilson, James B.: The module isomorphism problem reconsidered. (2015)
  3. Bryant, Roger M.; Danz, Susanne; Erdmann, Karin; Müller, Jürgen: Vertices of Lie modules. (2015)
  4. Corr, Brian P.: Estimation and computation with matrices over finite fields. (Abstract of thesis) (2015)
  5. Bäärnhielm, Henrik: Recognising the small Ree groups in their natural representations. (2014)
  6. Brooksbank, Peter A.; Wilson, James B.: Groups acting on tensor products. (2014)
  7. Koshitani, Shigeo; Müller, Jürgen; Noeske, Felix: Broué’s Abelian defect group conjecture for the sporadic simple Janko group $J_4$ revisited. (2014)
  8. Brooksbank, Peter A.; Wilson, James B.: Computing isometry groups of Hermitian maps. (2012)
  9. Green, David J.; King, Simon A.: The computation of the cohomology rings of all groups of order 128. (2011)
  10. Koshitani, Shigeo; Müller, Jürgen; Noeske, Felix: Broué’s Abelian defect group conjecture holds for the sporadic simple Conway group $Co_3$. (2011)
  11. Albrecht, Martin; Bard, Gregory; Hart, William: Algorithm 898: efficient multiplication of dense matrices over GF(2) (2010)
  12. Koshitani, Shigeo; Müller, Jürgen: Broué’s Abelian defect group conjecture holds for the Harada-Norton sporadic simple group $HN$. (2010)
  13. Lux, Klaus; Pahlings, Herbert: Representations of groups. A computational approach. (2010)
  14. Carlson, Jon F.; Neunhöffer, Max; Roney-Dougal, Colva M.: A polynomial-time reduction algorithm for groups of semilinear or subfield class. (2009)
  15. Geck, Meinolf; Müller, Jürgen: James’ conjecture for Hecke algebras of exceptional type. I. (2009)
  16. Glasby, S.P.; Praeger, Cheryl E.: Towards an efficient meat-axe algorithm using $f$-cyclic matrices: The density of uncyclic matrices in M$(n,q)$ (2009)
  17. Brooksbank, Peter A.; O’Brien, E.A.: Constructing the group preserving a system of forms. (2008)
  18. Danz, Susanne; Külshammer, Burkhard; Zimmermann, René: On vertices of simple modules for symmetric groups of small degrees. (2008)
  19. Müller, Jürgen: On the multiplicity-free actions of the sporadic simple groups. (2008)
  20. Müller, Jürgen: On the action of the sporadic simple Baby Monster group on its conjugacy class $2B$. (2008)

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