Matrix representations over finite fields

http://www.math.rwth-aachen.de/~MTX/

The MeatAxe is a set of programs for working with matrix representations

over finite fields. Permutation representations are supported to some

extent, too.

Command | Description |
---|---|

cfcomp | compare irreducible constituents of a module |

checksum | compute the CRC of a file |

chop | find irreducible constituents of a matrix |

decomp | decompose a module |

genmod | make submodule |

mkcycl | find cyclic subspaces of a condensed module |

mkdotl | find dotted lines between submodules |

mkgraph | draw the submodule lattice |

mkhom | calculate homomorphisms between modules |

mkhom_old | calculate homomorphisms between modules |

mkinc | compute mountains and incidence matrix of a module |

mksub | find submodules |

mktree | enumerate elements of a finitely generated matrix group |

orbrep | find a permutation which maps A to B |

precond | precondensation of tensor products |

pseudochop | chop with known peak words |

pwkond | peak word condensation |

rad | calculate the radical series of a module |

soc | Socle series |

symnew | symmetrized tensor product |

tcond | tensor product condensation |

tuc | tensor uncondense |

zad | add or subtract matrices |

zbl | make lower triangular matrix keeping bottom left |

zcf | change field |

zcl | clean matrix |

zcp | characteristic and minimal polynomial of a matrix |

zct | cut matrices or permutations |

zcv | convert text representation of a matrix to binary format |

zef | convert a matrix to echelon form |

zev | compute matrix eigenvalues |

zfr | apply Frobenius automorphism to a matrix |

ziv | invert matrix or permutation |

zkd | condense a permutation |

zmo | make orbits under a set of permutations |

zmu | multiply matrices or permutations |

zmw | make word from a set of matrices |

znu | compute a matrix null-space |

zor | calculate the order of a matrix or permutation |

zpo | power of a matrix or permutation |

zpr | print permutations or matrices |

zpt | paste matrices or permutations |

zqt | clean and quotient on a matrix |

zro | random orders of a group |

zsc | spin up with script on a matrix |

zsi | sum and intersection of spaces |

zsp | spin up, split, and standard basis on matrices or permutations |

zsy | symmetrized tensor product of a matrix or permutation |

ztc | calculate matrix or permutation trace |

zte | tensor product of two matrices or permutations |

ztr | transpose matrices |

zts | tensor spin of modules |

zuk | uncondense vectors |

zvp | vector permute on matrices |