Title | **Fraction-free row reduction of matrices of Ore polynomials** |

Author(s) | Bernhard Beckermann, Howard Cheng, George Labahn |

Type | Article in Journal |

Abstract | In this paper we give formulas for performing row reduction of a matrix of Ore polynomials in a fraction-free way. The reductions can be used for finding the rank and left nullspace of such matrices. When specialized to matrices of skew polynomials our reduction can be used for computing a weak Popov form of such matrices and for computing a GCRD and an LCLM of skew polynomials or matrices of skew polynomials. The algorithm is suitable for computation in exact arithmetic domains where the growth of coefficients in intermediate computations is a concern. This coefficient growth is controlled by using fraction-free methods. The known factor can be predicted and removed efficiently. |

Keywords | Ore polynomials, Exact arithmetic, Matrix normal forms |

ISSN | 0747-7171 |

URL |
http://www.sciencedirect.com/science/article/pii/S0747717105001513 |

Language | English |

Journal | Journal of Symbolic Computation |

Volume | 41 |

Number | 5 |

Pages | 513 - 543 |

Year | 2006 |

Edition | 0 |

Translation |
No |

Refereed |
No |