Description Usage Arguments Details Value References

View source: R/triang_sylvester.R

The function `triang_Sylvester`

triangularize the given polynomial matrix.

1 | ```
triang_Sylvester(pm, u, eps = ZERO_EPS)
``` |

`pm` |
an polynomial matrix to triangularize |

`u` |
the minimal degree of the triangularizator multiplicator |

`eps` |
threshold of non zero coefficients |

The `u`

parameter is a necessary supplementary input without default value.
This parameter give the minimal degree of the searched triangulizator to solve the problem.

In a polynomial matrix the head elements are the first non-zero polynomials of columns.
The sequence of row indices of this head elements form the *shape* of the polynomial matrix.
A polynomial matrix is in left-lower triangular form, if this sequence is monoton increasing.

This method search a solution of the triangulrization by the method of Sylvester matrix, descripted in the article Labhalla-Lombardi-Marlin (1996).

T - the left-lower triangularized version of the given polynomial matrix U - the right multiplicator to triangularize the given polynomial matrix

Salah Labhalla, Henri Lombardi, Roger Marlin: Algorithm de calcule de la reduction de Hermite d'une matrice a coefficients polynomiaux, Theoretical Computer Science 161 (1996) pp 69-92

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