triang_Sylvester: Triangularization of a polynomial matrix by Sylvester method
In polyMatrix: Infrastructure for Manipulation Polynomial Matrices

Description Usage Arguments Details Value References

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

polyMatrix documentation built on July 18, 2021, 5:06 p.m.