The function triang_Sylvester triangularize the given polynomial matrix.
triang_Sylvester(pm, u, eps = ZERO_EPS)an polynomial matrix to triangularize
the minimal degree of the triangularizator multiplicator
threshold of non zero coefficients
T - the left-lower triangularized version of the given polynomial matrix U - the right multiplicator to triangularize the given polynomial matrix
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).
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