High-order lifting and integrality erti ation
نویسنده
چکیده
Redu tions to polynomial matrix multipli ation are given for some lassi al problems involving a nonsingular input matrix over the ring of univariate polynomials with oeÆ ients from a eld. High-order lifting is used to ompute the determinant, the Smith form, and a rational system solution with about the same number of eld operations as required to multiply together two matri es having the same dimension and degree as the input matrix. Integrality erti ation is used to verify orre tness of the output. The algorithms are spa e eÆ ient.
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