Fast Parallel Computation of Hermite and Smith Forms of Polynomial Matrices

Erich Kaltofen, M. S. Krishnamoorthy, B. David Saunders
1987 SIAM Journal on Algebraic and Discrete Methods  
B oolean circuits of polynomial size and poly-logarithmic depth are givenf or computing the Hermite and Smith normal forms of polynomial matrices overfinite fields and the field of rational numbers. The circuits for the Smith normal form computation are probabilistic ones and also determine very efficient sequential algorithms. Furthermore, we give a polynomial-time deterministic sequential algorithm for the Smith normal form overthe rationals. The Smith normal form algorithms are applied to
more » ... s are applied to the Rational canonical form of matrices overfinite fields and the field of rational numbers.
doi:10.1137/0608057 fatcat:wi5nzwifljfifpxvshky2cd6pm