An algorithm for the exact reduction of a matrix to Frobenius form using modular arithmetic. I
Jo Ann Howell · Mathematics of Computation · 1973
This paper is in two parts. Part I contains a description of the Danilewski algorithm for reducing a matrix to Frobenius form using rational arithmetic. This algorithm is modified for use over the field of integers modulo p . The modified algorithm yields exact integral factors of the characteristic polynomial. A description of the single-modulus algorithm is given. Part II contains a description of the multiple-modulus algorithm. Since different moduli may yield different factorizations, an algorithm is given for determining which factorizations are not correct factorizations over the integers of the characteristic polynomial.