Exact Inversion of a Rational Polynomial Matrix Using Finite Field Transforms
E. V. Krishnamurthy · SIAM Journal on Applied Mathematics · 1978
A unique code (called Hensel’s code) is derived for a single variable rational polynomial function with integral coefficients, by converting its numerator and denominator into polynomials over a finite field and truncating the infinite expansion of the quotient. The four basic polynomial arithmetic algorithms for these codes are described; their application for the reduction of a rational polynomial matrix to the Hermite normal form (by a sequence of elementary transformations) and hence for the exact (generalized) inversion of the rational polynomial matrix is demonstrated.