Abstract :
A unique code (called Hensel´s code) is derived for a rational number by truncating its infinite p-adic expansion. The four basic arithmetic algorithms for these codes are described and their application to rational matrix computations is demonstrated by solving a system of linear equations exactly, using the Gaussian elimination procedure.
Keywords :
Computational complexity, exact linear computation, Galois-field arithmetic, Gaussian elimination, linear equations, matrix processor, p-adic arithmetic, rational arithmetic, residue arithmetic.; Africa; Computational complexity; Equations; Floating-point arithmetic; Galois fields; Mathematics; Roundoff errors; Symmetric matrices; Computational complexity, exact linear computation, Galois-field arithmetic, Gaussian elimination, linear equations, matrix processor, p-adic arithmetic, rational arithmetic, residue arithmetic.;
