Computing by homomorphic images

  • Franz Winkler
Part of the Texts and Monographs in Symbolic Computation book series (TEXTSMONOGR)


The Chinese remainder method has already been investigated by Chinese mathematicians more than 2000 years ago. For a short introduction to the history we refer to Knuth (1981). The main idea consists of solving a problem over the integers by solving this problem in several homomorphic images modulo various primes, and afterwards combining the solutions of the modular problems to a solution of the problem over the integers. In fact, the method can be generalized to work over arbitrary Euclidean domains, i.e., domains in which we can compute greatest common divisors by the Euclidean algorithm. An interesting list of different statements of the Chinese remainder theorem is given in Davis and Hersh (1981).


Fast Fourier Transform Discrete Fourier Transform Arithmetic Operation Homomorphic Image Great Common Divisor 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Wien 1996

Authors and Affiliations

  • Franz Winkler
    • 1
  1. 1.Research Institute for Symbolic ComputationJohannes-Kepler-University LinzLinzAustria

Personalised recommendations