Modular Integer Arithmetic

Christoph Schwarzweller

Formalized Mathematics (2008)

  • Volume: 16, Issue: 3, page 247-252
  • ISSN: 1426-2630

Abstract

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In this article we show the correctness of integer arithmetic based on Chinese Remainder theorem as described e.g. in [11]: Integers are transformed to finite sequences of modular integers, on which the arithmetic operations are performed. Retransformation of the results to the integers is then accomplished by means of the Chinese Remainder theorem. The method presented is a typical example for computing in homomorphic images.

How to cite

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Christoph Schwarzweller. "Modular Integer Arithmetic." Formalized Mathematics 16.3 (2008): 247-252. <http://eudml.org/doc/267141>.

@article{ChristophSchwarzweller2008,
abstract = {In this article we show the correctness of integer arithmetic based on Chinese Remainder theorem as described e.g. in [11]: Integers are transformed to finite sequences of modular integers, on which the arithmetic operations are performed. Retransformation of the results to the integers is then accomplished by means of the Chinese Remainder theorem. The method presented is a typical example for computing in homomorphic images.},
author = {Christoph Schwarzweller},
journal = {Formalized Mathematics},
language = {eng},
number = {3},
pages = {247-252},
title = {Modular Integer Arithmetic},
url = {http://eudml.org/doc/267141},
volume = {16},
year = {2008},
}

TY - JOUR
AU - Christoph Schwarzweller
TI - Modular Integer Arithmetic
JO - Formalized Mathematics
PY - 2008
VL - 16
IS - 3
SP - 247
EP - 252
AB - In this article we show the correctness of integer arithmetic based on Chinese Remainder theorem as described e.g. in [11]: Integers are transformed to finite sequences of modular integers, on which the arithmetic operations are performed. Retransformation of the results to the integers is then accomplished by means of the Chinese Remainder theorem. The method presented is a typical example for computing in homomorphic images.
LA - eng
UR - http://eudml.org/doc/267141
ER -

References

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  1. [1] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990. Zbl06213858
  2. [2] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990. 
  3. [3] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990. 
  4. [4] Czesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990. 
  5. [5] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990. 
  6. [6] Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990. 
  7. [7] Artur Korniłowicz. On the real valued functions. Formalized Mathematics, 13(1):181-187, 2005. 
  8. [8] Rafał Kwiatek and Grzegorz Zwara. The divisibility of integers and integer relative primes. Formalized Mathematics, 1(5):829-832, 1990. 
  9. [9] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990. 
  10. [10] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. 
  11. [11] J. von zur Gathen and J. Gerhard. Modern Computer Algebra. Cambridge University Press, 1999. Zbl0936.11069

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