Место издания:VVM Publisher St. Petersburg, Russia
Первая страница:36
Последняя страница:37
Аннотация:We consider applications of the modular arithmetic to cumbersome compu-
tational tasks, i.e. to problems with a lot of operations with cumbersome numbers.
Such problems often arise in computer algebra tasks. We mean evaluations of long
polynomials with huge numerical coeffcients. Traditionally a modular arithmetic
is used for each separate arithmetic operation. But It is more effective to execute
the programs from the beginning till the end modulo one prime. After several such
calculations in modulo different primes we can finally restore the right values of
all numbers of the result. With respect of the Chinese remainder theorem if you
know remainders from division of a natural number by a number of noncompa-
rable natural numbers you can restore the original number itself if it is not more
than multiplication of all these divisors. We assume that all numbers in the
problem are integer or rational. There is an generalization of the Chinese theorem
for integer and rational numbers.