Fast evaluation of iterated multiplication of very large polynomials: An application to chinese remainder theory
نویسندگان
چکیده
We consider the problem of exactly computing the number of integers in a Chinese Remainder Representation (crr) whose pseudorank does not equal the rank. We call this number the census. The rank is key in developing crr-intrinsic methods for comparing integers in crr, a problem known to be notoriously difficult. Pseudorank can be computed in highly restrictive computation models. We have developed and implemented a fast, efficient algorithm for computing the census based on using a variant of the fft to compute iterated products of polynomials of very large degree, and with arbitrary size integer coefficients. Experimental census results are tabulated. This census information makes possible a new approach to exploring the fine structure of crr. See http://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/article/view/112 for this article, c © Austral. Mathematical Soc. 2007. Published December 27, 2007. ISSN 1446-8735
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