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# ðŸ“™ Algorithms for rational function arithmetic by Horowitz. â€” free download

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Despite recent advances in speeding up many arithmetic and algebraic algorithms plus a general increase in algorithm analyses, no computing time study has ever been done for algorithms which perform the rational function arithmetic operations. Mathematical symbol manipulation systems which provide for operations on rational functions use algorithms which were initially given by P. Henrici in 1956. In this paper, these algorithms are precisely specified and their computing times analyzed. Then, new algorithms based on the use of modular arithmetic are developed and analyzed. It is shown that the computing time for adding and taking the derivative of rational functions is 2 orders of magnitude faster using the modular algorithms. Also, the computing time for rational function multiplication will be one order of magnitude faster using the modular algorithm.

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A terminating condition of the well-known Zeilberger's algorithm for a given hypergeometric term T(n, k) is presented. It is shown that the only information on T(n, k) that one needs in order to determine in advance whether this algorithm will succeed is ...

Algorithms for Computer Algebra is the first comprehensive textbook to be published on the topic of computational symbolic mathematics. The book first develops the foundational material from modern algebra that is required for subsequent topics. It then p...

One of the best known fast computational algorithms is the fast Fourier transform method. Its efficiency is based mainly on the special structure of the discrete Fourier transform matrix. Recently, many other algorithms of this type were discovered,...

One of the best known fast computational algorithms is the fast Fourier transform method. Its efficiency is based mainly on the special structure of the discrete Fourier transform matrix. Recently, many other algorithms of this type were discovered,...

In life, time is money, and on the Internet, the size of data is money. Small programs and small files take less disk space and cost less to send over the Internet. Compression Algorithms for Real Programmers describes the basic algorithms and approach...

One of the best known fast computational algorithms is the fast Fourier transform method. Its efficiency is based mainly on the special structure of the discrete Fourier transform matrix. Recently, many other algorithms of this type were discovered, and t...

A compiler translates a high-level language program into a functionally equivalent low-level language program that can be understood and executed by the computer. Crucial to any computer system, effective compiler design is also one of the most complex ar...