Algorithmic Number Theory: Efficient algorithms

Algorithmic Number Theory: Efficient algorithms

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Algorithmic Number Theory provides a thorough introduction to the design and analysisof algorithms for problems from the theory of numbers. Although not an elementary textbook, itincludes over 300 exercises with suggested solutions. Every theorem not proved in the text or leftas an exercise has a reference in the notes section that appears at the end of each chapter. Thebibliography contains over 1, 750 citations to the literature. Finally, it successfully blendscomputational theory with practice by covering some of the practical aspects of algorithmimplementations.The subject of algorithmic number theory represents the marriage of number theorywith the theory of computational complexity. It may be briefly defined as finding integer solutionsto equations, or proving their non-existence, making efficient use of resources such as time andspace. Implicit in this definition is the question of how to efficiently represent the objects inquestion on a computer. The problems of algorithmic number theory are important both for theirintrinsic mathematical interest and their application to random number generation, codes forreliable and secure information transmission, computer algebra, and other areas.Publisher's Note:Volume 2 was not written. Volume 1 is, therefore, a stand-alone publication.Table 3.2 Instructions and Their Costs Instr. No. Instruction Computation Cost 1 R , ^C I 2 R.^Rj+Rk \gRj + \gRk 3 R, Ala€”Rj-Rk lgR, + lg/?* 4 R, -RjRk dgR, )(lgR*) 5 K, . alt;-lV**J (lgR, )(lg/?*) 6 RiAla€”Rrj \gRj + \gRrj 1 RR, Ala€”Rj \gR, + \gRj 8 /?, alt;- DECODE /?y /?* Ig Rj + Rk 9 /?, a€” LENGth Rj lg/?; 1 0 ENCODE Rj AT /?; lg /?, + lg /?; 11 . IF/?, . XlGOTOm lg/?, 12 GOTOm 1 13 READR, lg/?, 14 WRITER, lgR, 15 END 1 instructions, it is assumed that addresses are non-negative, and base-fo digitsanbsp;...

Title:Algorithmic Number Theory: Efficient algorithms
Author: Eric Bach, Jeffrey Outlaw Shallit
Publisher:MIT Press - 1996

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