3. Algebraic and Number-theoretic Computations
| 3.1 | Introduction |
| 3.2 | Complexity Issues |
| 3.3 | Multiple-precision Integer Arithmetic |
| 3.4 | Elementary Number-theoretic Computations |
| 3.5 | Arithmetic in Finite Fields |
| 3.6 | Arithmetic on Elliptic Curves |
| 3.7 | Arithmetic on Hyperelliptic Curves |
| 3.8 | Random Numbers |
| Chapter Summary | |
| Sugestions for Further Reading |
From the start there has been a curious affinity between mathematics, mind and computing . . . It is perhaps no accident that Pascal and Leibniz in the seventeenth century, Babbage and George Boole in the nineteenth, and Alan Turing and John von Neumann in the twentieth – seminal figures in the history of computing – were all, among their other accomplishments, mathematicians, possessing a natural affinity for symbol, representation, abstraction and logic.
—Doron Swade [295]
. . . the laws of physics and of logic . . . the number system . . . the principle of algebraic substitution. These are ghosts. We just believe in them so thoroughly they seem real.
—Robert M. Pirsig [233]
The world is continuous, but the mind is discrete.
—David Mumford
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