The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The Use of Index Calculus and Mersenne Primes for the Design of a High-Speed Digital Multiplier
Journal of the ACM (JACM)
On Euclid's algorithm and the computation of polynomial greatest common divisors
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
The calculation of multivariate polynomial resultants
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
Algorithms for partial fraction decomposition and rational function integration
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
Algorithms for rational function arithmetic operations
STOC '72 Proceedings of the fourth annual ACM symposium on Theory of computing
Symbolic mathematical computation in a Ph.D. computer science program
SIGCSE '72 Proceedings of the second SIGCSE technical symposium on Education in computer science
Symbolic mathematical computation in a Ph. D. computer science program
ACM SIGCSE Bulletin
Symbolic mathematical computation in a Ph.D. Computer Science program
ACM SIGSAM Bulletin
Congruence arithmetic algorithms for polynomial real zero determination
Journal of Computer and System Sciences
Zombie memory: extending memory lifetime by reviving dead blocks
Proceedings of the 40th Annual International Symposium on Computer Architecture
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The paradigm of algorithm analysis has achieved major pre-eminence in the field of symbolic and algebraic manipulation in the last few years. A major factor in its success has been the use of modular arithmetic. Application of this technique has proved effective in reducing computing times for algorithms covering a wide variety of symbolic mathematical problems. This paper is intended to review the basic theory underlying modular arithmetic. In addition, attention will be paid to certain practical problems which arise in the construction of a modular arithmetic system. A second area of importance in symbol manipulation is the theory of finite fields. A recent algorithm for polynomial factorization over a finite field has led to faster algorithms for factorization over the field of rationals. Moreover, the work in modular arithmetic often consists of manipulating elements in a finite field. Hence, this paper will outline some of the major theorems for finite fields, hoping to provide a basis from which an easier grasp of these new algorithms can be made.