The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
ACM SIGSAM Bulletin
CABAL: polynomial and power series algebra on a parallel computer
PASCO '97 Proceedings of the second international symposium on Parallel symbolic computation
Two Fast Algorithms for Sparse Matrices: Multiplication and Permuted Transposition
ACM Transactions on Mathematical Software (TOMS)
A Parallel Symbolic Computation Environment: Structures and Mechanics
Euro-Par '99 Proceedings of the 5th International Euro-Par Conference on Parallel Processing
Universal classes of hash functions (Extended Abstract)
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
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In this paper, we show that addition and subtraction of unordered sparse polynomials can be done in time m+n and multiplication in time m+n. So we see already that if a particular sequence of polynomials computation involves a combination of these arithmetic operations as well as tests for equivalence or zero while intermediate expressions are not important enough to be displayed, then the unordered representation could amount to substantial savings in computation time. The visual demand of human users can still be satisfied at the cost of a single sort of the final answer as opposed to sorting each intermediate result in the case of ordered representations.