A fast, low-space algorithm for multiplying dense multivariate polynomials
ACM Transactions on Mathematical Software (TOMS)
A deterministic algorithm for sparse multivariate polynomial interpolation
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Communications of the ACM
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Practical fast polynomial multiplication
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Hashing LEMMAs on time complexities with applications to formula manipulation
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Use of VLSI in algebraic computation: Some suggestions
SYMSAC '81 Proceedings of the fourth ACM symposium on Symbolic and algebraic computation
Parallelism and algorithms for algebraic manipulation: current work
ACM SIGSAM Bulletin
On the bit-complexity of sparse polynomial and series multiplication
Journal of Symbolic Computation
Sparse polynomial powering using heaps
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
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This paper examines the most efficient known serial and parallel algorithms for multiplying and powering polynomials. For sparse polynomials the Simp algorithm multiplies using a simple divide and conquer approach, and the NOMC algorithm computes powers using a multinomial expansion. For dense polynomials the FFT multiplies and powers by evaluating polynomials at a set of points, performing pointwise multiplication or powering, and interpolating a polynomial through the results. Practical issues of applying these algorithms in algebraic manipulation systems are discussed.