The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Arithmetic complexity of unordered sparse polynomials
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
ALTRAN programs for SIGSAM problem #6
ACM SIGSAM Bulletin
On computing with factored rational expressions
ACM SIGSAM Bulletin
A comparative study of algorithms for sparse polynomial multiplication
ACM SIGSAM Bulletin
A p-adic division with remainder algorithm
ACM SIGSAM Bulletin
ACM SIGSAM Bulletin
Parallel sparse polynomial multiplication using heaps
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Lazy and Forgetful Polynomial Arithmetic and Applications
CASC '09 Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing
Parallel sparse polynomial division using heaps
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
Sparse polynomial multiplication and division in Maple 14
ACM Communications in Computer Algebra
Sparse polynomial division using a heap
Journal of Symbolic Computation
Chunky and equal-spaced polynomial multiplication
Journal of Symbolic Computation
Polynomial division using dynamic arrays, heaps, and packed exponent vectors
CASC'07 Proceedings of the 10th international conference on Computer Algebra in Scientific Computing
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
Structured FFT and TFT: symmetric and lattice polynomials
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
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Sparse polynomial representations are used in a number of algebraic manipulation systems, including Altran. This paper discusses the arithmetic operations with sparsely represented polynomials; we give particular attention to multiplication and division. We give new algorithms for multiplying two polynomials, with n and m terms, in time mnlogm;, these algorithms have the property that, in the usual univariate dense case, the algorithm is bounded by mn. Division algorithms are discussed which run in comparable time.