Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Computer algebra: systems and algorithms for algebraic computation
Computer algebra: systems and algorithms for algebraic computation
Algorithms for computer algebra
Algorithms for computer algebra
Inverting polynomials and formal power series
SIAM Journal on Computing
Polynomial and matrix computations (vol. 1): fundamental algorithms
Polynomial and matrix computations (vol. 1): fundamental algorithms
Fast Algorithms for Manipulating Formal Power Series
Journal of the ACM (JACM)
The Art of Computer Programming Volumes 1-3 Boxed Set
The Art of Computer Programming Volumes 1-3 Boxed Set
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
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We consider the problem of predicting long sequences of zero coefficients in a power series obtained by multiplication, division or reversion (where all coefficients are integers). We describe efficient randomized algorithms whose probability of error can be controlled by the user. A runtime analysis is given and some experimental results are also presented that compare our algorithms with classical ones for formal power series computations. We envisage the algorithms given here as being of greatest use in situations where several processors are available so that the possibility of a long sequence of zeros can be tested in parallel to the normal computation of coefficients. Copyright 2002 Elsevier Science Ltd.