Polynomial Decomposition Algorithms

@article{Kozen1989PolynomialDA,
  title={Polynomial Decomposition Algorithms},
  author={Dexter Kozen and Susan Landau},
  journal={J. Symb. Comput.},
  year={1989},
  volume={7},
  pages={445-456}
}
We examine the question of when a polynomial f over a commutative ring has a nontrivial functional decomposition f = g ◦ h. Previous algorithms [2, 3, 1] are exponential-time in the worst case, require polynomial factorization, and only work over fields of characteristic 0. We present an O(n2)-time algorithm. We also show that the problem is in NC . The algorithm does not use polynomial factorization, and works over any commutative ring containing a multiplicative inverse of r. Finally, we give… CONTINUE READING
Highly Influential
This paper has highly influenced 14 other papers. REVIEW HIGHLY INFLUENTIAL CITATIONS
Highly Cited
This paper has 95 citations. REVIEW CITATIONS

Citations

Publications citing this paper.
Showing 1-10 of 57 extracted citations

On Polynomial Decompositions

J. Symb. Comput. • 1999
View 5 Excerpts
Highly Influenced

Functional Decomposition

View 15 Excerpts
Highly Influenced

RTL datapath optimization using system-level transformations

Fifteenth International Symposium on Quality Electronic Design • 2014
View 4 Excerpts
Highly Influenced

Exact and approximate polynomial decomposition methods for signal processing applications

2013 IEEE International Conference on Acoustics, Speech and Signal Processing • 2013
View 9 Excerpts
Highly Influenced

Algorithms for the Functional Decomposition of Laurent Polynomials

Calculemus/MKM • 2009
View 4 Excerpts
Highly Influenced

Decomposition of ordinary difference polynomials

J. Symb. Comput. • 2009
View 7 Excerpts
Highly Influenced

96 Citations

051015'88'95'03'11'19
Citations per Year
Semantic Scholar estimates that this publication has 96 citations based on the available data.

See our FAQ for additional information.

References

Publications referenced by this paper.
Showing 1-10 of 14 references

Polynomial Decomposition Algorithms

J. Symb. Comput. • 1985
View 8 Excerpts
Highly Influenced

A polynomial decomposition algorithm

View 8 Excerpts
Highly Influenced

Fast Polynominal Decomposition Algorithms

European Conference on Computer Algebra • 1985
View 7 Excerpts
Highly Influenced

Functional decomposition of polynomials

28th Annual Symposium on Foundations of Computer Science (sfcs 1987) • 1987
View 1 Excerpt

Polynomial decomposition algorithms for multivariate polynomials

Matthew Dickerson
Technical Report TR87-826, • 1987
View 1 Excerpt

Ritt . Prime and composite polynomials

F. J.
Vetterling . Numerical Recipes : The Art of Scientific Computing • 1986

Fast Parallel Matrix Inversion Algorithms

SIAM J. Comput. • 1976
View 1 Excerpt

Similar Papers

Loading similar papers…