Parallel algorithms for algebraic problems
SIAM Journal on Computing
Irreducibility of multivariate polynomials
Journal of Computer and System Sciences
Polynomial decomposition algorithms
Journal of Symbolic Computation
Parallel arithmetic computations: a survey
Proceedings of the 12th symposium on Mathematical foundations of computer science 1986
Greatest common divisors of polynomials given by straight-line programs
Journal of the ACM (JACM)
Very fast parallel polynomial arithmetic
SIAM Journal on Computing
Fast Algorithms for Manipulating Formal Power Series
Journal of the ACM (JACM)
Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
Practical fast polynomial multiplication
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Functional decomposition of polynomials: The wild case
Journal of Symbolic Computation
Rational function decomposition
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
Homogeneous decomposition of polynomials
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
A practical implementation of two rational function decomposition algorithms
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
Fast computations in the lattice of polynomial rational function fields
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Fast algorithms for Taylor shifts and certain difference equations
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
On factorization of nonlinear ordinary differential equations
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Approximate polynomial decomposition
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Unirational fields of transcendence degree one and functional decomposition
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Weaknesses in the SL2(IFs2) Hashing Scheme
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
Computer algebra handbook
Decomposition of differential polynomials with constant coefficients
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
High order derivatives and decomposition of multivariate polynomials
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
The number of decomposable univariate polynomials. extended abstract
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
An efficient algorithm for decomposing multivariate polynomials and its applications to cryptography
Journal of Symbolic Computation
Algebraic Condition for Decomposition of Large-Scale Linear Dynamic Systems
International Journal of Applied Mathematics and Computer Science
Composition collisions and projective polynomials: statement of results
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Decomposition of generic multivariate polynomials
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
On decomposition of tame polynomials and rational functions
CASC'06 Proceedings of the 9th international conference on Computer Algebra in Scientific Computing
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Algebraic computation of resolvents without extraneous powers
European Journal of Combinatorics
Lower bounds for decomposable univariate wild polynomials
Journal of Symbolic Computation
Compositions and collisions at degree p 2
Journal of Symbolic Computation
Modular Composition Modulo Triangular Sets and Applications
Computational Complexity
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If g and h are polynomials of degrees r and s over a field, their functional composition f=g(h) has degree n=rs. The functional decomposition problem is: given f of degree n=rs, determine whether such g and h exist, and, in the affirmative case, compute them. We first deal with univariate polynomials, and present sequential algorithms that use O(n log^2n log log n) arithmetic operations, and a parallel algorithm with optimal depth O(log n). Then we consider the case where f and h are multivariate, and g is univariate. All algorithms work only in the ''tame'' case, where the characteristic of the field does not divide r.