Computer algebra: symbolic and algebraic computation (2nd ed.)
Computer algebra: symbolic and algebraic computation (2nd ed.)
Polynomial decomposition algorithms
Journal of Symbolic Computation
Polynomial decomposition algorithms
Journal of Symbolic Computation
Functional decomposition ofpolynomials: the tame case
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Functional decomposition of polynomials: The wild case
Journal of Symbolic Computation
On multivariate rational function decomposition
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
AAECC-10 Proceedings of the 10th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Fast Polynominal Decomposition Algorithms
EUROCAL '85 Research Contributions from the European Conference on Computer Algebra-Volume 2
A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Analytic models for token-ring networks
Analytic models for token-ring networks
The functional decomposition of polynomials
The functional decomposition of polynomials
Functional Decomposition of Symbolic Polynomials
ICCSA '08 Proceedings of the 2008 International Conference on Computational Sciences and Its Applications
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
Inherently improper surface parametric supports
Computer Aided Geometric Design
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We consider the composition f =g o h of two systems g= (g0, ..., gt) and h=(h0, ..., hs) of homogeneous multivariate polynomials over a field K, where each gj ∈ K[y0, ..., ys] has degree ℓ each hk ∈ K[x0, ..., xr] has degree m, and fi = gi(h0, ..., hs) ∈ K[x0, ..., xr] has degree n = ℓ · m, for 0 ≤ i ≤ t. The motivation of this paper is to investigate the behavior of the decomposition algorithm Multi-ComPoly proposed at ISSAC'09 [18]. We prove that the algorithm works correctly for generic decomposable instances -- in the special cases where ℓ is 2 or 3, and m is 2 -- and investigate the issue of uniqueness of a generic decomposable instance. The uniqueness is defined w.r.t. the "normal form" of a multivariate decomposition, a new notion introduced in this paper, which is of independent interest.