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
Asymmetric cryptography with S-Boxes
ICICS '97 Proceedings of the First International Conference on Information and Communication Security
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
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
Inherently improper surface parametric supports
Computer Aided Geometric Design
Functional Decomposition of Symbolic Polynomials
ICCSA '08 Proceedings of the 2008 International Conference on Computational Sciences and Its Applications
An efficient algorithm for decomposing multivariate polynomials and its applications to cryptography
Journal of Symbolic Computation
Decomposition of generic multivariate polynomials
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
On multivariate homogeneous polynomial decomposition
CASC'10 Proceedings of the 12th international conference on Computer algebra in scientific computing
A computer algebra user interface manifesto
ACM Communications in Computer Algebra
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In this paper, we present an improved method for decomposing multivariate polynomials. This problem, also known as the Functional Decomposition Problem (FDP) [17, 9, 27], is classical in computer algebra (e.g. [17, 18, 19, 23, 24, 7, 25]). Here, we propose to use high order partial derivatives to improve the algorithm described in [14]. Our new approach is more simple, and in some sense more natural. From a practical point of view, this new approach will lead to more efficient algorithms. The complexity of our algorithms will depend of the degree of the input polynomials, and the ratio n/u between the number of variables/polynomials.