Polynomial decomposition algorithms
Journal of Symbolic Computation
Rational function decomposition
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
Decomposition of algebraic functions
Journal of Symbolic Computation
A polynomial decomposition algorithm
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
On systems of algebraic equations with parametric exponents
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Uniform Gröbner bases for ideals generated by polynomials with parametric exponents
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Functional Decomposition of Symbolic Polynomials
ICCSA '08 Proceedings of the 2008 International Conference on Computational Sciences and Its Applications
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Recent work has detailed the conditions under which univariate Laurent polynomials have functional decompositions. This paper presents algorithms to compute such univariate Laurent polynomial decompositions efficiently and gives their multivariate generalization. One application of functional decomposition of Laurent polynomials is the functional decomposition of so-called "symbolic polynomials." These are polynomial-like objects whose exponents are themselves integer-valued polynomials rather than integers. The algebraic independence of X , X n , $X^{n^2/2}$, etc , and some elementary results on integer-valued polynomials allow problems with symbolic polynomials to be reduced to problems with multivariate Laurent polynomials. Hence we are interested in the functional decomposition of these objects.