Functional Decomposition of Symbolic Polynomials
Stephen M. Watt · 2008
Earlier work has presented algorithms to factor and compute GCDs of symbolic Laurent polynomials, that is multivariate polynomials whose exponents are themselves integer-valued polynomials. This article extends the notion of univariate polynomial decomposition to symbolic polynomials and presents an algorithm to compute these decompositions. For example, the symbolic polynomial f(X) = 2Xn2+n- 4Xn2+ 2Xn2-n+ 1 can be de-composed as f = g o h where g(X) = 2X2+ 1 and h(X) = Xn2/2+n/2- Xn2/2-n/2.