Functional Decomposition of Symbolic Polynomials

Stephen M. Watt
2008 2008 International Conference on Computational Sciences and Its Applications  
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) = 2X n 2 +n − 4X n 2 + 2X n 2 −n + 1 can be decomposed as f = g • h where g(X) = 2X 2 + 1 and h(X) = X n 2 /2+n/2 − X n 2 /2−n/2 .
doi:10.1109/iccsa.2008.71 dblp:conf/iccsa/Watt08 fatcat:iqyabbnyqrcc7he5t4im3rindm