SFA, a package on symmetric functions considered as operators over the ring of polynomials for the computer algebra system MAPLE

International audienceSymmetric functions can be considered as operators acting on the ring of polynomials with coefficients in R. We present the package SFA. an implementation of this action for the computer algebra system MAPLE. As an example, we show how to recover different classical expressions of Lagrange inversion, and of Faber polynomials. (C) 2000 Academic Press

SFA, a package on symmetric functions considered as operators over the ring of polynomials for the computer algebra system MAPLE

Introduction Up to now, two main implementations of the theory of symmetric functions in Maple were made in ACE [UV95] and SF [Ste93]. The ring of symmetric functions can act in both of them as operators on the ring of polynomials with coefficients in R. Implementations of symmetric functions for systems other than Maple are for instance SYMMETRICA [KKL92] and SYM for Macsyma [Val89]. In the SFA package --- Symmetric Functions on different Alphabets, we give the possibility of doing more formal computations by implementing the structure of-ring of symmetric functions viewed as operators. Symmetric functions are operators on the ring of polynomials. However, one can recover usual symmetric functions (i.e. invariant by permutation): SfAExpand(e[2](x1+x2+x3)) will produce x1x2 + x1x3